https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Arinkin&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-29T10:55:19ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=File:Putnam-032024.pdf&diff=26343File:Putnam-032024.pdf2024-03-20T02:07:22Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=26342Putnam Club2024-03-20T02:00:27Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Assorted algebra problems<br />
|-<br />
| bgcolor="#D0D0D0" | February 7<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" |<br />
|-<br />
| bgcolor="#D0D0D0" | February 14<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-021424.pdf|Multivariable Calculus]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 21<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-022124.pdf|Polynomials]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 28<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 6<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 13<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-031324.pdf|Sequences, series, and recurrences]]<br />
|-<br />
| bgcolor="#D0D0D0" | March 20<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-032024.pdf|Real numbers]]<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26323Algebra and Algebraic Geometry Seminar Spring 20242024-03-14T13:14:52Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''') 2:30-3:30pm in '''B123'''<br />
|[https://www.universiteitleiden.nl/en/staffmembers/marton-hablicsek Marton Hablicsek] (Leiden University)<br />
|[[#Marton Hablicsek|A formality result for logarithmic Hochschild (co)homology]]<br />
|Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.<br />
<br />
<br />
=== Marton Hablicsek ===<br />
==== A formality result for logarithmic Hochschild (co)homology ====<br />
Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For smooth and proper varieties X over a field of characteristic 0, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. For affine schemes, the Hochschild invariants are, in general, infinite dimensional. In this talk, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. Using the formality theorem of Arinkin and Căldăraru, we recover an HKR isomorphism for logarithmic schemes relating logarithmic Hochschild homology to logarithmic differential forms. I will also discuss simple applications of our framework. This is a joint work with Francesca Leonardi and Leo Herr.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=26322Putnam Club2024-03-13T20:06:11Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Assorted algebra problems<br />
|-<br />
| bgcolor="#D0D0D0" | February 7<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" |<br />
|-<br />
| bgcolor="#D0D0D0" | February 14<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-021424.pdf|Multivariable Calculus]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 21<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-022124.pdf|Polynomials]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 28<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 6<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 13<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-031324.pdf|Sequences, series, and recurrences]]<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=File:Putnam-031324.pdf&diff=26321File:Putnam-031324.pdf2024-03-13T19:37:13Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=26320Putnam Club2024-03-13T19:36:54Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Assorted algebra problems<br />
|-<br />
| bgcolor="#D0D0D0" | February 7<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" |<br />
|-<br />
| bgcolor="#D0D0D0" | February 14<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-021424.pdf|Multivariable Calculus]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 21<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-022124.pdf|Polynomials]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 28<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 6<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | <br />
|-<br />
| bgcolor="#D0D0D0" | March 13<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-031324.pdf|Sequences, series, and recursions]]<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26315Algebra and Algebraic Geometry Seminar Spring 20242024-03-12T20:57:28Z<p>Arinkin: /* A formality result for logarithmic Hochschild (co)homology */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''') 2:30-3:30pm<br />
|[https://www.universiteitleiden.nl/en/staffmembers/marton-hablicsek Marton Hablicsek] (Leiden University)<br />
|[[#Marton Hablicsek|A formality result for logarithmic Hochschild (co)homology]]<br />
|Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.<br />
<br />
<br />
=== Marton Hablicsek ===<br />
==== A formality result for logarithmic Hochschild (co)homology ====<br />
Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For smooth and proper varieties X over a field of characteristic 0, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. For affine schemes, the Hochschild invariants are, in general, infinite dimensional. In this talk, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. Using the formality theorem of Arinkin and Căldăraru, we recover an HKR isomorphism for logarithmic schemes relating logarithmic Hochschild homology to logarithmic differential forms. I will also discuss simple applications of our framework. This is a joint work with Francesca Leonardi and Leo Herr.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26314Algebra and Algebraic Geometry Seminar Spring 20242024-03-12T20:57:04Z<p>Arinkin: /* = A formality result for logarithmic Hochschild (co)homology */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''') 2:30-3:30pm<br />
|[https://www.universiteitleiden.nl/en/staffmembers/marton-hablicsek Marton Hablicsek] (Leiden University)<br />
|[[#Marton Hablicsek|A formality result for logarithmic Hochschild (co)homology]]<br />
|Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.<br />
<br />
<br />
=== Marton Hablicsek ===<br />
=== A formality result for logarithmic Hochschild (co)homology ===<br />
Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For smooth and proper varieties X over a field of characteristic 0, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. For affine schemes, the Hochschild invariants are, in general, infinite dimensional. In this talk, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. Using the formality theorem of Arinkin and Căldăraru, we recover an HKR isomorphism for logarithmic schemes relating logarithmic Hochschild homology to logarithmic differential forms. I will also discuss simple applications of our framework. This is a joint work with Francesca Leonardi and Leo Herr.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26313Algebra and Algebraic Geometry Seminar Spring 20242024-03-12T20:56:36Z<p>Arinkin: /* Abstracts */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''') 2:30-3:30pm<br />
|[https://www.universiteitleiden.nl/en/staffmembers/marton-hablicsek Marton Hablicsek] (Leiden University)<br />
|[[#Marton Hablicsek|A formality result for logarithmic Hochschild (co)homology]]<br />
|Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.<br />
<br />
<br />
=== Marton Hablicsek ===<br />
==== A formality result for logarithmic Hochschild (co)homology ===<br />
Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For smooth and proper varieties X over a field of characteristic 0, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. For affine schemes, the Hochschild invariants are, in general, infinite dimensional. In this talk, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. Using the formality theorem of Arinkin and Căldăraru, we recover an HKR isomorphism for logarithmic schemes relating logarithmic Hochschild homology to logarithmic differential forms. I will also discuss simple applications of our framework. This is a joint work with Francesca Leonardi and Leo Herr.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26312Algebra and Algebraic Geometry Seminar Spring 20242024-03-12T20:55:15Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''') 2:30-3:30pm<br />
|[https://www.universiteitleiden.nl/en/staffmembers/marton-hablicsek Marton Hablicsek] (Leiden University)<br />
|[[#Marton Hablicsek|A formality result for logarithmic Hochschild (co)homology]]<br />
|Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2023&diff=26311Algebra and Algebraic Geometry Seminar Fall 20232024-03-12T20:49:35Z<p>Arinkin: </p>
<hr />
<div>[[Algebra and Algebraic Geometry Seminar|Schedule for the current semester.]]<br />
<br />
The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B135.<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 />
== Fall 2023 Schedule==<br />
<br />
{| cellpadding="8"<br />
! align="left" | date<br />
! align="left" | speaker<br />
! align="left" | title<br />
! align="left" | host/link to talk<br />
|-<br />
|September 15<br />
|Joshua Mundinger<br />
|[[#Joshua Mundinger|Quantization in positive characteristic]]<br />
|local<br />
|-<br />
|September 22<br />
|Andrei Negut<br />
|[[#Andrei Negut|Computing K-HA's of quivers]]<br />
|local<br />
|-<br />
|October 6<br />
|[https://www.math.utah.edu/~bragg/ Daniel Bragg (Utah)]<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Daniel Bragg|A Stacky Murphy’s Law for the Stack of Curves]]<br />
|Josh<br />
|-<br />
|October 13<br />
|Xinchun Ma (UChicago)<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Xinchun Ma|Filtrations on the finite dimensional representations of rational Cherednik algebras]]<br />
|Josh<br />
|-<br />
|November 3<br />
|[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj2zfLYr9uBAxX0lYkEHbsEDLgQFnoECA8QAQ&url=https%3A%2F%2Fsites.google.com%2Fuic.edu%2Fjzhao&usg=AOvVaw3q6zkVU_weBiPpPLC9-QlK&opi=89978449 Junyan Zhao] <br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Junyan Zhao|Moduli of curves and K-stability]]<br />
|Peter W<br />
|-<br />
|November 17 <br />
|Purnaprajna Bangere<br />
|[[#Purnaprajna Bangere|Syzygies of adjoint linear series on projective varieties]]<br />
|Michael K<br />
|-<br />
|December 1<br />
|[https://www.math.harvard.edu/people/bogdanova-ekaterina/ Ekaterina Bogdanova (Harvard)]<br />
