https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Ashankar22&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-28T21:27:45ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=NTS&diff=23839NTS2022-10-10T16:20:39Z<p>Ashankar22: /* Fall 2022 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' '''Van Vleck B139''' or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Fall 2022 speakers in [https://wiki.math.wisc.edu/index.php/NTS_Fall_Semester_2022 Fall 2022]<br />
<br />
You can find our Spring 2022 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2022 Spring 2022].<br />
<br />
You can find our Fall 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2021 Fall 2021].<br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our Fall 2018 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
=Fall 2022 Semester=<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center" |'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" |Sep 8<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/zqyang Ziquan Yang]<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2022#Sep_07 The Tate conjecture for h^{2, 0} = 1 varieties over finite fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sep 15<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/qiucongling Congling Qiu]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_15 Modularity of arithmetic special divisors for unitary Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sep 22<br />
| bgcolor="#F0B0B0" align="center" |[https://people.math.wisc.edu/~shi/ Yousheng Shi]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_22 Special cycles on Shimura varieties and theta series]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" |Sep 29<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.duke.edu/pmgu/research/ Miao (Pam) Gu]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_29 A family of period integrals related to triple product L-functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 6<br />
| bgcolor="#F0B0B0" align="center" |(merged with weekend workshop)<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 13<br />
| bgcolor="#F0B0B0" align="center" |[https://notnotraju.github.io/ Raju Krishnamoorthy]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Oct_13 Rank 2 local systems and abelian varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 20<br />
| bgcolor="#F0B0B0" align="center" |Tian Wang<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 27<br />
| bgcolor="#F0B0B0" align="center" |Kazuhiro Ito<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 3<br />
| bgcolor="#F0B0B0" align="center" |Zhiyu Zhang<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 10<br />
| bgcolor="#F0B0B0" align="center" |Qiao He<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 17<br />
| bgcolor="#F0B0B0" align="center" |Tristan Phillips<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 24 (Thanksgiving)<br />
| bgcolor="#F0B0B0" align="center" |No Seminar<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Dec 1<br />
| bgcolor="#F0B0B0" align="center" |Sachi Hashimoto<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Dec 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
Boya Wen bwen25@wisc.edu or Ziquan Yang zy352@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=23838NTS2022-10-10T16:20:00Z<p>Ashankar22: /* Fall 2022 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' '''Van Vleck B139''' or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Fall 2022 speakers in [https://wiki.math.wisc.edu/index.php/NTS_Fall_Semester_2022 Fall 2022]<br />
<br />
You can find our Spring 2022 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2022 Spring 2022].<br />
<br />
You can find our Fall 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2021 Fall 2021].<br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our Fall 2018 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
=Fall 2022 Semester=<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center" |'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center" |'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center" |'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" |Sep 8<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/zqyang Ziquan Yang]<br />
| bgcolor="#BCE2FE" |[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2022#Sep_07 The Tate conjecture for h^{2, 0} = 1 varieties over finite fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sep 15<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.google.com/view/qiucongling Congling Qiu]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_15 Modularity of arithmetic special divisors for unitary Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Sep 22<br />
| bgcolor="#F0B0B0" align="center" |[https://people.math.wisc.edu/~shi/ Yousheng Shi]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_22 Special cycles on Shimura varieties and theta series]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" |Sep 29<br />
| bgcolor="#F0B0B0" align="center" |[https://sites.duke.edu/pmgu/research/ Miao (Pam) Gu]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Sep_29 A family of period integrals related to triple product L-functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 6<br />
| bgcolor="#F0B0B0" align="center" |(merged with weekend workshop)<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 13<br />
| bgcolor="#F0B0B0" align="center" |[https://notnotraju.github.io/ Raju Krishnamoorthy]<br />
| bgcolor="#BCE2FE" |[https://wiki.math.wisc.edu/index.php/NTS_ABSTRACTFall2022#Oct13 Rank 2 local systems and abelian varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 20<br />
| bgcolor="#F0B0B0" align="center" |Tian Wang<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Oct 27<br />
| bgcolor="#F0B0B0" align="center" |Kazuhiro Ito<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 3<br />
| bgcolor="#F0B0B0" align="center" |Zhiyu Zhang<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 10<br />
| bgcolor="#F0B0B0" align="center" |Qiao He<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 17<br />
| bgcolor="#F0B0B0" align="center" |Tristan Phillips<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Nov 24 (Thanksgiving)<br />
| bgcolor="#F0B0B0" align="center" |No Seminar<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Dec 1<br />
| bgcolor="#F0B0B0" align="center" |Sachi Hashimoto<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
| bgcolor="#E0E0E0" align="center" |Dec 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE" |<br />
|- <br />
<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
Boya Wen bwen25@wisc.edu or Ziquan Yang zy352@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2022&diff=23837NTS ABSTRACTFall20222022-10-10T16:16:46Z<p>Ashankar22: </p>
<hr />
<div>== Sep 08 ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Tate conjecture for h^{2, 0} = 1 varieties over finite fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The past decade has witnessed a great advancement on the Tate conjecture for varieties with Hodge number h^{2, 0} = 1. Charles, Madapusi-Pera and Maulik completely settled the conjecture for K3 surfaces over finite fields, and Moonen proved the Mumford-Tate (and hence also Tate) conjecture for more or less arbitrary h^{2, 0} = 1 varieties in characteristic 0. <br />
<br />
In this talk, I will explain that the Tate conjecture is true for mod $p$ reductions of complex projective h^{2, 0} = 1 varieties when p is big enough, under a mild assumption on moduli. By refining this general result, we prove that in characteristic p at least 5 the BSD conjecture holds for a height 1 elliptic curve E over a function field of genus 1, as long as E is subject to the generic condition that all singular fibers in its minimal compacification are irreducible. We also prove the Tate conjecture over finite fields for a class of surfaces of general type and a class of Fano varieties. The overall philosphy is that the connection between the Tate conjecture over finite fields and the Lefschetz (1, 1)-theorem over the complex numbers is very robust for h^{2, 0} = 1 varieties, and works well beyond the hyperkahler world.<br />
<br />
This is based on joint work with Paul Hamacher and Xiaolei Zhao. <br />
<br />
''Zoom ID: 93014934562 Password: The order of A9 (the alternating group of 9 elements)''<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Congling Qiu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modularity of arithmetic special divisors for unitary Shimura varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We construct explicit generating series of arithmetic extensions of Kudla's special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the arithmetic Chow groups. This provides a partial solution to Kudla's modularity problem. The main ingredient in our construction is S. Zhang's theory of admissible arithmetic divisors. The main ingredient in the proof is an arithmetic mixed Siegel-Weil formula.<br />
<br />
''Zoom ID: 93014934562 Password: The order of A9 (the alternating group of 9 elements)''<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special cycles on Shimura varieties and theta series<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will introduce special cycles on Shimura varieties and discuss how to use them to construct geometric and arithmetic theta series. Then I will briefly discuss the connection between these theta series and L functions. In particular I will introduce Kudla-Rapoport conjecture–one key ingredient to make the connection.<br />
<br />
''Zoom ID: 93014934562 Password: The order of A9 (the alternating group of 9 elements)''<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 29 ==<br />
<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Miao (Pam) Gu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A family of period integrals related to triple product L-functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Let be a number field with ring of adeles . Let be a triple of positive integers and let where the are all cuspidal automorphic representations of . We denote by the corresponding triple product L-function. It is the Langlands L-function defined by the tensor product representation . In this talk I will present a family of Eulerian period integrals, which are holomorphic multiples of the triple product -function in a domain that nontrivially intersects the critical strip. We expect that they satisfy a local multiplicity one statement and a local functional equation. This is joint work with Jayce Getz, Chun-Hsien Hsu and Spencer Leslie.<br />
<br />
''Zoom ID: 93014934562 Password: The order of A9 (the alternating group of 9 elements)''<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Raju Krishnamoorthy'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Rank 2 local systems and abelian varieties.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Motivated by work of Corlette-Simpson over the complex numbers, we conjecture that all rank 2 \ell-adic local systems with trivial determinant on a smooth variety over a finite field come from families of abelian varieties. We will survey partial results on a p-adic variant of this conjecture. Time permitting, we will provide indications of the proofs, which involve the work of Hironaka and Hartshorne on positivity, the answer to a question of Grothendieck on extending abelian schemes via their p-divisible groups, Drinfeld's first work on the Langlands correspondence for GL_2 over function fields, and the pigeonhole principle with infinitely many pigeons. This is joint with Ambrus Pál.<br />
<br />
<br />
<br />
''Zoom ID: 93014934562 Password: The order of A9 (the alternating group of 9 elements)''<br />
|} <br />
</center></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23793Colloquia2022-10-03T14:05:07Z<p>Ashankar22: /* October 7, 2022, Friday at 4pm Daniel Litt (University of Toronto) */</p>
<hr />
<div>__NOTOC__<br />
<br />
In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated. <br />
<br />
==September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma)==<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
'''On surface homeomorphisms'''<br />
<br />
In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.<br />
==September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of British Columbia) ==<br />
(host: Guo, Seeger)<br />
<br />
'''Incidences and line counting: from the discrete to the fractal setting'''<br />
<br />
How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the continuum setting, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.<br />
<br />
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison, Statistics) ==<br />
(host: Stovall)<br />
<br />
'''Dependent Stopping Times and an Application to Credit Risk Theory'''<br />
<br />
Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.<br />
<br />
In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.<br />
==October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==<br />
(host: Ananth Shankar)<br />
<br />
'''The search for special symmetries'''<br />
<br />
What are the canonical sets of symmetries of n-dimensional space? I'll describe the history of this question, going back to Schwarz, Fuchs, Painlevé, and others, and some new answers to it, obtained jointly with Aaron Landesman. While our results rely on low-dimensional topology, Hodge theory, and the Langlands program, and we'll get a peek into how these areas come into play, no knowledge of them will be assumed.<br />
<br />
==October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==<br />
(host: Mari-Beffa)<br />
<br />
== October 20, 2022, Thursday at 4pm, VV911 [https://tavarelab.cancerdynamics.columbia.edu/ Simon Tavaré] (Columbia University) ==<br />
(host: Kurtz, Roch)<br />
<br />
''Note the unusual time and room!''<br />
<br />
'''An introduction to counts-of-counts data'''<br />
<br />
Counts-of-counts data arise in many areas of biology and medicine, and have been studied by statisticians since the 1940s. One of the first examples, discussed by R. A. Fisher and collaborators in 1943 [1], concerns estimation of the number of unobserved species based on summary counts of the number of species observed once, twice, … in a sample of specimens. The data are summarized by the numbers ''C<sub>1</sub>, C<sub>2</sub>, …'' of species represented once, twice, … in a sample of size<br />
<br />
''N = C<sub>1</sub> + 2 C<sub>2</sub> + 3 C<sub>3</sub> + <sup>….</sup>'' containing ''S = C<sub>1</sub> + C<sub>2</sub> + <sup>…</sup>'' species; the vector ''C ='' ''(C<sub>1</sub>, C<sub>2</sub>, …)'' gives the counts-of-counts. Other examples include the frequencies of the distinct alleles in a human genetics sample, the counts of distinct variants of the SARS-CoV-2 S protein obtained from consensus sequencing experiments, counts of sizes of components in certain combinatorial structures [2], and counts of the numbers of SNVs arising in one cell, two cells, … in a cancer sequencing experiment.<br />
<br />
In this talk I will outline some of the stochastic models used to model the distribution of ''C,'' and some of the inferential issues that come from estimating the parameters of these models. I will touch on the celebrated Ewens Sampling Formula [3] and Fisher’s multiple sampling problem concerning the variance expected between values of ''S'' in samples taken from the same population [3]. Variants of birth-death-immigration processes can be used, for example when different variants grow at different rates. Some of these models are mechanistic in spirit, others more statistical. For example, a non-mechanistic model is useful for describing the arrival of covid sequences at a database. Sequences arrive one at a time, and are either a new variant, or a copy of a variant that has appeared before. The classical Yule process with immigration provides a starting point to model this process, as I will illustrate.<br />
