
Date Time 
Location  Speaker 
Title – click for abstract 

02/11 3:00pm 
Zoom 
Ryan Martin Iowa State University 
Counting paths, cycles, and other subgraphs in planar graphs
For a planar graph H, let N_P(n,H) denote the maximum number of copies of H in an nvertex planar graph. The case where H is the path on 3 vertices, H=P_3, was established by Alon and Caro. The case of H=P_4 was determined, also exactly, by Gy\H{o}ri, Paulos, Salia, Tompkins, and Zamora. In this talk, we will give the asymptotic values for H equal to P_5 and P_7 as well as the cycles C_6, C_8, C_{10} and C_{12} and discuss the general approach which can be used to compute the asymptotic value for many other graphs H. 

03/04 00:00am 


CombinaTexas
Conference website: https://www.math.tamu.edu/conferences/combinatexas/ 

03/05 00:00am 


CombinaTexas
Conference website: https://www.math.tamu.edu/conferences/combinatexas/ 

03/11 3:00pm 
BLOC 302 
Harshit Yadav Rice University 
Filtered Frobenius algebras in monoidal categories
We develop filteredgraded techniques for algebras in monoidal categories with the goal of establishing a categorical version of Bongale's 1967 result: A filtered deformation of a Frobenius algebra over a field is Frobenius as well. Towards the goal, we construct a monoidal associated graded functor, building on prior works of ArdizzoniMenini, of Galatius et al., and of GwillianPavlov. We then produce equivalent conditions for an algebra in a rigid monoidal category to be Frobenius in terms of the existence of categorical Frobenius form. These two results of independent interest are used to achieve our goal. As an application of our main result, we show that any exact module category over a symmetric finite tensor category is represented by a Frobenius algebra in it. This is joint work with Dr. Chelsea Walton (Rice University). 

04/01 3:00pm 
BLOC 302 
ChunHung Liu TAMU 
A decomposition theorem for immersionfree graphs with no 3edgecut
Structural decomposition theorems for graphs with forbidden minors and topological minors have been proved and led to many applications. Graph immersions is a notion related to graph minors and topological minors, and many analogous open problems about immersions have been proposed. In this talk we address the fundamental problem about the structure of a graph with forbidden immersions. We prove that every graph with no edgecut of size 3 that forbids a fixed graph H as an immersion can be decomposed into graphs that are "nearly simpler" than H. The condition for having no 3edgecut is necessary to have a clean theorem. 

04/22 3:00pm 
Zoom 
Anton Bernshteyn Georgia Tech 
Lower bounds for difference bases
A difference basis with respect to $n$ is a subset $A \subseteq \mathbb{Z}$ such that $A  A \supseteq [n]$. R\'{e}dei and R\'{e}nyi showed that the minimum size of a difference basis with respect to $n$ is $(c+o(1))\sqrt{n}$ for some positive constant $c$. The precise value of $c$ is not known, but some bounds are available, and I will discuss them in this talk. This is joint work with Michael Tait (Villanova University). 

05/03 3:00pm 
BLOC 302 
Daniel Perales University of Waterloo 
On the anticommutator of two free random variables
Let a, b be freely independent random variables in a noncommutative probability space. Based on some considerations on bipartite graphs, we provide a formula to express the nth free cumulant of the anticommutator ab+ba as a sum indexed by subset Y_{2n} of noncrossing partitions of {1,2,...,2n}. Specifically, Y_{2n} is the set of partitions that separate odd elements and where blocks with only even elements have even size. We will study the sets Y_{2n} and obtain new results regarding the distribution of ab+ba. For instance, the size Y_{2n} is closely related to the case when a,b have a MarchenkoPastur (free Poisson) distribution of parameter 1. We will also provide a formula with the sum indexed by cacti graphs, and discuss a natural generalization to study quadratic forms in $k$ free random variables. The talk is based on the preprint arXiv:2101.09444. 