Chase Meadors

Graduate Student — Mathematics


Fully-Commutative Kazdahn-Lusztig cells

In a project under the direction of Tianyuan Xu, we investigated the combinatorics of fully commutative elements and Kazdahn-Lusztig cells in Coxeter groups. We developed a robust library of code for working with these elements which we contributed to SageMath in #30243. We also fixed some bugs in the process (#30237, #30167).

The Hecke algebras of certain Coxeter groups have a natural identification with a class of diagram algebras called Generalized Temperley-Lieb algebras. I put together a visual portfolio of some notable diagrams related to our conjectures. Here are some slides from I talk I delievered about these diagram algebras.

Formalized Proofs

I've contributed a few features to Lean's library of formalized mathematics, including

  • A collection of results on lattice theory and order theory: #5825, #5871, #5942
  • A refactoring and simplification of existing proofs using the above results: #6082


2. A Brief Exploration of a Homological Theory of Functions | Course paper for Topology 2

1. Cohen-Macaulay Monomial Ideals Arising From Transitive Directed Hypergraphs | Masters Thesis at Oklahoma State University — Advised by Chris Francisco