|[[#Ekaterina Bogdanova|Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization]]<br />
|Dima<br />
|-<br />
|December 8<br />
|[https://sites.google.com/view/wanchun-shen?pli=1 Wanchun (Rosie) Shen (Harvard)]<br />
|[[#Wanchun (Rosie) Shen|Du Bois singularities, rational singularities, and beyond]]<br />
|Andrei<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Joshua Mundinger===<br />
<br />
'''Quantization in positive characteristic'''<br />
<br />
In order to answer basic questions in modular and geometric representation theory, Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties in positive characteristic. These are certain noncommutative algebras over a field of positive characteristic which have a large center. I will discuss recent work describing how to construct an important class of modules over such algebras.<br />
<br />
===Andrei Negut ===<br />
<br />
'''Computing K-HA's of quivers'''<br />
<br />
Many interesting moduli stacks M in geometric representation theory admit interesting K-theoretic Hall algebras (K-HAs), defined by endowing the algebraic K-theory of M with an appropriate convolution product. While these algebras are notoriously hard to compute, they have an interesting relative called the shuffle algebra S. When M is a moduli stack of quiver representations, S is given by a collection of ideals inside polynomial rings, and their study can be reduced to commutative algebra. Fortunately/unfortunately, the commutative algebra in question is challenging, and we do not yet know of a complete description for a general quiver. In this talk, I will explain the general framework behind this problem, and survey results for the following special cases of quivers:<br />
<br />
*double quivers arising in the theory of Nakajima quiver varieties<br />
* quivers corresponding to symmetric Cartan matrices, yielding simply laced quantum loop groups<br />
*quivers associated to toric Calabi-Yau threefolds in mathematical physics<br />
<br />
===Daniel Bragg===<br />
<br />
'''A Stacky Murphy’s Law for the Stack of Curves'''<br />
<br />
We show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. Informally, this means that the moduli space of curves fails to be a fine moduli space in every possible way. We also show the same result for a list of other natural moduli problems. This is joint work with Max Lieblich.<br />
<br />
===Xinchun Ma===<br />
<br />
'''Filtrations on the finite dimensional representations of rational Cherednik algebras'''<br />
<br />
Under the Gordon-Stafford functor, every filtered representation of the type A rational Cherednik algebra corresponds to an equivariant coherent sheaf on the Hilbert scheme of points on the plane. Under the decategorification of this functor, the images of the finite-dimensional representations are conjectured to be closely related to the torus knot superpolynomials (with some special cases proved). There are several candidates for the filtrations coming from algebraic or geometric formulations conjectured to coincide with each other. I'll talk about recent developments on these conjectures including my own work in progress.<br />
<br />
===Junyan Zhao===<br />
<br />
====Moduli of curves and K-stability ====<br />
The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.<br />
<br />
===Purnaprajna Bangere===<br />
<br />
'''Syzygies of adjoint linear series on projective varieties'''<br />
<br />
Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Mark Green on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.<br />
<br />
===Ekaterina Bogdanova===<br />
<br />
'''Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization'''<br />
<br />
Given a DG category acted on by the category of quasi-coherent sheaves on LocSys<sub>''G''</sub>(''D''&deg;) (the stack of ''G''-local systems on the punctured formal disk ''D''&deg;), one can define a factorization Rep(''G'')-module category. Following ideas of Beilinson and Drinfeld, Gaitsgory conjectured that this construction loses no information: that it gives a fully faithful 2-functor QCoh(LocSys<sub>''G''</sub>(''D''&deg;))-mod(DGCat)&rarr;Rep(''G'')-mod<sup>''fact''</sup>(DGCat). I will give a quick introduction to the local Geometric Langlands program, discuss preliminaries, and the role of the above conjecture in this context. If time permits, we will discuss a partial result in the direction of the conjecture. Namely, the fully faithfulness for QCoh(LocSys<sub>''G''</sub>(''D''&deg;))-modules set-theoretically supported over the stack of local systems with restricted variation on the formal punctured disk.<br />
<br />
===Wanchun (Rosie) Shen===<br />
<br />
'''Du Bois singularities, rational singularities, and beyond'''<br />
<br />
We survey some extensions of the classical notions of Du Bois and rational singularities, known as the k-Du Bois and k-rational singularities. By now, these notions are well-understood for local complete intersections (lci). We explain the difficulties beyond the lci case, and propose new definitions in general to make further progress in the theory. This is joint work (in progress) with Mihnea Popa, Matthew Satriano, Sridhar Venkatesh and Anh Duc Vo.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26267Algebra and Algebraic Geometry Seminar Spring 20242024-03-05T23:32:56Z<p>Arinkin: </p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B139'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26252Algebra and Algebraic Geometry Seminar Spring 20242024-03-02T02:21:36Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|-<br />
|April 18<br />
|Teresa Yu (Michigan)<br />
|TBA<br />
|Dima/Jose<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=26234Putnam Club2024-02-27T22:26:39Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Assorted algebra problems<br />
|-<br />
| bgcolor="#D0D0D0" | February 7<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBD<br />
|-<br />
| bgcolor="#D0D0D0" | February 14<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-021424.pdf|Multivariable Calculus]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 21<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-022124.pdf|Polynomials]].<br />
|-<br />
| bgcolor="#D0D0D0" | February 28<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBD<br />
|-<br />
| bgcolor="#D0D0D0" | March 6<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBD<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26207Algebra and Algebraic Geometry Seminar Spring 20242024-02-26T00:22:40Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Shravan Patankar|The absolute integral closure in equicharacteristic zero]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26206Algebra and Algebraic Geometry Seminar Spring 20242024-02-26T00:20:48Z<p>Arinkin: /* Abstracts */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|TBA<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.<br />
<br />
=== Shravan Patankar ===<br />
==== The absolute integral closure in equicharacteristic zero ====<br />
In spite of being large and non noetherian, the absolute integral closure of a domain R, R^{+}, carries great importance in positive characteristic commutative algebra and algebraic geometry. Recent advances due to Bhatt hint at a similar picture in mixed characteristic. In equicharacteristic zero however, this object seems largely unexplored. We answer a series of natural questions which suggest that it might play a similar central role in the study of singularities and algebraic geometry in equicharacteristic zero. More precisely, we show that it is rarely coherent, and facilitates a characterization of regular rings similar to Kunz's theorem. Both of these results, have in turn, applications back to positive characteristics.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26197Algebra and Algebraic Geometry Seminar Spring 20242024-02-22T22:30:24Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|TBA<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26196Algebra and Algebraic Geometry Seminar Spring 20242024-02-22T22:30:09Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 1<br />
|Shravan Patankar (UIC)<br />
|TBA<br />
|Dima/Josh<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=26181Algebra and Algebraic Geometry Seminar Spring 20242024-02-20T16:37:34Z<p>Arinkin: </p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room '''Van Vleck''' '''B317'''.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|February 16<br />
|Sean Cotner (Michigan)<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Sean Cotner|Schemes of homomorphisms]]<br />
|Josh<br />
|-<br />
|February 23<br />
|[https://sites.google.com/view/ylf/ Lingfei Yi (Minnesota)]<br />
|[[Algebra and Algebraic Geometry Seminar Spring 2024#Lingfei Yi|Slices in the loop spaces of symmetric varieties]]<br />
|Dima/Josh<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==<br />
===Sean Cotner===<br />
<br />
==== Schemes of homomorphisms ====<br />
Given two algebraic groups G and H, it is natural to ask whether the set Hom(G, H) of homomorphisms from G to H can be parameterized in a useful way. In general, this is not possible, but there are well-known partial positive results (mainly due to Grothendieck). In this talk I will describe essentially optimal conditions on G and H under which Hom(G, H) is a scheme. There will be many examples, and we will see how a geometric perspective on Hom(G, H) can be useful in studying concrete questions. Time permitting, I will discuss some aspects of the theory of Hom schemes over a base.<br />
<br />
=== Lingfei Yi ===<br />
<br />
==== Slices in the loop spaces of symmetric varieties ====<br />
Let X be a symmetric variety. J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are pointwise pure. This is an important geometric ingredient in their work providing a more geometric approach to the results of Lusztig-Vogan. In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will also explain its applications to the formality conjecture in the relative Langlands duality. If time permits, I will discuss similar constructions for Iwahori orbits. This is a joint work with Tsao-Hsien Chen.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=26027Putnam Club2024-02-02T01:01:34Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Assorted algebra problems<br />
