https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Kemeny&feedformat=atomUW-Math Wiki - User contributions [en]2022-10-03T17:52:29ZUser contributionsMediaWiki 1.35.6https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=22282Algebra and Algebraic Geometry Seminar Fall 20212021-12-03T04:36:37Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Yi (Peter) Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|Michael Perlman (Minnesota; virtual)<br />
|Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
|<br />
|Daniel<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|CA+ meeting [ https://www-users.cse.umn.edu/~cberkesc/CA/CA2021.html]<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
<br />
<br />
<br />
|<br />
|-<br />
|November 12 -- TALK AT NONSTANDARD TIME<br />
|Jinhyung Park at 9:00am (Zoom)<br />
|Asymptotic vanishing of syzygies of algebraic varieties<br />
|<br />
|<br />
|-<br />
|November 12 <br />
|Daniel Erman at usual time (2:30pm)<br />
|The geometry of virtual syzygies<br />
|<br />
|<br />
|-<br />
|November 19<br />
|Ritvik Ramkumar (UC Berkeley; Zoom)<br />
|Rational singularities of nested Hilbert schemes. <br />
|<br />
|Daniel<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|Federico Barbacovi (University College London; Zoom)<br />
|Categorical dynamical systems and Gromov—Yomdin type theorems<br />
|<br />
|Andrei<br />
|-<br />
|April 8<br />
|Haydee Lindo<br />
|<br />
|<br />
|Daniel<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.<br />
<br />
===Michael Perlman===<br />
Title: Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
<br />
Abstract: Given a closed subvariety Z in a smooth complex variety, the local cohomology modules with support in Z are functorially endowed with structures as mixed Hodge modules, implying that they are equipped with Hodge and weight filtrations that subtly measure the singularities of Z. We will discuss new calculations of these filtrations in the case when Z is a generic determinantal variety. As an application, we obtain the Hodge ideals for the determinant hypersurface. Joint work with Claudiu Raicu.<br />
<br />
===Jinhyung Park===<br />
Title: Asymptotic vanishing of syzygies of algebraic varieties<br />
<br />
Abstract: In this talk, we show Ein-Lazarsfeld's conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein-Lazarsfeld's asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows.<br />
<br />
===Daniel Erman===<br />
Title: The geometry of virtual syzygies<br />
<br />
Abstract: One of the foundational results connecting syzygies with algebraic geometry properties was Mark Green’s result on N_p conditions for smooth curves of high degree. A modern and streamlined proof of this result comes via Green’s Linear Syzygy Theorem. I will discuss very recent work with Michael Brown which proves a Multigraded Linear Syzygy Theorem and uses this to obtain the first known examples of “virtual" N_p conditions for smooth curves of high degree in other toric varieties. This is joint work with Michael Brown.<br />
<br />
===Ritvik Ramkumar===<br />
Title: Rational singularities of nested Hilbert schemes. <br />
<br />
Abstract: For a smooth surface S the Hilbert scheme of points S^(n) is a well studied smooth parameter space. In this talk I will consider a natural generalization, the nested Hilbert scheme of points S^(n,m) which parameterizes pairs of 0-dimensional subschemes X \supseteq Y of S with deg(X) = n and deg(Y) = m. In contrast to the usual Hilbert scheme of points, S^(n,m) is almost always singular and it is known that S(n,1) has rational singularities. I will discuss some general techniques to study S^(n,m) and apply them to show that S^(n,2) also has rational singularities. This relies on a connection between S^(n,2) and a certain variety of matrices, and involves square-free Gröbner degenerations as well as the Kempf-Weyman geometric technique. This is joint work with Alessio Sammartano.<br />
<br />
===Eric Ramos===<br />
Tite: Equivariant log-concavity<br />
<br />
Abstract: Log concave sequences have been ubiquitous in combinatorics for decades. For instance, June Huh famously proved that the Betti numbers of the complement of a complex hyperplane arrangement always form a log concave sequence. In this talk I will introduce an equivariant version of log concave sequences for representations of groups, and present a conjecture of Nick Proudfoot on such sequences arising from hyperplane arrangements. I will then show that one can use a numerical version of representation stability to prove infinitely many cases of this conjecture for configuration spaces. This is joint work with Jacob Matherne, Dane Miyata, and Nick Proudfoot.<br />
<br />
===Federico Barbacovi===<br />
Title: Categorical dynamical systems and Gromov—Yomdin type theorems<br />
<br />
Abstract: Categorical dynamical systems were introduced by Dimitrov—Haiden—Katzarkov—Kontsevich to give a categorification of topological dynamical systems. To every categorical dynamical system one can associate its entropy, which measures the complexity of the system. While in the topological world this measure is given by a number, in the categorical world the entropy is a function. The value at zero of this function takes the name of categorical entropy and mirrors the role of the topological entropy. In this talk I will report on joint work with Jongmyeong Kim in which we investigate a categorical version of a theorem of Gromov and Yomdin and we propose a categorical interpretation of one of the properties of holomorphic functions. Such interpretation allows us to give a sufficient condition for a categorified version of Gromov—Yomdin’s theorem to hold.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=22142Algebra and Algebraic Geometry Seminar Fall 20212021-11-11T20:14:00Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Yi (Peter) Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|Michael Perlman (Minnesota; virtual)<br />
|Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
|<br />
|Daniel<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|CA+ meeting [ https://www-users.cse.umn.edu/~cberkesc/CA/CA2021.html]<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
<br />
<br />
<br />
|<br />
|-<br />
|November 12 -- TALK AT NONSTANDARD TIME<br />
|Jinhyung Park at 9:00am (Zoom)<br />
|Asymptotic vanishing of syzygies of algebraic varieties<br />
|<br />
|<br />
|-<br />
|November 12 <br />
|Daniel Erman at usual time (2:30pm)<br />
|The geometry of virtual syzygies<br />
|<br />
|<br />
|-<br />
|November 19<br />
|Ritvik Ramkumar (UC Berkeley; Zoom)<br />
|Rational singularities of nested Hilbert schemes. <br />
|<br />
|Daniel<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|April 8<br />
|Haydee Lindo<br />
|<br />
|<br />
|Daniel<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.<br />
<br />
===Michael Perlman===<br />
Title: Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
<br />
Abstract: Given a closed subvariety Z in a smooth complex variety, the local cohomology modules with support in Z are functorially endowed with structures as mixed Hodge modules, implying that they are equipped with Hodge and weight filtrations that subtly measure the singularities of Z. We will discuss new calculations of these filtrations in the case when Z is a generic determinantal variety. As an application, we obtain the Hodge ideals for the determinant hypersurface. Joint work with Claudiu Raicu.<br />
<br />
===Jinhyung Park===<br />
Title: Asymptotic vanishing of syzygies of algebraic varieties<br />
<br />
Abstract: In this talk, we show Ein-Lazarsfeld's conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein-Lazarsfeld's asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows.<br />
<br />
===Daniel Erman===<br />
Title: The geometry of virtual syzygies<br />
<br />
Abstract: One of the foundational results connecting syzygies with algebraic geometry properties was Mark Green’s result on N_p conditions for smooth curves of high degree. A modern and streamlined proof of this result comes via Green’s Linear Syzygy Theorem. I will discuss very recent work with Michael Brown which proves a Multigraded Linear Syzygy Theorem and uses this to obtain the first known examples of “virtual" N_p conditions for smooth curves of high degree in other toric varieties. This is joint work with Michael Brown.<br />
<br />
===Ritvik Ramkumar===<br />
Title: Rational singularities of nested Hilbert schemes. <br />
<br />
Abstract: For a smooth surface S the Hilbert scheme of points S^(n) is a well studied smooth parameter space. In this talk I will consider a natural generalization, the nested Hilbert scheme of points S^(n,m) which parameterizes pairs of 0-dimensional subschemes X \supseteq Y of S with deg(X) = n and deg(Y) = m. In contrast to the usual Hilbert scheme of points, S^(n,m) is almost always singular and it is known that S(n,1) has rational singularities. I will discuss some general techniques to study S^(n,m) and apply them to show that S^(n,2) also has rational singularities. This relies on a connection between S^(n,2) and a certain variety of matrices, and involves square-free Gröbner degenerations as well as the Kempf-Weyman geometric technique. This is joint work with Alessio Sammartano.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=22141Algebra and Algebraic Geometry Seminar Fall 20212021-11-11T20:13:07Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Yi (Peter) Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|Michael Perlman (Minnesota; virtual)<br />
|Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
|<br />
|Daniel<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|CA+ meeting [ https://www-users.cse.umn.edu/~cberkesc/CA/CA2021.html]<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
<br />
<br />
<br />
|<br />
|-<br />
|November 12 -- TALK AT NONSTANDARD TIME<br />
|Jinhyung Park at 9:00am (Zoom)<br />
|Asymptotic vanishing of syzygies of algebraic varieties<br />
|<br />
|<br />
|-<br />
|November 12 <br />
|Daniel Erman at usual time (2:30pm)<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|Ritvik Ramkumar (UC Berkeley; Zoom)<br />
|Rational singularities of nested Hilbert schemes. <br />
|<br />
|Daniel<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|April 8<br />
|Haydee Lindo<br />
|<br />
|<br />
|Daniel<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.<br />
<br />
===Michael Perlman===<br />
Title: Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
<br />
Abstract: Given a closed subvariety Z in a smooth complex variety, the local cohomology modules with support in Z are functorially endowed with structures as mixed Hodge modules, implying that they are equipped with Hodge and weight filtrations that subtly measure the singularities of Z. We will discuss new calculations of these filtrations in the case when Z is a generic determinantal variety. As an application, we obtain the Hodge ideals for the determinant hypersurface. Joint work with Claudiu Raicu.<br />
<br />
===Jinhyung Park===<br />
Title: Asymptotic vanishing of syzygies of algebraic varieties<br />
<br />
Abstract: In this talk, we show Ein-Lazarsfeld's conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein-Lazarsfeld's asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows.<br />
<br />
===Daniel Erman===<br />
Title: The geometry of virtual syzygies<br />
<br />
Abstract: One of the foundational results connecting syzygies with algebraic geometry properties was Mark Green’s result on N_p conditions for smooth curves of high degree. A modern and streamlined proof of this result comes via Green’s Linear Syzygy Theorem. I will discuss very recent work with Michael Brown which proves a Multigraded Linear Syzygy Theorem and uses this to obtain the first known examples of “virtual" N_p conditions for smooth curves of high degree in other toric varieties. This is joint work with Michael Brown.<br />
<br />
===Ritvik Ramkumar===<br />
Title: Rational singularities of nested Hilbert schemes. <br />
<br />
Abstract: For a smooth surface S the Hilbert scheme of points S^(n) is a well studied smooth parameter space. In this talk I will consider a natural generalization, the nested Hilbert scheme of points S^(n,m) which parameterizes pairs of 0-dimensional subschemes X \supseteq Y of S with deg(X) = n and deg(Y) = m. In contrast to the usual Hilbert scheme of points, S^(n,m) is almost always singular and it is known that S(n,1) has rational singularities. I will discuss some general techniques to study S^(n,m) and apply them to show that S^(n,2) also has rational singularities. This relies on a connection between S^(n,2) and a certain variety of matrices, and involves square-free Gröbner degenerations as well as the Kempf-Weyman geometric technique. This is joint work with Alessio Sammartano.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21981Algebra and Algebraic Geometry Seminar Fall 20212021-10-21T18:32:26Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Yi (Peter) Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|Michael Perlman (Minnesota; virtual)<br />
|Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
|<br />
|Daniel<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|CA+ meeting [ https://www-users.cse.umn.edu/~cberkesc/CA/CA2021.html]<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12 -- TALK AT NONSTANDARD TIME<br />
|Jinhyung Park at 9:30am<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.<br />
<br />
===Michael Perlman===<br />
Title: Mixed Hodge structure on local cohomology with support in determinantal varieties<br />
<br />
Abstract: Given a closed subvariety Z in a smooth complex variety, the local cohomology modules with support in Z are functorially endowed with structures as mixed Hodge modules, implying that they are equipped with Hodge and weight filtrations that subtly measure the singularities of Z. We will discuss new calculations of these filtrations in the case when Z is a generic determinantal variety. As an application, we obtain the Hodge ideals for the determinant hypersurface. Joint work with Claudiu Raicu.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21861Algebra and Algebraic Geometry Seminar Fall 20212021-10-07T18:11:40Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Yi (Peter) Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21831Algebra and Algebraic Geometry Seminar Fall 20212021-10-02T20:28:24Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Peter Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.<br />
<br />
===Peter Wei===<br />
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
<br />
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21830Algebra and Algebraic Geometry Seminar Fall 20212021-10-02T20:26:31Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Tate resolutions as noncommutative Fourier-Mukai transforms<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Peter Wei (local)<br />
|Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.<br />
<br />
===Michael Brown===<br />
Title: Tate resolutions as noncommutative Fourier-Mukai transforms<br />
<br />
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21752Algebra and Algebraic Geometry Seminar Fall 20212021-09-24T15:32:13Z<p>Kemeny: </p>
<hr />
<div>The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local, in person)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Something about toric varieties, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Peter Wei (local)<br />
|TBD (talk will be about results of Ogus on K3 surfaces in char p and syzygies)<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21731Algebra and Algebraic Geometry Seminar Fall 20212021-09-22T15:43:44Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Something about toric varieties, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|Peter Wei (local)<br />
|TBD (talk will be about results of Ogus on K3 surfaces in char p and syzygies)<br />
|<br />
|Michael<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21730Algebra and Algebraic Geometry Seminar Fall 20212021-09-22T15:38:15Z<p>Kemeny: /* Speaker Name */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Something about toric varieties, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
===Michael Kemeny===<br />
Title: The Rank of Syzygies<br />
<br />
Abstract: I will explain a notion of ''rank'' for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! <br />
I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible<br />
rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank ''four''.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21729Algebra and Algebraic Geometry Seminar Fall 20212021-09-22T15:33:56Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny (local)<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Something about toric varieties, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
Title: <br />
<br />
Abstract:</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2021&diff=21728Algebra and Algebraic Geometry Seminar Fall 20212021-09-22T15:33:43Z<p>Kemeny: /* Fall 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2021 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 />
|-<br />
|September 24<br />
|Michael Kemeny<br />
|The Rank of Syzygies<br />
|<br />
|<br />
|-<br />
|September 24|<br />
|<br />
|<br />
|<br />
|-<br />
|October 1<br />
|Michael K Brown (Auburn University)<br />
|Something about toric varieties, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 8<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 15<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|October 22<br />
|Ritvik Ramkumar (UC Berkeley)<br />
|Something about Hilbert schemes, probably<br />
|<br />
|Daniel<br />
|-<br />
|October 29<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 5<br />
|Eric Ramos<br />
|Equivariant log-concavity<br />
|<br />
|-<br />
|November 12<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 19<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|November 26<br />
|Thanksgiving<br />
|<br />
|<br />
|<br />
|-<br />
|December 3<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|December 10<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Speaker Name===<br />
Title: <br />
<br />
Abstract:</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra&diff=21368Algebra2021-08-31T00:29:10Z<p>Kemeny: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<!--[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)--><br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[https://people.math.wisc.edu/~kemeny/homepage.html Michael Kemeny:] (Bonn, 2015) Algebraic geometry and commutative algebra, in particular the study of moduli and syzygies of algebraic varieties.<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics.<br />
<!--[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics--><br />
<br />
[https://sites.google.com/view/ashankar/home Ananth Shankar:] (Harvard, 2017) Arithmetic geometry and number theory.<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<!--[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.--><br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<!--[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers--><br />
<br />
[https://sites.google.com/site/dcorey2814/ Daniel Corey:] (Yale, 2018) Tropical geometry<br />
<!--[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry--><br />
<br />
Yousheng Shi: (Maryland, 2019) Number theory, automorphic forms<br />
<br />
<!--[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces--><br />
[https://markshus.wixsite.com/math Mark Shusterman:] (Tel Aviv, 2019) Number theory and group theory<br />
<br />
[https://www.math.wisc/edu/~asobieska Aleksandra (Ola) Sobieska:] (Texas A&M University, 2020) Commutative algebra, combinatorics<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
<!--[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories--><br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar Applied Algebra Seminar] (Thursdays)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
[https://docs.google.com/document/d/e/2PACX-1vQaFtI9Pvf7HYTmch19qftoBUR81hevJ9n3F1viS_b-QxfAMz4fcIo6-jxQjMkpZvZqSJn2IS33BrG6/pub Online Social Chit-Chats] (various times)<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra&diff=21367Algebra2021-08-31T00:27:49Z<p>Kemeny: /* Research at UW-Madison in algebra */</p>
<hr />
<div>[[http://www.math.wisc.edu/algrtg/]]http://www.math.wisc.edu/algrtg/ is the RTG homepage.<br />
<br />
== '''Research at UW-Madison in algebra''' ==<br />
<br />
<br />
UW-Madison offers a large, active, and varied research group in algebra, including researchers in number theory, combinatorics, group theory, algebraic geometry, representation theory, and algebra with applications to science and engineering.<br />
<br />
'''Tenured and tenure-track faculty in algebra'''<br />
<br />
[http://www.math.wisc.edu/~arinkin/ Dima Arinkin]: (Harvard, 2002) Algebraic geometry, geometric representation theory, especially geometric Langlands conjecture.<br />
<br />
[http://pages.cs.wisc.edu/~bach/bach.html Eric Bach:] (Berkeley, 1984) Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata. (Joint appointment with CS.)<br />
<!--[http://www.math.wisc.edu/~boston/ Nigel Boston:] (Harvard, 1987) Algebraic number theory, group theory, arithmetic geometry, computational algebra, coding theory, cryptography, and other applications of algebra to electrical engineering. (Joint appointments with ECE and CS.)--><br />
<br />
[http://www.math.wisc.edu/~andreic/ Andrei Caldararu:] (Cornell, 2000) Algebraic geometry, homological algebra, string theory.<br />
<br />
[http://www.math.yale.edu/~td252/ Tullia Dymarz:] (Chicago, 2007) Geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~ellenber/ Jordan Ellenberg:] (Harvard, 1998) Arithmetic geometry and algebraic number theory, especially rational points on varieties over global fields.<br />
<br />
[http://www.math.wisc.edu/~derman/ Daniel Erman:] (Berkeley, 2010) Algebraic geometry and commutative algebra<br />
<br />
[http://www.math.wisc.edu/~shamgar/ Shamgar Gurevich:] (Tel Aviv, 2006) Geometric representation theory, with applications to harmonic analysis, signal processing, mathematical physics, and three-dimensional structuring of molecules.<br />
<br />
[https://people.math.wisc.edu/~kemeny/homepage.html Michael Kemeny:] (Bonn, 2015) Algebraic geometry and commutative algebra, in particular curves, K3 surfaces and syzygies.<br />
<br />
<br />
[http://www.math.wisc.edu/~marshall/ Simon Marshall:] (Princeton, 2010) Analytic number theory (also in the analysis group.)<br />
<br />
[https://www.math.wisc.edu/~maxim/ Laurentiu Maxim:] (Penn, 2005) Topology of algebraic varieties, singularities (also in the geometry/topology group.)<br />
<br />
[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez:] (Berkeley, 2014) Applied algebraic geometry and algebraic methods for statistics.<br />
<!--[http://www.math.wisc.edu/~svs/ Steven Sam:] (MIT, 2012) Commutative algebra, invariant theory, algebraic combinatorics--><br />
<br />
[https://sites.google.com/view/ashankar/home Ananth Shankar:] (Harvard, 2017) Arithmetic geometry and number theory.<br />
<br />
[http://www.math.wisc.edu/~terwilli/ Paul Terwilliger:] (Illinois, 1982) Combinatorics, representation theory and special functions. <br />
<!--[http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood:] (Princeton, 2009) Number theory and arithmetic geometry.--><br />
<br />
[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Complex algebraic geometry, algebraic statistics and combinatorics. (Also in the geometry/topology group)<br />
<br />
[http://www.math.wisc.edu/~thyang/ Tonghai Yang:] (Maryland, 1995) number theory, representation theory, and arithmetic geometry: especially L-functions, Eisenstein series, theta series, Shimura varieties, intersection theory, and elliptic curves.<br />
<br />
<br />
'''Postdoctoral fellows in algebra'''<br />
<br />
<!--[http://www.math.wisc.edu/~brownda/ David Brown:] (Berkeley, 2010) Number theory and arithmetic geometry, especially: p-adic cohomology, arithmetic of varieties, stacks, moduli, Galois representations, non-abelian techniques.<br />
<br />
[http://www.math.wisc.edu/~cais/ Bryden Cais:] (Michigan, 2007) Algebraic and arithmetic geometry, with a strong number theory bias.<br />
<br />
[http://www.math.wisc.edu/~ballard/ Matthew Ballard:] (U Washington, 2008) Homological mirror symmetry.<br />
<br />
[http://www.math.wisc.edu/~rharron/ Robert Harron:] (Princeton, 2009): Algebraic number theory, Iwasawa theory, p-adic Galois representations and automorphic forms.<br />
<br />
[http://www.math.wisc.edu/~klagsbru/ Zev Klagsbrun:] (UC-Irvine, 2011): Algebraic number theory and arithmetic geometry.<br />
<br />
Parker Lowrey: (University of Texas-Austin, 2010) Algebraic geometry and algebraic topology<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami:] (University of Maryland, 2012): representation theory of algebraic groups, local models of Shimura varieties<br />
<br />
[http://www.math.wisc.edu/~josizemore/ Owen Sizemore:] (UCLA, 2012) Operator Algebras, Orbit Equivalence Ergodic Theory, Measure Equivalence Rigidity of Groups <br />
<br />
[http://www.math.wisc.edu/~grizzard/ Robert Grizzard:] (U Texas, 2014) Algebraic number theory, diophantine geometry, heights<br />
--><br />
<br />
[http://www.math.wisc.edu/~mkbrown5/ Michael Brown:] (Nebraska, 2015) K-theory, commutative algebra, (noncommutative) algebraic geometry. <br />
<!--[https://sites.google.com/a/wisc.edu/alexandra-a-kjuchukova/home Alexandra Kjuchukova:] (Penn, 2015) Topology of algebraic varieties, branched covers--><br />
<br />
[https://sites.google.com/site/dcorey2814/ Daniel Corey:] (Yale, 2018) Tropical geometry<br />
<!--[http://www.math.wisc.edu/~pavlov/ Alexander Pavlov:] (U Toronto, 2015) Commutative algebra, algebraic geometry--><br />
<br />
Yousheng Shi: (Maryland, 2019) Number theory, automorphic forms<br />
<br />
<!--[http://www.math.wisc.edu/~ntalebiz Naser T. Sardari:] (Princeton, 2016) Number theory, especially: quadratic forms, automorphic forms, locally symmetric spaces--><br />
[https://markshus.wixsite.com/math Mark Shusterman:] (Tel Aviv, 2019) Number theory and group theory<br />
<br />
[https://www.math.wisc/edu/~asobieska Aleksandra (Ola) Sobieska:] (Texas A&M University, 2020) Commutative algebra, combinatorics<br />
<br />
<!--[http://www.math.wisc.edu/~wang/ Botong Wang:] (Purdue, 2012) Topology of algebraic varieties, topological methods in statistics--><br />
<!--[https://sites.google.com/wisc.edu/jwg/home John Wiltshire-Gordon:] (Michigan, 2016) Algebra, topology and combinatorics, especially: representation theory of categories--><br />
<br />
'''Seminars in algebra'''<br />
<br />
The weekly schedule at UW features many seminars in the algebraic research areas of the faculty.<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Algebraic_Geometry_Seminar Algebraic Geometry Seminar] (Fridays at 2:30)<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Applied_Algebra_Seminar Applied Algebra Seminar] (Thursdays)<br />
<br />
[http://www.math.wisc.edu/~terwilli/combsemsched.html Combinatorics Seminar] (Mondays at 2:25)<br />
<br />
Lie Theory Seminar (Mondays at 1:20 in VV901)<br />
<!--<br />
[https://www.math.wisc.edu/wiki/index.php/Group_Theory_Seminar Group Theory Seminar (mostly local speakers)] (Tuesdays at 4:00)--><br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTS Number Theory Seminar (outside speakers)](Thursdays at 2:30)<br />
<br />
[http://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2018 Number Theory Seminar (grad student speakers)] (Tuesdays at 2:30)<br />
<br />
[http://silo.ece.wisc.edu/web/content/seminars SILO (Systems, Information, Learning and Optimization)] (Wednesdays at 12:30)<br />
<br />
[https://docs.google.com/document/d/e/2PACX-1vQaFtI9Pvf7HYTmch19qftoBUR81hevJ9n3F1viS_b-QxfAMz4fcIo6-jxQjMkpZvZqSJn2IS33BrG6/pub Online Social Chit-Chats] (various times)<br />
<br />
<br />
'''Upcoming conferences in algebra held at UW'''<br />
<br />
[http://www.math.grinnell.edu/~paulhusj/ants2018/ ANTS XIII] (Algorithmic Number Theory Symposium), July 2018<br />
<br />
[https://www.math.wisc.edu/~rdavis/conference/ Arithmetic of Algebraic Curves], April 2018<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing18.html Singularities in the Midwest V], March 2018<br />
<br />
'''Previous conferences in algebra held at UW'''<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing17.html Singularities in the Midwest IV], March 2017<br />
<br />
[http://www.math.wisc.edu/~boston/applalg3.html Applied Algebra Days 3], May 2016<br />
<br />
[http://www.math.wisc.edu/~derman/UMW.html Upper midwest commutative algebra colloquium], November 2015<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing15.html Stratified spaces in geometric and computational topology and physics (Shaneson 70)], March 2015<br />
<br />
[http://www.math.wisc.edu/~boston/applalg2.html Applied Algebra Days 2], May 2014<br />
<br />
[https://sites.google.com/site/gtntd2013/ Group Theory, Number Theory, and Topology Day], January 2013<br />
<br />
[https://sites.google.com/site/mirrorsymmetryinthemidwest/ Mirror Symmetry in the Midwest], November 2012<br />
<br />
[https://sites.google.com/site/uwmagc/ Midwest Algebraic Geometry Graduate Conference], November 2012<br />
<br />
[http://www.math.wisc.edu/~boston/applalg.html Applied Algebra Days], October 2011<br />
<br />
[https://sites.google.com/site/mntcg2011/ Midwest Number Theory Conference for Graduate Students], November 2011<br />
<br />
[http://sites.google.com/site/uwmagc/ RTG Graduate Student Workshop in Algebraic Geometry], October 2010<br />
<br />
[http://www.math.wisc.edu/~jeanluc/pAconf.html Workshop on Pseudo-Anosovs with Small Dilatation], April 2010<br />
<br />
[http://www.math.wisc.edu/~maxim/Sing10.html Singularities in the Midwest], March 2010<br />
<br />
[http://www.math.wisc.edu/~ellenber/mntcg/index.html RTG Midwest Graduate Student Conference in Number Theory], November 2009<br />
<br />
[http://www.math.wisc.edu/~ellenber/MNTD09.html Midwest Number Theory Day], November 2009<br />
<br />
Miniconference on pro-p groups in number theory, April 2008<br />
<br />
[http://www.math.wisc.edu/~ellenber/ProPday.html Pro-p groups and pro-p algebras in number theory], April 2007<br />
<br />
<br />
'''Graduate study at UW-Madison in algebra'''<br />
<br />
Algebra is among the most popular specializations for UW Ph.D. students. Regularly offered courses include a four-semester sequence in number theory; a two-semester sequence in algebraic geometry; homological algebra; representation theory; advanced topics in group theory. We also regularly offer more advanced topics courses, which in recent years have included the Gross-Zagier formula, classification of algebraic surfaces, and p-adic Hodge theory. Here is [http://www.math.wisc.edu/graduate/gcourses_fall a list of this fall's graduate courses].<br />
<br />
The department holds an [http://www.nsf.gov/awardsearch/showAward.do?AwardNumber=0838210&version=noscript NSF-RTG grant in number theory and algebraic geometry], which funds several research assistantships for graduate students (U.S. citizens and permanent residents) working in those areas. <br />
<br />
Recent Ph.D. graduates from the group have been very successful on the job market; in the last few years, we have sent alumni to postdoctoral fellowships at Berkeley, Harvard, Chicago, Michigan, Penn, Imperial (UK), MIT, Princeton, Stanford, University of Cologne(Germany), Max Planck Institut, and UT-Austin, to tenure-track jobs at Oregon, Wake Forest, SUNY-Geneseo, Bogacizi (Turkey), Chennai Mathematical Institute (India), CUNY, the University of Sheffield (UK), the University of Missouri, and the University of South Carolina, and to non-academic positions at places such as Google, Robart GMBH, Microsoft, Credit Suisse and the Center for Communications Research, La Jolla.<br />
<br />
<br />
'''Emeritus faculty in algebra'''<br />
<br />
Steven Bauman <br />
Professor, University of Illinois at Urbana-Champaign (1962) <br />
Research: Finite group theory<br />
<br />
Georgia Benkart <br />
E. B. Van Vleck Professor of Mathematics, Ph.D. Yale University (1974) <br />
Research: Lie Theory, Quantum Groups and Representation Theory.<br />
<br />
Michael Bleicher <br />
Professor, Ph.D. Tulane University and University of Warsaw (1961) <br />
Research: Number theory and convex geometry<br />
<br />
Richard A. Brualdi <br />
Beckwith Bascom Professor of Mathematics, Ph.D. Syracuse University (1964) <br />
Research: Combinatorics, Graph Theory, Matrix Theory, Coding Theory<br />
<br />
Donald Crowe <br />
Professor, Ph.D. University of Michigan (1959) <br />
Research: Classical geometry and African patterns<br />
<br />
I. Martin Isaacs <br />
Professor, Ph.D. Harvard University (1964) <br />
Research: Group Theory, Algebra<br />
<br />
J. Marshall Osborn <br />
Professor, Ph.D. University of Chicago (1957) <br />
Research: Non-associative rings and Lie algebras<br />
<br />
Donald Passman <br />
Richard Brauer Professor of Mathematics, Ph.D. Harvard University (1964) <br />
Research: Associative Rings and Algebras, Group Theory<br />
<br />
Louis Solomon <br />
Professor, Ph.D. Harvard University (1958) <br />
Research: Finite group theory and hyperplane arrangements <br />
<br />
Robert Wilson <br />
Professor, Ph.D. University of Wisconsin-Madison (1969) <br />
Research: Algebra, Math. Education.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21170Algebra and Algebraic Geometry Seminar Spring 20212021-04-23T17:03:54Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| Algebraic symmetries of the hydrogen atom]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| The QR decomposition for radial neural networks]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
===Eyal Subag===<br />
Title: Algebraic symmetries of the hydrogen atom.<br />
<br />
Abstract. In this talk we will examine symmetries of the hydrogen atom from two related algebraic perspectives. The first is in the context of algebraic families of groups. The second comes from a new suggested model for the Schrödinger equation of the hydrogen atom within the algebra of differential operators on a complex null cone. Time permit I will discuss related questions in representation theory of SL(2,R).<br />
<br />
This talk is based on joint work with J. Bernstein and N. Higson.<br />
<br />
===Gurbir Dhillon===<br />
'''The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras'''<br />
<br />
Abstract: The affine W-algebras are a family of algebras whose representation theory plays an important role in conformal field theory and the geometric Langlands program. In the original paper which introduced W-algebras into mathematics, Feigin and Frenkel conclude with a striking conjecture, joint with Kac and Wakimoto, relating certain irreducible representations of affine Lie algebras and affine W-algebras via a functor since called the `plus' Drinfeld--Sokolov reduction. We have proven this conjecture in forthcoming work. The primary goal of the talk will be to give a motivated introduction to the conjecture, its history, and the objects appearing in it for non-specialists.<br />
<br />
<br />
===Iordan Ganev===<br />
The QR decomposition for radial neural networks<br />
<br />
Abstract: We present a perspective on neural networks stemming from quiver representation theory. This point of view emphasizes the symmetries inherent in neural networks, interacts nicely with gradient descent, and has the potential to improve training algorithms. As an application, we establish an analogue of the QR decomposition for radial neural networks, which leads to a dimensional reduction result. This talk is intended for a broad mathematical audience, and we explain all concepts relating to neural networks and machine learning from first principles. It is based on joint work-in-progress with Robin Walters.</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21099Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:24:09Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
===Hannah Larson===<br />
Title: The rational Chow rings of M_7, M_8, and M_9<br />
<br />
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g \leq 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I will give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21098Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:23:10Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21097Algebra and Algebraic Geometry Seminar Spring 20212021-04-02T17:22:53Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| The rational Chow rings of M_7, M_8, and M_9]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21015Algebra and Algebraic Geometry Seminar Spring 20212021-03-18T16:41:29Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
===Gavril Farkas===<br />
Title: The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.<br />
<br />
Abstract: The problem of determining the birational nature of the moduli<br />
space of curves of genus g has received constant attention in the last<br />
century and inspired a lot of development in moduli theory. I will<br />
discuss progress achieved in the last 12 months. On the one hand, making<br />
essential of tropical methods it has been showed that both moduli spaces<br />
of curves of genus 22 and 23 are of general type (joint with D. Jensen<br />
and S. Payne). On the other hand I will discuss a proof (joint with A.<br />
Verra) of the uniruledness of the moduli space of curves of genus 16.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=21014Algebra and Algebraic Geometry Seminar Spring 20212021-03-18T16:39:59Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| The Kodaira dimension of the moduli space of curves: recent<br />
progress on a century-old problem.]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 30<br />
