https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Shamgar&feedformat=atomUW-Math Wiki - User contributions [en]2022-10-03T14:31:03ZUser contributionsMediaWiki 1.35.6https://wiki.math.wisc.edu/index.php?title=Algebra&diff=22881Algebra2022-02-25T01:17:54Z<p>Shamgar: /* Research at UW-Madison in algebra */</p>
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<div><!-->[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.--><br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<!--[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)--><br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[https://people.math.wisc.edu/~vadicgor/ Vadim Gorin:] (Moscow, 2011) Integrable probability, random matrices, asymptotic representation theory (also in the probability group.)<br />
<br />
[https://people.math.wisc.edu/~sguo223/ Shaoming Guo:] (Bonn, 2015) Harmonic analysis, analytic number theory, combinatorics, geometric measure theory, partial differential equations (also in the analysis group.)<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Representation theory, with applications to harmonic analysis, signal processing, mathematical physics.<br />
<br />
[https://people.math.wisc.edu/~kemeny/homepage.html Michael Kemeny:] (Bonn, 2015) Algebraic geometry and commutative algebra, in particular the study of moduli and syzygies of algebraic varieties.<br />
<br />
[https://hanbaeklyu.com/ Hanbaek Lyu:] (Ohio State, 2018) Discrete probability, dynamical systems, networks, optimization, machine learning (also in the probability group.) <br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics.<br />
<!--[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics--><br />
<br />
[https://pages.cs.wisc.edu/~amos/ Amos Ron:] (Tel Aviv, 1987) Approximation theory, wavelets, Gabor systems, splines, polynomial interpolation, data representation, frames, scientific data, applications (joint appointment with CS.)<br />
<br />
[https://sites.google.com/view/ashankar/home Ananth Shankar:] (Harvard, 2017) Arithmetic geometry and number theory.<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Algebraic combinatorics, representation theory, Lie algebras, quantum groups, special functions. <br />
<!--[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.--><br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<!--[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry.--> <br />
<!--[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers--><br />
<!--[https://sites.google.com/site/dcorey2814/ Daniel Corey:] (Yale, 2018) Tropical geometry--><br />
<!--[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry--><br />
<br />
[https://people.math.wisc.edu/~shi/ Yousheng Shi:] (Maryland, 2019) Number theory and arithmetic algebraic geometry.<br />
<br />
<!--[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces--><br />
<!--[https://markshus.wixsite.com/math Mark Shusterman:] (Tel Aviv, 2019) Number theory and group theory--><br />
[https://people.math.wisc.edu/~asobieska/ Aleksandra (Ola) Sobieska:] (Texas A&M University, 2020) Commutative algebra, combinatorics<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
<!--[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories--><br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[http://hilbert.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar Algebra and Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<!--[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)--><br />
<br />
[https://hilbert.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar Graduate Algebraic Geometry Seminar] (Wednesdays at 4:00)<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar Applied Algebra Seminar] (Thursdays)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<!--Lie Theory Seminar (Mondays at 1:20 in VV901)--><br />
<!--[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
[https://docs.google.com/document/d/e/2PACX-1vQaFtI9Pvf7HYTmch19qftoBUR81hevJ9n3F1viS_b-QxfAMz4fcIo6-jxQjMkpZvZqSJn2IS33BrG6/pub Online Social Chit-Chats] (various times)<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
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[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. <br />
<!-->Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].--><br />
<!--The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas.--> <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Nigel Boston<br />
Professor, Ph.D. Harvard (1987) <br />
Research: Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21445Colloquia2021-09-08T17:23:46Z<p>Shamgar: /* October 22, 2021 , vera-serganova (UC Berkeley) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021, B239, [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
'''Finitely Presented Groups in Arithmetic Geometry'''<br />
<br />
I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.<br />
<br />
== Sep. 24, 2021 , [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==<br />
<br />
<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevich)<br />
<br />
== October 22, 2021 , [https://math.berkeley.edu/people/faculty/vera-serganova Vera Serganova] (UC Berkeley) ==<br />
<br />
(hosted by Gurevich/Gorin)<br />
<br />
== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==<br />