<br />
''References''<br />
<br />
[1] Fisher RA, Corbet AS & Williams CB. J Animal Ecology, 12, 1943<br />
<br />
[2] Arratia R, Barbour AD & Tavaré S. ''Logarithmic Combinatorial Structures,'' EMS, 2002<br />
<br />
[3] Ewens WJ. Theoret Popul Biol, 3, 1972<br />
<br />
[4] Da Silva P, Jamshidpey A, McCullagh P & Tavaré S. Bernoulli Journal, in press, 2022 (online)<br />
<br />
==October 21, 2022, Friday at 4pm [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas)==<br />
(host: Rodriguez)<br />
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kristen Lauter] (Facebook) ==<br />
Distinguished lectures<br />
<br />
(host: Yang).<br />
<br />
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech)==<br />
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.<br />
<br />
(host: Qin, Jordan)<br />
==November 18, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 2, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 9, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23667Colloquia2022-09-16T16:50:46Z<p>Ashankar22: /* September 23, 2022, Friday at 4pm Pablo Shmerkin (University of Washington) */</p>
<hr />
<div>__NOTOC__<br />
<br />
In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated. <br />
<br />
==September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma)==<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
'''On surface homeomorphisms'''<br />
<br />
In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.<br />
==September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of British Columbia) ==<br />
(host: Guo, Seeger)<br />
<br />
'''Incidences and line counting: from the discrete to the fractal setting'''<br />
<br />
How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the continuum setting, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.<br />
<br />
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison) ==<br />
(host: Stovall)<br />
==October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==<br />
(host: Ananth Shankar)<br />
<br />
==October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==<br />
(host: Mari-Beffa)<br />
<br />
==October 21, 2022, Friday at 4pm [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas)==<br />
(host: Rodriguez)<br />
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kristen Lauter] (Facebook) ==<br />
Distinguished lectures<br />
<br />
(host: Yang).<br />
<br />
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech)==<br />
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.<br />
<br />
(host: Qin, Jordan)<br />
==November 18, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 2, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 9, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23564Colloquia2022-09-05T14:35:29Z<p>Ashankar22: /* November 7-9, 2022, Kriten Lauter (Facebook) */</p>
<hr />
<div>__NOTOC__<br />
<br />
In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated. <br />
<br />
==September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma)==<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
'''On surface homeomorphisms'''<br />
<br />
In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.<br />
==September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of Washington) ==<br />
(host: Guo, Seeger)<br />
<br />
<br />
==October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==<br />
(host: Ananth Shankar)<br />
<br />
==October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==<br />
(host: Mari-Beffa)<br />
<br />
==October 21, 2022, Friday at 4pm [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas)==<br />
(host: Rodriguez)<br />
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kristen Lauter] (Facebook) ==<br />
Distinguished lectures<br />
<br />
(host: Yang).<br />
<br />
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech)==<br />
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.<br />
<br />
(host: Qin, Jordan)<br />
==November 18, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 2, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 9, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23554Colloquia2022-09-02T16:44:07Z<p>Ashankar22: </p>
<hr />
<div>__NOTOC__<br />
<br />
==September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma)==<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
'''On surface homeomorphisms'''<br />
<br />
In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.<br />
==September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of Washington) ==<br />
(host: Guo, Seeger)<br />
<br />
<br />
==October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==<br />
(host: Ananth Shankar)<br />
<br />
==October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State)==<br />
(host: Mari-Beffa)<br />
<br />
==October 21, 2022, Friday at 4pm [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas)==<br />
(host: Rodriguez)<br />
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kriten Lauter] (Facebook) ==<br />
Distinguished lectures<br />
<br />
(host: Yang).<br />
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech)==<br />
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.<br />
<br />
(host: Qin, Jordan)<br />
==November 18, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 2, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
==December 9, 2022, Friday at 4pm [TBD]==<br />
(reserved by HC. contact: Stechmann)<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia/Fall2022&diff=23545Colloquia/Fall20222022-09-01T19:01:44Z<p>Ashankar22: </p>
<hr />
<div>== September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma) ==<br />
<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
== September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of Washington) ==<br />
<br />
(host: Guo, Seeger)<br />
<br />
== September 30, 2022, Friday at 4pm ==<br />
<br />
(reserved. contact: Kent)<br />
<br />
<br />
== October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto) ==<br />
<br />
(host: Ananth Shankar)<br />
<br />
<br />
== October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State) ==<br />
<br />
(host: Mari-Beffa)<br />
<br />
<br />
== October 21, 2022, Friday at 4pm [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (Texas) ==<br />
<br />
(host: Rodriguez)<br />
<br />
== November 7-9, 2022, [https://ai.facebook.com/people/kristin-lauter/ Kriten Lauter] (Facebook) ==<br />
Distinguished lectures<br />
<br />
(host: Yang).<br />
<br />
== November 11, 2022, Friday at 4pm [http://users.cms.caltech.edu/~jtropp/ Joel Tropp] (Caltech) ==<br />
This is the Annual LAA lecture. See [https://math.wisc.edu/laa-lecture/ this] for its history.<br />
<br />
(host: Qin, Jordan)<br />
<br />
== November 18, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)<br />
<br />
== December 2, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)<br />
<br />
== December 9, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Colloquia/Fall2022&diff=23448Colloquia/Fall20222022-08-18T17:23:52Z<p>Ashankar22: </p>
<hr />
<div>== September 9 , 2022, Friday at 4pm [https://math.ou.edu/~jing/ Jing Tao] (University of Oklahoma) ==<br />
<br />
(host: Dymarz, Uyanik, WIMAW)<br />
<br />
== September 23, 2022, Friday at 4pm [https://www.pabloshmerkin.org/ Pablo Shmerkin] (University of Washington) ==<br />
<br />
(host: Guo, Seeger)<br />
<br />
== October 7, 2022, Friday at 4pm [https://www.daniellitt.com/ Daniel Litt] (University of Toronto) ==<br />
<br />
(host: Ananth Shankar)<br />
<br />
<br />
== October 14, 2022, Friday at 4pm [https://math.sciences.ncsu.edu/people/asagema/ Andrew Sageman-Furnas] (North Carolina State) ==<br />
<br />
(host: Mari-Beffa)<br />
<br />
== November 18, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)<br />
<br />
== December 2, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)<br />
<br />
== December 9, 2022, Friday at 4pm [TBD] ==<br />
<br />
(reserved by HC. contact: Stechmann)</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21382NTS2021-09-01T21:59:19Z<p>Ashankar22: /* Organizer contact information */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Fall 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2021 Fall 2021].<br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our Fall 2018 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2021 Semester =<br />
<br />
<center><br />
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{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 9<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center" | <br />
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|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center" | <br />
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|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
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|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 7<br />
| bgcolor="#F0B0B0" align="center" | <br />
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|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 4<br />
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| bgcolor="#E0E0E0" align="center" | Nov 11<br />
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| bgcolor="#E0E0E0" align="center" | Nov 18<br />
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| bgcolor="#E0E0E0" align="center" | Dec 2<br />
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| bgcolor="#E0E0E0" align="center" | Dec 9<br />
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</center><br />
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*to be confirmed<br />
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= Organizer contact information =<br />
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<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21193NTS ABSTRACTSpring20212021-04-29T22:39:20Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
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</center><br />
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== Feb 4 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
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</center><br />
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== Feb 11 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
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|} <br />
</center><br />
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== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
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|} <br />
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== Feb 25 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
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|} <br />
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== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
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== Mar 11 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
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</center><br />
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== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
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</center><br />
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== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
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== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
|-<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
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</center><br />
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== Apr 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Henri Darmon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Hilbert’s twelfth problem and deformations of modular forms<br />
|-<br />
| bgcolor="#BCD2EE" | Hilbert’s twelfth problem asks for the construction of abelian extensions of number fields via special values of (complex) analytic functions. An early prototype for a solution is the theory of complex multiplication, culminating in the landmark treatise of Shimura and Taniyama which provides a satisfying answer for CM ground fields.<br />
<br />
For more general number fields, Stark’s conjecture leads to a conjectural framework for explicit class field theory based on the leading terms of abelian complex L-series at s=1 or s=0. While there has been very little no progress on the original conjecture, Benedict Gross formulated seminal p-adic and ``tame’’ analogues in the mid 1980’s which have turned out to be far more amenable to available techniques, growing out of the proof of the ``main conjectures” by Mazur and Wiles, and culminating in the recent work of Samit Dasgupta and Mahesh Kakde which, by proving a strong refinement of the p-adic Gross-Stark conjecture, leads to what might be touted as a {\em p-adic solution} to Hilbert’s twelfth problem for all totally real fields.<br />
<br />
I will compare and contrast this work with a different approach (in collaboration with Alice Pozzi and Jan Vonk) which proves a similar result for real quadratic fields. While limited for now to real quadratic fields, this approach is part of the broader program of extending the full panoply of the theory of complex multiplication to real quadratic, and possibly other non CM base fields.<br />
|} <br />
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== Apr 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Joshua Lam'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | CM liftings on Shimura varieties<br />
|-<br />
| bgcolor="#BCD2EE" | I will discuss results on CM liftings of mod p points of Shimura varieties, for example the finiteness of supersingular points admitting CM lifts. I’ll also discuss the structure of CM liftable points in the case of Hilbert modular varieties, by applying results of Helm-Tian-Xiao on the Goren-Oort stratification. This is joint work with Mark Kisin, Ananth Shankar and Padma Srinivasan.<br />
|} <br />
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<br><br />
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== Apr 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brian Lawrence'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Shafarevich conjecture for hypersurfaces in abelian varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Let K be a number field, S a finite set of primes of O_K, and g a positive integer. Shafarevich conjectured, and Faltings proved, that there are only finitely many curves of genus g, defined over K and having good reduction outside S. Analogous results have been proven for other families, replacing "curves of genus g" with "K3 surfaces", "del Pezzo surfaces" etc.; these results are also called Shafarevich conjectures. There are good reasons to expect the Shafarevich conjecture to hold for many families of varieties: the moduli space should have only finitely many integral points. Will Sawin and I prove this for hypersurfaces in a fixed abelian variety of dimension not equal to 3.<br />
|} <br />
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== Apr 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Maria Fox'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Supersingular Loci of Some Unitary Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Unitary Shimura varieties are moduli spaces of abelian varieties with an action of a quadratic imaginary field, and extra structure. In this talk, we'll discuss specific examples of unitary Shimura varieties whose supersingular loci can be concretely described in terms of Deligne-Lusztig varieties. By Rapoport-Zink uniformization, much of the structure of these supersingular loci can be understood by studying an associated moduli space of p-divisible groups (a Rapoport-Zink space). We'll discuss the geometric structure of these associated Rapoport-Zink spaces as well as some techniques for studying them. <br />