|[https://ivganev.github.io Iordan Ganev (Weizmann)]<br />
|[[#Iordan Ganev| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20984Algebra and Algebraic Geometry Seminar Spring 20212021-03-10T16:30:49Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
===Daniele Agostini===<br />
Title: Effective Torelli theorem<br />
<br />
Abstract: Torelli's theorem is a foundational result of classical algebraic geometry, asserting that<br />
a smooth curve can be recovered from its Jacobian. There are many effective proofs of this result, that<br />
can even be implemented on a computer. In this talk, I will present this circle of ideas. In particular, I<br />
will focus on a method based on the KP equation in mathematical physics, that I have recently implemented<br />
together with Türkü Çelik and Demir Eken.<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20983Algebra and Algebraic Geometry Seminar Spring 20212021-03-10T16:29:34Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| Effective Torelli theorem]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20966Algebra and Algebraic Geometry Seminar Spring 20212021-03-09T17:46:42Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 19<br />
|[https://personal-homepages.mis.mpg.de/agostini/ Daniele Agostini (MPI Leipzig)]<br />
|[[#Daniele Agostini| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20950Algebra and Algebraic Geometry Seminar Spring 20212021-03-07T02:45:40Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| Rigid local systems]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 26<br />
|[https://www.mathematik.hu-berlin.de/~farkas/ Gavril Farkas (Humboldt-Universitaet zu Berlin)]<br />
|[[#Gavril Farkas| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Michael Groechenig===<br />
Title: Rigid Local Systems<br />
<br />
Abstract: An irreducible representation of a finitely generated group G is called rigid, if it induces an isolated point in the moduli space of representations. For G being the fundamental group of a complex projective manifold, Simpson conjectured that rigid representations should have integral monodromy and more generally, be of geometric origin. In this talk I will give an overview about what is currently known about Simpson’s conjectures and will present a few results joint with H. Esnault.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20861Algebra and Algebraic Geometry Seminar Spring 20212021-02-21T19:02:44Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Andreas Knutsen===<br />
Title: Genus two curves on abelian surfaces<br />
<br />
Abstract: Let (S,L) be a general polarized abelian surface of type<br />
(d_1,d_2). The minimal geometric genus of any curve in the linear system<br />
|L| is two and there are finitely many curves of such genus. In analogy<br />
with Chen's results concerning rational curves in primitive linear<br />
systems on K3 surfaces, it is natural to ask whether all such curves are<br />
nodal. In the seminar I will present joint work with Margherita<br />
Lelli-Chiesa (arXiv:1901.07603) where we prove that this holds true if<br />
and only if d_2 is not divisible by 4. In the cases where d_2 is a<br />
multiple of 4, we show the existence of curves in |L| having a triple,<br />
4-tuple or 6-tuple point, and prove that these are the only types of<br />
unnodal singularities a genus 2 curve in |L| may acquire.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20860Algebra and Algebraic Geometry Seminar Spring 20212021-02-21T19:01:25Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| Genus two curves on abelian surfaces]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20829Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:25:21Z<p>Kemeny: /* Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. <br />
<br />
Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20828Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:25:05Z<p>Kemeny: /* Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications. Slides available here [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing]<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20827Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:23:47Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]] <br />
[https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20826Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:22:41Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]][https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20825Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:22:22Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20824Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:21:55Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20823Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:18:28Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications][https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20822Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:17:45Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[#Marian Aprodu| Koszul modules, resonance varieties and applications. ] [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20821Algebra and Algebraic Geometry Seminar Spring 20212021-02-12T23:16:49Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications. [https://drive.google.com/file/d/1FCSQNOHbVaht7I1ubdg2ktTPqGO7joU6/view?usp=sharing Slides from talk] ]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20806Algebra and Algebraic Geometry Seminar Spring 20212021-02-09T23:00:34Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 9<br />
|[http://web.stanford.edu/~hlarson/ Hannah Larson (Stanford)]<br />
|[[#Hannah Larson| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20792Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:31Z<p>Kemeny: /* February 26: Philip Engel */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20791Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:19Z<p>Kemeny: /* February 19: Dhruv Ranganathan */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik.<br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20790Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:27:05Z<p>Kemeny: /* February 12: Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20789Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:26:52Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20788Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:25:19Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
Title: Koszul modules, resonance varieties and applications.<br />
<br />
Abstract: This talk is based on joint works with Gabi Farkas, Stefan Papadima, Claudiu Raicu, Alex Suciu and Jerzy Weyman. I plan to discuss various aspects of the geometry of resonance varieties, Hilbert series of Koszul modules and applications.<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20787Algebra and Algebraic Geometry Seminar Spring 20212021-02-06T23:24:16Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| Koszul modules, resonance varieties and applications]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| Compact K3 moduli]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
'''TBA'''<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===February 26: Philip Engel===<br />
Title: Compact K3 moduli<br />
<br />