<br />
(hosted by Wainger)<br />
<br />
== November 5, 2021 , [https://faculty.washington.edu/jathreya/ Jayadev S. Athreya] (University of Washington) ==<br />
<br />
(hosted by Uyanik)<br />
<br />
== November 12, 2021 , [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==<br />
<br />
(hosted by Stovall)<br />
<br />
== Nov. 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
<br />
<br />
== Future ==<br />
<br />
[[Colloquia/Spring2022|Spring 2022]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21444Colloquia2021-09-08T17:23:10Z<p>Shamgar: /* Fall 2021 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021, B239, [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
'''Finitely Presented Groups in Arithmetic Geometry'''<br />
<br />
I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.<br />
<br />
== Sep. 24, 2021 , [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==<br />
<br />
<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevich)<br />
<br />
== October 22, 2021 , [https://math.berkeley.edu/people/faculty/vera-serganova vera-serganova] (UC Berkeley) ==<br />
<br />
(hosted by Gurevich/Gorin)<br />
<br />
== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==<br />
<br />
(hosted by Wainger)<br />
<br />
== November 5, 2021 , [https://faculty.washington.edu/jathreya/ Jayadev S. Athreya] (University of Washington) ==<br />
<br />
(hosted by Uyanik)<br />
<br />
== November 12, 2021 , [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==<br />
<br />
(hosted by Stovall)<br />
<br />
== Nov. 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
<br />
<br />
== Future ==<br />
<br />
[[Colloquia/Spring2022|Spring 2022]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21381Colloquia2021-09-01T15:54:28Z<p>Shamgar: /* Sep. 17, 2021 , Mark Shusterman (Harvard) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021 , [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
Title: Finitely Presented Groups in Arithmetic Geometry<br />
<br />
Abstract:<br />
<br />
I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.<br />
<br />
== Sep. 24, 2021 , [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==<br />
<br />
<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevich)<br />
<br />
== October 29, 2021 , [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==<br />
<br />
(hosted by Wainger)<br />
<br />
== November 12, 2021 , [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==<br />
<br />
(hosted by Stovall)<br />
<br />
== Nov. 19, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 3, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
== Dec. 10, 2021 , [https://math.wisc.edu/ TBA] (TBA) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
<br />
<br />
== Future ==<br />
<br />
[[Colloquia/Spring2022|Spring 2022]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21249Colloquia2021-07-19T19:24:47Z<p>Shamgar: /* Fall 2021 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021 , [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevitch)<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21248Colloquia2021-07-19T19:24:05Z<p>Shamgar: /* Fall 2021 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021 , Mark Shusterman[https://markshus.wixsite.com/math] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevitch)<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=21247Colloquia2021-07-19T19:23:37Z<p>Shamgar: /* Fall 2021 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
=Fall 2021=<br />
<br />
== Sep. 17, 2021 , [https://markshus.wixsite.com/math] (Harvard) ==<br />
<br />
(hosted by Gurevich)<br />
<br />
== October 8, 2021 , [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==<br />
<br />
(Wasow lecture; hosted by Thiffeault)<br />
<br />
== October 11, 13, 15, 2021 '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==<br />
<br />
(Special lecture series; hosted by Gurevitch)<br />
<br />
<br />
<br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21169Algebra and Algebraic Geometry Seminar Spring 20212021-04-23T15:51:35Z<p>Shamgar: /* Iordan Ganev */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| The QR decomposition for radial neural networks]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.<br />
<br />
<br />
===Iordan Ganev===<br />
The QR decomposition for radial neural networks<br />
<br />
Abstract: We present a perspective on neural networks stemming from quiver representation theory. This point of view emphasizes the symmetries inherent in neural networks, interacts nicely with gradient descent, and has the potential to improve training algorithms. As an application, we establish an analogue of the QR decomposition for radial neural networks, which leads to a dimensional reduction result. This talk is intended for a broad mathematical audience, and we explain all concepts relating to neural networks and machine learning from first principles. It is based on joint work-in-progress with Robin Walters.</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21168Algebra and Algebraic Geometry Seminar Spring 20212021-04-23T14:10:00Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| The QR decomposition for radial neural networks]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.<br />
