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 / Fall 2020 / Fall 2021 / Fall 2023
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. Credit not granted for this course and MATH 2002.
MATH 3001 - Analysis 1
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
MATH 3140 - Abstract Algebra 1
Fall 2019 / Fall 2023
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
Fall 2018 / Fall 2020 / Fall 2022
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates.