
Date Time 
Location  Speaker 
Title – click for abstract 

01/19 3:00pm 
BLOC 628 
Anton Dochtermann Texas State University 
Coparking functions and hvectors of matroids
The hvector of a simplicial complex X is a wellstudied invariant with connections to algebraic aspects of its StanleyReisner ring. When X is the independence complex of a matroid Stanley has conjectured that its hvector is a ‘pure Osequence’, i.e. the degree sequence of a monomial order ideal where all maximal elements have the same degree. The conjecture has inspired a good deal of research and is proven for some classes of matroids, but is open in general. Merino has established the conjecture for the case that X is a cographical matroid by relating the hvector to properties of chipfiring and `Gparking functions' on the underlying graph G. We introduce and study the notion of a ‘coparking’ function on a graph (and more general matroids) inspired by a dual version of chipfiring. As an application we establish Stanley’s conjecture for certain classes of binary matroids that admit a wellbehaved `circuit covering'. Joint work with Kolja Knauer 

01/26 3:00pm 
BLOC 628 
Karina Batistelli U. N. Cordoba 
Some Lie subalgebras of the matrix quantum pseudodifferential operators
In this talk, we will characterize the irreducible quasifinite highest weight modules of some subalgebras of the Lie algebra of matrix quantum pseudodifferential operators N x N.
In order to do this, we will first give a complete description of the antiinvolutions that preserve the principal gradation of the algebra of NxN matrix quantum pseudodifferential operators and we will describe the Lie subalgebras of its minus fixed points. We will obtain, up to conjugation, two families of antiinvolutions that show quite different results when n=N and n 

01/30 4:00pm 
BLOC 220 
Davis Penneys The Ohio State University 
Exotic fusion categories: EH3 exists!
Fusion categories generalize the representation categories
of (quantum) groups, and we think of them as objects which encode
quantum symmetry. All currently known fusion categories fit into 4
families: those coming from groups, those coming from quantum groups,
quadratic categories, and those related to the extended Haagerup (EH)
subfactor. First, I'll explain what I mean by the preceding sentence.
We'll then discuss the extended Haagerup subfactor, along with the
newly constructed EH3 fusion category (in joint work with Grossman,
Izumi, Morrison, Peters, and Snyder), and the possibility of the
existence of EH4. 

02/02 3:00pm 
BLOC 628 
Daniel Creamer Texas A&M University 
A Computational Approach to Classifying Modular Categories by Rank
Modular categories are of interest in a variety of disciplines stretching from abstract algebra to theoretical physics. It was recently proved by Bruillard, Ng, Rowell, and Wang, that there are a finite number of modular categories given a fixed rank. I present a computer assisted approach to classifying modular categories by their rank. 

02/09 3:00pm 
BLOC 628 
Nathan Williams UT Dallas 
Fixed Points of Parking Functions
We define an action of words in [m]^n on R^m to give
a new characterization of rational parking functions. We use
this viewpoint to give a simple definition of Gorsky, Mazin,
and Vazirani's zeta map on rational parking functions when m and n
are coprime, and prove that this zeta map is invertible. A
specialization recovers Loehr and Warrington's sweep map on
rational Dyck paths. This is joint work with Jon McCammond and Hugh Thomas. 

02/10 08:00am 
BLOCKER 
Combinatexas 


02/11 8:00pm 
BLOCKER 
Combinatexas 


02/16 3:00pm 
BLOC 628 
Alex Kunin Penn State University 
Hyperplane neural codes and the polar complex
This talk concerns combinatorial and algebraic questions arising from neuroscience. Combinatorial codes arise in a neuroscience setting as sets of cofiring neurons in a population; abstractly, they record intersection patterns of sets in a cover of a space. Hyperplane codes are a class of combinatorial codes that arise as the output of a one layer feedforward neural network, such as Perceptron. Here we establish several natural properties of nondegenerate hyperplane codes, in terms of the {\it polar complex} of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a nondegenerate hyperplane code is shellable. Moreover, we show that all currently known properties of hyperplane codes follow from the shellability of the appropriate polar complex. Lastly, we connect this to previous work by examining some algebraic properties of the StanleyReisner ideal associated to the polar complex. This is joint work with Vladimir Itskov and Zvi Rosen.