|-<br />
| bgcolor="#D0D0D0" | February 7<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBD<br />
|-<br />
| bgcolor="#D0D0D0" | February 14<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBD<br />
|-<br />
| bgcolor="#D0D0D0" | February 21<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBD<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25981Colloquia2024-01-27T17:23:51Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm in B239</b><br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|[[#Li|Arithmetic of real-analytic modular forms]]<br />
|Yang<br />
|-<br />
|'''Thursday Jan 25 at 4pm in VV911'''<br />
|[https://chimeraki.weebly.com/scientificresearch.html Sanjukta Krishnagopal] (UCLA/UC Berkeley)<br />
|Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes<br />
|Smith<br />
|-<br />
|Jan 26<br />
|[https://www.math.ucla.edu/~jacob/ Jacob Bedrossian] (UCLA)<br />
|Lyapunov exponents in stochastic systems<br />
|Tran<br />
|-<br />
|Feb 2<br />
|William Chen<br />
|[[#Chen|Orbit problems and the mod p properties of Markoff numbers]]<br />
|Arinkin<br />
|-<br />
|Feb 9<br />
|(held for town hall)<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<div id="Li">'''Monday, January 22. Yingkun Li''' <br />
<br />
'''Arithmetic of real-analytic modular forms'''<br />
<br />
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions. <br />
<br />
'''Thursday, January 25. Sanjukta Krishnagopal''' <br />
<br />
'''Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes'''<br />
<br />
In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application. <br />
<br />
First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a graph limit or a graph with infinitely many nodes. I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.<br />
<br />
Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some recent results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of ''multilayer'' simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, and hate speech in social media.<br />
<br />
<br />
<br />
'''Friday, January 26. Jacob Bedrossian'''<br />
<br />
'''Lyapunov exponents in stochastic systems'''<br />
<br />
In this overview talk we discuss several results regarding positive Lyapunov exponents in stochastic systems. First we discuss proving "Lagrangian chaos" in stochastic fluid mechanics, that is, demonstrating a positive Lyapunov exponent for the motion of a particle in the velocity field arising from the stochastic Navier-Stokes equations. We describe how this chaos can be used to deduce qualitatively optimal almost-sure exponential mixing of passive scalars. Next we describe more recently developed methods for obtaining strictly positive lower bounds and some quantitative estimates on the top Lyapunov exponent of weakly-damped stochastic differential equations, such as Lorenz-96 model or Galerkin truncations of the 2d Navier-Stokes equations (called "Eulerian chaos" in fluid mechanics). Further applications of the ideas to the chaotic motion of charged particles in fluctuating magnetic fields and the non-uniqueness of stationary measures for Lorenz 96 in degenerate forcing situations will be discussed if time permits. All of the work except for the charged particles (joint with Chi-Hao Wu) is joint with Alex Blumenthal and Sam Punshon-Smith.<br />
<br />
<div id="Chen">'''Friday, February 2. William Chen'''<br />
<br />
'''Orbit problems and the mod p properties of Markoff numbers'''<br />
<br />
Markoff numbers are positive integers which encode how resistant certain irrational numbers are to being approximated by rationals. In 1913, Frobenius asked for a description of all congruence conditions satisfied by Markoff numbers modulo primes p. In 1991 and 2016, Baragar, Bourgain, Gamburd, and Sarnak conjectured a refinement of Frobenius’s question, which amounts to showing that the Markoff equation x^2 + y^2 + z^2 - xyz = 0 satisfies “strong approximation”; that is to say: they conjecture that its integral points surject onto its mod p points for every prime p. In this talk we will show how to prove this conjecture for all but finitely many primes p, thus reducing the conjecture to a finite computation. A key step is to understand this problem in the context of describing the orbits of certain group actions. Primarily, we will consider the action of the mapping class group of a topological surface S on (a) the set of G-covers of S, where G is a finite group, and (b) on the character variety of local systems on S. Questions of this type have been related to many classical problems, from proving that the moduli space of curves of a given genus is connected, to Grothendieck’s ambitious plan to understand the structure of the absolute Galois group of the rationals by studying its action on “dessins d’enfant”. We will explain some of this history and why such problems can be surprisingly difficult.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25980Colloquia2024-01-27T17:22:10Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm in B239</b><br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|[[#Li|Arithmetic of real-analytic modular forms]]<br />
|Yang<br />
|-<br />
|'''Thursday Jan 25 at 4pm in VV911'''<br />
|[https://chimeraki.weebly.com/scientificresearch.html Sanjukta Krishnagopal] (UCLA/UC Berkeley)<br />
|Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes<br />
|Smith<br />
|-<br />
|Jan 26<br />
|[https://www.math.ucla.edu/~jacob/ Jacob Bedrossian] (UCLA)<br />
|Lyapunov exponents in stochastic systems<br />
|Tran<br />
|-<br />
|Feb 2<br />
|William Chen<br />
|[[#Chen|Orbit problems and the mod p properties of Markoff numbers]]<br />
|Arinkin<br />
|-<br />
|Feb 9<br />
|(held for town hall)<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<div id="Li">'''Monday, January 22. Yingkun Li''' <br />
<br />
'''Arithmetic of real-analytic modular forms'''<br />
<br />
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions. <br />
<br />
'''Thursday, January 25. Sanjukta Krishnagopal''' <br />
<br />
'''Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes'''<br />
<br />
In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application. <br />
<br />
First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a graph limit or a graph with infinitely many nodes. I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.<br />
<br />
Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some recent results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of ''multilayer'' simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, and hate speech in social media.<br />
<br />
<br />
<br />
'''Friday, January 26. Jacob Bedrossian'''<br />
<br />
'''Lyapunov exponents in stochastic systems'''<br />
<br />
In this overview talk we discuss several results regarding positive Lyapunov exponents in stochastic systems. First we discuss proving "Lagrangian chaos" in stochastic fluid mechanics, that is, demonstrating a positive Lyapunov exponent for the motion of a particle in the velocity field arising from the stochastic Navier-Stokes equations. We describe how this chaos can be used to deduce qualitatively optimal almost-sure exponential mixing of passive scalars. Next we describe more recently developed methods for obtaining strictly positive lower bounds and some quantitative estimates on the top Lyapunov exponent of weakly-damped stochastic differential equations, such as Lorenz-96 model or Galerkin truncations of the 2d Navier-Stokes equations (called "Eulerian chaos" in fluid mechanics). Further applications of the ideas to the chaotic motion of charged particles in fluctuating magnetic fields and the non-uniqueness of stationary measures for Lorenz 96 in degenerate forcing situations will be discussed if time permits. All of the work except for the charged particles (joint with Chi-Hao Wu) is joint with Alex Blumenthal and Sam Punshon-Smith.<br />
<br />
<div id="Chen">'''Friday, February 2nd. William Chen'''<br />
<br />
'''Orbit problems and the mod p properties of Markoff numbers'''<br />
<br />
Markoff numbers are positive integers which encode how resistant certain irrational numbers are to being approximated by rationals. In 1913, Frobenius asked for a description of all congruence conditions satisfied by Markoff numbers modulo primes p. In 1991 and 2016, Baragar, Bourgain, Gamburd, and Sarnak conjectured a refinement of Frobenius’s question, which amounts to showing that the Markoff equation x^2 + y^2 + z^2 - xyz = 0 satisfies “strong approximation”; that is to say: they conjecture that its integral points surject onto its mod p points for every prime p. In this talk we will show how to prove this conjecture for all but finitely many primes p, thus reducing the conjecture to a finite computation. A key step is to understand this problem in the context of describing the orbits of certain group actions. Primarily, we will consider the action of the mapping class group of a topological surface S on (a) the set of G-covers of S, where G is a finite group, and (b) on the character variety of local systems on S. Questions of this type have been related to many classical problems, from proving that the moduli space of curves of a given genus is connected, to Grothendieck’s ambitious plan to understand the structure of the absolute Galois group of the rationals by studying its action on “dessins d’enfant”. We will explain some of this history and why such problems can be surprisingly difficult.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25968Putnam Club2024-01-24T18:01:30Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | TBD<br />
| bgcolor="yellow" | TBD<br />
|-<br />
|}<br />
</center><br />
<br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25967Putnam Club2024-01-24T18:00:49Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Spring 2024 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (first meeting on Jan 31st) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
In the spring, the UW holds our own in-house Undergraduate Math Contest. It is (tentatively) scheduled for Saturday, April 13th. <br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old Putnam exams and more information on the Putnam competition.] The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students.</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | January 31<br />
