https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Soumyasankar&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-28T10:44:45ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19389NTS ABSTRACTSpring20202020-05-07T21:18:49Z<p>Soumyasankar: /* May 7 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
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<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
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<br><br />
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== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
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== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
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<br><br />
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== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
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<br />
<br />
|} <br />
</center><br />
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== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
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<br><br />
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== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
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<br><br />
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== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
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<br><br />
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== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
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== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the étale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the étale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree <math>p</math> and <math>K</math> is the cyclotomic field containing a <math>p</math>th root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod <math>p</math>. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod <math>p</math>. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
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== April 9 ==<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%" | '''Rahul Dalal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Statistics of Automorphic Representations through the Stable Trace Formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since individual automorphic representations are very difficult to access, it is helpful to study families of them instead. In particular, statistics over families can be computed through various forms of Arthur's trace formula. One refinement---the stable trace formula---has recently developed to the point where explicit computations with it are feasible. I will present one result on statistics that this new technique can prove. <br />
|} <br />
</center><br />
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== April 23 ==<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%" | '''Jayce Getz'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On triple product $L$-functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Establishing the conjectured analytic properties of triple product $L$-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on $\mathrm{GL}_3$; in some sense this is the smallest case that appears out of reach via standard techniques. The approach involves a relative trace formula and Poisson summation on spherical varieties in the sense of Braverman-Kazhdan, Ngo, and Sakellaridis. <br />
<br />
https://zoom.us/j/96864496800 <br />
|} <br />
</center><br />
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== April 30 ==<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%" | '''Noah Taylor'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Sato Tate Conjecture on Abelian Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sato-Tate conjecture says that the normalized point counts of genus $g$ curves are equidistributed with respect to a certain measure. We will construct the Sato-Tate group, state the conjecture precisely, prove a case, and in the cases where not everything is known, we will discuss how much we can say about the point counts anyway.<br />
<br />
https://us02web.zoom.us/j/81526488221<br />
<br />
|} <br />
</center><br />
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== May 7 ==<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 Landesman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The geometric distribution of Selmer groups of Elliptic curves over function fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Bhargava, Kane, Lenstra, Poonen, and Rains proposed heuristics for the distribution of arithmetic data relating to elliptic curves, such as their ranks, Selmer groups, and Tate-Shafarevich groups. As a special case of their heuristics, they obtain the minimalist conjecture, which predicts that 50% of elliptic curves have rank 0 and 50% of elliptic curves have rank 1. After surveying these conjectures, we will explain joint work with Tony Feng and Eric Rains, verifying many of these conjectures over function fields of the form <math>\mathbb F_q(t)</math>, after taking a certain large <math>q</math> limit.<br />
<br />
Zoom link: https://us02web.zoom.us/j/84813855575<br />
<br />
Notes: http://web.stanford.edu/~aaronlan/assets/longer-selmer-distribution-talk-notes.pdf<br />
|} <br />
</center><br />
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<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19388NTS ABSTRACTSpring20202020-05-03T21:29:14Z<p>Soumyasankar: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
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<br><br />
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== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
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<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
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== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
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<br><br />
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== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the étale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the étale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree <math>p</math> and <math>K</math> is the cyclotomic field containing a <math>p</math>th root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod <math>p</math>. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod <math>p</math>. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 9 ==<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%" | '''Rahul Dalal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Statistics of Automorphic Representations through the Stable Trace Formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since individual automorphic representations are very difficult to access, it is helpful to study families of them instead. In particular, statistics over families can be computed through various forms of Arthur's trace formula. One refinement---the stable trace formula---has recently developed to the point where explicit computations with it are feasible. I will present one result on statistics that this new technique can prove. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 23 ==<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%" | '''Jayce Getz'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On triple product $L$-functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Establishing the conjectured analytic properties of triple product $L$-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on $\mathrm{GL}_3$; in some sense this is the smallest case that appears out of reach via standard techniques. The approach involves a relative trace formula and Poisson summation on spherical varieties in the sense of Braverman-Kazhdan, Ngo, and Sakellaridis. <br />
<br />