<br />
<br />
===Iordan Ganev===<br />
<br />
Abstract: We present a perspective on neural networks stemming from quiver representation theory. This point of view emphasizes the symmetries inherent in neural networks, interacts nicely with gradient descent, and has the potential to improve training algorithms. As an application, we establish an analogue of the QR decomposition for radial neural networks, which leads to a dimensional reduction result. This talk is intended for a broad mathematical audience, and we explain all concepts relating to neural networks and machine learning from first principles. It is based on joint work-in-progress with Robin Walters.</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21167Algebra and Algebraic Geometry Seminar Spring 20212021-04-23T14:07:51Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| The QR decomposition for radial neural networks]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21153Algebra and Algebraic Geometry Seminar Spring 20212021-04-16T18:04:19Z<p>Shamgar: /* Gurbir Dhillon */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21152Algebra and Algebraic Geometry Seminar Spring 20212021-04-16T18:03:50Z<p>Shamgar: /* Gurbir Dhillon */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21151Algebra and Algebraic Geometry Seminar Spring 20212021-04-16T18:03:30Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21121Algebra and Algebraic Geometry Seminar Spring 20212021-04-08T20:21:58Z<p>Shamgar: /* Hannah Larson */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21120Algebra and Algebraic Geometry Seminar Spring 20212021-04-08T20:20:52Z<p>Shamgar: /* Eyal Subag */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21119Algebra and Algebraic Geometry Seminar Spring 20212021-04-08T20:20:01Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20999Algebra and Algebraic Geometry Seminar Spring 20212021-03-15T13:04:35Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20998Algebra and Algebraic Geometry Seminar Spring 20212021-03-15T13:03:39Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20997Algebra and Algebraic Geometry Seminar Spring 20212021-03-15T13:02:49Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|<br />
}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20996Algebra and Algebraic Geometry Seminar Spring 20212021-03-15T13:00:35Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io/ Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20699Algebra and Algebraic Geometry Seminar Spring 20212021-01-29T18:21:59Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20698Algebra and Algebraic Geometry Seminar Spring 20212021-01-29T18:21:17Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20561Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T18:17:25Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20560Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T18:16:07Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20559Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T18:15:24Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20545Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T15:48:07Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20527Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T16:55:24Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20526Algebra and Algebraic Geometry Seminar Spring 20212021-01-17T16:54:07Z<p>Shamgar: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|TBA March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Penn State)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA (April)<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19576NTS2020-08-26T03:31:21Z<p>Shamgar: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19575NTS2020-08-26T03:29:50Z<p>Shamgar: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(abstract + registration for link https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19574NTS2020-08-26T03:27:20Z<p>Shamgar: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields (zoom link https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19573NTS2020-08-26T03:25:47Z<p>Shamgar: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19572NTS2020-08-26T03:24:47Z<p>Shamgar: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9：00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=19037Colloquia/Spring20202020-02-15T20:45:00Z<p>Shamgar: /* Spring 2020 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |Fluctuations for products of random matrices]]<br />
|Roch<br />
|-<br />
|Feb 19<br />
|[https://www.math.upenn.edu/~zwang423// Zhenfu Wang] (University of Pennsylvania)<br />
|[[#Zhenfu Wang (University of Pennsylvania) |Quantitative Methods for the Mean Field Limit Problem]]<br />
|Tran<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|[[#Shai Evra (IAS) |Golden Gates in PU(n) and the Density Hypothesis]]<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|JM Landsberg (TAMU)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinzi Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
=== Yi Sun (Columbia) ===<br />
<br />
Title: Fluctuations for products of random matrices<br />
<br />
