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Fall 2021 ANT ZoominarFridays @ 10AM California Time Meeting ID: 941 6843 5061, Passcode: 821454 [Direct link]
[Give feedback]For further information please contactProfessor Robert Boltje
Schedule (click dates for title and abstract)
10/1 
NO TALK 
NO TALK 
10/8 
NO TALK 
NO TALK 
10/15, 9am

ChanHo Kim 
Korea Institute for Advanced Studies (KIAS) 
10/22 
Nadia Romero 
University of Guanajuato 
10/29 
Yunqing Tang 
Princeton 
11/5 
Caroline Lassueur 
University of Kaiserslautern 
11/12 
Mandi Schaeffer Fry 
MSU Denver 
11/19 
David Holmes 
University of Leiden 
11/26 
BLACK FRIDAY 

12/3 
Baptiste Rognerud 
University of Paris, Jussieu 
Friday, October 15, at *9* am PST
ChanHo Kim, Korea Institute for Advanced Studies (KIAS)
On the pconverse to a theorem of GrossZagier and Kolyvagin
The celebrated Birch and SwinnertonDyer (BSD) conjecture predicts the equality between the rank of the rational points on elliptic curves and the vanishing order of their Lfunctions at s=1. One of the most striking results on the BSD conjecture is the work of GrossZagier and Kolyvagin: if the vanishing order is ≤1, then the predicted equality holds and the TateShafarevich group is finite. Around 2013, Skinner and W. Zhang independently proved the pconverse of the aforementioned result under certain mild assumptions: If the Selmer corank is one, then the vanishing order is one. After their work, pconverse theorems are extensively studied in various forms. We discuss a simple proof of the pconverse theorem based on recent developments on PerrinRiou's conjecture.
Friday, October 22, at 10 am PST
Nadia Romero, University of Guanajuato
Green Fields
Green fields were discovered by Serge Bouc in 2019. To be precise, the terminology was introduced at the very end of his paper "Relative Bgroups", published in 2019. A Green field is a commutative Green biset functor with no nontrivial ideals. In this talk I will present some properties of a Green field and examples of known Green biset functors which are Green fields. This is a joint work with Serge Bouc.
Friday, October 29, at 10 am PST
Yunqing Tang, Princeton
The unbounded denominators conjecture
The unbounded denominators conjecture, first raised by Atkin and SwinnertonDyer, asserts that a modular form for a finite index subgroup of SL_2(Z) whose Fourier coefficients have bounded denominators must be a modular form for some congruence subgroup. In this talk, we will give a sketch of the proof of this conjecture based on a new arithmetic algebraization theorem. (Joint work with Frank Calegari and Vesselin Dimitrov.)
Friday, November 5, at 10 am PST
Caroline Lassueur, University of Kaiserslautern
Classifying trivial source modules in blocks with cyclic defect groups
In the modular representation theory of finite groups the class of trivial source modules  by definition the direct summands of the permutation modules  is omnipresent and it is essential to understand them better in order to shed new light on main open questions concerned with the structure of blocks up to different kind of categorical equivalences. The aim of this talk is to present a concrete classification of the indecomposable trivial source modules belonging to a block B of a finite group with nontrivial cyclic defect groups. To achieve this goal, we rely on the classification of the indecomposable Bmodules (by Janusz and dating back to the 1960's) and of the indecomposable liftable Bmodules (by Hiß and Naehrig, 2012), both of which are determined up to Morita equivalence, hence by the Brauer tree of the block. Trivial source modules are not invariant under Morita equivalences in general. However, they are invariant under the stronger sourcealgebra equivalences. In this respect, besides the Brauer tree, two further parameters come into play. In particular, we will see how to recover the trivial source modules from the source algebra of the block in this case. This is joint work with Gerhard Hiß.
Friday, November 12, at 10 am PST
Mandi Schaeffer Fry, MSU Denver
The McKayNavarro Conjecture: the Conjecture That Keeps on Giving!
The McKay conjecture is one of the main open conjectures in the realm of the localglobal philosophy in character theory. It posits a bijection between the set of irreducible characters of a group with p’degree and the corresponding set in the normalizer of a Sylow psubgroup. In this talk, I’ll give an overview of a refinement of the McKay conjecture due to Gabriel Navarro, which brings the action of Galois automorphisms into the picture. A lot of recent work has been done on this conjecture, but possibly even more interesting is the amount of information it yields about the character table of a finite group. I’ll discuss some recent results on the McKay—Navarro conjecture, as well as some of the implications the conjecture has had for other interesting charactertheoretic problems.
Friday, November 19, at 10 am PST
David Holmes, University of Leiden
How often is a divisor on a curve principal?
A divisor on an algebraic curve (or Riemann surface) is called principal if it is the divisor of a rational (or meromorphic) function. If one has a family C/S of curves, and a family of divisors D on C, it is natural to study the locus of points s in S such that D becomes principal when restricted to the fibre over S (the `double ramification' locus). We will talk about how to extend the definition of this locus to families of singular curves, and how to compute the class of the resulting locus in the (logarithmic) Chow ring of S. If time allows we will briefly discuss connections to cohomological field theories and to localisation computations in GromovWitten theory.
Friday, December 3, at 10 am PST
Baptiste Rognerud, University of Paris, Jussieu
Coxeter matrices of finite posets and fractionally CalabiYau categories
The Coxeter matrix of a finite poset is defined by an easy formula involving the incidence matrix of the poset and its inverse. If its definition is combinatorial, many of its properties are in fact shadows of representation theoretical properties of the poset. One interesting question is to understand which posets have a Coxeter matrix of finite order. We will see examples of such posets and how this phenomenon is related to the notion of fractionally CalabiYau categories.