|} <br />
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== May 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Padmavathi Srinivasan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Towards a unified theory of canonical heights on abelian varieties<br />
|-<br />
| bgcolor="#BCD2EE" | p-adic heights have been a rich source of explicit functions vanishing on rational points on a curve. In this talk, we will outline a new construction of canonical p-adic heights on abelian varieties from p-adic adelic metrics, using p-adic Arakelov theory developed by Besser. This construction closely mirrors Zhang's construction of canonical real valued heights from real-valued adelic metrics. We will use this new construction to give direct explanations (avoiding p-adic Hodge theory) of the key properties of height pairings needed for the quadratic Chabauty method for rational points. This is joint work in progress with Amnon Besser and Steffen Mueller.<br />
|} <br />
</center><br />
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<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21192NTS2021-04-29T22:38:20Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_25 Remembrances of polynomial values: Fourier's way]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_1 A non-archimedean definable Chow theorem]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" | Henri Darmon<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_8 Hilbert’s twelfth problem and deformations of modular forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_15 CM liftings on Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_22 The Shafarevich conjecture for hypersurfaces in abelian varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_29 Supersingular Loci of Some Unitary Shimura Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#May_6 Towards a unified theory of canonical heights on abelian varieties]<br />
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|}<br />
</center><br />
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<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21190NTS ABSTRACTSpring20212021-04-28T17:25:36Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
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== Feb 4 ==<br />
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
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== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
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|} <br />
</center><br />
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== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
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|} <br />
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== Feb 25 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
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|} <br />
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== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
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== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
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<br><br />
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== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
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== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
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== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
|-<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
|} <br />
</center><br />
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== Apr 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Henri Darmon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Hilbert’s twelfth problem and deformations of modular forms<br />
|-<br />
| bgcolor="#BCD2EE" | Hilbert’s twelfth problem asks for the construction of abelian extensions of number fields via special values of (complex) analytic functions. An early prototype for a solution is the theory of complex multiplication, culminating in the landmark treatise of Shimura and Taniyama which provides a satisfying answer for CM ground fields.<br />
<br />
For more general number fields, Stark’s conjecture leads to a conjectural framework for explicit class field theory based on the leading terms of abelian complex L-series at s=1 or s=0. While there has been very little no progress on the original conjecture, Benedict Gross formulated seminal p-adic and ``tame’’ analogues in the mid 1980’s which have turned out to be far more amenable to available techniques, growing out of the proof of the ``main conjectures” by Mazur and Wiles, and culminating in the recent work of Samit Dasgupta and Mahesh Kakde which, by proving a strong refinement of the p-adic Gross-Stark conjecture, leads to what might be touted as a {\em p-adic solution} to Hilbert’s twelfth problem for all totally real fields.<br />
<br />
I will compare and contrast this work with a different approach (in collaboration with Alice Pozzi and Jan Vonk) which proves a similar result for real quadratic fields. While limited for now to real quadratic fields, this approach is part of the broader program of extending the full panoply of the theory of complex multiplication to real quadratic, and possibly other non CM base fields.<br />
|} <br />
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== Apr 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Joshua Lam'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | CM liftings on Shimura varieties<br />
|-<br />
| bgcolor="#BCD2EE" | I will discuss results on CM liftings of mod p points of Shimura varieties, for example the finiteness of supersingular points admitting CM lifts. I’ll also discuss the structure of CM liftable points in the case of Hilbert modular varieties, by applying results of Helm-Tian-Xiao on the Goren-Oort stratification. This is joint work with Mark Kisin, Ananth Shankar and Padma Srinivasan.<br />
|} <br />
</center><br />
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<br />
<br><br />
<br />
== Apr 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brian Lawrence'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Shafarevich conjecture for hypersurfaces in abelian varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Let K be a number field, S a finite set of primes of O_K, and g a positive integer. Shafarevich conjectured, and Faltings proved, that there are only finitely many curves of genus g, defined over K and having good reduction outside S. Analogous results have been proven for other families, replacing "curves of genus g" with "K3 surfaces", "del Pezzo surfaces" etc.; these results are also called Shafarevich conjectures. There are good reasons to expect the Shafarevich conjecture to hold for many families of varieties: the moduli space should have only finitely many integral points. Will Sawin and I prove this for hypersurfaces in a fixed abelian variety of dimension not equal to 3.<br />
|} <br />
</center><br />
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== Apr 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Maria Fox'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Supersingular Loci of Some Unitary Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Unitary Shimura varieties are moduli spaces of abelian varieties with an action of a quadratic imaginary field, and extra structure. In this talk, we'll discuss specific examples of unitary Shimura varieties whose supersingular loci can be concretely described in terms of Deligne-Lusztig varieties. By Rapoport-Zink uniformization, much of the structure of these supersingular loci can be understood by studying an associated moduli space of p-divisible groups (a Rapoport-Zink space). We'll discuss the geometric structure of these associated Rapoport-Zink spaces as well as some techniques for studying them. <br />
|} <br />
</center><br />
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<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21189NTS2021-04-28T17:24:32Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_25 Remembrances of polynomial values: Fourier's way]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_1 A non-archimedean definable Chow theorem]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" | Henri Darmon<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_8 Hilbert’s twelfth problem and deformations of modular forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_15 CM liftings on Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_22 The Shafarevich conjecture for hypersurfaces in abelian varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_29 Supersingular Loci of Some Unitary Shimura Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
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<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21165NTS ABSTRACTSpring20212021-04-21T22:09:07Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
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== Feb 4 ==<br />
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
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== Feb 11 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
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</center><br />
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== Feb 18 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
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|} <br />
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== Feb 25 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
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== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
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== Mar 11 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
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<br><br />
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== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
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== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
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== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
|-<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
|} <br />
</center><br />
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== Apr 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Henri Darmon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Hilbert’s twelfth problem and deformations of modular forms<br />
|-<br />
| bgcolor="#BCD2EE" | Hilbert’s twelfth problem asks for the construction of abelian extensions of number fields via special values of (complex) analytic functions. An early prototype for a solution is the theory of complex multiplication, culminating in the landmark treatise of Shimura and Taniyama which provides a satisfying answer for CM ground fields.<br />
<br />
For more general number fields, Stark’s conjecture leads to a conjectural framework for explicit class field theory based on the leading terms of abelian complex L-series at s=1 or s=0. While there has been very little no progress on the original conjecture, Benedict Gross formulated seminal p-adic and ``tame’’ analogues in the mid 1980’s which have turned out to be far more amenable to available techniques, growing out of the proof of the ``main conjectures” by Mazur and Wiles, and culminating in the recent work of Samit Dasgupta and Mahesh Kakde which, by proving a strong refinement of the p-adic Gross-Stark conjecture, leads to what might be touted as a {\em p-adic solution} to Hilbert’s twelfth problem for all totally real fields.<br />
<br />
I will compare and contrast this work with a different approach (in collaboration with Alice Pozzi and Jan Vonk) which proves a similar result for real quadratic fields. While limited for now to real quadratic fields, this approach is part of the broader program of extending the full panoply of the theory of complex multiplication to real quadratic, and possibly other non CM base fields.<br />
|} <br />
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== Apr 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Joshua Lam'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | CM liftings on Shimura varieties<br />
|-<br />
| bgcolor="#BCD2EE" | I will discuss results on CM liftings of mod p points of Shimura varieties, for example the finiteness of supersingular points admitting CM lifts. I’ll also discuss the structure of CM liftable points in the case of Hilbert modular varieties, by applying results of Helm-Tian-Xiao on the Goren-Oort stratification. This is joint work with Mark Kisin, Ananth Shankar and Padma Srinivasan.<br />
|} <br />
</center><br />
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<br><br />
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== Apr 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Brian Lawrence'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Shafarevich conjecture for hypersurfaces in abelian varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Let K be a number field, S a finite set of primes of O_K, and g a positive integer. Shafarevich conjectured, and Faltings proved, that there are only finitely many curves of genus g, defined over K and having good reduction outside S. Analogous results have been proven for other families, replacing "curves of genus g" with "K3 surfaces", "del Pezzo surfaces" etc.; these results are also called Shafarevich conjectures. There are good reasons to expect the Shafarevich conjecture to hold for many families of varieties: the moduli space should have only finitely many integral points. Will Sawin and I prove this for hypersurfaces in a fixed abelian variety of dimension not equal to 3.<br />
|} <br />
</center><br />
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<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21164NTS2021-04-21T22:07:47Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_25 Remembrances of polynomial values: Fourier's way]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_1 A non-archimedean definable Chow theorem]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" | Henri Darmon<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_8 Hilbert’s twelfth problem and deformations of modular forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_15 CM liftings on Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_22 The Shafarevich conjecture for hypersurfaces in abelian varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21126NTS ABSTRACTSpring20212021-04-09T15:31:40Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
|} <br />
</center><br />
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== Feb 4 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
|} <br />
</center><br />
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== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
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|} <br />
</center><br />
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== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
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|} <br />
</center><br />
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== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
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|} <br />
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== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
<br />
|} <br />
</center><br />
