Events for 08/26/2022 from all calendars

Student/Postdoc Working Geometry Seminar

Time: 1:30PM - 2:30PM

Location: BLOC 628

Speaker: JM Landsberg, TAMU

Title: Spaces of matrices of constant rank

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Galen Dorpalen-Barry, Ruhr-Universität Bochum

Title: Real Hyperplane Arrangements and the Varchenko-Gelfand Ring

Abstract: For a real hyperplane arrangement A, Varchenko--Gelfand ring is the ring of functions from the chambers of A to the integers with pointwise addition and multiplication. Varchenko and Gelfand gave a simple presentation for this ring, along with a filtration whose associated graded ring has its Hilbert function given by the coefficients of the Poincaré polynomial. Their work was extended to oriented matroids by Gelfand—Rybnikov, who gave an analogous presentation and filtration. We extend this work first to pairs (A,K) consisting of an arrangement A in a real vector space and open convex set K, and then to conditional oriented matroids. Time permitting, we will discuss an interesting special case arising in Coxeter theory: Weyl cones of Shi arrangements. We find that the coefficients of the cone Poincaré polynomial of a Weyl cone are described by antichains in the root poset. This talk contains joint work with Christian Stump, Nicholas Proudfoot, and Jayden Wang.

Promotion Talk by Chun-Hung Liu

Time: 4:00PM - 5:00PM

Location: Bloc 117

Description: Title: Coarse graph colorings on minor-closed families
Abstract: Hadwiger's conjecture addresses graph minors and graph coloring and is widely considered as one of the most important open questions in graph theory. It states that the complete graph on t+1 vertices (i.e. the most obvious non-properly t-colorable graph) is a minor of any non-properly t-colorable graph. In this talk, we will present optimal results or nearly optimal results for coarse versions of Hadwiger's conjecture by relaxing the notion of proper coloring. Those versions are fundamental graph partitioning problems, and our results are incomparable with Hadwiger's conjecture and solve a number of open questions. Some of those versions are studied in other areas of mathematics.