My research area is Algebraic combinatorics. My recent research located at the intersection of Combinatorics and Representation Theory with natural links to Theoretical Physics. For some families of groups, it is not possible to find a satisfactory classification of irreducible representations (or equivalently conjugacy classes). Most recently, I defined normal supercharacter theory, which is a mechanism to replace conjugacy classes by normal subgroups in such a way that this 'coarsening' simulates many desirable properties of representation theory. This construction gives new tools to construct algebraic structures isomorphic to combinatorial structures. For instance, we build a supercharacter theory for unipotent uppertriangular matrices in which Dyck paths index supercharacters.
Teaching
courses taught
MATH 2001  Introduction to Discrete Mathematics
Primary Instructor

Summer 2018 / Fall 2018
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 2130  Introduction to Linear Algebra for NonMathematics Majors
Primary Instructor

Spring 2018
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who do not plan to major in Mathematics. Degree credit not granted for this course and MATH 2135 or APPM 3310. Formerly MATH 3130.
MATH 2135  Introduction to Linear Algebra for Mathematics Majors
Primary Instructor

Spring 2019
Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
MATH 4140  Abstract Algebra 2
Primary Instructor

Spring 2018
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Same as MATH 5140.
MATH 5140  Abstract Algebra 2
Primary Instructor

Spring 2018
Explores some topic that builds on material in MATH 3140. Possible topics include (but are not limited to) Galois theory, representation theory, advanced linear algebra or commutative algebra. Department enforced prerequisite: MATH 3140. Same as MATH 4140.
MATH 6250  Theory of Rings
Primary Instructor

Spring 2019
Studies semisimple Artinian rings, the Jacobson radical, group rings, representations of finite groups, central simple algebras, division rings and the Brauer group. Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
International Activities
global connections related to teaching and scholarly work (in recent years)