Abstract: This is joint work with Valery Alexeev. A well-known consequence of the Torelli theorem is that the moduli space F_{2d} of degree 2d K3 surfaces (X,L) is the quotient of a 19-dimensional Hermitian symmetric space by the action of an arithmetic group. In this capacity, it admits a natural class of "semitoroidal compactifications." These are built from periodic tilings of 18-dimensional hyperbolic space, and were studied by Looijenga, who built on earlier work of Baily-Borel and Ash-Mumford-Rapaport-Tai. On the other hand, F_{2d} also admits "stable pair compactifications": Choose canonically on any polarized K3 surface X an ample divisor R. Then the works of Kollar-Shepherd-Barron, Alexeev, and others provide for the existence of a compact moduli space of so-called stable pairs (X,R) containing, as an open subset, the K3 pairs.<br />
<br />
I will discuss two theorems in the talk: (1) There is a simple criterion on R, called "recognizability" ensuring that the normalization of a stable pair compactification is semitoroidal and (2) the rational curves divisor, generically the sum of geometric genus zero curves in |L|, is recognizable for all 2d. This gives a modular semitoroidal compactification for all degrees 2d.<br />
<br />
<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20711Algebra and Algebraic Geometry Seminar Spring 20212021-01-31T19:33:14Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| Logarithmic Donaldson-Thomas theory<br />
]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[https://folk.uib.no/st00895/ Andreas Knutsen (University of Bergen)]<br />
|[[#Andreas Knutsen| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===February 12: Marian Aprodu===<br />
'''TBA'''<br />
<br />
===February 19: Dhruv Ranganathan===<br />
Title: Logarithmic Donaldson-Thomas theory<br />
<br />
Abstract: I will give an introduction to a circle ideas surrounding the enumerative geometry of pairs, and in particular, intersection theory on a new models of the Hilbert schemes of curves on threefolds. These give rise to “logarithmic” DT and PT invariants. I will explain the conjectural relationship between this geometry and Gromov-Witten theory, and give some sense of the role of tropical geometry in the story. The talk is based on joint work, some of it in progress, with Davesh Maulik. <br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20552Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:59Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20551Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:37Z<p>Kemeny: /* =Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20550Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:39:15Z<p>Kemeny: /* =Marian Aprodu */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Marian Aprodu==<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20549Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:38:52Z<p>Kemeny: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Marian Aprodu==<br />
'''TBA'''<br />
<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20548Algebra and Algebraic Geometry Seminar Spring 20212021-01-18T16:38:31Z<p>Kemeny: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|TBA <br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA<br />
===Nir Avni===<br />
'''TBA'''<br />
<br />
TBA</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar&diff=20525Algebra and Algebraic Geometry Seminar2021-01-17T00:33:52Z<p>Kemeny: Redirected page to Algebra and Algebraic Geometry Seminar Spring 2021</p>
<hr />
<div>#REDIRECT [[Algebra and Algebraic Geometry Seminar Spring 2021]]</div>Kemenyhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2020&diff=20524Algebra and Algebraic Geometry Seminar Fall 20202021-01-17T00:26:14Z<p>Kemeny: </p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar. The link to the Spring 2021 seminar is here: [https://www.math.wisc.edu/wiki/index.php/Algebra_and_Algebraic_Geometry_Seminar_Spring_2021 Spring 2021 Seminar]<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Fall 2020 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|September 14 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 1/4 in lecture series at Imperial College - Register here to get the link to the talk!]<br />
|-<br />
|September 18 <br />
|[https://www.math.wisc.edu/~arinkin/ Dima Arinkin (Madison)]<br />
|[[#Dima Arinkin|Singular support of categories]]<br />
|[https://uwmadison.zoom.us/j/91919237303?pwd=SzhtYVpwSHhoVVFmQWx1NFpBVVNBQT09 Zoom link]<br />
|-<br />
|September 21 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 2/4 in lecture series at Imperial College]<br />
|-<br />
|September 25<br />
|[https://www.math.tamu.edu/~ola/ Aleksandra Sobieska (Madison)]<br />
|[[#Aleksandra Sobieska|Toward Free Resolutions Over Scrolls]]<br />
|<br />
|-<br />
|September 28 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 3/4 in lecture series at Imperial College]<br />
|-<br />
|October 2<br />
|Robert Scherer (UC Davis)<br />
|[[#Robert Scherer|A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 5 @ 10am<br />
|[http://www.math.wisc.edu/~andreic/ Andrei Căldăraru (Madison)]<br />
|[[#Andrei Căldăraru|Categorical Enumerative Invariants]]<br />
|[https://sites.google.com/view/catgw/ Talk 4/4 in lecture series at Imperial College]<br />
|-<br />
|October 7 @ 7pm<br />
|[https://www.math.wisc.edu/~shamgar// Shamgar Gurevich (Madison)]<br />
|[[#Shamgar Gurevich|Harmonic Analysis on GLn over Finite Fields]]<br />
| [https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ Register here to get link to talk at University of Sydney]<br />
|-<br />
|October 9<br />
|[https://math.berkeley.edu/~germans/ German Stefanich (Berkeley) ]<br />
|[[#German Stefanich|Categorified sheaf theory and the spectral Langlands TQFT]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 16<br />
|[https://sites.google.com/view/ruijie-yang/ Ruijie Yang (Stony Brook)]<br />
|[[#Ruijie Yang|Decomposition theorem for semisimple local systems]]<br />
| [https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|October 23 <br />
|[http://www-users.math.umn.edu/~ottxx141/ Nadia Ott (Mittag-Leffler Institute)]<br />
|[[#Nadia Ott|The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|October 30<br />
|[http://w3.impa.br/~heluani/ Reimundo Heluani (IMPA, Rio de Janeiro)]<br />
|[[#Reimundo Heluani|Rogers Ramanujan type identities coming from representation theory]]<br />
| <br />
|-<br />
|November 6<br />
|[https://bakker.people.uic.edu/ Ben Bakker (UIC)]<br />
|[[#Ben Bakker|Quasiprojectivity of images of mixed period maps]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link] <br />
|-<br />
|November 13<br />
|[https://pages.uoregon.edu/honigs/ Katrina Honigs (Oregon)]<br />
|[[#Katrina Honigs|An obstruction to weak approximation on some Calabi-Yau threefolds]]<br />
|<br />
|-<br />
|December 4<br />
|[https://www.iag.uni-hannover.de/de/institut/personenverzeichnis/stefan-schreieder/?&L=1 Stefan Schreieder (Hannover)]<br />
|[[#Stefan Schreieder|Refined unramified cohomology and algebraic cycles]]<br />
|<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
===Andrei Căldăraru===<br />
'''Categorical Enumerative Invariants'''<br />
<br />
I will talk about recent papers with Junwu Tu, Si Li, and Kevin Costello where we give a computable definition of Costello's 2005 invariants and compute some of them. These invariants are associated to a pair (A,s) consisting of a cyclic A∞-algebra and a choice of splitting s of its non-commutative Hodge filtration. They are expected to recover classical Gromov-Witten invariants when A is obtained from the Fukaya category of a symplectic manifold, as well as extend various B-model invariants (solutions of Picard-Fuchs equations, BCOV invariants, B-model FJRW invariants) when A is obtained from the derived category of a manifold or a matrix factorization category.<br />
<br />
===Dima Arinkin===<br />
<br />