Abstract: Products of large random matrices appear in many modern applications such as high dimensional statistics (MANOVA estimators), machine learning (Jacobians of neural networks), and population ecology (transition matrices of dynamical systems). Inspired by these situations, this talk concerns global limits and fluctuations of singular values of products of independent random matrices as both the size N and number M of matrices grow. As N grows, I will show for a variety of ensembles that fluctuations of the Lyapunov exponents converge to explicit Gaussian fields which transition from log-correlated for fixed M to having a white noise component for M growing with N. I will sketch our method, which uses multivariate generalizations of the Laplace transform based on the multivariate Bessel function from representation theory.<br />
<br />
=== Zhenfu Wang (University of Pennsylvania) ===<br />
<br />
Title: Quantitative Methods for the Mean Field Limit Problem<br />
<br />
Abstract: We study the mean field limit of large systems of interacting particles. Classical mean field limit results require that the interaction kernels be essentially Lipschitz. To handle more singular interaction kernels is a longstanding and challenging question but which now has some successes. Joint with P.-E. Jabin, we use the relative entropy between the joint law of all particles and the tensorized law at the limit to quantify the convergence from the particle systems towards the macroscopic PDEs. This method requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit convergence rates for all marginals. This in particular can be applied to the Biot-Savart law for 2D Navier-Stokes. To treat more general and singular kernels, joint with D. Bresch and P.-E. Jabin, we introduce the modulated free energy, combination of the relative entropy that we had previously developed and of the modulated energy introduced by S. Serfaty. This modulated free energy may be understood as introducing appropriate weights in the relative entropy to cancel the most singular terms involving the divergence of the kernels. Our modulated free energy allows to treat gradient flows with singular potentials which combine large smooth part, small attractive singular part and large repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as the Patlak-Keller-Segel system in the subcritical regimes, is obtained.<br />
<br />
===Shai Evra (IAS)===<br />
<br />
Title: Golden Gates in PU(n) and the Density Hypothesis.<br />
<br />
Abstract: In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. In this talk I will describe some recent works that extend the construction of LPS to higher rank compact Lie groups. <br />
<br />
A key ingredient in the work of LPS is the Ramanujan conjecture for U(2), which follows from Deligne's proof of the Ramanujan-Petersson conjecture for GL(2). Unfortunately, the naive generalization of the Ramanujan conjecture is false for higher rank groups. Following a program initiated by Sarnak in the 90's, we prove a density hypothesis and use it as a replacement of the naive Ramanujan conjecture.<br />
<br />
This talk is based on some joint works with Ori Parzanchevski and Amitay Kamber.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=19036Colloquia/Spring20202020-02-15T20:43:58Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |Fluctuations for products of random matrices]]<br />
|Roch<br />
|-<br />
|Feb 19<br />
|[https://www.math.upenn.edu/~zwang423// Zhenfu Wang] (University of Pennsylvania)<br />
|[[#Zhenfu Wang (University of Pennsylvania) |Quantitative Methods for the Mean Field Limit Problem]]<br />
|Tran<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|JM Landsberg (TAMU)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
<br />
== Abstracts ==<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinzi Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
=== Yi Sun (Columbia) ===<br />
<br />
Title: Fluctuations for products of random matrices<br />
<br />
Abstract: Products of large random matrices appear in many modern applications such as high dimensional statistics (MANOVA estimators), machine learning (Jacobians of neural networks), and population ecology (transition matrices of dynamical systems). Inspired by these situations, this talk concerns global limits and fluctuations of singular values of products of independent random matrices as both the size N and number M of matrices grow. As N grows, I will show for a variety of ensembles that fluctuations of the Lyapunov exponents converge to explicit Gaussian fields which transition from log-correlated for fixed M to having a white noise component for M growing with N. I will sketch our method, which uses multivariate generalizations of the Laplace transform based on the multivariate Bessel function from representation theory.<br />
<br />
=== Zhenfu Wang (University of Pennsylvania) ===<br />
<br />
Title: Quantitative Methods for the Mean Field Limit Problem<br />
<br />
