Chase Meadors

Graduate Student — Mathematics
chase.meadors@colorado.edu

Papers

• Local finiteness in varieties of MS4-algebras
• Cohen-Macaulay Monomial Ideals Arising From Transitive Directed Hypergraphs | Masters Thesis at Oklahoma State University — Advised by Chris Francisco

Topics and Projects

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 mathematics

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

Talks and presentations

• Galois Theory: Syntax and Semantics
  An introduction to "Galois Theory", but instead of field extensions, we discuss the various Galois connections between syntax and semantics in logic.

• Coxeter Groups and Diagram Algebras
  An expository presentation of diagram algebras that arise in the study of Coxeter Groups; related to a project with Tianyuan Xu that investigated Fully commutative Kazdahn-Lusztig cells.

• A Tour of Type Theory
  Part introduction to Lean, and part introduction to Type Theory. Introduces type-theoretic foundations and compares to usual foundations based on Set Theory.

• A Brief Exploration of a Homological Theory of Functions
  A course paper for Algebraic Topology.