| bgcolor="#D0D0D0" | TBD<br />
| bgcolor="yellow" | TBD<br />
|-<br />
|}<br />
</center><br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">Fall 2023</div></font></span><br />
<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25966Putnam Club2024-01-24T17:53:04Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Probability<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | Combinatorics<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | [[Media:Putnam-112923.pdf|Geometry]].<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | Putnam review<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25959Colloquia2024-01-23T15:04:12Z<p>Arinkin: /* Spring 2024 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm in B239</b><br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|[[#Li|Arithmetic of real-analytic modular forms]]<br />
|Yang<br />
|-<br />
|'''Thursday Jan 25 at 4pm in VV911'''<br />
|[https://chimeraki.weebly.com/scientificresearch.html Sanjukta Krishnagopal] (UCLA/UC Berkeley)<br />
|Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes<br />
|Smith<br />
|-<br />
|Jan 26<br />
|[https://www.math.ucla.edu/~jacob/ Jacob Bedrossian] (UCLA)<br />
|Lyapunov exponents in stochastic systems<br />
|Tran<br />
|-<br />
|Feb 2<br />
|William Chen<br />
|<br />
|<br />
|-<br />
|Feb 9<br />
|(held for town hall)<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<div id="Li">'''Monday, January 22. Yingkun Li''' <br />
<br />
'''Arithmetic of real-analytic modular forms'''<br />
<br />
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions. <br />
<br />
'''Thursday, January 25. Sanjukta Krinshagopal''' <br />
<br />
'''Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes'''<br />
<br />
In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application. <br />
<br />
First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a graph limit or a graph with infinitely many nodes. I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.<br />
<br />
Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some recent results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of ''multilayer'' simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, and hate speech in social media.<br />
<br />
<br />
<br />
'''Friday, January 26. Jacob Bedrossian'''<br />
<br />
'''Lyapunov exponents in stochastic systems'''<br />
<br />
In this overview talk we discuss several results regarding positive Lyapunov exponents in stochastic systems. First we discuss proving "Lagrangian chaos" in stochastic fluid mechanics, that is, demonstrating a positive Lyapunov exponent for the motion of a particle in the velocity field arising from the stochastic Navier-Stokes equations. We describe how this chaos can be used to deduce qualitatively optimal almost-sure exponential mixing of passive scalars. Next we describe more recently developed methods for obtaining strictly positive lower bounds and some quantitative estimates on the top Lyapunov exponent of weakly-damped stochastic differential equations, such as Lorenz-96 model or Galerkin truncations of the 2d Navier-Stokes equations (called "Eulerian chaos" in fluid mechanics). Further applications of the ideas to the chaotic motion of charged particles in fluctuating magnetic fields and the non-uniqueness of stationary measures for Lorenz 96 in degenerate forcing situations will be discussed if time permits. All of the work except for the charged particles (joint with Chi-Hao Wu) is joint with Alex Blumenthal and Sam Punshon-Smith.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25951Colloquia2024-01-22T03:29:05Z<p>Arinkin: /* Spring 2024 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm in B239</b><br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|[[#Li|Arithmetic of real-analytic modular forms]]<br />
|Yang<br />
|-<br />
|'''Thursday Jan 25 at 4pm in VV911'''<br />
|[https://chimeraki.weebly.com/scientificresearch.html Sanjukta Krishnagopal] (UCLA/UC Berkeley)<br />
|<br />
|Smith<br />
|-<br />
|Jan 26<br />
|[https://www.math.ucla.edu/~jacob/ Jacob Bedrossian] (UCLA)<br />
|<br />
|Tran<br />
|-<br />
|Feb 2<br />
|William Chen (to be confirmed)<br />
|<br />
|<br />
|-<br />
|Feb 9<br />
|(held for town hall)<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<div id="Li">'''Monday, January 22. Yingkun Li''' <br />
<br />
'''Arithmetic of real-analytic modular forms'''<br />
<br />
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions. <br />
<br />
'''Thursday, January 25. Sanjukta Krinshagopal''' <br />
<br />
'''Theoretical methods for data-driven complex systems: from mathematical machine learning to simplicial complexes'''<br />
<br />
In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application. <br />
<br />
First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a graph limit or a graph with infinitely many nodes. I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.<br />
<br />
Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some recent results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of ''multilayer'' simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, and hate speech in social media.<br />
<br />
<br />
'''Friday, January 26. Jacob Bedrossian'''<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25927Colloquia2024-01-18T17:32:13Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm</b> (Room TBD)<br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|[[#Li|Arithmetic of real-analytic modular forms]]<br />
|Yang<br />
|-<br />
|Jan 25<br />
|Sanjukta Krishnagopal (UCLA/UC Berkeley)<br />
|<br />
|Smith<br />
|-<br />
|Jan 26<br />
|Jacob Bedrossian (UCLA)<br />
|<br />
|Tran<br />
|-<br />
|Feb 2<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 9<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<div id="Li">'''Monday, January 22. Yingkun Li''' <br />
<br />
'''Arithmetic of real-analytic modular forms'''<br />
<br />
Modular form is a classical mathematical object dating back to the 19th century. Because of its connections to and appearances in many different areas of math and physics, it remains a popular subject today. Since the work of Hans Maass in 1949, real-analytic modular form has found important applications in arithmetic geometry and number theory. In this talk, I will discuss the amazing works in this area over the past 20 years, and give a glimpse of its fascinating future directions. <br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25926Colloquia2024-01-18T17:27:07Z<p>Arinkin: /* Spring 2024 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
<br />
Contacts for the colloquium are Simon Marshall and Dallas Albritton.<br />
<br />
<br />
<br />
==Spring 2024==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" | host(s)<br />
|-<br />
|<b>Monday Jan 22 at 4pm</b> (Room TBD)<br />
|[https://www.mathematik.tu-darmstadt.de/fb/personal/details/yingkun_li.en.jsp Yingkun Li] (Darmstadt Tech U, Germany)<br />
|Arithmetic of real-analytic modular forms<br />
|Yang<br />
|-<br />
|Jan 25<br />
|Sanjukta Krishnagopal (UCLA/UC Berkeley)<br />
|<br />
|Smith<br />
|-<br />
|Jan 26<br />
|Jacob Bedrossian (UCLA)<br />
|<br />
|Tran<br />
|-<br />
|Feb 2<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 9<br />
|<br />
|<br />
|<br />
|-<br />
|Feb 16<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
|Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
|Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
|Mar 15<br />
|[https://sites.google.com/view/peterhumphries/ Peter Humphries] (Virginia)<br />
|<br />
|Marshall<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
|Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
|Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
|-<br />
|Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
|Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
[[Colloquia/Fall 2023|Fall 2023]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=25919Algebra and Algebraic Geometry Seminar Spring 20242024-01-17T22:53:35Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room TBA.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|March 18 ('''Monday''')<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2024&diff=25918Algebra and Algebraic Geometry Seminar Spring 20242024-01-17T22:52:50Z<p>Arinkin: /* Spring 2024 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room TBA.<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 />
==Spring 2024 Schedule==<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host/link to talk<br />
|-<br />
|March 18 (**Monday**)<br />
|Marton Hablicsek<br />
|TBA<br />
|Andrei/Dima<br />
|-<br />
|March 29<br />
|TBA<br />
|TBA<br />
|Josh<br />
|}<br />
<br />
==Abstracts==</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2023&diff=25636Algebra and Algebraic Geometry Seminar Fall 20232023-11-22T23:54:48Z<p>Arinkin: /* Ekaterina Bogdanova */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B135.<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 />
== Fall 2023 Schedule==<br />
<br />
{| cellpadding="8"<br />
! align="left" | date<br />
! align="left" | speaker<br />
! align="left" | title<br />
! align="left" | host/link to talk<br />
|-<br />
|September 15<br />
|Joshua Mundinger<br />
|[[#Joshua Mundinger|Quantization in positive characteristic]]<br />
|local<br />
|-<br />
|September 22<br />
|Andrei Negut<br />
|[[#Andrei Negut|Computing K-HA's of quivers]]<br />
|local<br />
|-<br />
|October 6<br />
|[https://www.math.utah.edu/~bragg/ Daniel Bragg (Utah)]<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Daniel Bragg|A Stacky Murphy’s Law for the Stack of Curves]]<br />
|Josh<br />
|-<br />
|October 13<br />
|Xinchun Ma (UChicago)<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Xinchun Ma|Filtrations on the finite dimensional representations of rational Cherednik algebras]]<br />
|Josh<br />
|-<br />
|November 3<br />
|[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj2zfLYr9uBAxX0lYkEHbsEDLgQFnoECA8QAQ&url=https%3A%2F%2Fsites.google.com%2Fuic.edu%2Fjzhao&usg=AOvVaw3q6zkVU_weBiPpPLC9-QlK&opi=89978449 Junyan Zhao] <br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Junyan Zhao|Moduli of curves and K-stability]]<br />