https://zoom.us/j/96864496800 <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 30 ==<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%" | '''Noah Taylor'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Sato Tate Conjecture on Abelian Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sato-Tate conjecture says that the normalized point counts of genus $g$ curves are equidistributed with respect to a certain measure. We will construct the Sato-Tate group, state the conjecture precisely, prove a case, and in the cases where not everything is known, we will discuss how much we can say about the point counts anyway.<br />
<br />
https://us02web.zoom.us/j/81526488221<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== May 7 ==<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 Landesman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The geometric distribution of Selmer groups of Elliptic curves over function fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Bhargava, Kane, Lenstra, Poonen, and Rains proposed heuristics for the distribution of arithmetic data relating to elliptic curves, such as their ranks, Selmer groups, and Tate-Shafarevich groups. As a special case of their heuristics, they obtain the minimalist conjecture, which predicts that 50% of elliptic curves have rank 0 and 50% of elliptic curves have rank 1. After surveying these conjectures, we will explain joint work with Tony Feng and Eric Rains, verifying many of these conjectures over function fields of the form <math>\mathbb F_q(t)</math>, after taking a certain large <math>q</math> limit.<br />
<br />
Zoom link: https://us02web.zoom.us/j/84813855575<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19387NTS ABSTRACTSpring20202020-05-03T21:28:59Z<p>Soumyasankar: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the étale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the étale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree <math>p</math> and <math>K</math> is the cyclotomic field containing a <math>p</math>th root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod <math>p</math>. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod <math>p</math>. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 9 ==<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%" | '''Rahul Dalal'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Statistics of Automorphic Representations through the Stable Trace Formula<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Since individual automorphic representations are very difficult to access, it is helpful to study families of them instead. In particular, statistics over families can be computed through various forms of Arthur's trace formula. One refinement---the stable trace formula---has recently developed to the point where explicit computations with it are feasible. I will present one result on statistics that this new technique can prove. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 23 ==<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%" | '''Jayce Getz'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On triple product $L$-functions<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Establishing the conjectured analytic properties of triple product $L$-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on $\mathrm{GL}_3$; in some sense this is the smallest case that appears out of reach via standard techniques. The approach involves a relative trace formula and Poisson summation on spherical varieties in the sense of Braverman-Kazhdan, Ngo, and Sakellaridis. <br />
<br />
https://zoom.us/j/96864496800 <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 30 ==<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%" | '''Noah Taylor'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Sato Tate Conjecture on Abelian Surfaces<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sato-Tate conjecture says that the normalized point counts of genus $g$ curves are equidistributed with respect to a certain measure. We will construct the Sato-Tate group, state the conjecture precisely, prove a case, and in the cases where not everything is known, we will discuss how much we can say about the point counts anyway.<br />
<br />
https://us02web.zoom.us/j/81526488221<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== April 30 ==<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 Landesman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The geometric distribution of Selmer groups of Elliptic curves over function fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Bhargava, Kane, Lenstra, Poonen, and Rains proposed heuristics for the distribution of arithmetic data relating to elliptic curves, such as their ranks, Selmer groups, and Tate-Shafarevich groups. As a special case of their heuristics, they obtain the minimalist conjecture, which predicts that 50% of elliptic curves have rank 0 and 50% of elliptic curves have rank 1. After surveying these conjectures, we will explain joint work with Tony Feng and Eric Rains, verifying many of these conjectures over function fields of the form <math>\mathbb F_q(t)</math>, after taking a certain large <math>q</math> limit.<br />
<br />
Zoom link: https://us02web.zoom.us/j/84813855575<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19386NTS2020-05-03T21:26:05Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_2 Galois action on the etale fundamental group of the Fermat curve]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_9 Statistics of Automorphic Representations through the Stable Trace Formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| CANCELLED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_23 On triple product L-functions]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_30 The Sato Tate Conjecture on Abelian Surfaces]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | Aaron Landesman <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#May_7 The geometric distribution of Selmer groups of Elliptic curves over function fields]<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19357NTS2020-04-15T18:38:46Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_2 Galois action on the etale fundamental group of the Fermat curve]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_9 Statistics of Automorphic Representations through the Stable Trace Formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| CANCELLED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | Aaron Landesman <br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19354NTS2020-04-13T19:38:59Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_2 Galois action on the etale fundamental group of the Fermat curve]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_9 Statistics of Automorphic Representations through the Stable Trace Formula]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| CANCELLED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | Aaron Landesman <br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19330NTS2020-04-05T15:58:36Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_2 Galois action on the etale fundamental group of the Fermat curve]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| CANCELLED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | Aaron Landesman <br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19320NTS ABSTRACTSpring20202020-03-31T20:49:59Z<p>Soumyasankar: /* April 2 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the étale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the étale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree <math>p</math> and <math>K</math> is the cyclotomic field containing a <math>p</math>th root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod <math>p</math>. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod <math>p</math>. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19319NTS ABSTRACTSpring20202020-03-31T20:43:57Z<p>Soumyasankar: /* April 2 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the \'etale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the \'etale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree <math>p</math> and <math>K</math> is the cyclotomic field containing a <math>p</math>th root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod <math>p</math>. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod <math>p</math>. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19318NTS ABSTRACTSpring20202020-03-31T20:43:10Z<p>Soumyasankar: /* April 2 */</p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the \'etale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X</math> is a curve over a number field <math>K</math>, then we are motivated to understand the action of the absolute Galois group <math>G_K</math> on the \'etale fundamental group <math>\pi_1(X)</math>. When <math>X</math> is the Fermat curve of degree p and <math>K</math> is the cyclotomic field containing a pth root of unity, Anderson proved theorems about this action on the homology of <math>X</math>, with coefficients mod p. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K</math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod p. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19317NTS ABSTRACTSpring20202020-03-31T20:40:11Z<p>Soumyasankar: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== April 2 ==<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%" | '''Rachel Pries'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Galois action on the \'etale fundamental group of the Fermat curve<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
