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 superrepresentation 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.
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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
Primary Instructor

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
Primary Instructor

Fall 2019
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
Primary Instructor

Fall 2018
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.