
Date Time 
Location  Speaker 
Title – click for abstract 

09/01 3:00pm 
BLOC 506A 
Eric Rowell Texas A&M University 
Organizational meeting 

09/15 3:00pm 
BLOC 117 
Michael Anshelevich Texas A&M University 
Product formulas on posets and Wick products.
We will construct "incomplete" version of several familiar posets, and prove a product formula on posets. Then we will apply these results to the study of Wick products corresponding to the Charlier, free Charlier, and Laguerre polynomials. For the fourth and perhaps most interesting example of Wick products, I do not know the appropriate poset structure. However their inversion and product formulas can still be obtained by less conceptual techniques. As a consequence, we obtain the formula for the linearization coefficients of the free Meixner polynomials. 

09/22 3:00pm 
BLOC 117 
Patrick Brosnan University of Maryland 
Hessenberg varieties and a conjecture of ShareshianWachs
I will explain joint work with Tim Chow proving a conjecture of ShareshianWachs which
relates a combinatorial object, the socalled chromatic symmetric function of a certain graph, to a certain action of the symmetric on the cohomology of a Hessenberg variety first studied by J. Tymoczko.
I should mention that, shortly after Chow and I posted our proof to the ArXiv, a completely independent proof relying on a map of Hopf algebras and the theorem of AguiarBergeronSottile was posted by M. GuayPaquet.
The Hessenberg varieties in the title are certain smooth subvarieties of the the complete flag variety studied first by the applied mathematicians de Mari and Shayman. They were later generalized by de Mari, Procesi and Shayman to a setting where the general linear group is replaced with an arbitrary reductive group.
In this case, Tymoczko's dot action becomes a representation of the Weyl group, and it is an interesting problem to determine this representation. I will present some results in this direction. In particular, I will explain a restriction formula that generalizes GuayPaquet's proof that his Hopf algebra map respects comultiplication. 

09/29 3:00pm 
BLOC 117 
Sarah Witherspoon Texas A&M University 
Algebraic deformation theory and the structure of Hochschild cohomology
Some questions about deformations of algebras can
be answered by using Hochschild cohomology, and in
particular by using its Lie/Gerstenhaber brackets.
Until very recently there was no independent
description of this Lie structure for an arbitrary
resolution, a big disadvantage both theoretically
and computationally. In this talk, we will first
introduce Hochschild cohomology and explain its role
in algebraic deformation theory. We will then
summarize recent progress by several mathematicians,
focusing on examples. 

10/06 3:00pm 
BLOC 117 
Tian Yang Texas A&M University 
Volume conjectures for quantum invariants
Supported by numerical evidences, Chen and I conjectured that at the root of unity exp(2π i/r) instead of the usually considered root exp(π i/r), the TuraevViro and the ReshetikhinTuraev invariants of a hyperbolic 3manifold
grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold. This reveals a different asymptotic behavior of the relevant quantum invariants than that of Wittens invariants (that grow polynomially by the Asymptotic Expansion Conjecture), which may indicate a different geometric interpretation of those invariants than the SU(2) ChernSimons gauge theory. In this talk, I will introduce the conjecture and show further supporting evidences, including recent joint works with Detcherry and DetcherryKalfagianni. 

10/13 3:00pm 
BLOC 117 
Yiby Morales Universidad de los Andes 
The fiveterm exact sequence for Kac cohomology
The group of equivalence classes of abelian extensions of Hopf algebras associated to a matched pair of finite groups was described by Kac in the 60’s as the first cohomology group of a double complex, whose total cohomology is known as the Kac cohomology. Masuoka generalized this result and used it to compute some groups of abelian Hopf algebra extensions. Since Kac cohomology is defined as the total cohomology of a double complex, there is an associated spectral sequence. I will explain how we compute the fiveterm exact sequence associated to this double complex, which can be used to compute some other groups of abelian extensions.
This is joint work with César Galindo.


10/20 3:00pm 
BLOC 117 
Benjamin Schröter TUBerlin 
Multisplits in hypersimplicies and split matroids
Multisplits are a class of coarsest regular subdivisions of convex polytopes. In this talk I will present a characterization of all multisplits of two types of polytopes, namely products of simplices and hypersimplices. It turns out that the multisplits of these polytopes are in correspondence with one another and matroid theory is the key in their analysis, as all cells in a multisplit of a hypersimplex are matroid polytopes. Conversely, the simplest case of multisplits of hypersimplices give rise to a new class of matroids, which we call split matroids. The structural properties of split matroids can be exploited to obtain new results in tropical geometry. 

10/27 3:00pm 
BLOC 117 
Laura Colmenarejo York University 
TBA 

11/10 3:00pm 
BLOC 117 
Henry Tucker UC San Diego 
TBA 

11/17 3:00pm 
BLOC 117 
X. Shawn Cui Stanford University 
TBA
TBA 

12/01 3:00pm 
BLOC 117 
Carlos Arreche UT Dallas 
TBA
TBA 