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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 and analytic combinatorics. Algebraic combinatorics is a field of mathematics which 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). Analytic combinatorics seeks to give effective asymptotic estimates of combinatorial quantities, often by exploiting generating function identities. Such estimates make frequent use of tools from real and complex analysis (e.g. contour integrals, the saddle point method) and probability theory (e.g. the method of moments). A famous example combining both areas is the Hardy--Ramanujan estimate for the number of ways to write n as an unordered sum of positive integers. Much of my research is related to Young tableau, coinvariant algebras, and the surrounding combinatorics, commutative algebra, and representation theory, especially major index statistics. More technical topics of interest are listed below.
Research interests: Algebraic combinatorics, analytic combinatorics, combinatorial representation theory, symmetric functions, complex reflection groups, Coxeter groups, major index statistics, tableaux combinatorics, invariant theory, cyclic sieving, \{classical, super, diagonal\} coinvariant algebras, $q$-analogues, generating function factorizations, free Lie algebras, cumulants, limit laws, local limit theorems