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== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
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<br><br />
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== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
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== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
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<br><br />
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== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
|-<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
|} <br />
</center><br />
<br><br />
== Apr 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Henri Darmon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Hilbert’s twelfth problem and deformations of modular forms<br />
|-<br />
| bgcolor="#BCD2EE" | Hilbert’s twelfth problem asks for the construction of abelian extensions of number fields via special values of (complex) analytic functions. An early prototype for a solution is the theory of complex multiplication, culminating in the landmark treatise of Shimura and Taniyama which provides a satisfying answer for CM ground fields.<br />
<br />
For more general number fields, Stark’s conjecture leads to a conjectural framework for explicit class field theory based on the leading terms of abelian complex L-series at s=1 or s=0. While there has been very little no progress on the original conjecture, Benedict Gross formulated seminal p-adic and ``tame’’ analogues in the mid 1980’s which have turned out to be far more amenable to available techniques, growing out of the proof of the ``main conjectures” by Mazur and Wiles, and culminating in the recent work of Samit Dasgupta and Mahesh Kakde which, by proving a strong refinement of the p-adic Gross-Stark conjecture, leads to what might be touted as a {\em p-adic solution} to Hilbert’s twelfth problem for all totally real fields.<br />
<br />
I will compare and contrast this work with a different approach (in collaboration with Alice Pozzi and Jan Vonk) which proves a similar result for real quadratic fields. While limited for now to real quadratic fields, this approach is part of the broader program of extending the full panoply of the theory of complex multiplication to real quadratic, and possibly other non CM base fields.<br />
|} <br />
</center><br />
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<br><br />
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<br />
== Apr 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Joshua Lam'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | CM liftings on Shimura varieties<br />
|-<br />
| bgcolor="#BCD2EE" | I will discuss results on CM liftings of mod p points of Shimura varieties, for example the finiteness of supersingular points admitting CM lifts. I’ll also discuss the structure of CM liftable points in the case of Hilbert modular varieties, by applying results of Helm-Tian-Xiao on the Goren-Oort stratification. This is joint work with Mark Kisin, Ananth Shankar and Padma Srinivasan.<br />
|} <br />
</center><br />
<br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21125NTS2021-04-09T15:29:24Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_25 Remembrances of polynomial values: Fourier's way]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_1 A non-archimedean definable Chow theorem]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" | Henri Darmon<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_8 Hilbert’s twelfth problem and deformations of modular forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_15 CM liftings on Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21049NTS ABSTRACTSpring20212021-03-23T18:34:55Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
|-<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=21048NTS ABSTRACTSpring20212021-03-23T18:34:10Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Emmanuel Kowalski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Remembrances of polynomial values: Fourier's way<br />
|-<br />
| bgcolor="#BCD2EE" | The talk will begin by a survey of questions about the value sets of<br />
polynomials over finite fields. We will then focus in particular on a<br />
new phase-retrieval problem for the exponential sums associated to two<br />
polynomials; under suitable genericity assumptions, we determine all<br />
solutions to this problem. We will attempt to highlight the remarkably<br />
varied combination of tools and results of algebraic geometry, group<br />
theory and number theory that appear in this study.<br />
<br />
(Joint work with K. Soundararajan)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Abhishek Oswal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A non-archimedean definable Chow theorem<br />
<br />
| bgcolor="#BCD2EE" | In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context.<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=21047NTS2021-03-23T18:31:02Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_25 Remembrances of polynomial values: Fourier's way]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Apr_1 A non-archimedean definable Chow theorem]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2021&diff=20987NTS ABSTRACTSpring20212021-03-11T20:13:10Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS Main Page]<br />
<br />
<br />
== Jan 28 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Monica Nevins'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Interpreting the local character expansion of p-adic SL(2)<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Harish-Chandra—Howe local character expansion expresses the character of an admissible representation of a p-adic group G as a linear combination with complex coefficients of the (finitely many!) Fourier transforms of nilpotent orbital integrals \(\widehat{\mu}_{\mathcal{O}}\) --- near the identity. Approaching from another direction: we can restrict the representation to any compact open subgroup K of G, obtaining its branching rules, which also describe the representation near the identity, in a different sense. <br />
We show that for G=SL(2,k), k a nonarchimedean local field, where the branching rules to maximal compact open subgroups K are known, each of these terms \(\widehat{\mu}_{\mathcal{O}}\) can be interpreted as the character \(\tau_{\mathcal{O}}\) of a representation of K, up to an error term arising from the zero orbit. Moreover, the irreducible components of \(\tau_{\mathcal{O}}\) are explicitly constructed from the K -orbits in \(\mathcal{O}\). This work in progress offers a conjectural alternative interpretation of branching rules of admissible representations. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ke Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On CM points away from the Torelli locus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Coleman conjectured in 1980's that when g is an integer sufficiently large, the open Torelli locus T_g in the Siegel modular variety A_g should contain at most finitely many CM points, namely Jacobians of ''general'' curves of high genus should not admit complex multiplication. We show that certain CM points do not lie in T_g if they parametrize abelian varieties isogeneous to products of simple CM abelian varieties of low dimension. The proof relies on known results on Faltings height and Sato-Tate equidistributions. This is a joint work with Kang Zuo and Xin Lv.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Dmitry Gourevitch'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In recent works with H. P. A. Gustafsson, A. Kleinschmidt, D. Persson, and<br />
S. Sahi, we found a way to express any automorphic form through its Fourier coefficients, using adelic integrals, period integrals and discrete summation – generalizing the Piatetski-Shapiro – Shalika decomposition for GL(n).<br />
I will explain the general idea behind our formulas, and illustrate it on examples.<br />
I will also show applications to vanishing and Eulerianity of Fourier coefficients.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Eyal Kaplan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The generalized doubling method, multiplicity one and the application to global functoriality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
One of the fundamental difficulties in the Langlands program is to handle the non-generic case.<br />
The doubling method, developed by Piatetski-Shapiro and Rallis in the 80s, pioneered the study of L-functions<br />
for cuspidal non-generic automorphic representations of classical groups. Recently, this method has been generalized<br />
in several aspects with interesting applications. In this talk I will survey the different components of the <br />
generalized doubling method, describe the fundamental multiplicity one result obtained recently in a joint <br />
work with Aizenbud and Gourevitch, and outline the application to global functoriality.<br />
Parts of the talk are also based on a collaboration with Cai, Friedberg and Ginzburg.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Feb 25 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Roger Van Peski'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Random matrices, random groups, singular values, and symmetric functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since the 1989 work of Friedman-Washington, the cokernels of random p-adic matrices drawn from various distributions have provided models for random finite abelian p-groups arising in number theory and combinatorics, the most famous being the class groups of quadratic imaginary number fields. Since any finite abelian p-group is isomorphic to a direct sum of cyclic groups $\bigoplus_i \mathbb{Z}/p^{\lambda_i}\mathbb{Z}$, it is equivalent to study the random integer partition $\lambda = (\lambda_1, \lambda_2,\ldots)$, which is analogous to the singular values of a complex random matrix. We show that the behavior of such partitions under taking products and corners of random p-adic matrices is governed by the Hall-Littlewood polynomials, recovering and explaining some previous results relating p-adic matrix cokernels to these polynomials. We use these exact results to study the joint asymptotic behavior of the cokernels of products of many random p-adic matrices $A_\tau \cdots A_1$, with $\tau$ acting as a discrete time parameter. We show that the parts $\lambda_i$ of the corresponding partition have a simple description via an interacting particle system, and their fluctuations converge under rescaling to independent Brownian motions. At both the exact and asymptotic level we explain connections between our results and existing results on singular values of complex random matrices: both are in fact degenerations of the same operations on random partitions coming from Macdonald polynomials.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 4 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Amos Nevo'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intrinsic Diophantine approximation on homogeneous algebraic varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Classical Diophantine approximation quantifies the denseness of the set of rational vectors in their ambient Euclidean space. A far-reaching extension of the classical theory calls for quantifying the denseness of rational points in general homogeneous algebraic varieties. This was raised as an open problem by Serge Lang already half a century ago, but progress towards it was achieved only in a limited number of special cases. A systematic approach to this problem for homogeneous varieties associated with semi-simple groups has been developed in recent years, in joint work with A. Ghosh and A. Gorodnik. The methods employ dynamical arguments and effective ergodic theory, and employ spectral estimates in the automorphic representation of semi-simple groups. In the case of homogeneous spaces with semi-simple stability group, this approach leads to the derivation of pointwise uniform and almost sure Diophantine exponents, as well as analogs of Khinchin's and W. Schmidt's theorems, with some of the results being best possible. We will explain some of the main results and some of the ingredients in their proof, focusing on some easily accessible examples.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Mar 11 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Carlo Pagano'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the negative Pell conjecture<br />
|-<br />
| bgcolor="#BCD2EE" | The negative Pell equation has been studied since many centuries. Euler already provided an interesting criterion in terms of continued fractions. In 1995 Peter Stevenhagen proposed a conjecture for the frequency of the solvability of this equation, when one varies the real quadratic field. I will discuss an upcoming joint work with Peter Koymans where we establish Stevenhagen's conjecture. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 18 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Siddhi Pathak'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Special values of L-series with periodic coefficients<br />
|-<br />
| bgcolor="#BCD2EE" | A crucial ingredient in Dirichlet's proof of infinitude of primes in arithmetic progressions is the non-vanishing of $L(1,\chi)$, for any non-principal Dirichlet character $\chi$. Inspired by this result, one can ask if the same remains true when $\chi$ is replaced by a general periodic arithmetic function. This problem has received significant attention in the literature, beginning with the work of S. Chowla and that of Baker, Birch and Wirsing. Nonetheless, tantalizing questions such as the conjecture of Erdos regarding non-vanishing of $L(1,f)$, for certain periodic $f$, remain open. In this talk, I will present various facets of this problem and discuss recent progress in generalizing the theorems of Baker-Birch-Wirsing and Okada. <br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20986NTS2021-03-11T20:11:25Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [[NTSGrad|graduate seminar]], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_25 Random matrices, random groups, singular values, and symmetric functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_4 Intrinsic Diophantine approximation on homogeneous algebraic varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_11 On the negative Pell conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Mar_18 Special values of L-series with periodic coefficients]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20948Algebra and Algebraic Geometry Seminar Spring 20212021-03-05T19:41:42Z<p>Ashankar22: /* 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 />
|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>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20947Algebra and Algebraic Geometry Seminar Spring 20212021-03-05T19:39:19Z<p>Ashankar22: /* 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 />