If <math>X<\math> is a curve over a number field K, then we are motivated to understand the action of the absolute Galois group <math>G_K<\math> on the \'etale fundamental group <math>\pi_1(X)</math>. When <math>X<\math> is the Fermat curve of degree p and K is the cyclotomic field containing a pth root of unity, Anderson proved theorems about this action on the homology of <math>X<\math>, with coefficients mod p. In earlier work, we extended Anderson's results to give explicit formulas for this action on the homology. Recently, we use a cup product in cohomology to determine the action of <math>G_K<\math> on the lower central series of <math>\pi_1(X)</math>, with coefficients mod p. The proof involves some fun Galois theory and combinatorics. This is joint work with Davis and Wickelgren. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19316NTS2020-03-31T20:31:00Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#April_2 Galois action on the etale fundamental group of the Fermat curve]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19314NTS2020-03-27T17:40:48Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Rachel Pries (Note different time: 2 pm)<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19309NTS2020-03-26T16:57:47Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| ONLINE<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_ABSTRACTSpring2020&diff=19279NTS ABSTRACTSpring20202020-03-18T19:55:48Z<p>Soumyasankar: </p>
<hr />
<div>Return to [https://www.math.wisc.edu/wiki/index.php/NTS ]<br />
<br />
<br />
== Jan 23 ==<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%" | '''Rahul Krishna'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The global Gross-Prasad conjecture (really its refinement by Ichino and Ikeda) is a remarkable conjectural formula generalizing Waldspurger's formula for the central value of a Rankin-Selberg $L$ function. I will explain a relative trace formula approach to this conjecture, akin in spirit to the successful comparison for unitary groups. The approach relies on a somewhat strange matching of orbits, and on two local conjectures of smooth transfer and fundamental lemma type, which I will formulate. If time permits, I will discuss some recent evidence for these local identities in some low rank cases.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Jan 30 ==<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%" | '''Eric Stubley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Class Groups, Congruences, and Cup Products<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The structure of class groups of number fields can be computed in some cases with explicit congruence conditions, for example as in Kummer's criterion which relates the $p$-part of the class group of the $p$-th cyclotomic field to congruences of Bernoulli numbers mod $p$. For $p$ and $N$ prime with $N = 1$ mod $p$, a similar result of Calegari and Emerton relates the rank of the $p$-part of the class group of $\mathbb{Q}(N^{1/p})$ to whether or not a certain quantity (Merel's number) is a $p$-th power mod $N$. We study this rank by building off of an idea of Wake and Wang-Erickson, namely to relate elements of the class group to the vanishing of certain cup products in Galois cohomology. Using this idea, we prove new bounds on the rank in terms of similar $p$-th power conditions, and we give exact characterizations of the rank for small $p$. This talk will aim to explain the interplay between ranks of class groups, explicit congruences, and cup products in Galois cohomology. This is joint work with Karl Schaefer.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 6 ==<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%" | '''Brian Smithling'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | On Shimura varieties for unitary groups<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Shimura varieties attached to unitary similitude groups are a well-studied class of Shimura varieties of PEL type (i.e., admitting moduli interpretations in terms of abelian varieties with additional structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 20 ==<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%" | '''Shai Evra'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Ramanujan Conjectures and Density Theorems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Generalized Ramanujan Conjecture (GRC) for the group $GL(n)$ is a central open problem in modern number theory. The (GRC) is known to imply the solution of many Diophantine problems associated to arithmetic congruence subgroups of $GL(n)$. One can also state analogous (Naive) Ramanujan Conjectures (NRC) for other reductive groups $G$, whose validity would imply various applications for the congruence subgroups of $G$. However, already in the 70s Howe and Piatetski-Shapiro proved that the (NRC) fails even for the class of classical split and quasi-split groups. In the 90s Sarnak and Xue put forth the conjecture that a Density Hypothesis (DH) version of the (NRC) should hold, and that these Density Hypotheses can serve as a replacement of the (NRC) in many applications. In this talk I will describe the (GRC), (NRC) and (DH), and explain how to prove the (DH) for certain classical groups, by invoking deep and recent results coming from the Langlands program. <br />
<br />
<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 27 ==<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%" | '''Mathilde Gerbelli-Gauthier'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Cohomology of Arithmetic Groups and Endoscopy<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How fast do Betti numbers grow in a congruence tower of compact arithmetic manifolds? The dimension of the middle degree of cohomology is proportional to the volume of the manifold, but away from the middle the growth is known to be sub-linear in the volume. I will explain how automorphic representations and the phenomenon of endoscopy provide a framework to understand and quantify this slow growth. Specifically, I will discuss how to obtain explicit bounds in the case of unitary groups using the character identities appearing in Arthur’s stable trace formula. This is joint work in progress with Simon Marshall.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== March 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%" | '''Jessica Fintzen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | From representations of p-adic groups to congruences of automorphic forms<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The theory of automorphic forms and the global Langlands program have been very active research areas for the past 30 years. Significant progress has been achieved by developing intricate geometric methods, but most results to date are restricted to general linear groups (and general unitary groups).<br />
In this talk I will present new results about the representation theory of p-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at p. This simplifies earlier constructions of attaching Galois representations to automorphic representations, i.e. the global Langlands correspondence, for general linear groups. Moreover, our results apply to general p-adic groups and have therefore the potential to become widely applicable beyond the case of the general linear group.<br />