Abstract: We study the mean field limit of large systems of interacting particles. Classical mean field limit results require that the interaction kernels be essentially Lipschitz. To handle more singular interaction kernels is a longstanding and challenging question but which now has some successes. Joint with P.-E. Jabin, we use the relative entropy between the joint law of all particles and the tensorized law at the limit to quantify the convergence from the particle systems towards the macroscopic PDEs. This method requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit convergence rates for all marginals. This in particular can be applied to the Biot-Savart law for 2D Navier-Stokes. To treat more general and singular kernels, joint with D. Bresch and P.-E. Jabin, we introduce the modulated free energy, combination of the relative entropy that we had previously developed and of the modulated energy introduced by S. Serfaty. This modulated free energy may be understood as introducing appropriate weights in the relative entropy to cancel the most singular terms involving the divergence of the kernels. Our modulated free energy allows to treat gradient flows with singular potentials which combine large smooth part, small attractive singular part and large repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as the Patlak-Keller-Segel system in the subcritical regimes, is obtained.<br />
<br />
===Shai Evra (IAS)===<br />
<br />
Title: Golden Gates in PU(n) and the Density Hypothesis.<br />
<br />
Abstract: In their seminal work from the 80’s, Lubotzky, Phillips and Sarnak gave explicit constructions of topological generators for PU(2) with optimal covering properties. In this talk I will describe some recent works that extend the construction of LPS to higher rank compact Lie groups. <br />
<br />
A key ingredient in the work of LPS is the Ramanujan conjecture for U(2), which follows from Deligne's proof of the Ramanujan-Petersson conjecture for GL(2). Unfortunately, the naive generalization of the Ramanujan conjecture is false for higher rank groups. Following a program initiated by Sarnak in the 90's, we prove a density hypothesis and use it as a replacement of the naive Ramanujan conjecture.<br />
<br />
This talk is based on some joint works with Ori Parzanchevski and Amitay Kamber.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18969Colloquia/Spring20202020-02-10T15:04:22Z<p>Shamgar: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |TBA]]<br />
|Roch<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|JM Landsberg (TAMU)<br />
|TBA<br />
|Gurevich<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinzi Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18968Colloquia/Spring20202020-02-10T15:03:30Z<p>Shamgar: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |TBA]]<br />
|Roch<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|JM Landsberg (TAMU)<br />
|<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinzi Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17913Colloquia/Spring20202019-09-18T00:57:44Z<p>Shamgar: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17780Colloquia/Spring20202019-09-06T22:18:19Z<p>Shamgar: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
| Omer Mermelstein (Madison)<br />
|<br />
|Andrews<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17722Colloquia/Spring20202019-08-31T23:24:35Z<p>Shamgar: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
| Omer Mermelstein (Madison)<br />
|<br />
|Andrews<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 18<br />
| <br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17688Colloquia/Spring20202019-08-28T16:22:05Z<p>Shamgar: /* Abstracts */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 18<br />
| Thomas Strohmer (UC Davis)<br />
|<br />
|Gurevich<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17687Colloquia/Spring20202019-08-28T16:12:18Z<p>Shamgar: /* Mathematics Colloquium */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 18<br />
| Thomas Strohmer (UC Davis)<br />
|<br />
|Gurevich<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17647Colloquia/Spring20202019-08-19T17:17:12Z<p>Shamgar: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
|<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
| Thomas Strohmer (UC Davis)<br />
|<br />
|Gurevich<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=17646Colloquia/Spring20202019-08-19T17:15:50Z<p>Shamgar: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
|<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
| Thomas Strohmer (UC Davis)<br />
|Mathematics and Engineering<br />
|Gurevich<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=16095Colloquia/Fall182018-10-01T16:33:48Z<p>Shamgar: /* Fall 2018 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)| Harry Potter's Cloak via Transformation Optics ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 14 '''Room 911'''<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21 '''Room 911'''<br />
| [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture<br />
|[[#Sep 21: Andrew Stuart (Caltech) | The Legacy of Rudolph Kalman ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)<br />
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)<br />
|[[#Oct 5: Eyal Subag (Penn State)| Symmetries of the hydrogen atom and algebraic families ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 12<br />
| ...<br />
|[[# TBA| TBA ]]<br />
| ...<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===<br />
Harry Potter's Cloak via Transformation Optics<br />
<br />