|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>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20805NTS2021-02-09T01:17:33Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_11 Relations between Fourier coefficients of automorphic forms, with applications to vanishing and to Eulerianity]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_18 The generalized doubling method, multiplicity one and the application to global functoriality]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | Abhishek Oswal<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20766Algebra and Algebraic Geometry Seminar Spring 20212021-02-05T19:24:05Z<p>Ashankar22: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|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>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20765Algebra and Algebraic Geometry Seminar Spring 20212021-02-05T19:22:46Z<p>Ashankar22: /* 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| 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 />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20701Algebra and Algebraic Geometry Seminar Spring 20212021-01-29T23:27:11Z<p>Ashankar22: /* Abstracts */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|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 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>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20700Algebra and Algebraic Geometry Seminar Spring 20212021-01-29T23:24:14Z<p>Ashankar22: </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 12<br />
|[http://individual.utoronto.ca/groechenig/ Michael Groechenig (University of Toronto)]<br />
|[[#Michael Groechenig| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 16<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20652Algebra and Algebraic Geometry Seminar Spring 20212021-01-26T22:32:47Z<p>Ashankar22: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 26<br />
|[http://people.math.harvard.edu/~engel/ Philip Engel (UGA)]<br />
|[[#Philip Engel| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 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 />
|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 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20651Algebra and Algebraic Geometry Seminar Spring 20212021-01-26T20:11:39Z<p>Ashankar22: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|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 />
|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 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20650Algebra and Algebraic Geometry Seminar Spring 20212021-01-26T20:11:30Z<p>Ashankar22: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|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 />
|March 5<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 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Spring_2021&diff=20640Algebra and Algebraic Geometry Seminar Spring 20212021-01-24T22:47:24Z<p>Ashankar22: /* Spring 2021 Schedule */</p>
<hr />
<div>The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).<br />
<br />
== COVID-19 Update ==<br />
As a result of Covid-19, the seminar for this semester will be held virtually. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes<br />
we will have to use a different meeting link, if Michael K cannot host that day).<br />
<br />
== Spring 2021 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | link to talk<br />
|-<br />
|January 29<br />
|[https://sites.math.northwestern.edu/~nir/ Nir Avni (Northwestern)]<br />
|[[#Nir Avni| First order rigidity for higher rank lattices]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
<br />
|-<br />
|February 12<br />
|[https://sites.google.com/site/aprodupage/ Marian Aprodu (Bucharest)]<br />
|[[#Marian Aprodu| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|February 19<br />
|[https://www.dhruvrnathan.net/ Dhruv Ranganathan (Cambridge)]<br />
|[[#Dhruv Ranganathan| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|March 5<br />
|[http://www.personal.psu.edu/eus25/ Eyal Subag (Bar Ilan - Israel)]<br />
|[[#Eyal Subag| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|April 23<br />
|[https://sites.google.com/view/gurbir-dhillon/home Gurbir Dhillon (Yale)]<br />
|[[#Gurbir Dhillon| TBA]]<br />
|[https://uwmadison.zoom.us/j/9502605167 Zoom link]<br />
|-<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===January 29: Nir Avni===<br />
Title: First order rigidity for higher rank lattices.<br />
<br />
Abstract: I'll describe a new rigidity phenomenon for lattices in higher rank simple algebraic groups. Specifically, I'll explain why the first order theories of such groups do not have (finitely generated) deformations and why they are determined (in the class of finitely generated groups) by a single first order axiom.<br />
<br />
The results are from joint works with Alex Lubotzky and Chen Meiri.<br />
<br />
===Marian Aprodu===<br />
'''TBA'''<br />
<br />
TBA<br />
===Eyal Subag===<br />
'''TBA'''<br />
<br />
TBA<br />
===Gurbir Dhillon===<br />
'''TBA'''<br />
<br />
TBA</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20603NTS2021-01-21T18:28:29Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Feb_4 On CM points away from the Torelli locus]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~ylam/ Joshua Lam]<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20499NTS2021-01-13T20:22:33Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20498NTS2021-01-13T20:22:19Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Fall 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2020 Fall 2020].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2021#Jan_28 Interpreting the local character expansion of p-adic SL(2)]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | [ https://padmask.github.io/ Padmavathi Srinivasan]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_Spring_Semester_2021&diff=20476NTS Spring Semester 20212021-01-09T20:43:18Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div><br />
= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/mariafox/ Maria Fox]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_Spring_Semester_2021&diff=20475NTS Spring Semester 20212021-01-09T20:42:29Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div><br />
= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | Maria Fox<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_Spring_Semester_2021&diff=20467NTS Spring Semester 20212021-01-07T00:51:40Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div><br />
= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | Monica Nevins<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | Ke Chen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | Dmitry Gourevitch<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | Eyal Kaplan<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | Roger Van Peski<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | Amos Nevo<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" | [http://guests.mpim-bonn.mpg.de/carlo.pagano90/ Carlo Pagano]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | [https://people.math.ethz.ch/~kowalski/ Emmanuel Kowalski]<br />
| bgcolor="#BCE2FE"| Remembrances of polynomial values: Fourier's way<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | Brian Lawrence<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20433NTS2020-12-09T15:54:46Z<p>Ashankar22: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9:00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_3 Beilinson-Bloch conjecture and arithmetic inner product formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_10 The joints problem for varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | Ziquan Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_17 A Crystalline Torelli Theorem for Supersingular K3^&#91;n&#93;-type Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | Yousheng Shi<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_24 Kudla Rapoport conjecture over the ramified primes]<br />
|- <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | Liyang Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_1 Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(Register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~yujiex/ Yujie Xu] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_15 On normalization in the integral models of Shimura varieties of Hodge type]<br />
(Register at https://harvard.zoom.us/meeting/register/tJYlduqrrDgqGNRmtfw245PNXp_XGCzMlkYm)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | Artane Siad <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_22 Average 2-torsion in the class group of monogenic fields]<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/guillermo-mantilla-soler Guillermo Mantilla-Soler]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_29 A complete invariant for real S_n number fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5(11 AM)<br />
| bgcolor="#F0B0B0" align="center" | Anup Dixit<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_5 On generalized Brauer-Siegel conjecture and Euler-Kronecker constants]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | Si Ying Lee<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_12 Eichler-Shimura relations for Hodge type Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_19 On the Kudla-Rapoport conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | Thanksgiving (no seminar)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_3 Singular modular forms on quaternionic E_8]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10 (9:00 AM)<br />
| bgcolor="#F0B0B0" align="center" | Daxin Xu<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_10 Bessel F-isocrystals for reductive groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | Qirui Li<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_17 Biquadratic Guo-Jacquet Fundamental Lemma and its arithmetic generalizations]<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2020&diff=20417NTS ABSTRACTFall20202020-12-03T18:56:49Z<p>Ashankar22: /* Dec 10 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yifeng Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Beilinson-Bloch conjecture and arithmetic inner product formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yufei Zhao'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The joints problem for varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). <br />
<br />
Our main innovation is a new way to extend the polynomial method to higher dimensional objects. A simple, yet key step in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk, I will explain how we generalize the vanishing lemma to multivariable polynomials, for our application to the joints problem.<br />
<br />
Joint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1983, Ogus proved that a supersingular K3 surface in characteristic at least 5 is determined up to isomorphism by the Frobenius action and the Poincaré pairing on its second crystalline cohomology. This is an analogue of the classical Torelli theorem for K3's, due to Shapiro and Shafarevich, which says that a complex algebraic K3 surface is determined up to isomorphism by the Hodge structure and the Poinaré pairing on its second singular cohomology. I will explain how to re-interpret Ogus' theorem from a motivic point of view and generalize the stronger form of the theorem to a class of higher dimensional analogues of K3 surfaces, called K3^[n]-type varieties. This is also an analogue of Verbitsky's global Torelli theorem for general irreducible symplectic manifolds. A new feature in Verbitsky's theorem, which did not appear in the classical Torelli theorem for K3's, is the notion of "parallel transport operators". I will explain how to work with this notion in an arithmetic setting. <br />
<br />
As an application, I will also present a similar crystalline Torelli theorem for supersingular cubic fourfolds, the Hodge theoretic counterpart of which is a theorem of Voisin. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Kudla Rapoport conjecture over the ramified primes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In the nineties, Kudla formulated a conjecture relating central derivative of certain Eisenstein series to arithmetic intersection numbers of special cycles on Shimura varieties. Later Kudla and Rapoport formulated a local version of the conjecture which compares intersection numbers of special cycles on the unitary Rapoport Zink spaces over an inert prime of an imaginary quadratic field with derivatives of local density of hermitian forms. In this talk, I will review Kudla-Rapoport conjecture and its global motivation. Then I will talk about an attempt to formulate a Kudla-Rapoport type of conjecture over the ramified primes. In case of unitary Shimura curves, this new conjecture can be proved. This is a joint work with Qiao He and Tonghai Yang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Liyang Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study an average of automorphic periods on $U(2,1)\times U(1,1).$ We also compute local factors in Ichino-Ikeda formulas for these periods to obtain an explicit asymptotic expression. Combining them together we would deduce some important properties of central $L$-values on $U(2,1)\times U(1,1)$ over certain family: the first moment, nonvanishing and subconvexity. This is joint work with Philippe Michel and Dinakar Ramakrishnan.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yujie Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On normalization in the integral models of Shimura varieties of Hodge type<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties are moduli spaces of abelian varieties (in characteristic zero) with extra structures. Interests in mod p points of Shimura varieties motivated the constructions of integral models of Shimura varieties by various mathematicians. <br />
In this talk, I will discuss some motivic aspects of integral models of Hodge type at hyperspecial level, constructed by Kisin. I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Artane Siad'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average 2-torsion in the class group of monogenic fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Let n greater than or equal to 3 be a fixed degree. In this talk, we prove an upper bound on the average size of the 2-torsion in the class groups of monogenised fields of degree $n$, and, conditional on a widely expected tail estimate, compute it exactly. For odd degree, we find that this average is different from the value predicted for the full family of fields by the Cohen-Lenstra-Martinet-Malle heuristic, generalising a result of Bhargava-Hanke-Shankar. For even degree at least 4, no heuristic is available about the distribution of the 2-part over the full family. In fact, it is the first time that p-torsion averages are computed for a "bad" prime in the sense of Cohen-Lenstra in degree at least 3. A corollary of our results is that in each fixed degree and signature, there are infinitely many monogenic S_n-number fields with odd class number and units of every signature.<br />
<br />