This is joint work with Sug Woo Shin. <br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 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%" | '''Andrea Dotto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Functoriality of Serre weights<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
By work of Gee--Geraghty and myself, one can transfer Serre weights from the maximal compact subgroup of an inner form $D^*$ of $GL(n)$ to a maximal compact subgroup of $GL(n)$. Because of the congruence properties of the Jacquet--Langlands correspondence this transfer is compatible with the Breuil--Mezard formalism, which allows one to extend the Serre weight conjectures to $D^*$ (at least for a tame and generic residual representation). This talk aims to explain all of the above and to discuss a possible generalization to inner forms of unramified groups.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== March 26 ==<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%" | '''Daniel Litt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The section conjecture at the boundary of moduli space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Grothendieck's section conjecture predicts that over<br />
arithmetically interesting fields (e.g. number fields or <math>p</math>-adic fields),<br />
rational points on a smooth projective curve X of genus at least 2 can be<br />
detected via the arithmetic of the etale fundamental group of X. We<br />
construct infinitely many curves of each genus satisfying the section<br />
conjecture in interesting ways, building on work of Stix, Harari, and<br />
Szamuely. The main input to our result is an analysis of the degeneration<br />
of certain torsion cohomology classes on the moduli space of curves at<br />
various boundary components. This is (preliminary) joint work with<br />
Padmavathi Srinivasan, Wanlin Li, and Nick Salter.<br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19278NTS2020-03-18T19:54:32Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_26 The section conjecture at the boundary of moduli space]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Caroline Turnage-Butterbaugh<br />
| bgcolor="#BCE2FE"| CANCELED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| CANCELED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=19274NTS2020-03-17T21:55:44Z<p>Soumyasankar: /* Spring 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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_23 A relative trace formula comparison for the global Gross-Prasad conjecture for orthogonal groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Jan_30 Class Groups, Congruences, and Cup Products]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|[https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_6 On Shimura varieties for unitary groups]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_20 Ramanujan Conjectures and Density Theorems]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | Mathilde Gerbelli-Gauthier<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#Feb_27 Cohomology of Arithmetic Groups and Endoscopy]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_6 From representations of p-adic groups to congruences of automorphic forms]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto (CANCELED)<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTS_ABSTRACTSpring2020#March_12 Functoriality of Serre weights]<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt (ONLINE)<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Caroline Turnage-Butterbaugh<br />
| bgcolor="#BCE2FE"| CANCELED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| CANCELED<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Noah Taylor <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<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]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=18990NTSGrad Spring 2020/Abstracts2020-02-10T20:28:49Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<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%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <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%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><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%" | '''Will Hardt and John Yin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.<br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18989NTSGrad Spring 20202020-02-10T20:27:35Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://will-hardt.com/ Will Hardt] and John Yin<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_11|Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=18958NTSGrad Spring 2020/Abstracts2020-02-08T22:35:10Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<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%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <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%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''ABC's of Shimura Varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term ''Shimura variety''. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18957NTSGrad Spring 20202020-02-08T22:33:37Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Feb_4| ABC’s of Shimura Varieties]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.linkedin.com/in/will-hardt-330167149 Will Hardt]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18956Colloquia/Spring20202020-02-08T22:30:44Z<p>Soumyasankar: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm in 911'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|[https://web.math.princeton.edu/~jkileel/ Joe Kileel] (Princeton)<br />
|[[#Joe Kileel (Princeton) |Inverse Problems, Imaging and Tensor Decomposition]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|[https://clvinzan.math.ncsu.edu/ Cynthia Vinzant] (NCSU)<br />
|[[#Cynthia Vinzant (NCSU) |Matroids, log-concavity, and expanders]]<br />
|Roch/Erman<br />
|-<br />
|Feb 12 '''Wednesday 4-5 pm in VV 911'''<br />
|[https://www.machuang.org/ Jinzi Mac Huang] (UCSD)<br />
|[[#Jinzi Mac Huang (UCSD) |Mass transfer through fluid-structure interactions]]<br />
|Spagnolie<br />
|-<br />
|Feb 14<br />
|[https://math.unt.edu/people/william-chan/ William Chan] (University of North Texas)<br />
|[[#William Chan (University of North Texas) |Definable infinitary combinatorics under determinacy]]<br />
|Soskova/Lempp<br />
|-<br />
|Feb 17<br />
|[https://yisun.io/ Yi Sun] (Columbia)<br />
|[[#Yi Sun (Columbia) |TBA]]<br />
|Roch<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|[https://max.lieblich.us/ Max Lieblich] (Univ. of Washington, Seattle)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|<br />
|<br />
|<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
=== Joe Kileel (Princeton) ===<br />
<br />
Title: Inverse Problems, Imaging and Tensor Decomposition<br />
<br />
Abstract: Perspectives from computational algebra and optimization are brought <br />
to bear on a scientific application and a data science application. <br />
In the first part of the talk, I will discuss cryo-electron microscopy <br />
(cryo-EM), an imaging technique to determine the 3-D shape of <br />
macromolecules from many noisy 2-D projections, recognized by the 2017 <br />
Chemistry Nobel Prize. Mathematically, cryo-EM presents a <br />
particularly rich inverse problem, with unknown orientations, extreme <br />
noise, big data and conformational heterogeneity. In particular, this <br />
motivates a general framework for statistical estimation under compact <br />
group actions, connecting information theory and group invariant <br />
theory. In the second part of the talk, I will discuss tensor rank <br />
decomposition, a higher-order variant of PCA broadly applicable in <br />
data science. A fast algorithm is introduced and analyzed, combining <br />
ideas of Sylvester and the power method.<br />
<br />
=== Cynthia Vinzant (NCSU) ===<br />
<br />
Title: Matroids, log-concavity, and expanders<br />
<br />