Can we make objects invisible? This has been a subject of human<br />
fascination for millennia in Greek mythology, movies, science fiction,<br />
etc. including the legend of Perseus versus Medusa and the more recent<br />
Star Trek and Harry Potter. In the last fifteen years or so there have been<br />
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion<br />
one of them, the so-called "traansformation optics"<br />
in a non-technical fashion n the so-called that has received the most attention in the<br />
scientific literature.<br />
<br />
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===<br />
Journey to the Center of the Earth<br />
<br />
We will consider the inverse problem of determining the sound<br />
speed or index of refraction of a medium by measuring the travel times of<br />
waves going through the medium. This problem arises in global seismology<br />
in an attempt to determine the inner structure of the Earth by measuring<br />
travel times of earthquakes. It has also several applications in optics<br />
and medical imaging among others.<br />
<br />
The problem can be recast as a geometric problem: Can one determine the<br />
Riemannian metric of a Riemannian manifold with boundary by measuring<br />
the distance function between boundary points? This is the boundary<br />
rigidity problem. We will also consider the problem of determining<br />
the metric from the scattering relation, the so-called lens rigidity<br />
problem. The linearization of these problems involve the integration<br />
of a tensor along geodesics, similar to the X-ray transform.<br />
<br />
We will also describe some recent results, join with Plamen Stefanov<br />
and Andras Vasy, on the partial data case, where you are making<br />
measurements on a subset of the boundary. No previous knowledge of<br />
Riemannian geometry will be assumed.<br />
<br />
=== Sep 21: Andrew Stuart (Caltech) ===<br />
<br />
The Legacy of Rudolph Kalman<br />
<br />
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.<br />
<br />
=== Sep 28: Gautam Iyer (CMU) ===<br />
<br />
Stirring and Mixing<br />
<br />
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical<br />
aspects of mixing that arise in the context of fluid dynamics:<br />
<br />
1. How efficiently can stirring "mix"?<br />
<br />
2. What is the interaction between diffusion and mixing.<br />
<br />
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing<br />
results, and talk about a few open problems.<br />
<br />
=== Oct 5: Eyal Subag (Penn State)===<br />
<br />
Symmetries of the hydrogen atom and algebraic families<br />
<br />
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2019&diff=16032Colloquia/Spring20192018-09-20T21:27:25Z<p>Shamgar: /* Spring 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State)<br />
|[[# TBA| TBA ]]<br />
| Erman and Corey<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| Jennifer Park (OSU)<br />
|[[# TBA| TBA ]]<br />
| Marshall<br />
|<br />
|-<br />
|April 5<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 26<br />
| [https://www.brown.edu/academics/applied-mathematics/faculty/kavita-ramanan/home Kavita Ramanan] (Brown University)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
|May 3<br />
| Tomasz Przebinda (Oklahoma)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2019&diff=15770Colloquia/Spring20192018-08-26T21:52:37Z<p>Shamgar: /* Mathematics Colloquium */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State)<br />
|[[# TBA| TBA ]]<br />
| Erman<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 5<br />
| [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University)<br />
|[[# TBA| TBA ]]<br />
| Jean-Luc<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| Ju-Lee Kim (MIT)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 26<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|May 3<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2019&diff=15710Colloquia/Spring20192018-08-15T17:45:39Z<p>Shamgar: /* Spring 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
== Spring 2019 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Jan 25<br />
| [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW<br />
|[[# TBA| TBA ]]<br />
| Tullia Dymarz<br />
|<br />
|-<br />
|Feb 1<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Feb 8<br />
| [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 15<br />
| [https://math.uchicago.edu/~smart/ Charles Smart] (University of Chicago)<br />
|[[# TBA| TBA ]]<br />
| Street<br />
|<br />
|-<br />
|Feb 22<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 4<br />
| Vladimir Sverak (Minnesota) Wasow lecture<br />
|[[# TBA| TBA ]]<br />
| Kim<br />
|<br />
|-<br />
|March 8<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 15<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|March 29<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 12<br />
| Evitar Procaccia (TAMU)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|April 19<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|April 26<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|May 3<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=15619Colloquia/Fall182018-07-18T06:08:11Z<p>Shamgar: /* Fall 2018 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''. The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].<br />