|Peter W<br />
|-<br />
|November 17 <br />
|Purnaprajna Bangere<br />
|[[#Purnaprajna Bangere|Syzygies of adjoint linear series on projective varieties]]<br />
|Michael K<br />
|-<br />
|December 1<br />
|[https://www.math.harvard.edu/people/bogdanova-ekaterina/ Ekaterina Bogdanova (Harvard)]<br />
|[[#Ekaterina Bogdanova|Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization]]<br />
|Dima<br />
|-<br />
|December 8<br />
|[https://sites.google.com/view/wanchun-shen?pli=1 Wanchun (Rosie) Shen (Harvard)]<br />
|TBA<br />
|Andrei<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Joshua Mundinger===<br />
<br />
'''Quantization in positive characteristic'''<br />
<br />
In order to answer basic questions in modular and geometric representation theory, Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties in positive characteristic. These are certain noncommutative algebras over a field of positive characteristic which have a large center. I will discuss recent work describing how to construct an important class of modules over such algebras.<br />
<br />
===Andrei Negut ===<br />
<br />
'''Computing K-HA's of quivers'''<br />
<br />
Many interesting moduli stacks M in geometric representation theory admit interesting K-theoretic Hall algebras (K-HAs), defined by endowing the algebraic K-theory of M with an appropriate convolution product. While these algebras are notoriously hard to compute, they have an interesting relative called the shuffle algebra S. When M is a moduli stack of quiver representations, S is given by a collection of ideals inside polynomial rings, and their study can be reduced to commutative algebra. Fortunately/unfortunately, the commutative algebra in question is challenging, and we do not yet know of a complete description for a general quiver. In this talk, I will explain the general framework behind this problem, and survey results for the following special cases of quivers:<br />
<br />
*double quivers arising in the theory of Nakajima quiver varieties<br />
* quivers corresponding to symmetric Cartan matrices, yielding simply laced quantum loop groups<br />
*quivers associated to toric Calabi-Yau threefolds in mathematical physics<br />
<br />
===Daniel Bragg===<br />
<br />
'''A Stacky Murphy’s Law for the Stack of Curves'''<br />
<br />
We show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. Informally, this means that the moduli space of curves fails to be a fine moduli space in every possible way. We also show the same result for a list of other natural moduli problems. This is joint work with Max Lieblich.<br />
<br />
===Xinchun Ma===<br />
<br />
'''Filtrations on the finite dimensional representations of rational Cherednik algebras'''<br />
<br />
Under the Gordon-Stafford functor, every filtered representation of the type A rational Cherednik algebra corresponds to an equivariant coherent sheaf on the Hilbert scheme of points on the plane. Under the decategorification of this functor, the images of the finite-dimensional representations are conjectured to be closely related to the torus knot superpolynomials (with some special cases proved). There are several candidates for the filtrations coming from algebraic or geometric formulations conjectured to coincide with each other. I'll talk about recent developments on these conjectures including my own work in progress.<br />
<br />
===Junyan Zhao===<br />
<br />
====Moduli of curves and K-stability ====<br />
The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.<br />
<br />
===Purnaprajna Bangere===<br />
<br />
'''Syzygies of adjoint linear series on projective varieties'''<br />
<br />
Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Mark Green on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.<br />
<br />
===Ekaterina Bogdanova===<br />
<br />
'''Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization'''<br />
<br />
Given a DG category acted on by the category of quasi-coherent sheaves on LocSys<sub>''G''</sub>(''D''&deg;) (the stack of ''G''-local systems on the punctured formal disk ''D''&deg;), one can define a factorization Rep(''G'')-module category. Following ideas of Beilinson and Drinfeld, Gaitsgory conjectured that this construction loses no information: that it gives a fully faithful 2-functor QCoh(LocSys<sub>''G''</sub>(''D''&deg;))-mod(DGCat)&rarr;Rep(''G'')-mod<sup>''fact''</sup>(DGCat). I will give a quick introduction to the local Geometric Langlands program, discuss preliminaries, and the role of the above conjecture in this context. If time permits, we will discuss a partial result in the direction of the conjecture. Namely, the fully faithfulness for QCoh(LocSys<sub>''G''</sub>(''D''&deg;))-modules set-theoretically supported over the stack of local systems with restricted variation on the formal punctured disk.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2023&diff=25635Algebra and Algebraic Geometry Seminar Fall 20232023-11-22T23:49:35Z<p>Arinkin: </p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B135.<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 />
== Fall 2023 Schedule==<br />
<br />
{| cellpadding="8"<br />
! align="left" | date<br />
! align="left" | speaker<br />
! align="left" | title<br />
! align="left" | host/link to talk<br />
|-<br />
|September 15<br />
|Joshua Mundinger<br />
|[[#Joshua Mundinger|Quantization in positive characteristic]]<br />
|local<br />
|-<br />
|September 22<br />
|Andrei Negut<br />
|[[#Andrei Negut|Computing K-HA's of quivers]]<br />
|local<br />
|-<br />
|October 6<br />
|[https://www.math.utah.edu/~bragg/ Daniel Bragg (Utah)]<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Daniel Bragg|A Stacky Murphy’s Law for the Stack of Curves]]<br />
|Josh<br />
|-<br />
|October 13<br />
|Xinchun Ma (UChicago)<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Xinchun Ma|Filtrations on the finite dimensional representations of rational Cherednik algebras]]<br />
|Josh<br />
|-<br />
|November 3<br />
|[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj2zfLYr9uBAxX0lYkEHbsEDLgQFnoECA8QAQ&url=https%3A%2F%2Fsites.google.com%2Fuic.edu%2Fjzhao&usg=AOvVaw3q6zkVU_weBiPpPLC9-QlK&opi=89978449 Junyan Zhao] <br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Junyan Zhao|Moduli of curves and K-stability]]<br />
|Peter W<br />
|-<br />
|November 17 <br />
|Purnaprajna Bangere<br />
|[[#Purnaprajna Bangere|Syzygies of adjoint linear series on projective varieties]]<br />
|Michael K<br />
|-<br />
|December 1<br />
|[https://www.math.harvard.edu/people/bogdanova-ekaterina/ Ekaterina Bogdanova (Harvard)]<br />
|[[#Ekaterina Bogdanova|Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization]]<br />
|Dima<br />
|-<br />
|December 8<br />
|[https://sites.google.com/view/wanchun-shen?pli=1 Wanchun (Rosie) Shen (Harvard)]<br />
|TBA<br />
|Andrei<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Joshua Mundinger===<br />
<br />
'''Quantization in positive characteristic'''<br />
<br />
In order to answer basic questions in modular and geometric representation theory, Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties in positive characteristic. These are certain noncommutative algebras over a field of positive characteristic which have a large center. I will discuss recent work describing how to construct an important class of modules over such algebras.<br />
<br />
===Andrei Negut ===<br />
<br />
'''Computing K-HA's of quivers'''<br />
<br />
Many interesting moduli stacks M in geometric representation theory admit interesting K-theoretic Hall algebras (K-HAs), defined by endowing the algebraic K-theory of M with an appropriate convolution product. While these algebras are notoriously hard to compute, they have an interesting relative called the shuffle algebra S. When M is a moduli stack of quiver representations, S is given by a collection of ideals inside polynomial rings, and their study can be reduced to commutative algebra. Fortunately/unfortunately, the commutative algebra in question is challenging, and we do not yet know of a complete description for a general quiver. In this talk, I will explain the general framework behind this problem, and survey results for the following special cases of quivers:<br />
<br />
*double quivers arising in the theory of Nakajima quiver varieties<br />
* quivers corresponding to symmetric Cartan matrices, yielding simply laced quantum loop groups<br />
*quivers associated to toric Calabi-Yau threefolds in mathematical physics<br />
<br />
===Daniel Bragg===<br />
<br />
'''A Stacky Murphy’s Law for the Stack of Curves'''<br />
<br />
We show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. Informally, this means that the moduli space of curves fails to be a fine moduli space in every possible way. We also show the same result for a list of other natural moduli problems. This is joint work with Max Lieblich.<br />
<br />
===Xinchun Ma===<br />
<br />
'''Filtrations on the finite dimensional representations of rational Cherednik algebras'''<br />
<br />
Under the Gordon-Stafford functor, every filtered representation of the type A rational Cherednik algebra corresponds to an equivariant coherent sheaf on the Hilbert scheme of points on the plane. Under the decategorification of this functor, the images of the finite-dimensional representations are conjectured to be closely related to the torus knot superpolynomials (with some special cases proved). There are several candidates for the filtrations coming from algebraic or geometric formulations conjectured to coincide with each other. I'll talk about recent developments on these conjectures including my own work in progress.<br />
<br />
===Junyan Zhao===<br />
<br />
====Moduli of curves and K-stability ====<br />
The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.<br />
<br />
===Purnaprajna Bangere===<br />
<br />
'''Syzygies of adjoint linear series on projective varieties'''<br />
<br />
Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Mark Green on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.<br />
<br />
===Ekaterina Bogdanova===<br />
<br />
'''Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization'''<br />
<br />