Abstract: Matroids are combinatorial objects that model various types of independence. They appear several fields mathematics, including graph theory, combinatorial optimization, and algebraic geometry. In this talk, I will introduce the theory of matroids along with the closely related class of polynomials called strongly log-concave polynomials. Strong log-concavity is a functional property of a real multivariate polynomial that translates to useful conditions on its coefficients. Discrete probability distributions defined by these coefficients inherit several of these nice properties. I will discuss the beautiful real and combinatorial geometry underlying these polynomials and describe applications to random walks on the faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets of a matroid is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.<br />
<br />
=== Jinz Mac Huang (UCSD) ===<br />
<br />
Title: Mass transfer through fluid-structure interactions<br />
<br />
Abstract: The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and how many licks it takes to get to the center of a Tootsie Pop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusiophoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.<br />
<br />
=== William Chan (University of North Texas) ===<br />
<br />
Title: Definable infinitary combinatorics under determinacy<br />
<br />
Abstract: The axiom of determinacy, AD, states that in any infinite two player integer game of a certain form, one of the two players must have a winning strategy. It is incompatible with the ZFC set theory axioms with choice; however, it is a succinct extension of ZF which implies many subsets of the real line possess familiar regularity properties and eliminates many pathological sets. For instance, AD implies all sets of reals are Lebesgue measurable and every function from the reals to the reals is continuous on a comeager set. Determinacy also implies that the first uncountable cardinal has the strong partition property which can be used to define the partition measures. This talk will give an overview of the axiom of determinacy and will discuss recent results on the infinitary combinatorics surrounding the first uncountable cardinal and its partition measures. I will discuss the almost everywhere continuity phenomenon for functions outputting countable ordinals and the almost-everywhere uniformization results for closed and unbounded subsets of the first uncountable cardinal. These will be used to describe the rich structure of the cardinals below the powerset of the first and second uncountable cardinals under determinacy assumptions and to investigate the ultrapowers by these partition measures.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18801NTSGrad Spring 20202020-01-27T15:11:53Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.linkedin.com/in/will-hardt-330167149 Will Hardt]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=18800NTSGrad Spring 2020/Abstracts2020-01-27T15:02:39Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<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%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms and class groups''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem. <br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18799NTSGrad Spring 20202020-01-27T14:59:55Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18798NTSGrad Spring 20202020-01-27T14:58:00Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Brandon Boggess<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18797NTSGrad Spring 20202020-01-27T14:57:43Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://sites.google.com/site/soumya3sankar/ | Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Brandon Boggess<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18796NTSGrad Spring 20202020-01-27T14:56:32Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Spring 2020/Abstracts#Jan_28|Modular forms and class groups]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Johnnie Han<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ivan Aidun<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Soumya Sankar<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|No Talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Brandon Boggess<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yi Wei<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|May 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Eiki Norizuki<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18727NTSGrad Spring 20202020-01-21T19:20:00Z<p>Soumyasankar: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
This semester, we will be watching lectures of the [https://sites.google.com/view/vantageseminar| VaNTAGe Seminar], every other Tuesday (starting January 21st). VaNTAGe is an online seminar on open conjectures in Number Theory. The schedule can be found on the website. The watch-party will be held in 901 VV at Noon. <br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS&diff=18726NTS2020-01-21T19:07:01Z<p>Soumyasankar: </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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our 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 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" | Jan 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | '''Friday Jan 31, 3-4 pm'''<br />
| bgcolor="#F0B0B0" align="center" | Lillian Pierce <br /> (joint analysis / NT seminar)<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Caroline Turnage-Butterbaugh<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed<br />
<br />
= Organizer contact information =<br />
<br />
[http://www.math.wisc.edu/~shusterman/ Mark Shusterman]<br />
----<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020/Abstracts&diff=18725NTSGrad Spring 2020/Abstracts2020-01-21T19:06:16Z<p>Soumyasankar: Created page with "This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click here. == Jan 21 =..."</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click [[NTSGrad_Spring_2020|here.]]<br />
<br />
== Jan 21 ==<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation theory and arithmetic geometry''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.<br />
|} <br />
</center><br />
<br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18724NTSGrad Spring 20202020-01-21T19:02:31Z<p>Soumyasankar: /* Spring 2020 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Spring 2020/Abstracts#Jan_21|Representation theory and arithmetic geometry]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18669NTSGrad Spring 20202020-01-18T16:33:52Z<p>Soumyasankar: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| TBA<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18668NTSGrad Fall 20192020-01-18T16:33:17Z<p>Soumyasankar: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Fall 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_19| Cohomology Juggle]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Dec_3| A brief introduction to the Bloch-Kato conjecture and motivic cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2020 is [[NTSGrad_Spring_2020|here]].<br><br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Spring_2020&diff=18592NTSGrad Spring 20202020-01-02T04:19:25Z<p>Soumyasankar: Created page with "= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison = *'''When:''' Tuesdays, 2:30 PM – 3:30 PM *'''Where:''' B321 Van Vlec..."</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
= Spring 2020 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Jan 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Jan 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 4th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 11th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 18th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Feb 25th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"|Arizona Winter School Week<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"|Spring Break<br />
| bgcolor="#BCD2EE" width="300" align="center"|No talk<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Mar 31st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 7th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 14th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 21st<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|Apr 28th<br />
