Chase Meadors

Graduate Student — Mathematics
chase.meadors@colorado.edu

Papers

Other 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 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.