Given a DG category acted on by the category of quasi-coherent sheaves on ''LocSys''<sub>G</sub>(''D''{{sup|&circ}}) (the stack of G-local systems on the punctured formal disk <math>D^{\circ}</math>), one can define a factorization Rep(G)-module category. Following ideas of Beilinson and Drinfeld, Gaitsgory conjectured that this construction loses no information: that it gives a fully faithful 2-functor QCoh(LocSys_G(D^{\circ}))-mod (DGCat) —> Rep(G)-mod^fact(DGCat). I will give a quick introduction to the local Geometric Langlands program, discuss preliminaries, and the role of the above conjecture in this context. If time permits, we will discuss a partial result in the direction of the conjecture. Namely, the fully faithfulness for QCoh(LocSys_G(D^{\circ}))-modules set-theoretically supported over the stack of local systems with restricted variation on the formal punctured disk.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Abelian_varieties_2023&diff=25621Abelian varieties 20232023-11-20T23:08:06Z<p>Arinkin: </p>
<hr />
<div>We are following Polishchuk's book "Abelian varieties, theta functions, and the Fourier transform". All references are to the book<br />
<br />
=== Meeting schedule ===<br />
Starting with the second part of the book, please sign up!<br />
<br />
Our normal meeting time is on Mondays, 3:30-5pm.<br />
<br />
* November 6: Chapter 8: Abelian varieties, rigidity lemma, and the seesaw principle.<br />
* November 13 (Kevin Dao): Chapters 8, 9: Line bundles on abelian varieties.<br />
* <s>November 20 (Alex Vischer) Chapter 9.</s> Cancelled<br />
* November 27 at '''2:30''' (Alex Vischer) Chapter 9. <br />
* December 4 (Jameson Auger) Chapter 10.<br />
* December 11 (Sign up here) Chapter 11?</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2023&diff=25618Algebra and Algebraic Geometry Seminar Fall 20232023-11-20T21:23:01Z<p>Arinkin: /* Fall 2023 Schedule */</p>
<hr />
<div>The seminar normally meets 2:30-3:30pm on Fridays, in the room VV B135.<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 />
== Fall 2023 Schedule==<br />
<br />
{| cellpadding="8"<br />
! align="left" | date<br />
! align="left" | speaker<br />
! align="left" | title<br />
! align="left" | host/link to talk<br />
|-<br />
|September 15<br />
|Joshua Mundinger<br />
|[[#Joshua Mundinger|Quantization in positive characteristic]]<br />
|local<br />
|-<br />
|September 22<br />
|Andrei Negut<br />
|[[#Andrei Negut|Computing K-HA's of quivers]]<br />
|local<br />
|-<br />
|October 6<br />
|[https://www.math.utah.edu/~bragg/ Daniel Bragg (Utah)]<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Daniel Bragg|A Stacky Murphy’s Law for the Stack of Curves]]<br />
|Josh<br />
|-<br />
|October 13<br />
|Xinchun Ma (UChicago)<br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Xinchun Ma|Filtrations on the finite dimensional representations of rational Cherednik algebras]]<br />
|Josh<br />
|-<br />
|November 3<br />
|[https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj2zfLYr9uBAxX0lYkEHbsEDLgQFnoECA8QAQ&url=https%3A%2F%2Fsites.google.com%2Fuic.edu%2Fjzhao&usg=AOvVaw3q6zkVU_weBiPpPLC9-QlK&opi=89978449 Junyan Zhao] <br />
|[[Algebra and Algebraic Geometry Seminar Fall 2023#Junyan Zhao|Moduli of curves and K-stability]]<br />
|Peter W<br />
|-<br />
|November 17 <br />
|Purnaprajna Bangere<br />
|[[#Purnaprajna Bangere|Syzygies of adjoint linear series on projective varieties]]<br />
|Michael K<br />
|-<br />
|December 1<br />
|[https://www.math.harvard.edu/people/bogdanova-ekaterina/ Ekaterina Bogdanova (Harvard)]<br />
|Sheaves of categories on the moduli stack of local systems on the formal punctured disk via factorization<br />
|Dima<br />
|-<br />
|December 8<br />
|[https://sites.google.com/view/wanchun-shen?pli=1 Wanchun (Rosie) Shen (Harvard)]<br />
|TBA<br />
|Andrei<br />
|}<br />
<br />
==Abstracts==<br />
<br />
===Joshua Mundinger===<br />
<br />
'''Quantization in positive characteristic'''<br />
<br />
In order to answer basic questions in modular and geometric representation theory, Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties in positive characteristic. These are certain noncommutative algebras over a field of positive characteristic which have a large center. I will discuss recent work describing how to construct an important class of modules over such algebras.<br />
<br />
===Andrei Negut===<br />
<br />
'''Computing K-HA's of quivers'''<br />
<br />
Many interesting moduli stacks M in geometric representation theory admit interesting K-theoretic Hall algebras (K-HAs), defined by endowing the algebraic K-theory of M with an appropriate convolution product. While these algebras are notoriously hard to compute, they have an interesting relative called the shuffle algebra S. When M is a moduli stack of quiver representations, S is given by a collection of ideals inside polynomial rings, and their study can be reduced to commutative algebra. Fortunately/unfortunately, the commutative algebra in question is challenging, and we do not yet know of a complete description for a general quiver. In this talk, I will explain the general framework behind this problem, and survey results for the following special cases of quivers:<br />
<br />
* double quivers arising in the theory of Nakajima quiver varieties<br />
* quivers corresponding to symmetric Cartan matrices, yielding simply laced quantum loop groups<br />
* quivers associated to toric Calabi-Yau threefolds in mathematical physics<br />
<br />
=== Daniel Bragg ===<br />
<br />
'''A Stacky Murphy’s Law for the Stack of Curves'''<br />
<br />
We show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. Informally, this means that the moduli space of curves fails to be a fine moduli space in every possible way. We also show the same result for a list of other natural moduli problems. This is joint work with Max Lieblich.<br />
<br />
=== Xinchun Ma ===<br />
<br />
'''Filtrations on the finite dimensional representations of rational Cherednik algebras'''<br />
<br />
Under the Gordon-Stafford functor, every filtered representation of the type A rational Cherednik algebra corresponds to an equivariant coherent sheaf on the Hilbert scheme of points on the plane. Under the decategorification of this functor, the images of the finite-dimensional representations are conjectured to be closely related to the torus knot superpolynomials (with some special cases proved). There are several candidates for the filtrations coming from algebraic or geometric formulations conjectured to coincide with each other. I'll talk about recent developments on these conjectures including my own work in progress.<br />
<br />
=== Junyan Zhao ===<br />
<br />
==== Moduli of curves and K-stability ====<br />
The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.<br />
<br />
===Purnaprajna Bangere===<br />
<br />
'''Syzygies of adjoint linear series on projective varieties'''<br />
<br />
Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Mark Green on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Abelian_varieties_2023&diff=25606Abelian varieties 20232023-11-17T22:53:51Z<p>Arinkin: /* Meeting schedule */</p>
<hr />
<div>We are following Polishchuk's book "Abelian varieties, theta functions, and the Fourier transform". All references are to the book<br />
<br />
=== Meeting schedule ===<br />
Starting with the second part of the book, please sign up!<br />
<br />
Our normal meeting time is on Mondays, 3:30-5pm.<br />
<br />
* November 6: Chapter 8: Abelian varieties, rigidity lemma, and the seesaw principle.<br />
* November 13 (Kevin Dao): Chapters 8, 9: Line bundles on abelian varieties.<br />
* November 20 (Alex Vischer) Chapter 9.<br />
* November 27 (Sign up here) Chapter 10?:<br />
* December 4 (Jameson Auger) Chapter 11?:<br />
* December 11 (Sign up here):</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25566Colloquia2023-11-10T21:49:19Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|''no colloquium (see Monday)''<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures: On the Solvability of the Navier-Stokes and Euler Equations, where do we stand?<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Some new results in Higher Teichmüller Theory<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|The Schrödinger equations as inspiration of beautiful mathematics<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|Probabilistic tools in discrete harmonic analysis<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Tuesday Nov 14 at 4 pm (Room TBD!)</b><br />
|[https://www.iazd.uni-hannover.de/en/gao Ziyang Gao] (Leibniz University Hannover)<br />
|[[#Gao|Sparsity of rational and algebraic points]]<br />
|Arinkin, Yang<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
<br />
'''Friday, September 22. David Dumas'''<br />
<br />
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.<br />
<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
<br />
<br />
''' Friday, October 20. Sara Maloni'''<br />
<br />
The Teichmüller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, the Teichmüller space can also be seen as a connected component of (conjugacy classes of) representations from the fundamental group of S into PSL(2,R), consisting entirely of discrete and faithful representations. Generalizing this point of view, Higher Teichmüller Theory studies connected components of (conjugacy classes of) representations from the fundamental group of S into more general semisimple Lie groups which consist entirely of discrete and faithful representations.<br />
<br />
We will give a survey of some aspects of Higher Teichmüller Theory and will make links with the recent powerful notion of Anosov representation. We will conclude by focusing on two separate questions: Do these representations correspond to deformation of geometric structures? <br />
Can we generalize the important notion of pleated surfaces to higher rank Lie groups like PSL(d, C)?<br />
The answer to question 1 is joint work with Alessandrini, Tholozan and Wienhard, while the answer to question 2 is joint work with Martone, Mazzoli and Zhang.<br />
<br />
<br />
'''Wednesday, October 25. Gigliola Staffilani'''<br />
<br />
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed <br />
to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic <br />
nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.<br />
<br />
<br />
'''Friday, October 27. Rodrigo Bañuelos'''<br />
<br />
'''Probabilistic tools in discrete harmonic analysis'''<br />
<br />
The discrete Hilbert transform was introduced by David Hilbert at the beginning of the 20th century as an example of a singular quadratic form. Its boundedness on the space of square summable sequences appeared in H. Weyl’s doctoral dissertation (under Hilbert) in 1908. In 1925, M. Riesz proved that the continuous version of this operator is bounded on L^p(R), 1 < p < \infty, and that the same holds for the discrete version on the integers. Shortly thereafter (1926), E. C. Titchmarsh gave a different proof and from it concluded that the operators have the same p-norm. Unfortunately, Titchmarsh’s argument for equality was incorrect. The question of equality of the norms had been a “simple tantalizing" problem ever since.<br />
<br />
In this general colloquium talk the speaker will discuss a probabilistic construction, based on Doob’s “h-Brownian motion," that leads to sharp inequalities for a collection of discrete operators on the d-dimensional lattice Z^d, d ≥ 1. The case d = 1 verifies equality of the norms for the discrete and continuous Hilbert transforms. The case d > 1 leads to similar questions and conjectures for other Calderón-Zygmund singular integrals in higher dimensions.<br />
<br />
<br />
<div id="Gao">'''Tuesday, November 14. Ziyang Gao'''</div><br />
<br />
'''Sparsity of rational and algebraic points'''<br />
<br />
It is a fundamental question in mathematics to find rational solutions to a given system of polynomials, and in modern language this question translates into finding rational points in algebraic varieties. This question is already very deep for algebraic curves defined over Q. An intrinsic natural number associated with the curve, called its genus, plays an important role in studying the rational points on the curve. In 1983, Faltings proved the famous Mordell Conjecture (proposed in 1922), which asserts that any curve of genus at least 2 has only finitely many rational points. Thus the problem for curves of genus at least 2 can be divided into several grades: finiteness, bound, uniform bound, effectiveness. An answer to each grade requires a better understanding of the distribution of the rational points.<br />
In my talk, I will explain the historical and recent developments of this problem according to the different grades. Another important topic on studying points on curves is the torsion packets. This topic goes beyond rational points. I will also discuss briefly about it in my talk.<br />
<br />
==Future Colloquia==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25565Colloquia2023-11-10T21:48:35Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|''no colloquium (see Monday)''<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures: On the Solvability of the Navier-Stokes and Euler Equations, where do we stand?<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Some new results in Higher Teichmüller Theory<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|The Schrödinger equations as inspiration of beautiful mathematics<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|Probabilistic tools in discrete harmonic analysis<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Tuesday Nov 14 at 4 pm</b><br />
|[https://www.iazd.uni-hannover.de/en/gao Ziyang Gao] (Leibniz University Hannover)<br />
|[[#Gao|Sparsity of rational and algebraic points]]<br />
|Arinkin, Yang<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
<br />
'''Friday, September 22. David Dumas'''<br />
<br />
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.<br />
<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
<br />
<br />
''' Friday, October 20. Sara Maloni'''<br />
<br />
The Teichmüller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, the Teichmüller space can also be seen as a connected component of (conjugacy classes of) representations from the fundamental group of S into PSL(2,R), consisting entirely of discrete and faithful representations. Generalizing this point of view, Higher Teichmüller Theory studies connected components of (conjugacy classes of) representations from the fundamental group of S into more general semisimple Lie groups which consist entirely of discrete and faithful representations.<br />
<br />
We will give a survey of some aspects of Higher Teichmüller Theory and will make links with the recent powerful notion of Anosov representation. We will conclude by focusing on two separate questions: Do these representations correspond to deformation of geometric structures? <br />
Can we generalize the important notion of pleated surfaces to higher rank Lie groups like PSL(d, C)?<br />
The answer to question 1 is joint work with Alessandrini, Tholozan and Wienhard, while the answer to question 2 is joint work with Martone, Mazzoli and Zhang.<br />
<br />
<br />
'''Wednesday, October 25. Gigliola Staffilani'''<br />
<br />
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed <br />
to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic <br />
nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.<br />
<br />
<br />
'''Friday, October 27. Rodrigo Bañuelos'''<br />
<br />
'''Probabilistic tools in discrete harmonic analysis'''<br />
<br />
The discrete Hilbert transform was introduced by David Hilbert at the beginning of the 20th century as an example of a singular quadratic form. Its boundedness on the space of square summable sequences appeared in H. Weyl’s doctoral dissertation (under Hilbert) in 1908. In 1925, M. Riesz proved that the continuous version of this operator is bounded on L^p(R), 1 < p < \infty, and that the same holds for the discrete version on the integers. Shortly thereafter (1926), E. C. Titchmarsh gave a different proof and from it concluded that the operators have the same p-norm. Unfortunately, Titchmarsh’s argument for equality was incorrect. The question of equality of the norms had been a “simple tantalizing" problem ever since.<br />
<br />
In this general colloquium talk the speaker will discuss a probabilistic construction, based on Doob’s “h-Brownian motion," that leads to sharp inequalities for a collection of discrete operators on the d-dimensional lattice Z^d, d ≥ 1. The case d = 1 verifies equality of the norms for the discrete and continuous Hilbert transforms. The case d > 1 leads to similar questions and conjectures for other Calderón-Zygmund singular integrals in higher dimensions.<br />
<br />
<br />
<div id="Gao">'''Tuesday, November 14. Ziyang Gao'''</div><br />
<br />
'''Sparsity of rational and algebraic points'''<br />
<br />
It is a fundamental question in mathematics to find rational solutions to a given system of polynomials, and in modern language this question translates into finding rational points in algebraic varieties. This question is already very deep for algebraic curves defined over Q. An intrinsic natural number associated with the curve, called its genus, plays an important role in studying the rational points on the curve. In 1983, Faltings proved the famous Mordell Conjecture (proposed in 1922), which asserts that any curve of genus at least 2 has only finitely many rational points. Thus the problem for curves of genus at least 2 can be divided into several grades: finiteness, bound, uniform bound, effectiveness. An answer to each grade requires a better understanding of the distribution of the rational points.<br />
In my talk, I will explain the historical and recent developments of this problem according to the different grades. Another important topic on studying points on curves is the torsion packets. This topic goes beyond rational points. I will also discuss briefly about it in my talk.<br />
<br />
==Future Colloquia==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25563Colloquia2023-11-10T21:40:16Z<p>Arinkin: </p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b><br />
==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|''no colloquium (see Monday)''<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures: On the Solvability of the Navier-Stokes and Euler Equations, where do we stand?<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Some new results in Higher Teichmüller Theory<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|The Schrödinger equations as inspiration of beautiful mathematics<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|Probabilistic tools in discrete harmonic analysis<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|<s>Distinguished lectures</s> Cancelled<br />
|Gurevich<br />
|-<br />
|<b>Tuesday Nov 14 at 4 pm</b><br />
|[https://www.iazd.uni-hannover.de/en/gao Ziyang Gao] (Leibniz University Hannover)<br />
|[[#Gao|Sparsity of rational and algebraic points]]<br />
|Arinkin<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
<br />
'''Friday, September 22. David Dumas'''<br />
<br />
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.<br />
<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
<br />
<br />
''' Friday, October 20. Sara Maloni'''<br />
<br />
The Teichmüller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, the Teichmüller space can also be seen as a connected component of (conjugacy classes of) representations from the fundamental group of S into PSL(2,R), consisting entirely of discrete and faithful representations. Generalizing this point of view, Higher Teichmüller Theory studies connected components of (conjugacy classes of) representations from the fundamental group of S into more general semisimple Lie groups which consist entirely of discrete and faithful representations.<br />
<br />
We will give a survey of some aspects of Higher Teichmüller Theory and will make links with the recent powerful notion of Anosov representation. We will conclude by focusing on two separate questions: Do these representations correspond to deformation of geometric structures? <br />
Can we generalize the important notion of pleated surfaces to higher rank Lie groups like PSL(d, C)?<br />
The answer to question 1 is joint work with Alessandrini, Tholozan and Wienhard, while the answer to question 2 is joint work with Martone, Mazzoli and Zhang.<br />
