My research explores the interplay between algebra and combinatorics. I specialize in combinatorial representation theory, which observes that we can gain insights into abstract mathematical structures by realizing them in more concrete ways. In recent years, I have become especially involved in an emerging area known as super-representation theory, a theory that uses a precise form of fudging to better understand problems that are known to be mathematically impossible. This new interest has also inspired me to study combinatorial Hopf algebras in more detail.
Topics of interest: Representation theory, character theory, supercharacter theory, groups of Lie type, Hecke algebras, symmetric functions, Hopf algebras and monoids
MATH 2001 - Introduction to Discrete Mathematics
Fall 2018 / Fall 2019
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).
MATH 3140 - Abstract Algebra 1
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields.
MATH 6130 - Algebra 1
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.