| bgcolor="#F0A0A0" width="300" align="center"|<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18591NTSGrad Fall 20192020-01-02T04:10:34Z<p>Soumyasankar: </p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Fall 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_19| Cohomology Juggle]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Dec_3| A brief introduction to the Bloch-Kato conjecture and motivic cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTS_Spring_Semester_2020&diff=18590NTS Spring Semester 20202020-01-02T04:08:04Z<p>Soumyasankar: </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<br />
*Please join the [https://mailhost.math.wisc.edu/mailman/listinfo/nts NT/RT mailing list:] (you must be on a math department computer to use this link).<br />
<br />
There is also an accompanying [https://www.math.wisc.edu/wiki/index.php/NTSGrad_Spring_2020 graduate-level seminar], which meets on Tuesdays.<br><br />
<br />
You can find our last semester speakers in [https://www.math.wisc.edu/wiki/index.php/NTS Fall 2019].<br />
<br><br />
You can find our previous speakers in [https://www.math.wisc.edu/wiki/index.php/NTS_Spring_2018_Semester Spring 2018].<br />
<br />
<br />
= Schedule =<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 23<br />
| bgcolor="#F0B0B0" align="center" | Rahul Krishna<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Jan 30<br />
| bgcolor="#F0B0B0" align="center" | Eric Stubley<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 6<br />
| bgcolor="#F0B0B0" align="center" | Brian Smithling<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 20<br />
| bgcolor="#F0B0B0" align="center" | Shai Evra<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | Jessica Fintzen<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | Andrea Dotto<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | Spring Break<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | Daniel Litt<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Caroline Turnage-Butterbaugh<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Rahul Dalal<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 16 <br />
| bgcolor="#F0B0B0" align="center" | Aaron Pollack<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Jayce Getz<br />
| bgcolor="#BCE2FE"|<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"|<br />
|- <br />
|}<br />
</center><br />
<br />
<br><br />
<br />
*to be confirmed</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18514NTSGrad Fall 2019/Abstracts2019-12-02T15:43:38Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<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%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><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%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><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%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><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%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><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%" | '''Hyun Jong'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Tate's Thesis and Rankin-Selberg theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Yang's talk at the number theory seminar is related to Tate's thesis and Rankin-Selberg theory, so I'm going to introduce both. Tate's thesis generalizes the functional equation of the Riemann zeta function to a function defined using the adeles. Furthermore, the Rankin-Selberg method uncovers a functional equation for an L-function. I will focus on the classical Rankin-Selberg method, but I may also be able to talk about adelic Rankin-Selberg, which seems to be good to know for Yang's talk.<br />
|} <br />
</center><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%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Cohomology Juggle''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
A brief review of Chern class, Etale cohomology and spectral sequences with classical examples and also a slight touch on Steenrod operations which will be a key tool for Tony's talk.<br />
|} <br />
</center><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%" | '''Ruofan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''A brief introduction to Bloch-Kato conjecture and motivic cohomology.''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will start by introducing the Bloch-Kato conjecture (now known as the norm residue theorem) and motivic cohomology, and briefly show how the conjecture can be reduced to certain comparison result of etale and Zariski motivic cohomology groups. We will focus mainly on basic properties of the motivic cohomology. Time permitting, I will also discuss the idea underlying the proof of the conjecture.<br />
|} <br />
</center><br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18513NTSGrad Fall 20192019-12-02T15:42:10Z<p>Soumyasankar: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_19| Cohomology Juggle]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Dec_3| A brief introduction to the Bloch-Kato conjecture and motivic cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18447NTSGrad Fall 2019/Abstracts2019-11-18T16:59:16Z<p>Soumyasankar: /* Nov 19 */</p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<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%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><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%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><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%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><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%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><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%" | '''Hyun Jong'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Tate's Thesis and Rankin-Selberg theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Yang's talk at the number theory seminar is related to Tate's thesis and Rankin-Selberg theory, so I'm going to introduce both. Tate's thesis generalizes the functional equation of the Riemann zeta function to a function defined using the adeles. Furthermore, the Rankin-Selberg method uncovers a functional equation for an L-function. I will focus on the classical Rankin-Selberg method, but I may also be able to talk about adelic Rankin-Selberg, which seems to be good to know for Yang's talk.<br />
|} <br />
</center><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%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Cohomology Juggle''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
A brief review of Chern class, Etale cohomology and spectral sequences with classical examples and also a slight touch on Steenrod operations which will be a key tool for Tony's talk.<br />
|} <br />
</center><br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18445NTSGrad Fall 2019/Abstracts2019-11-18T16:58:39Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<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%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><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%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><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%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><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%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><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%" | '''Hyun Jong'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Tate's Thesis and Rankin-Selberg theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Yang's talk at the number theory seminar is related to Tate's thesis and Rankin-Selberg theory, so I'm going to introduce both. Tate's thesis generalizes the functional equation of the Riemann zeta function to a function defined using the adeles. Furthermore, the Rankin-Selberg method uncovers a functional equation for an L-function. I will focus on the classical Rankin-Selberg method, but I may also be able to talk about adelic Rankin-Selberg, which seems to be good to know for Yang's talk.<br />