<br />
<br />
'''Wednesday, October 25. Gigliola Staffilani'''<br />
<br />
In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed <br />
to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrödinger equation. I will start by giving a physical derivation of the equation from a quantum many-particles system, I will introduce periodic Strichartz estimates along with some remarkable connections to analytic number theory, I will move on the concept of energy transfer and its connection to dynamical systems, and I will end with some results following from viewing the periodic <br />
nonlinear Schrödinger equation as an infinite dimensional Hamiltonian system.<br />
<br />
<br />
'''Friday, October 27. Rodrigo Bañuelos'''<br />
<br />
'''Probabilistic tools in discrete harmonic analysis'''<br />
<br />
The discrete Hilbert transform was introduced by David Hilbert at the beginning of the 20th century as an example of a singular quadratic form. Its boundedness on the space of square summable sequences appeared in H. Weyl’s doctoral dissertation (under Hilbert) in 1908. In 1925, M. Riesz proved that the continuous version of this operator is bounded on L^p(R), 1 < p < \infty, and that the same holds for the discrete version on the integers. Shortly thereafter (1926), E. C. Titchmarsh gave a different proof and from it concluded that the operators have the same p-norm. Unfortunately, Titchmarsh’s argument for equality was incorrect. The question of equality of the norms had been a “simple tantalizing" problem ever since.<br />
<br />
In this general colloquium talk the speaker will discuss a probabilistic construction, based on Doob’s “h-Brownian motion," that leads to sharp inequalities for a collection of discrete operators on the d-dimensional lattice Z^d, d ≥ 1. The case d = 1 verifies equality of the norms for the discrete and continuous Hilbert transforms. The case d > 1 leads to similar questions and conjectures for other Calderón-Zygmund singular integrals in higher dimensions.<br />
<br />
<br />
<div id="Gao">'''Tuesday, November 14. Ziyang Gao'''</div><br />
<br />
'''Sparsity of rational and algebraic points'''<br />
<br />
It is a fundamental question in mathematics to find rational solutions to a given system of polynomials, and in modern language this question translates into finding rational points in algebraic varieties. This question is already very deep for algebraic curves defined over Q. An intrinsic natural number associated with the curve, called its genus, plays an important role in studying the rational points on the curve. In 1983, Faltings proved the famous Mordell Conjecture (proposed in 1922), which asserts that any curve of genus at least 2 has only finitely many rational points. Thus the problem for curves of genus at least 2 can be divided into several grades: finiteness, bound, uniform bound, effectiveness. An answer to each grade requires a better understanding of the distribution of the rational points.<br />
In my talk, I will explain the historical and recent developments of this problem according to the different grades. Another important topic on studying points on curves is the torsion packets. This topic goes beyond rational points. I will also discuss briefly about it in my talk.<br />
<br />
==Future Colloquia==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<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>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Abelian_varieties_2023&diff=25551Abelian varieties 20232023-11-07T20:28:13Z<p>Arinkin: </p>
<hr />
<div>We are following Polishchuk's book "Abelian varieties, theta functions, and the Fourier transform". All references are to the book<br />
<br />
=== Meeting schedule ===<br />
Starting with the second part of the book, please sign up!<br />
<br />
Our normal meeting time is on Mondays, 3:30-5pm.<br />
<br />
* November 6: Chapter 8: Abelian varieties, rigidity lemma, and the seesaw principle.<br />
* November 13 (Sign up here): Chapters 8, 9: Line bundles on abelian varieties.<br />
* November 20 (Sign up here) Chapter 9?:<br />
* November 27 (Sign up here) Chapter 10?:<br />
* December 4 (Sign up here) Chapter 11?:<br />
* December 11 (Sign up here):</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Abelian_varieties_2023&diff=25550Abelian varieties 20232023-11-07T20:21:45Z<p>Arinkin: </p>
<hr />
<div>We are following Polishchuk's book "Abelian varieties, theta functions, and the Fourier transform". All references are to the book<br />
<br />
=== Meeting schedule ===<br />
Starting with the second part of the book, please sign up!<br />
<br />
Our normal meeting time is on Mondays, 3:30-5pm.<br />
<br />
* November 6: Abelian varieties, rigidity lemma, and the seesaw principle.<br />
* November 13 (Sign up here): Line bundles on abelian varieties.<br />
* November 20 (Sign up here):<br />
* November 27 (Sign up here):<br />
* December 4 (Sign up here):<br />
* December 11 (Sign up here):</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Abelian_varieties_2023&diff=25549Abelian varieties 20232023-11-07T20:20:59Z<p>Arinkin: Wiki page for the reading seminar</p>
<hr />
<div>We are following Polishchuk's book "Abelian varieties, theta functions, and the Fourier transform". All references are to the book<br />
<br />
=== Meeting schedule (starting with the second part of the book), please sign up! ===<br />
<br />
Our normal time is on Mondays, 3:30-5pm.<br />
<br />
* November 6: Abelian varieties, rigidity lemma, and the seesaw principle.<br />
* November 13 (Sign up here): Line bundles on abelian varieties.<br />
* November 20 (Sign up here):<br />
* November 27 (Sign up here):<br />
* December 4 (Sign up here):<br />
* December 11 (Sign up here):</div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25523Putnam Club2023-11-01T01:39:16Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Let us try something different today: a mock math contest. Let's look at a past [https://intranet.math.vt.edu/vtrmc/exams/37th%20VTRMC.pdf Virginia Tech Contests].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=File:Putnam-102523.pdf&diff=25494File:Putnam-102523.pdf2023-10-24T16:45:12Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25493Putnam Club2023-10-24T16:44:26Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 22<br />
| <br />
| No meeting (Wednesday before Thanksgiving)<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25492Putnam Club2023-10-24T16:42:59Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | Even numbered problems from last time and [https://drive.google.com/file/d/1fe4Dxp7w3C3u5IvnM-U11dVyCWL1S0DA/view?usp=drive_link additional calculus problems]<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-102523.pdf|Number theory]].<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | November 8<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | November 15<br />
| bgcolor="#D0D0D0" | Brian Lawrence<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
<br />
| bgcolor="#D0D0D0" | November 29<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | December 6<br />
| bgcolor="#D0D0D0" | Paul Apisa<br />
| bgcolor="yellow" | TBA<br />
|-<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25427Putnam Club2023-10-12T23:29:48Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:Putnam-092723.pdf|assorted problems]].<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:Putnam-100423.pdf|Polynomials]].<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 11<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | [https://drive.google.com/file/d/1yonONnXcFyI7VRaAyqnYodZuJIXoTfrJ/view?usp=drive_link Calculus problems].<br />
|-<br />
| bgcolor="#D0D0D0" | October 18<br />
| bgcolor="#D0D0D0" | Laurel Ohm<br />
| bgcolor="yellow" | TBA<br />
|-<br />
<br />
| bgcolor="#D0D0D0" | October 25<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | TBA<br />
|-<br />
| bgcolor="#D0D0D0" | November 1<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | TBA<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=File:Putnam-100423.pdf&diff=25365File:Putnam-100423.pdf2023-10-03T22:45:53Z<p>Arinkin: </p>
<hr />
<div></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25364Putnam Club2023-10-03T22:45:19Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:putnam-092723.pdf|assorted problems]].<br />
<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | [[Media:putnam-100423.pdf|Polynomials]].<br />
|}<br />
</center></div>Arinkinhttps://wiki.math.wisc.edu/index.php?title=Putnam_Club&diff=25323Putnam Club2023-09-26T16:05:55Z<p>Arinkin: </p>
<hr />
<div>[[File:Bascom-fall-1500x500-1500x500.jpg]] <br />
<br />
<span style="color:Indigo"><font size="5"> <div style="text-align: center;">WELCOME TO THE Fall 2023 PUTNAM CLUB!</div></font></span><br />
<br />
<div style="text-align: center;"><span style="color:crimson"><font size="3">Organizers: Paul Apisa, Dima Arinkin, Brian Lawrence, Laurel Ohm </font></span><br />
<br />
'''Join us on Wednesdays 5:00-6:30pm (from September 27th) in Van Vleck B325 for some challenging questions, pizza and soda!!!'''<br />
<br />
The Putnam Exam, offered by the Mathematical Association of America, is the premier American math competition for undergraduate students. This year, the exam is on Saturday, December 2nd. <br />
The exam is run in two three-hour sessions of six problems each. This is a difficult exam with many interesting and fun problems.<br />
<br />
<div style="text-align: center;">[http://kskedlaya.org/putnam-archive/ Old exams and more information on the Putnam competition.]</div><br />
<div style="text-align: center;">[[Putnam Club Archive | The archive of the Putnam Club from past years, with many practice problems.]]</div><br />
<br />
'''To sign up for Putnam club email announcements, please send an email to ''putnam-club+join@g-groups.wisc.edu'' (empty subject and body works). '''<br />
<br />
<center><br />
{|style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" | September 27<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | Introductory meeting - [[Media:putnam-092723.pdf|assorted problems]].<br />
<br />
|-<br />
| bgcolor="#D0D0D0" | October 4<br />
| bgcolor="#D0D0D0" | Dima Arinkin<br />
| bgcolor="yellow" | TBA<br />
|}<br />
</center></div>Arinkin