Our proof exploits an orbit parametrisation due to Wood, clarifies the roles of genus theory in even degree, and reveals an interesting structure explaining the deviation of the odd monogenic averages from the values expected for the full family.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Guillermo Mantilla-Soler'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A complete invariant for real S_n number fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | In this talk we will review some of the most common invariants from algebraic number theory. We divide number fields in families, by Galois groups or signature, and study the trace form in each collection of fields. We will show how this division on number fields led us to the discovery that for real S_n number fields, with restricted ramification, the trace is a complete invariant. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anup Dixit'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On generalized Brauer-Siegel conjecture and Euler-Kronecker constants<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | For a number field K, let h_K denote its class number. It is an important theme in number theory to study how h_K varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regulator varies over a family of Galois fields. An analogue of this statement for general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant gamma, Ihara introduced the Euler-Kronecker constants attached to any number field. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constants, thus proving the Brauer-Siegel conjecture in some special cases.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Si Ying Lee'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Eichler-Shimura relations for Hodge type Shimura varieties<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschebung. Blasius and Rogawski proposed a generalization of this result for general Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for Shimura varieties of Hodge type, assuming a technical condition on the unramified sigma-conjugacy classes in the Kottwitz set.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Chao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the Kudla-Rapoport conjecture<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic Siegel-Weil formula and the arithmetic inner product formula. We will motivate this conjecture from the classical Hurwitz class number formula, explain a proof based on the uncertainty principle, and discuss global applications. This is joint work with Wei Zhang.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Dec 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Aaron Pollack'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Singular modular forms on quaternionic E_8<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The exceptional group $E_{7,3}$ has a symmetric space with Hermitian tube structure. On it, Henry Kim wrote down low weight holomorphic modular forms that are "singular" in the sense that their Fourier expansion has many terms equal to zero. The symmetric space associated to the exceptional group $E_{8,4}$ does not have a Hermitian structure, but it has what might be the next best thing: a quaternionic structure and associated "modular forms". I will explain the construction of singular modular forms on $E_{8,4}$, and the proof that these special modular forms have rational Fourier expansions, in a precise sense. This builds off of work of Wee Teck Gan and uses key input from Gordan Savin.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Daxin Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Bessel F-isocrystals for reductive groups<br />
<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | I will first review relationship between the Bessel differential equation and the classical Kloosterman sums.<br />
<br />
Recently, there are two generalizations of this story (corresponding to GL<sub>2</sub>-case) for reductive groups: one is due to Frenkel and Gross from the viewpoint of the Bessel differential equation; another one, due to Heinloth, Ng\^o and Yun, uses the geometric Langlands correspondence to produce $\ell$-adic sheaves.<br />
<br />
I will report my joint work with Xinwen Zhu, where we study the p-adic aspect of this theory and unify previous two constructions.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2020&diff=20416NTS ABSTRACTFall20202020-12-03T18:55:37Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yifeng Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Beilinson-Bloch conjecture and arithmetic inner product formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yufei Zhao'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The joints problem for varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). <br />
<br />
Our main innovation is a new way to extend the polynomial method to higher dimensional objects. A simple, yet key step in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk, I will explain how we generalize the vanishing lemma to multivariable polynomials, for our application to the joints problem.<br />
<br />
Joint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1983, Ogus proved that a supersingular K3 surface in characteristic at least 5 is determined up to isomorphism by the Frobenius action and the Poincaré pairing on its second crystalline cohomology. This is an analogue of the classical Torelli theorem for K3's, due to Shapiro and Shafarevich, which says that a complex algebraic K3 surface is determined up to isomorphism by the Hodge structure and the Poinaré pairing on its second singular cohomology. I will explain how to re-interpret Ogus' theorem from a motivic point of view and generalize the stronger form of the theorem to a class of higher dimensional analogues of K3 surfaces, called K3^[n]-type varieties. This is also an analogue of Verbitsky's global Torelli theorem for general irreducible symplectic manifolds. A new feature in Verbitsky's theorem, which did not appear in the classical Torelli theorem for K3's, is the notion of "parallel transport operators". I will explain how to work with this notion in an arithmetic setting. <br />
<br />
As an application, I will also present a similar crystalline Torelli theorem for supersingular cubic fourfolds, the Hodge theoretic counterpart of which is a theorem of Voisin. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Kudla Rapoport conjecture over the ramified primes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In the nineties, Kudla formulated a conjecture relating central derivative of certain Eisenstein series to arithmetic intersection numbers of special cycles on Shimura varieties. Later Kudla and Rapoport formulated a local version of the conjecture which compares intersection numbers of special cycles on the unitary Rapoport Zink spaces over an inert prime of an imaginary quadratic field with derivatives of local density of hermitian forms. In this talk, I will review Kudla-Rapoport conjecture and its global motivation. Then I will talk about an attempt to formulate a Kudla-Rapoport type of conjecture over the ramified primes. In case of unitary Shimura curves, this new conjecture can be proved. This is a joint work with Qiao He and Tonghai Yang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Liyang Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study an average of automorphic periods on $U(2,1)\times U(1,1).$ We also compute local factors in Ichino-Ikeda formulas for these periods to obtain an explicit asymptotic expression. Combining them together we would deduce some important properties of central $L$-values on $U(2,1)\times U(1,1)$ over certain family: the first moment, nonvanishing and subconvexity. This is joint work with Philippe Michel and Dinakar Ramakrishnan.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yujie Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On normalization in the integral models of Shimura varieties of Hodge type<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties are moduli spaces of abelian varieties (in characteristic zero) with extra structures. Interests in mod p points of Shimura varieties motivated the constructions of integral models of Shimura varieties by various mathematicians. <br />
In this talk, I will discuss some motivic aspects of integral models of Hodge type at hyperspecial level, constructed by Kisin. I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Artane Siad'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average 2-torsion in the class group of monogenic fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Let n greater than or equal to 3 be a fixed degree. In this talk, we prove an upper bound on the average size of the 2-torsion in the class groups of monogenised fields of degree $n$, and, conditional on a widely expected tail estimate, compute it exactly. For odd degree, we find that this average is different from the value predicted for the full family of fields by the Cohen-Lenstra-Martinet-Malle heuristic, generalising a result of Bhargava-Hanke-Shankar. For even degree at least 4, no heuristic is available about the distribution of the 2-part over the full family. In fact, it is the first time that p-torsion averages are computed for a "bad" prime in the sense of Cohen-Lenstra in degree at least 3. A corollary of our results is that in each fixed degree and signature, there are infinitely many monogenic S_n-number fields with odd class number and units of every signature.<br />
<br />
Our proof exploits an orbit parametrisation due to Wood, clarifies the roles of genus theory in even degree, and reveals an interesting structure explaining the deviation of the odd monogenic averages from the values expected for the full family.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Guillermo Mantilla-Soler'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A complete invariant for real S_n number fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | In this talk we will review some of the most common invariants from algebraic number theory. We divide number fields in families, by Galois groups or signature, and study the trace form in each collection of fields. We will show how this division on number fields led us to the discovery that for real S_n number fields, with restricted ramification, the trace is a complete invariant. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anup Dixit'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On generalized Brauer-Siegel conjecture and Euler-Kronecker constants<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | For a number field K, let h_K denote its class number. It is an important theme in number theory to study how h_K varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regulator varies over a family of Galois fields. An analogue of this statement for general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant gamma, Ihara introduced the Euler-Kronecker constants attached to any number field. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constants, thus proving the Brauer-Siegel conjecture in some special cases.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Si Ying Lee'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Eichler-Shimura relations for Hodge type Shimura varieties<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschebung. Blasius and Rogawski proposed a generalization of this result for general Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for Shimura varieties of Hodge type, assuming a technical condition on the unramified sigma-conjugacy classes in the Kottwitz set.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Chao Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On the Kudla-Rapoport conjecture<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic Siegel-Weil formula and the arithmetic inner product formula. We will motivate this conjecture from the classical Hurwitz class number formula, explain a proof based on the uncertainty principle, and discuss global applications. This is joint work with Wei Zhang.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Dec 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Aaron Pollack'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Singular modular forms on quaternionic E_8<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The exceptional group $E_{7,3}$ has a symmetric space with Hermitian tube structure. On it, Henry Kim wrote down low weight holomorphic modular forms that are "singular" in the sense that their Fourier expansion has many terms equal to zero. The symmetric space associated to the exceptional group $E_{8,4}$ does not have a Hermitian structure, but it has what might be the next best thing: a quaternionic structure and associated "modular forms". I will explain the construction of singular modular forms on $E_{8,4}$, and the proof that these special modular forms have rational Fourier expansions, in a precise sense. This builds off of work of Wee Teck Gan and uses key input from Gordan Savin.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Daxin Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Bessel F-isocrystals for reductive groups<br />
<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | I will first review relationship between the Bessel differential equation and the classical Kloosterman sums.<br />
<br />
Recently, there are two generalizations of this story (corresponding to $\GL_2$-case) for reductive groups: one is due to Frenkel and Gross from the viewpoint of the Bessel differential equation; another one, due to Heinloth, Ng\^o and Yun, uses the geometric Langlands correspondence to produce $\ell$-adic sheaves.<br />
<br />
I will report my joint work with Xinwen Zhu, where we study the p-adic aspect of this theory and unify previous two constructions.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20415NTS2020-12-03T18:54:21Z<p>Ashankar22: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2021 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2021 Spring 2021].<br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9:00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_3 Beilinson-Bloch conjecture and arithmetic inner product formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_10 The joints problem for varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | Ziquan Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_17 A Crystalline Torelli Theorem for Supersingular K3^&#91;n&#93;-type Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | Yousheng Shi<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_24 Kudla Rapoport conjecture over the ramified primes]<br />
|- <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | Liyang Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_1 Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(Register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~yujiex/ Yujie Xu] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_15 On normalization in the integral models of Shimura varieties of Hodge type]<br />
(Register at https://harvard.zoom.us/meeting/register/tJYlduqrrDgqGNRmtfw245PNXp_XGCzMlkYm)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | Artane Siad <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_22 Average 2-torsion in the class group of monogenic fields]<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/guillermo-mantilla-soler Guillermo Mantilla-Soler]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_29 A complete invariant for real S_n number fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5(11 AM)<br />
| bgcolor="#F0B0B0" align="center" | Anup Dixit<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_5 On generalized Brauer-Siegel conjecture and Euler-Kronecker constants]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | Si Ying Lee<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_12 Eichler-Shimura relations for Hodge type Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_19 On the Kudla-Rapoport conjecture]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | Thanksgiving (no seminar)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_3 Singular modular forms on quaternionic E_8]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" | Daxin Xu<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Dec_10 Bessel F-isocrystals for reductive groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | Qirui Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_Spring_Semester_2021&diff=20350NTS Spring Semester 20212020-11-15T04:11:28Z<p>Ashankar22: /* Spring 2021 Semester */</p>
<hr />
<div><br />
= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
Back to the number theory seminar main webpage: [https://www.math.wisc.edu/wiki/index.php/NTS Main page]<br />
<br />
<br />
= Spring 2021 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Jan 28<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 11<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 18<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 4<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 11<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 18<br />