<br />
== Fall 2018 ==<br />
<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sep 12, 14<br />
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series<br />
|[[# TBA| TBA ]]<br />
| Li<br />
|<br />
|-<br />
|Sep 21<br />
| Andrew Stuart (Caltech) LAA lecture<br />
|[[# TBA| TBA ]]<br />
| Jin<br />
|<br />
|-<br />
|Sep 28<br />
| Gautam Iyer (CMU)<br />
|[[# TBA| TBA ]]<br />
| Thiffeault<br />
|<br />
|-<br />
|Oct 5<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Oct 12<br />
| Arie Levit (Yale)<br />
|[[# TBA| TBA ]]<br />
| Gurevich<br />
|<br />
|-<br />
|Oct 19<br />
| Jeremy Teitelbaum (U Connecticut)<br />
|[[# TBA| TBA ]]<br />
| Boston<br />
|<br />
|-<br />
|Oct 26<br />
| Douglas Ulmer (Arizona)<br />
|[[# TBA| TBA ]]<br />
| Yang<br />
|<br />
|-<br />
|Nov 2<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 9<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 16<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Nov 30<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|Dec 7<br />
| Reserved for job talk<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Fall18&diff=14360Colloquia/Fall182017-10-13T19:10:39Z<p>Shamgar: /* Fall 2017 */</p>
<hr />
<div>__NOTOC__<br />
<br />
= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == --><br />
<br />
==Fall 2017==<br />
<br />
{| cellpadding="8"<br />
!align="left" | Date <br />
!align="left" | Speaker<br />
!align="left" | Title<br />
!align="left" | Host(s)<br />
|-<br />
|September 8<br />
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)<br />
|[[#September 8: Tess Anderson (Madison) | A Spherical Maximal Function along the Primes ]]<br />
| Yang<br />
|<br />
|-<br />
|September 15<br />
|<br />
|[[#| ]]<br />
|<br />
|<br />
|<br />
|-<br />
|September 22, '''9th floor'''<br />
| Jaeyoung Byeon (KAIST)<br />
|[[#September 22: Jaeyoung Byeon (KAIST) | Patterns formation for elliptic systems with large interaction forces ]]<br />
| Rabinowitz & Kim<br />
|<br />
|-<br />
|September 29<br />
|<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|October 6, '''9th floor'''<br />
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)<br />
|[[#October 6: Jonathan Hauenstein (Notre Dame) | Real solutions of polynomial equations ]]<br />
| Boston<br />
| <br />
|-<br />
|October 13, '''9th floor'''<br />
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)<br />
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]<br />
| Max<br />
|<br />
|-<br />
|October 20<br />
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU) <br />
|[[#October 13: Pierre Germain (Courant, NYU) | Stability of the Couette flow in the Euler and Navier-Stokes equations ]]<br />
| Minh-Binh Tran<br />
|<br />
|-<br />
|October 27<br />
|Stefanie Petermichl (Toulouse)<br />
|[[# TBA| TBA ]]<br />
| Stovall, Seeger<br />
|<br />
|-<br />
|We, November 1<br />
|Shaoming Guo (Indiana)<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 3<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 10<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 17<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|November 24<br />
|'''Thanksgiving break'''<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 1<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
|December 8<br />
| Reserved for possible job talks<br />
|[[# TBA| TBA ]]<br />
|<br />
|<br />
|-<br />
<br />
|}<br />
<br />
== Fall Abstracts ==<br />
=== September 8: Tess Anderson (Madison) ===<br />
Title: A Spherical Maximal Function along the Primes<br />
<br />
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.<br />
<br />
<br />
=== September 22: Jaeyoung Byeon (KAIST) ===<br />
Title: Patterns formation for elliptic systems with large interaction forces<br />
<br />
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.<br />
<br />
===October 6: Jonathan Hauenstein (Notre Dame) ===<br />
Title: Real solutions of polynomial equations<br />
<br />
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions. Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.<br />
<br />
===October 13: Tomoko Kitagawa (Berkeley) ===<br />
Title: A Global History of Mathematics from 1650 to 2017<br />
<br />
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?<br />
<br />
===October 13: Pierre Germain (Courant, NYU) ===<br />
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations<br />
<br />
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).<br />
<br />
== Spring 2018 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| March 16<br />
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)<br />
|[[# TBA| TBA ]]<br />
| WIMAW<br />
|<br />
|-<br />
| April 6<br />
| Reserved<br />
|[[# TBA| TBA ]]<br />
| Melanie<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|-<br />
|date<br />
| person (institution)<br />
|[[# TBA| TBA ]]<br />
| hosting faculty<br />
|<br />
|}<br />
<br />
== Spring Abstracts ==<br />
<br />
=== <DATE>: <PERSON> (INSTITUTION) ===<br />
Title: <TITLE><br />
<br />
Abstract: <ABSTRACT><br />
<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank Colloquia]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Shamgar