02/23 3:00pm 
BLOC 628 
Ka Ho Wong Chinese University of Hong Kong 
Asymptotic expansion formula for the colored Jones polynomial and TuraevViro invariant for the figure eight knot
The volume conjecture of the TuraevViro invariant is a new topic in quantum topology. It has been shown that the $(2N+1)$th TuraevViro invariant for the knot complement $\SS^3 \backslash K$ can be expressed as a sum of the colored Jones polynomial of $K$ evaluated at $\exp(2\pi i/ (N+1/2))$. That leads to the study of the asymptotic expansion formula (AEF) for the colored Jones polynomial of $K$ evaluated at halfinteger root of unity.
When $K$ is the figure eight knot, by using saddle point approximation, H.Murakami had already found out the AEF for the $N$th colored Jones polynomial of $K$ evaluated at $\exp(2\pi i/N)$. In this talk, I will first review the strategy Murakami used to prove the AEF of the colored Jones polynomial. Then, I will further discuss, for $M$ with a fixed limiting ratio of $M$ and $(N+1/2)$, how the AEF for the $M$th colored Jones polynomial for the figure eight knot evaluated at $(N+1/2)$th root of unity can be obtained. As an application of the asymptotic behavior of the colored Jones polynomials mentioned above, we obtain the asymptotic expansion formula for the TuraevViro invariant of the figure eight knot. Finally, we suggest a possible generalization of our approach so as to relate the AEF for the colored Jones polynomials and the AEF for the TuraevViro invariants for general hyperbolic knots. 

03/02 3:00pm 
BLOC 628 
Shilin Yu Texas A&M University 
Quantization and representation theory
In this talk, I will talk about a geometric way to construct representations of noncompact semisimple Lie groups, though no prior knowledge is required. Kirillov's coadjoint orbit method suggests that (unitary) irreducible representations can be constructed as geometric quantization of coadjoint orbits of the group. Except for a lot of evidence, the quantization scheme meets strong resistance in the case of noncompact semisimple groups. I will give a new perspective on the problem using deformation quantization of symplectic varieties and their Lagrangian subvarieties. This is joint work in progress with Conan Leung. 

03/23 3:00pm 
BLOC 628 
Dimitar Grantcharov UT Arlington 
Singular GelfandTsetlin Modules and BGG Differential Operators
Every irreducible finitedimensional module of the general linear Lie
algebra gl(n) can be described with the aid of the classical GelfandTsetlin
formulas. The same formulas can be used to define a gl(n)module structure
on some infinitedimensional modules  the socalled generic (nonsingular)
GelfandTsetlin modules. In this talk we will introduce GelfandTsetlin modules and discuss recent progress on the study of singular GelfandTsetlin
gl(n)modules and relations with BGG differential operators. The talk is based on a joint work with V. Futorny, L. E. Ramirez, and P. Zadunaisky. 

04/13 3:00pm 
BLOC 628 
Sarah Witherspoon & Catherine Yan 
Algebra and Combinatorics Spring 2019 Course Discussion. 

04/13 4:00pm 
BLOC 220 
Jurij Volcic BenGurion University of the Negev 
TBA  (Joint Algebra and Combinatorics  Linear Analysis seminar) 

04/27 3:00pm 
BLOC 628 
Xingting Wang Temple University 
Noncommutative algebra from a geometric point of view
In this talk, I will discuss how to use algebrogeometric and Poisson geometric methods
to study the representation theory of 3dimensional Sklyanin algebras, which are
noncommutative analogues of polynomial algebras of three variables. The fundamental tools
we are employing in this work include the noncommutative projective algebraic geometry
developed by ArtinSchelterTateVan den Bergh in 1990s and the theory of Poisson order
axiomatized by Brown and Gordon in 2002, which is based on De ConciniKacPriocesi’s
earlier work on the applications of Poisson geometry in the representation theory of
quantum groups at roots of unity. This talk demonstrates a strong connection between
noncommutative algebra and geometry when the underlining algebra satisfies a polynomial
identity or roughly speaking is almost commutative. 