# Combinatorics Seminars

**Upcoming Combinatorics Seminars**

**Past Combinatorics Seminars**

**DMS Combinatorics Seminar**

Apr 25, 2024 02:00 PM

328 Parker Hall

Speaker: **Kyungyong Lee **(University of Alabama)

Title: The Kazhdan-Lusztig polynomial of a matroid

Abstract: In 2016, Elias, Proudfoot, and Wakefield introduced the Kazhdan-Lusztig polynomial for every matroid. We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan-Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation. No background is required.

This is joint work with George D. Nasr and Jamie Radcliffe.

**DMS Combinatorics Seminar**

Apr 23, 2024 02:00 PM

328 Parker Hall

Speaker: **Isabel Harris **(Auburn)

Title: Avoiding k-Rainbow Graphs in Edge Colorings of K_{n} and other Families of Graphs

Abstract: A simple graph, G, avoids a k-rainbow edge coloring if any color appears on at least k+1 edges of G. For any positive integer k, the k-Anti-Ramsey Number, AR_{k}(G, H), is the maximum number of colors in an edge coloring of the graph H on such that no k-rainbow edge colored copy of G is a subgraph of H. This talk will focus specifically on the edge colorings of complete graphs with n vertices, AR_{k}(G,K_{n})=AR_{k}(G,n). We will say G is AR_{k}-bounded if AR_{k}(G,n) is bounded by some positive integer c for all n sufficiently large. In this talk we will discuss which simple graphs are AR_{k}-bounded on the complete graph for any k. Additionally, we will explore some results for AR_{k}(G,H), where H is not the complete graph.

**DMS Combinatorics Seminar**

Apr 11, 2024 02:00 PM

ZOOM

Speaker: **Ellen Veomett** (University of San Francisco)

Title: Mathematical Questions in Redistricting and Detecting Gerrymandering

Abstract: Please come learn how your skills and expertise as a mathematician can be used to improve our democracy! We'll discuss what redistricting is, and mathematical metrics that can help to determine whether or not a redistricting map is "fair." We'll also learn about the redistricting "metagraph," which is (as you probably guessed) a graph of graphs. (This is the kind of graph you've heard of in your discrete math or combinatorics class). The structure of this metagraph is unknown, and has impacts on whether a tool that is frequently cited in courts does a good job of sampling potential redistricting maps. Finally, we'll look at two-player-games in redistricting. In particular, we'll look at trees that arise from the "Connected Recursive Bisection" protocol, which is a two-player game to create a redistricting map.

**DMS Combinatorics Seminar**

Apr 09, 2024 02:00 PM

328 Parker Hall

Speaker: **Zach Walsh** (Georgia Tech/Auburn)

Title: New lift matroids for gain graphs

Abstract: Given a graph G with edges labeled by a group, a construction of Zaslavsky gives a rank-1 lift of the graphic matroid of G that respects the group labeling. For which finite groups can we construct a rank-t lift of the graphic matroid of G with t > 1 that respects the group labeling? We show that this is possible if and only if the group is the additive group of a non-prime finite field. We assume no knowledge of matroid theory.

This is joint work with Daniel Bernstein.

**DMS Combinatorics Seminar**

Apr 02, 2024 02:00 PM

328 Parker Hall

Speaker: **Aseem Dalal **(IIT Delhi)

Title: On Total Chromatic Number of Graphs Having Triangle-Free Core

**DMS Combinatorics Seminar**

Mar 26, 2024 11:00 AM

228 Parker Hall

Speaker: **Ben Baker **

Title: Searching for a Conway-99 Graph

**DMS Combinatorics Seminar**

Mar 21, 2024 02:00 PM

328 Parker Hall

Speaker: **Evan Leonard **(Auburn)

Title: Constructions based on a refinement of list coloring

**DMS Combinatorics Seminar**

Mar 14, 2024 02:00 PM

328 Parker Hall

Speaker: **Colby Muir **(Auburn University)

Title: Modified Feng-Rao Decoding for Two-Point Codes

Abstract: Matthews introduces a class of two-point algebraic-geometry codes with better parameters than the correlated one-point codes. However, there was no decoding scheme provided. We develop a decoding scheme (with codes as well) by reducing the two-point code into one-point form and use a modified Feng-Rao algorithm to produce the error positions and magnitudes.

**DMS Combinatorics Seminar**

Feb 29, 2024 02:00 PM

328 Parker Hall

Speaker: **Jie Ma** (University of Science and Technology of China)

Title: On extremal problems on k-critical graphs

Abstract: A graph is called k-critical if its chromatic number is k but any proper subgraph has chromatic number less than k. There has been extensive research on k-critical graphs over the past decades, yet several basic problems remain widely open. One of such problems is to determine the maximum number of edges in an n-vertex k-critical graph. In this talk, we will discuss some recent results on extremal aspects of k-critical graphs.

**DMS Combinatorics Seminar**

Feb 27, 2024 02:00 PM

328 Parker Hall

Speaker: **Manuel Fernandez** (Georgia Tech)

Title: On the \(\ell_0\)-Isoperimetry of Measurable Sets

Abstract: Gibbs-sampling, also known as coordinate hit-and-run (CHAR), is a random walk used to sample points uniformly from convex bodies. Its transition rule is simple: Given the current point p, pick a random coordinate i and resample the i'th coordinate of p according to the distribution induced by fixing all other coordinates. Despite its use in practice, strong theoretical guarantees regarding the mixing time of CHAR for sampling from convex bodies were only recently shown in works of Laddha and Vempala, Narayanan and Srivastava, and Narayanam, Rajaraman and Srivastava. In the work of Laddha and Vempala, as part of their proof strategy, the authors introduced the notion of the \(\ell_0\) isoperimetric coefficient of a measurable set and provided a lower bound for the quantity in the case of axis-aligned cubes. In this talk we will present some new results regarding the \(\ell_0\) isoperimetric coefficient of measurable sets. In particular we pin down the exact order of magnitude of the \(\ell_0\) isoperimetric coefficient of axis-aligned cubes and present a general upper bound of the \(\ell_0\) isoperimetric coefficient for any measurable set. As an application, we will mention how the results give a moderate improvement in the mixing time of CHAR.