| bgcolor="#F0B0B0" align="center" | [http://personal.psu.edu/spp5684/ Siddhi Pathak] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 25<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 8<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 15 <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 29<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 6<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2020&diff=20302NTS ABSTRACTFall20202020-11-06T17:15:12Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yifeng Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Beilinson-Bloch conjecture and arithmetic inner product formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yufei Zhao'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The joints problem for varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). <br />
<br />
Our main innovation is a new way to extend the polynomial method to higher dimensional objects. A simple, yet key step in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk, I will explain how we generalize the vanishing lemma to multivariable polynomials, for our application to the joints problem.<br />
<br />
Joint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1983, Ogus proved that a supersingular K3 surface in characteristic at least 5 is determined up to isomorphism by the Frobenius action and the Poincaré pairing on its second crystalline cohomology. This is an analogue of the classical Torelli theorem for K3's, due to Shapiro and Shafarevich, which says that a complex algebraic K3 surface is determined up to isomorphism by the Hodge structure and the Poinaré pairing on its second singular cohomology. I will explain how to re-interpret Ogus' theorem from a motivic point of view and generalize the stronger form of the theorem to a class of higher dimensional analogues of K3 surfaces, called K3^[n]-type varieties. This is also an analogue of Verbitsky's global Torelli theorem for general irreducible symplectic manifolds. A new feature in Verbitsky's theorem, which did not appear in the classical Torelli theorem for K3's, is the notion of "parallel transport operators". I will explain how to work with this notion in an arithmetic setting. <br />
<br />
As an application, I will also present a similar crystalline Torelli theorem for supersingular cubic fourfolds, the Hodge theoretic counterpart of which is a theorem of Voisin. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Kudla Rapoport conjecture over the ramified primes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In the nineties, Kudla formulated a conjecture relating central derivative of certain Eisenstein series to arithmetic intersection numbers of special cycles on Shimura varieties. Later Kudla and Rapoport formulated a local version of the conjecture which compares intersection numbers of special cycles on the unitary Rapoport Zink spaces over an inert prime of an imaginary quadratic field with derivatives of local density of hermitian forms. In this talk, I will review Kudla-Rapoport conjecture and its global motivation. Then I will talk about an attempt to formulate a Kudla-Rapoport type of conjecture over the ramified primes. In case of unitary Shimura curves, this new conjecture can be proved. This is a joint work with Qiao He and Tonghai Yang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Liyang Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study an average of automorphic periods on $U(2,1)\times U(1,1).$ We also compute local factors in Ichino-Ikeda formulas for these periods to obtain an explicit asymptotic expression. Combining them together we would deduce some important properties of central $L$-values on $U(2,1)\times U(1,1)$ over certain family: the first moment, nonvanishing and subconvexity. This is joint work with Philippe Michel and Dinakar Ramakrishnan.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yujie Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On normalization in the integral models of Shimura varieties of Hodge type<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties are moduli spaces of abelian varieties (in characteristic zero) with extra structures. Interests in mod p points of Shimura varieties motivated the constructions of integral models of Shimura varieties by various mathematicians. <br />
In this talk, I will discuss some motivic aspects of integral models of Hodge type at hyperspecial level, constructed by Kisin. I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Artane Siad'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average 2-torsion in the class group of monogenic fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Let n greater than or equal to 3 be a fixed degree. In this talk, we prove an upper bound on the average size of the 2-torsion in the class groups of monogenised fields of degree $n$, and, conditional on a widely expected tail estimate, compute it exactly. For odd degree, we find that this average is different from the value predicted for the full family of fields by the Cohen-Lenstra-Martinet-Malle heuristic, generalising a result of Bhargava-Hanke-Shankar. For even degree at least 4, no heuristic is available about the distribution of the 2-part over the full family. In fact, it is the first time that p-torsion averages are computed for a "bad" prime in the sense of Cohen-Lenstra in degree at least 3. A corollary of our results is that in each fixed degree and signature, there are infinitely many monogenic S_n-number fields with odd class number and units of every signature.<br />
<br />
Our proof exploits an orbit parametrisation due to Wood, clarifies the roles of genus theory in even degree, and reveals an interesting structure explaining the deviation of the odd monogenic averages from the values expected for the full family.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Guillermo Mantilla-Soler'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A complete invariant for real S_n number fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | In this talk we will review some of the most common invariants from algebraic number theory. We divide number fields in families, by Galois groups or signature, and study the trace form in each collection of fields. We will show how this division on number fields led us to the discovery that for real S_n number fields, with restricted ramification, the trace is a complete invariant. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anup Dixit'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On generalized Brauer-Siegel conjecture and Euler-Kronecker constants<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | For a number field K, let h_K denote its class number. It is an important theme in number theory to study how h_K varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regulator varies over a family of Galois fields. An analogue of this statement for general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant gamma, Ihara introduced the Euler-Kronecker constants attached to any number field. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constants, thus proving the Brauer-Siegel conjecture in some special cases.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Si Ying Lee'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Eichler-Shimura relations for Hodge type Shimura varieties<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschebung. Blasius and Rogawski proposed a generalization of this result for general Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for Shimura varieties of Hodge type, assuming a technical condition on the unramified sigma-conjugacy classes in the Kottwitz set.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2020&diff=20301NTS ABSTRACTFall20202020-11-06T17:14:31Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yifeng Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Beilinson-Bloch conjecture and arithmetic inner product formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yufei Zhao'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The joints problem for varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). <br />
<br />
Our main innovation is a new way to extend the polynomial method to higher dimensional objects. A simple, yet key step in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk, I will explain how we generalize the vanishing lemma to multivariable polynomials, for our application to the joints problem.<br />
<br />
Joint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1983, Ogus proved that a supersingular K3 surface in characteristic at least 5 is determined up to isomorphism by the Frobenius action and the Poincaré pairing on its second crystalline cohomology. This is an analogue of the classical Torelli theorem for K3's, due to Shapiro and Shafarevich, which says that a complex algebraic K3 surface is determined up to isomorphism by the Hodge structure and the Poinaré pairing on its second singular cohomology. I will explain how to re-interpret Ogus' theorem from a motivic point of view and generalize the stronger form of the theorem to a class of higher dimensional analogues of K3 surfaces, called K3^[n]-type varieties. This is also an analogue of Verbitsky's global Torelli theorem for general irreducible symplectic manifolds. A new feature in Verbitsky's theorem, which did not appear in the classical Torelli theorem for K3's, is the notion of "parallel transport operators". I will explain how to work with this notion in an arithmetic setting. <br />
<br />
As an application, I will also present a similar crystalline Torelli theorem for supersingular cubic fourfolds, the Hodge theoretic counterpart of which is a theorem of Voisin. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Kudla Rapoport conjecture over the ramified primes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In the nineties, Kudla formulated a conjecture relating central derivative of certain Eisenstein series to arithmetic intersection numbers of special cycles on Shimura varieties. Later Kudla and Rapoport formulated a local version of the conjecture which compares intersection numbers of special cycles on the unitary Rapoport Zink spaces over an inert prime of an imaginary quadratic field with derivatives of local density of hermitian forms. In this talk, I will review Kudla-Rapoport conjecture and its global motivation. Then I will talk about an attempt to formulate a Kudla-Rapoport type of conjecture over the ramified primes. In case of unitary Shimura curves, this new conjecture can be proved. This is a joint work with Qiao He and Tonghai Yang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Liyang Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study an average of automorphic periods on $U(2,1)\times U(1,1).$ We also compute local factors in Ichino-Ikeda formulas for these periods to obtain an explicit asymptotic expression. Combining them together we would deduce some important properties of central $L$-values on $U(2,1)\times U(1,1)$ over certain family: the first moment, nonvanishing and subconvexity. This is joint work with Philippe Michel and Dinakar Ramakrishnan.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yujie Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On normalization in the integral models of Shimura varieties of Hodge type<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties are moduli spaces of abelian varieties (in characteristic zero) with extra structures. Interests in mod p points of Shimura varieties motivated the constructions of integral models of Shimura varieties by various mathematicians. <br />
In this talk, I will discuss some motivic aspects of integral models of Hodge type at hyperspecial level, constructed by Kisin. I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Artane Siad'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average 2-torsion in the class group of monogenic fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Let n greater than or equal to 3 be a fixed degree. In this talk, we prove an upper bound on the average size of the 2-torsion in the class groups of monogenised fields of degree $n$, and, conditional on a widely expected tail estimate, compute it exactly. For odd degree, we find that this average is different from the value predicted for the full family of fields by the Cohen-Lenstra-Martinet-Malle heuristic, generalising a result of Bhargava-Hanke-Shankar. For even degree at least 4, no heuristic is available about the distribution of the 2-part over the full family. In fact, it is the first time that p-torsion averages are computed for a "bad" prime in the sense of Cohen-Lenstra in degree at least 3. A corollary of our results is that in each fixed degree and signature, there are infinitely many monogenic S_n-number fields with odd class number and units of every signature.<br />
<br />
Our proof exploits an orbit parametrisation due to Wood, clarifies the roles of genus theory in even degree, and reveals an interesting structure explaining the deviation of the odd monogenic averages from the values expected for the full family.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Guillermo Mantilla-Soler'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A complete invariant for real S_n number fields.<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | In this talk we will review some of the most common invariants from algebraic number theory. We divide number fields in families, by Galois groups or signature, and study the trace form in each collection of fields. We will show how this division on number fields led us to the discovery that for real S_n number fields, with restricted ramification, the trace is a complete invariant. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anup Dixit'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On generalized Brauer-Siegel conjecture and Euler-Kronecker constants<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | For a number field K, let h_K denote its class number. It is an important theme in number theory to study how h_K varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regulator varies over a family of Galois fields. An analogue of this statement for general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant gamma, Ihara introduced the Euler-Kronecker constants attached to any number field. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constants, thus proving the Brauer-Siegel conjecture in some special cases.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Si Ying Lee'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Eichler-Shimura relations for Hodge type Shimura varieties<br />
<br />
<br />
|-<br />
| bgcolor="#BCD2EE" | The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschebung. Blasius and Rogawski proposed a generalization of this result for general Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for Shimura varieties of Hodge type, assuming a technical condition on the unramified sigma-conjugacy classes in the Kottwitz set.<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20300NTS2020-11-06T17:13:25Z<p>Ashankar22: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9:00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_3 Beilinson-Bloch conjecture and arithmetic inner product formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_10 The joints problem for varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | Ziquan Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_17 A Crystalline Torelli Theorem for Supersingular K3^&#91;n&#93;-type Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | Yousheng Shi<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_24 Kudla Rapoport conjecture over the ramified primes]<br />