|} <br />
</center><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%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Cohomology Juggle''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
A brief review of Chern class, <math>\'{E}</math>tale cohomology and spectral sequences with classical examples and also a slight touch on Steenrod operations which would be a key tool for Tony's talk.<br />
|} <br />
</center><br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18444NTSGrad Fall 20192019-11-18T16:56:26Z<p>Soumyasankar: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_12| Tate's Thesis and Rankin-Selberg theory]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_19| Cohomology Juggle]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18361Algebra and Algebraic Geometry Seminar Fall 20192019-11-08T04:52:38Z<p>Soumyasankar: /* Abstracts */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] 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 />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Libby Taylor<br />
|<math>\mathbb{A}^1</math>-local degree via stacks<br />
|Daniel/Soumya<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|Cynthia Vinzant<br />
|TBD<br />
| Matroids Day<br />
|-<br />
|December 13<br />
|Taylor Brysiewicz<br />
|<br />
| Jose<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
===Libby Taylor===<br />
'''<math>\mathbb{A}^1</math>-local degree via stacks'''<br />
<br />
We extend results of Kass-Wickelgren to to define an Euler class for a non-orientable vector bundle on a smooth scheme, valued in the Grothendieck-Witt group of the ground field. We use a root stack construction to produce this Euler class and discuss its relation to <math>\mathbb{A}^1</math>-homotopy-theoretic definitions of an Euler class. This allows one to apply Kass-Wickelgren's technique for arithmetic enrichments of enumerative geometry to a larger class of problems; as an example, we use our construction to give an arithmetic count of the number of lines meeting $6$ planes in <math>\mathbb{P}^4</math>.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18360Algebra and Algebraic Geometry Seminar Fall 20192019-11-08T04:49:39Z<p>Soumyasankar: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] 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 />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Libby Taylor<br />
|<math>\mathbb{A}^1</math>-local degree via stacks<br />
|Daniel/Soumya<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|Cynthia Vinzant<br />
|TBD<br />
| Matroids Day<br />
|-<br />
|December 13<br />
|Taylor Brysiewicz<br />
|<br />
| Jose<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=Algebra_and_Algebraic_Geometry_Seminar_Fall_2019&diff=18359Algebra and Algebraic Geometry Seminar Fall 20192019-11-08T04:47:24Z<p>Soumyasankar: /* Fall 2019 Schedule */</p>
<hr />
<div>The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.<br />
<br />
Here is the schedule for [[Algebra and Algebraic Geometry Seminar Spring 2019 | the previous semester]], for [[Algebra and Algebraic Geometry Seminar Spring 2020 | the next semester]], and for [[Algebra and Algebraic Geometry Seminar | this semester]].<br />
<br />
==Algebra and Algebraic Geometry Mailing List==<br />
*Please join the [https://admin.lists.wisc.edu/index.php?p=11&l=ags AGS Mailing List] 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 />
<br />
== Fall 2019 Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s) <br />
|-<br />
|September 6<br />
|Yuki Matsubara<br />
|[[#Yuki Matsubara|On the cohomology of the moduli space of parabolic connections]]<br />
|Dima<br />
|-<br />
|September 13<br />
|Juliette Bruce<br />
|Semi-Ample Asymptotic Syzygies<br />
|Local<br />
|-<br />
|September 20<br />
|Michael Kemeny<br />
|The geometric syzygy conjecture<br />
|Local<br />
|-<br />
|September 27<br />
|<br />
|<br />
|<br />
|-<br />
|October 4<br />
|<br />
|<br />
|<br />
|-<br />
|October 11<br />
|<br />
|<br />
|<br />
|-<br />
|October 18<br />
|Kevin Tucker (UIC)<br />
|TBD<br />
|Daniel<br />
|-<br />
|October 25<br />
|Reserved<br />
|<br />
|Dima<br />
|-<br />
|November 1<br />
|Michael Brown<br />
|Standard Conjecture D for Matrix Factorizations<br />
|Local<br />
|-<br />
|November 8<br />
|Patricia Klein<br />
|Geometric vertex decomposition and liaison<br />
|Daniel<br />
|-<br />
|November 15<br />
|Libby Taylor<br />
|<math>\mathbb{A}^1<\math>-local degree via stacks<br />
|Daniel/Soumya<br />
|-<br />
|November 22<br />
|Daniel Corey<br />
|Topology of moduli spaces of tropical curves with low genus<br />
|Local<br />
|-<br />
|November 29<br />
| No Seminar<br />
| Thanksgiving Break<br />
|<br />
|-<br />
|December 6<br />
|Cynthia Vinzant<br />
|TBD<br />
| Matroids Day<br />
|-<br />
|December 13<br />
|Taylor Brysiewicz<br />
|<br />
| Jose<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yuki Matsubara===<br />
'''On the cohomology of the moduli space of parabolic connections'''<br />
<br />
We consider the moduli space of logarithmic connections of rank 2<br />
on the projective line minus 5 points with fixed spectral data.<br />
We compute the cohomology of such moduli space, <br />
and this computation will be used to extend the results of <br />
Geometric Langlands correspondence due to D. Arinkin <br />
to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.<br />
<br />
In this talk, I will review the Geometric Langlands Correspondence <br />
in the tamely ramified cases, and after that, <br />
I will explain how the cohomology of above moduli space will be used.<br />
<br />
===Juliette Bruce===<br />
'''Semi-Ample Asymptotic Syzygies'''<br />
<br />
I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.<br />
<br />
<br />
===Michael Kemeny===<br />
'''The geometric syzygy conjecture'''<br />
<br />
A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called <br />
Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture <br />
for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of <br />
syzygies of K3 surfaces.<br />
<br />
===Michael Brown===<br />
'''Standard Conjecture D for Matrix Factorizations'''<br />
<br />
In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.<br />
<br />
<br />
===Patricia Klein===<br />
'''Geometric vertex decomposition and liaison'''<br />
<br />
Geometric vertex decomposition and liaison are two frameworks that can be used to study algebraic varieties. These approaches have been used historically by two distinct communities of mathematicians. In this talk, we will describe a connection between the two. In particular, we will see how each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, how every G-biliaison of a certain type gives rise to geometric vertex decomposition. As a consequence, we establish that several families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes, and defining ideals of lower bound cluster algebras. This talk is based on joint work with Jenna Rajchgot.<br />
<br />
== Notes ==<br />
Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18295NTSGrad Fall 2019/Abstracts2019-11-03T18:55:48Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<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%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><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%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><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%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><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%" | '''Di Chen'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Artin-Hecke <math>L</math>-functions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to Artin-Hecke <math>L</math>-functions, their basic algebraic and analytic properties, and “equivalence” via class field theory. If time permits, I will briefly introduce what the Rankin-Selberg <math>L</math>-function is and what it’s meant for.<br />
|} <br />
</center><br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18294NTSGrad Fall 20192019-11-03T18:49:41Z<p>Soumyasankar: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Nov_5| Artin-Hecke <math>L</math>-functions]] <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019/Abstracts&diff=18264NTSGrad Fall 2019/Abstracts2019-10-28T02:34:36Z<p>Soumyasankar: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Fall 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Fall_2019|here.]]<br />
