Mathematics Home Page
I'm a postdoc at the University of California, San Diego (UCSD) under the mentorship of Brendon Rhoades. I graduated from the University of Washington in June 2018 with a PhD in mathematics. My advisor was Sara Billey. My thesis was on "Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics".
My research is in Algebraic Combinatorics. This field of mathematics is broadly interested in applying a wide variety of combinatorial methods (e.g. generating functions, Möbius inversion, recursive constructions, explicit bijections, polytopes) to analyze a vast array of algebraic structures (e.g. cohomology rings, irreducible decompositions, independent sets, Grothendieck groups, graphs). Much of my own work is related to Young tableau and the surrounding combinatorics and representation theory, especially major index statistics. I am also interested in exploiting combinatorial generating functions for enumerative and asymptotic purposes.
Research interests: Coxeter groups, representation theory of reflection groups, symmetric functions, tableaux combinatorics, invariant theory of reflection groups, coinvariant algebras, diagonal coinvariants, cyclic sieving, major index statistics, descent statistics, generating function factorizations, plethysms, Thrall's problem, induced characters, cumulants, limit laws