Calendar

Posted August 18, 2025

Discussion and Training in Combinatorics

Gyaneshwar Agrahari, LSU
Emmanuel Astante, Louisiana State University
Organizational Meeting of DTC Seminar

The first meeting of the Discussion and Combinatorics Seminar will be held on this day and time. In this meeting, we will introduce everyone and give the details of how the seminar will be run.

Posted September 1, 2025

Discussion and Training in Combinatorics

Week 2: Review of Topology

This week, our speaker, Sayani Mukherjee, will kick off our discussion on the applications of the Borsuk-Ulam Theorem. Ms. Mukherjee is a second-year PhD student in our department. She will review the first two sections of the textbook: "Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry"

Posted February 3, 2026

Discussion and Training in Combinatorics

Joy Harris
Ramsey Number of Daisies

Given the set of vertices $[n]=\{1,\ldots,n\}$, an \emph{$r$-daisy}, given by disjoint sets $K,M \subset [n]$, is the $(r+|K|)$-uniform hypergraph defined as \[ \{K \cup P : P \subset M \text{ and } |P|=r\}. \] In this talk, we will discuss the \emph{Ramsey number of daisies}. This is the minimum number of vertices $n$ such that no coloring of the subsets of $[n]$ by $\ell$ colors yields a monochromatic daisy. We will give a probabilistic proof showing a lower bound for this number.

Event contact: Gyaneshwar Agrahari and Emmanuel Asante

Posted February 17, 2026

Discussion and Training in Combinatorics

Gyaneshwar Agrahari, LSU
An Introduction to the Crapo Beta Invariant in Matroid Theory

We will define the Crapo beta invariant of a matroid and prove a few of its fundamental properties, including how it behaves under standard matroid operations. We will also investigate the connection of certain matroid properties like connectivity with the invariant.

Event contact: Gyaneshwar Agrahari and Emmanuel Asante

Posted August 27, 2026

Discussion and Training in Combinatorics

Joy Harris
Intro to Graphs and Matroids

We will give a brief introduction to both Matroid Theory and Graph Theory. From the basic ideas of linear independence, we will define, in many equivalent ways, matroids derived from matrices. We will then discuss core definitions of Graph Theory, important properties and classes, and the way that all graphs give rise to matroids.

Event contact: Sean Boros

Posted September 10, 2026

Discussion and Training in Combinatorics

Teegan Bailey, LSU
Legends, Tales, and Minor Figures: The Mythology of Graph Theory

The Greeks had Zeus, Hercules, Jason, the Sirens, and more. The Vikings had Odin, Loki, the Valkries, and Ragnarok. We have Ramsey, Dilsworth, Menger, Szemer\'edi, and Erd\'os. Our talk will focus on a lesser known mythos, the lore of Graph Theory. Our story will begin with the tale of creation in K\"onigsberg. We will then proceed to present a broad overview of the cornerstone tales that every practicing graph theorist is familiar with. Time permitting, audience members can expect to walk away from this talk knowing not only the basic terminology essential to this diverse field, but also some of the fundamental questions and results central to studying and conducting research in Graph Theory. This talk will primarily be expository and no background in graph theory will be assumed. The main purpose of this talk will be to equip audience members with the essential definitions needed to attend other talks or presentations on Graph Theory. Minor elementary results may be proved to give a flavor of what a ``typical'' Graph Theory result entails.

Event contact: jgarc86@lsu.edu

Posted September 17, 2026

Discussion and Training in Combinatorics

Cayleigh Ritter, LSU
Explanation and Proof of the Five-Color Theorem with Application on the Louisiana Parish Map

Given a geographical map, it is possible to properly color each region a distinct color. Mathematicians have been investigating the minimum number of distinct colors that can be used to properly color a geographical map for centuries. We discuss Heawood’s Five-Color theorem with proof, then apply our results to create an algorithm for coloring a geographical map. Specifically, coloring a parish map of the state of Louisiana.

Event contact: jgarc86@lsu.edu