Research

Algebraic Combinatorics:

Many objects in representation theory has combinatorial structures, and thus by studying their combinatorics we can get new information on the representation theory, also vice versa. In this paper, I used the representation stability result of diagonal harmonics to get an explicit formula for its bigraded dimension, and improving its stability bound. 

Paper:

• Dimension of the Bigraded Subspace of Diagonal Harmonics are Polynomials in n, preprint

Thesis:

• Dimension of the Bigraded Subspace of Diagonal Harmonics are Polynomials in n

Talks and Slides:

• “Dimensions of the Bigraded Components of Diagonal Harmonics are Polynomials in n” Combinatorics, Algebra and Geometry Seminar, University of Pennsylvania, October 2024. Slides

• "Generating Function, Rook Theory and Problème Des Ménages", UPenn Math Graduate Pizza Seminar, University of Pennsylvania, March 2022. Talk

Mathematical Biology:

Ever since COVID I have been interested in applying tools in mathematics to the biological systems in the real world. I am specifically interested in evolutionary game theory and social dynamics. 

Project:

Parameter estimation of the Wright Fisher Model, in progress