Research

My current research interests are principally in algebraic combinatorics, although I dip into topological and geometric combinatorics a fair amount. I am currently studying combinatorial Hopf structures in my work with my advisor Jeremy Martin. I also have an ongoing research project emerging from the Graduate Research Workshop in Combinatorics studying the cut complexes of graphs, which generalize a construction of Eagon and Reiner in their proof of Fröberg's theorem.

Papers and Preprints

• Total Cut Complexes of Graphs - Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Rowan Rowlands, Sheila Sundaram, and Lei Xue - Preprint

• Extension of Fröberg's Theorem to Other Graph Ideals - Mark Denker - Formal Report for the completion of a Master's Degree

• Predicting the evolutionary dynamic behavior of a laser with injected signal using Lyapunov exponents - D. K. Bandy, J. R. Hall, and M. E. Denker - Phys. Rev. A

Recorded Talks

• "Cut Complexes and Total Cut Complexes of Graphs" - Graduate Online Combinatorics Colloquium 9/29/2022 - Slides

• "Cut Complexes and Extending Fröberg's Theorem" - Graduate Student Combinatorics Conference 3/26/2022 - Slides

• "Hopf Monoids" - Expository Talk for KU Combinatorics Seminar 9/25/2020 - Slides