# CMU Algebra and Combinatorics Seminar

## Fall 2018

### Meeting Times

Fridays, 11:15am–12:15pm, in Pearce 226.

### Schedule

 Date Speaker Affiliation Title 09/14 Botong Wang University of Wisconsin–Madison The log-concave conjectures of graphs and matroids 10/12 Paramasamy Karuppuchamy University of Toledo Schubert varieties and toric varieties 10/19 10/26 Olivia Dumitrescu Central Michigan University TBD 11/02 Jordan Watts Central Michigan University Diffeological Groups 11/09 Dmitry Zakharov Central Michigan University TBD 11/16 Takumi Murayama University of Michigan TBD 11/30 12/07

### Abstracts

Speaker: Botong Wang
Title: The log-concave conjectures of graphs and matroids
Abstract: The chromatic polynomial is an important invariant in graph theory introduced by Birkhoff. A generalization of chromatic polynomial is the characteristic polynomial in matroid theory. It was conjectured by Rota, Heron and Welsh in the 70’s that the coefficients of the characteristic polynomials are log-concave. I will talk about a beautiful proof of this conjecture by Karim Adiprisito, June Huh and Eric Katz. I will also discuss a log-concavity result about the number of independent sets, which is joint work with June Huh and Benjamin Schroter. The key idea to proof the log-concavity properties is to use the Hodge-Riemann relation in algebraic geometry.

Speaker: Paramasamy Karuppuchamy
Title: Schubert varieties and toric varieties
Abstract: Degeneration of Schubert varieties to toric varieties is completed in the paper "Toric degeneration of Schubert varieties" by Philippe Caldero. In an attempt to find a geometric proof of this result we realized that certain Schubert varieties are already toric varieties: A Schubert variety $X_w$ is a toric variety if and only if $w$ is a product of distinct simple reflections. Part of this result can be found (not explicitly mentioned) in Deodhar's article "On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cell." The author was unaware of this fact while writing his article. In $A_n$ type, Masuda and Lee have different approach to get this result in their recent paper "Generic torus orbit closure in Schubert varieties." In this talk we give an overview of this topic.

Speaker: Olivia Dumitrescu
Title: TBD
Abstract: Coming soon …

Speaker: Jordan Watts
Title: Diffeological Groups
Abstract: Coming soon …

Speaker: Dmitry Zakharov
Title: TBD
Abstract: Coming soon …

Speaker: Takumi Murayama
Title: TBD
Abstract: Coming soon …