'''Singular support of categories'''<br />
<br />
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support.<br />
For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset<br />
of the cotangent bundle; there is also a version of this notion for coherent sheaves on local complete intersections.<br />
I would like to describe a higher categorical version of this notion.<br />
<br />
Let X be a smooth variety, and let Z be a closed conical isotropic subset of the cotangent bundle of X. I will define a<br />
2-category associated with Z; its objects may be viewed as `categories over X with singular support in Z'. In particular, if Z is<br />
the zero section, this gives the notion of categories over Z in the usual sense.<br />
<br />
The project is motivated by the local geometric Langlands correspondence; I will sketch the relation with the Langlands correspondence without <br />
going into details.<br />
<br />
===Aleksandra Sobieska===<br />
'''Toward Free Resolutions Over Scrolls'''<br />
<br />
Free resolutions over the polynomial ring have a storied and active record of study. However, resolutions over other rings are much more mysterious; even simple examples can be infinite! In these cases, we look to any combinatorics of the ring to glean information. This talk will present a minimal free resolution of the ground field over the semigroup ring arising from rational normal $2$-scrolls, and (if time permits) a computation of the Betti numbers of the ground field for all rational normal $k$-scrolls.<br />
<br />
===Robert Scherer===<br />
'''A Criterion for Asymptotic Sharpness in the Enumeration of Simply Generated Trees'''<br />
<br />
We study the identity $y(x)=xA(y(x))$, from the theory of rooted trees, for appropriate generating functions $y(x)$ and $A(x)$ with non-negative integer coefficients. A problem that has been studied extensively is to determine the asymptotics of the coefficients of $y(x)$ from analytic properties of the complex function $z\mapsto A(z)$, assumed to have a positive radius of convergence $R$. It is well-known that the vanishing of $A(x)-xA'(x)$ on $(0,R)$ is sufficient to ensure that $y(r)<R$, where $r$ is the radius of convergence of $y(x)$. This result has been generalized in the literature to account for more general functional equations than the one above, and used to determine asymptotics for the Taylor coefficients of $y(x)$. What has not been shown is whether that sufficient condition is also necessary. We show here that it is, thus establishing a criterion for sharpness of the inequality $y(r)\leq R$. As an application, we prove, and significantly extend, a 1996 conjecture of Kuperberg regarding the asymptotic growth rate of an integer sequence arising in the study of Lie algebra representations. <br />
<br />
===Shamgar Gurevich===<br />
'''Harmonic Analysis on GLn over Finite Fields'''<br />
<br />
There are many formulas that express interesting properties of a finite group G in terms of sums over<br />
its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
Trace(ρ(g)) / dim(ρ), for an irreducible representation ρ of G and an element g of G. For example, Diaconis<br />
and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. Recently,<br />
we discovered that for classical groups G over finite fields there is a natural invariant of representations that<br />
provides strong information on the character ratio. We call this invariant rank. Rank suggests a new<br />
organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s<br />
“philosophy of cusp forms”, which is (since the 60s) the main organization principle, and is based on the (huge<br />
collection) of “Large” representations. This talk will discuss the notion of rank for the group GLn over finite<br />
fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify<br />
mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&M). The<br />
numerics for this work was carried with Steve Goldstein (Madison) and John Cannon (Sydney).<br />
<br />
===German Stefanich===<br />
'''Categorified sheaf theory and the spectral Langlands TQFT'''<br />
<br />
It is expected that the Betti version of the geometric Langlands program should ultimately be about the equivalence of two 4-dimensional topological field theories. In this talk I will give an overview of ongoing work in categorified sheaf theory and explain how one can use it to describe the categories of boundary conditions arising on the spectral side.<br />
<br />
===Ruijie Yang===<br />
'''Decomposition theorem for semisimple local systems<br />
'''<br />
<br />
In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of very long papers via harmonic analysis and $D$-modules. In this talk, I would like to explain a simpler proof in the case of semisimple local systems using a more geometric approach. This is joint work in progress with Chuanhao Wei. <br />
<br />
===Nadia Ott===<br />
'''The Supermoduli Space of Genus Zero SUSY Curves with Ramond Punctures<br />
<br />
Super Riemann surfaces (SUSY curves) arise in the formulation of superstring theory, and their moduli spaces, called supermoduli space, are the integration spaces for superstring scattering amplitudes. I will focus specifically on genus zero SUSY curves. As with ordinary curves, genus zero SUSY curves present a certain challenge, as they have an infinitesimal group of automorphisms, and so in order for the moduli problem to be representable by a Deligne-Mumford superstack, we must introduce punctures. In fact, there are two kinds of punctures on a SUSY curve of Neveu-Schwarz or Ramond type. Neveu-Schwarz punctures are entirely analogous to the marked points in ordinary moduli theory. By contrast, the Ramond punctures are more subtle and have no ordinary analog. I will give a construction of the moduli space M_{0,n}^R of genus zero SUSY curves with Ramond punctures as a Deligne-Mumford superstack by an explicit quotient presentation (rather than by an abstract existence argument).<br />
<br />
===Reimundo Heluani===<br />
'''A Rogers-Ramanujan-Slater type identity related to the Ising model'''<br />
<br />
We prove three new q-series identities of the Rogers-Ramanujan-Slater<br />
type. We find a PBW basis for the Ising model as a consequence of one of these<br />
identities. If time permits it will be shown that the singular support of the<br />
Ising model is a hyper-surface (in the differential sense) on the arc space of<br />
it's associated scheme. This is joint work with G. E. Andrews and J. van Ekeren<br />
and is available online at https://arxiv.org/abs/2005.10769<br />
<br />
===Ben Bakker===<br />
'''Quasiprojectivity of images of mixed period maps'''<br />
<br />
Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J. Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case. In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications. <br />
<br />
===Katrina Honigs===<br />
'''An obstruction to weak approximation on some Calabi-Yau threefolds'''<br />
<br />
The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.<br />
<br />
===Stefan Schreieder===<br />
'''Refined unramified cohomology and algebraic cycles'''<br />
<br />
We introduce refined unramified cohomology groups, explain their relation to classical unramified cohomology, and prove some general comparison theorems to certain cycle groups. This generalizes and simplifies work of Bloch—Ogus, Colliot-Thélène—Voisin, Voisin, and Ma who dealt with cycles of low (co-)dimension. Our approach has several applications. Most notably, it allows to construct the first example of a variety with infinite torsion in its Griffiths group.</div>Kemeny