|- <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | Liyang Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_1 Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(Register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~yujiex/ Yujie Xu] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_15 On normalization in the integral models of Shimura varieties of Hodge type]<br />
(Register at https://harvard.zoom.us/meeting/register/tJYlduqrrDgqGNRmtfw245PNXp_XGCzMlkYm)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | Artane Siad <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_22 Average 2-torsion in the class group of monogenic fields]<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/guillermo-mantilla-soler Guillermo Mantilla-Soler]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_29 A complete invariant for real S_n number fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5(11 AM)<br />
| bgcolor="#F0B0B0" align="center" | Anup Dixit<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_5 On generalized Brauer-Siegel conjecture and Euler-Kronecker constants]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | Si Ying Lee<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_12 Eichler-Shimura relations for Hodge type Shimura varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | Thanksgiving (no seminar)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" | Daxin Xu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | Qirui Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTFall2020&diff=20266NTS ABSTRACTFall20202020-10-30T19:06:53Z<p>Ashankar22: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Sep 3 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yifeng Liu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Beilinson-Bloch conjecture and arithmetic inner product formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 10 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yufei Zhao'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The joints problem for varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We generalize the Guth-Katz joints theorem from lines to varieties. A special case of our result says that N planes (2-flats) in 6 dimensions (over any field) have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of these planes not all lying in some hyperplane. Our most general result gives upper bounds, tight up to constant factors, for joints with multiplicities for several sets of varieties of arbitrary dimensions (known as Carbery's conjecture). <br />
<br />
Our main innovation is a new way to extend the polynomial method to higher dimensional objects. A simple, yet key step in many applications of the polynomial method is the "vanishing lemma": a single-variable degree-d polynomial has at most d zeros. In this talk, I will explain how we generalize the vanishing lemma to multivariable polynomials, for our application to the joints problem.<br />
<br />
Joint work with Jonathan Tidor and Hung-Hsun Hans Yu (https://arxiv.org/abs/2008.01610)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 17 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ziquan Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A Crystalline Torelli Theorem for Supersingular K3^[n]-type Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In 1983, Ogus proved that a supersingular K3 surface in characteristic at least 5 is determined up to isomorphism by the Frobenius action and the Poincaré pairing on its second crystalline cohomology. This is an analogue of the classical Torelli theorem for K3's, due to Shapiro and Shafarevich, which says that a complex algebraic K3 surface is determined up to isomorphism by the Hodge structure and the Poinaré pairing on its second singular cohomology. I will explain how to re-interpret Ogus' theorem from a motivic point of view and generalize the stronger form of the theorem to a class of higher dimensional analogues of K3 surfaces, called K3^[n]-type varieties. This is also an analogue of Verbitsky's global Torelli theorem for general irreducible symplectic manifolds. A new feature in Verbitsky's theorem, which did not appear in the classical Torelli theorem for K3's, is the notion of "parallel transport operators". I will explain how to work with this notion in an arithmetic setting. <br />
<br />
As an application, I will also present a similar crystalline Torelli theorem for supersingular cubic fourfolds, the Hodge theoretic counterpart of which is a theorem of Voisin. <br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 24 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yousheng Shi'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Kudla Rapoport conjecture over the ramified primes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In the nineties, Kudla formulated a conjecture relating central derivative of certain Eisenstein series to arithmetic intersection numbers of special cycles on Shimura varieties. Later Kudla and Rapoport formulated a local version of the conjecture which compares intersection numbers of special cycles on the unitary Rapoport Zink spaces over an inert prime of an imaginary quadratic field with derivatives of local density of hermitian forms. In this talk, I will review Kudla-Rapoport conjecture and its global motivation. Then I will talk about an attempt to formulate a Kudla-Rapoport type of conjecture over the ramified primes. In case of unitary Shimura curves, this new conjecture can be proved. This is a joint work with Qiao He and Tonghai Yang.<br />
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== Oct 1 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Liyang Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, we study an average of automorphic periods on $U(2,1)\times U(1,1).$ We also compute local factors in Ichino-Ikeda formulas for these periods to obtain an explicit asymptotic expression. Combining them together we would deduce some important properties of central $L$-values on $U(2,1)\times U(1,1)$ over certain family: the first moment, nonvanishing and subconvexity. This is joint work with Philippe Michel and Dinakar Ramakrishnan.<br />
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== Oct 15 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Yujie Xu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On normalization in the integral models of Shimura varieties of Hodge type<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties are moduli spaces of abelian varieties (in characteristic zero) with extra structures. Interests in mod p points of Shimura varieties motivated the constructions of integral models of Shimura varieties by various mathematicians. <br />
In this talk, I will discuss some motivic aspects of integral models of Hodge type at hyperspecial level, constructed by Kisin. I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. <br />
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== Oct 22 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Artane Siad'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Average 2-torsion in the class group of monogenic fields.<br />
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|-<br />
| bgcolor="#BCD2EE" | <br />
Let n greater than or equal to 3 be a fixed degree. In this talk, we prove an upper bound on the average size of the 2-torsion in the class groups of monogenised fields of degree $n$, and, conditional on a widely expected tail estimate, compute it exactly. For odd degree, we find that this average is different from the value predicted for the full family of fields by the Cohen-Lenstra-Martinet-Malle heuristic, generalising a result of Bhargava-Hanke-Shankar. For even degree at least 4, no heuristic is available about the distribution of the 2-part over the full family. In fact, it is the first time that p-torsion averages are computed for a "bad" prime in the sense of Cohen-Lenstra in degree at least 3. A corollary of our results is that in each fixed degree and signature, there are infinitely many monogenic S_n-number fields with odd class number and units of every signature.<br />
<br />
Our proof exploits an orbit parametrisation due to Wood, clarifies the roles of genus theory in even degree, and reveals an interesting structure explaining the deviation of the odd monogenic averages from the values expected for the full family.<br />
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== Oct 29 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Guillermo Mantilla-Soler'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A complete invariant for real S_n number fields.<br />
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|-<br />
| bgcolor="#BCD2EE" | In this talk we will review some of the most common invariants from algebraic number theory. We divide number fields in families, by Galois groups or signature, and study the trace form in each collection of fields. We will show how this division on number fields led us to the discovery that for real S_n number fields, with restricted ramification, the trace is a complete invariant. <br />
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|} <br />
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== Nov 5 ==<br />
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<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Anup Dixit'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On generalized Brauer-Siegel conjecture and Euler-Kronecker constants<br />
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|-<br />
| bgcolor="#BCD2EE" | For a number field K, let h_K denote its class number. It is an important theme in number theory to study how h_K varies over a family of number fields. In this context, the classical Brauer-Siegel theorem describes how the class number times the regulator varies over a family of Galois fields. An analogue of this statement for general families was conjectured by Tsfasman and Vladut in 2002. On another front, as a natural generalization of Euler's constant gamma, Ihara introduced the Euler-Kronecker constants attached to any number field. In this talk, we will discuss a connection between the generalized Brauer-Siegel conjecture and bounds on the Euler-Kronecker constants, thus proving the Brauer-Siegel conjecture in some special cases.<br />
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</center><br />
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<br></div>Ashankar22https://wiki.math.wisc.edu/index.php?title=NTS&diff=20265NTS2020-10-30T19:05:09Z<p>Ashankar22: /* Fall 2020 Semester */</p>
<hr />
<div>= Number Theory / Representation Theory Seminar, University of Wisconsin - Madison =<br />
<br />
<br />
*'''When:''' Thursdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' Van Vleck B321 or remotely<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Fall_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our Spring 2020 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2020 Spring 2020]. <br />
<br><br />
You can find our Fall 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_Semester_2019 Fall 2019]. <br />
<br><br />
You can find our Spring 2019 speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_Semester_2019 Spring 2019]. <br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Fall_2018_Semester Fall 2018].<br />
<br />
= Fall 2020 Semester =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Sep 3 (9:00 am)<br />
| bgcolor="#F0B0B0" align="center" | Yifeng Liu<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_3 Beilinson-Bloch conjecture and arithmetic inner product formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 10<br />
| bgcolor="#F0B0B0" align="center" | Yufei Zhao<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_10 The joints problem for varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 17<br />
| bgcolor="#F0B0B0" align="center" | Ziquan Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_17 A Crystalline Torelli Theorem for Supersingular K3^&#91;n&#93;-type Varieties]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 24<br />
| bgcolor="#F0B0B0" align="center" | Yousheng Shi<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Sep_24 Kudla Rapoport conjecture over the ramified primes]<br />
|- <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 1<br />
| bgcolor="#F0B0B0" align="center" | Liyang Yang<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_1 Average Central L-values on U(2,1)$\times$ U(1,1), Nonvanishing and Subconvexity]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 7 (Wed. at 7pm)<br />
| bgcolor="#F0B0B0" align="center" | Shamgar Gurevich (UW - Madison)<br />
| bgcolor="#BCE2FE"|Harmonic Analysis on GLn over Finite Fields <br />
(Register at https://uni-sydney.zoom.us/meeting/register/tJAocOGhqjwiE91DEddxUhCudfQX5mzp-cPQ)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 15<br />
| bgcolor="#F0B0B0" align="center" | [http://people.math.harvard.edu/~yujiex/ Yujie Xu] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_15 On normalization in the integral models of Shimura varieties of Hodge type]<br />
(Register at https://harvard.zoom.us/meeting/register/tJYlduqrrDgqGNRmtfw245PNXp_XGCzMlkYm)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 22<br />
| bgcolor="#F0B0B0" align="center" | Artane Siad <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_22 Average 2-torsion in the class group of monogenic fields]<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 29<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/view/guillermo-mantilla-soler Guillermo Mantilla-Soler]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Oct_29 A complete invariant for real S_n number fields]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 5(11 AM)<br />
| bgcolor="#F0B0B0" align="center" | Anup Dixit<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTFall2020#Nov_5 On generalized Brauer-Siegel conjecture and Euler-Kronecker constants]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 12<br />
| bgcolor="#F0B0B0" align="center" | Si Ying Lee<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 19<br />
| bgcolor="#F0B0B0" align="center" | Chao Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 26<br />
| bgcolor="#F0B0B0" align="center" | Thanksgiving (no seminar)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 3<br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 10<br />
| bgcolor="#F0B0B0" align="center" | Daxin Xu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 17<br />
| bgcolor="#F0B0B0" align="center" | Qirui Li<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
|}<br />
</center><br />
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<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
<br />
<br />
[mailto:shi58@wisc.edu Yousheng Shi]<br />
Yousheng Shi:shi58@wisc.edu<br />
<br />
[mailto:ashankar@math.wisc.edu Ananth Shankar]<br />
Ananth Shankar:ashankar@math.wisc.edu<br />
<br />
= VaNTAGe =<br />
This is a virtual math seminar on open conjectures in<br />
number theory and arithmetic geometry. The seminar will be presented in English at (1 pm Eastern time)=(10 am Pacific time), every first and third Tuesday of the month. The Math Department of UW, Madison broadcasts the seminar in the math lounge room at Room 911, Van Vleck Building.<br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/vantageseminar VaNTAGe]<br />
----<br />
<br />
= New Developments in Number Theory =<br />
This is a new seminar series that features the work of early career number theorists from around the globe. <br />
For more information, please visit the official website: <br />
[https://sites.google.com/view/peopleonlinent/contributed-talks NDNT]<br />
----<br />
<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Ashankar22