<br />
== Sept 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Law and Orders in Quadratic Imaginary Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
To prepare for Thursday's talk, I will give a gentle introduction to the basic theory of complex multiplication for elliptic curves, beginning with a quick review of elliptic curves over the complex numbers.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Siegel-Weil Formula''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Theta functions, Eisenstein series, and Adeles, Oh my!<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sept 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%" | '''Dionel Jamie'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On The Discrete Fuglede Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It's well known that the set of functions from a finite abelian group to the complex numbers forms an inner product space and that any such function can be written as a unique linear combination of characters which are orthogonal with respect to this inner product. We will look specifically at copies of the integers modulo a fixed prime and I will talk about under what conditions can we take a subset of this group, E, and express a function from E to the complex numbers as a linear combination of characters which are orthogonal with respect to the inner product induced on E. <br />
|} <br />
</center><br />
<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%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modularity Theorem''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will describe the modularity theorem of elliptic curve. I will state the main theorem first, and then give some consequences of the theorem. If time permitted, I will try to sketch how to construct Galois representation from modular form and describe Langlands-Tunnell theorem, which will be related with Thursday's talk. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 7 ==<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%" | '''Yu Fu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Abhyankar's Conjectures''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
I'll talk about the Etale fundamental group and the equivalence between finite Galois covers and topological monodromy. Then I'll get into the topic of Abhyankar's Conjectures, which deal with Galois covers of curves in positive characteristics.<br />
<br />
|} <br />
</center><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%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Some examples of cohomology in action''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
Cohomology plays an important role throughout number theory however it can seem overly abstract and difficult at first, especially if one is not particularly familiar with topology where most people first develop some intuition for it. In this talk I will describe a number of scenarios(some fun, some serious) where we can concretely observe cohomology telling us something which lie outside these normal first examples. No prior knowledge of cohomology will be assumed.<br />
<br />
|} <br />
</center><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%" | '''Will Hardt'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Spectral Sequences and Completed Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In preparation for Thursday's talk, I will begin by introducing spectral sequences, a tool that gives increasingly accurate approximations converging to the homology groups of a filtered chain complex. Next, I will briefly introduce the theory of completed cohomology developed by Calegari and Emerton. I will state a main theorem, which utilizes spectral sequences, then finish with a simple example.<br />
|} <br />
</center><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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Chabauty, Coleman and Kim''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This talk is an introduction to the method of Chabauty and Coleman, which is often used to bound the number of rational points on curves of high genus. We will discuss some examples of this method, as well as some limitations. Time permitting, I will talk about non-abelian Chabauty and describe the motivation behind the work of Kim. <br />
<br />
|} <br />
</center><br />
<br></div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18263NTSGrad Fall 20192019-10-28T02:25:37Z<p>Soumyasankar: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_29| Chabauty, Coleman and Kim]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankarhttps://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2019&diff=18256NTSGrad Fall 20192019-10-27T17:43:22Z<p>Soumyasankar: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B321 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
<br />
As a part of the Graduate Number Theory Seminar this semester, we will be conducting a mini SAGE workshop ([https://sites.google.com/wisc.edu/saw SAW]) on the 16th of November, 2019. If you would like to participate in these, please email the organizers: Brandon Boggess, Solly Parenti, Soumya Sankar, Connor Simpson.<br />
<br />
= Spring 2019 Semester: Schedule =<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="#D0D0D0" width="300" align="center"|Sept 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"|[https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Sept_10|Law and Orders in Quadratic Imaginary Fields]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 17th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_17|The Siegel-Weil Formula]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Sept 24th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Dionel Jamie<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Sept_24|On The Discrete Fuglede Conjecture]]<br />
|-<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 1st<br />
| bgcolor="#F0A0A0" width="300" align="center"| Qiao He<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_1|Modularity Theorem]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 8th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Yu Fu<br />
| bgcolor="#BCD2EE" width="300" align="center"|[[NTSGrad_Fall_2019/Abstracts#Oct_7|Abhyankar's Conjectures]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 15th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ewan Dalby<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_15|Some examples of cohomology in action]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 22nd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Will Hardt<br />
| bgcolor="#BCD2EE" width="300" align="center"| [[NTSGrad_Fall_2019/Abstracts#Oct_22| Spectral Sequences and Completed Cohomology]]<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Oct 29th<br />
| bgcolor="#F0A0A0" width="300" align="center"| [https://www.math.wisc.edu/~soumyasankar/ Soumya Sankar]<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 5th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Di Chen<br />
| bgcolor="#BCD2EE" width="300" align="center"| <br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 12th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Hyun Jong Kim<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 19th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Niudun Wang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Nov 26th<br />
| bgcolor="#F0A0A0" width="300" align="center"| N/A (NTS Talk)<br />
| bgcolor="#BCD2EE" width="300" align="center"| N/A<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 3rd<br />
| bgcolor="#F0A0A0" width="300" align="center"| Ruofan Jiang<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"| Dec 10th<br />
| bgcolor="#F0A0A0" width="300" align="center"| Asvin Gothandaraman<br />
| bgcolor="#BCD2EE" width="300" align="center"|<br />
|-<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Spring 2019 is [[NTSGrad_Spring_2019|here]].<br><br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Soumyasankar