Research

My research is in algebraic combinatorics. A central problem in algebraic combinatorics is to show that certain symmetric functions expand with positive integer coefficients in certain bases. A positive integer coefficient could count the number of some combinatorial objects. It could also be an intersection number of varieties, a Betti number of a topological space, or a rank of a module, connecting combinatorics to geometry, topology, and representation theory. During my Ph.D. at UC Berkeley, I studied Schur-positivity of LLT symmetric functions. During my position at MIT, I studied e-positivity of chromatic (quasi)-symmetric functions. I am continuing this work at Dartmouth College.

Submitted

• The chromatic symmetric function of graphs glued at a single vertex with Aarush Vailaya
  

• Chromatic symmetric functions and change of basis with Bruce Sagan
  

Accepted

• On e-positivity of trees and connected partitions
  Advances in Applied Mathematics (2025)

• Adjacent cycle chains are e-positive with Aarush Vailaya
  Electronic Journal of Combinatorics (2025)

Appeared

• A signed e-expansion of the chromatic quasisymmetric function
  Combinatorial Theory, Vol. 5 No. 2 (2025)

• A horizontal-strip LLT polynomial is determined by its weighted graph
  Combinatorial Theory, Vol. 3 No. 3 (2023)

• A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
  Combinatorial Theory, Vol. 1 No. 14 (2021)

• Classifying the near-equality of ribbon Schur functions
  European Journal of Combinatorics, Vol. 90, 103197 (2020)

• The number of rational points of hyperelliptic curves over subsets of finite fields with Kristina Nelson, Jozsef Solymosi, and Ching Wong
  Involve, a Journal of Mathematics, Vol. 12 No. 5, 755--765 (2019)

• Necessary conditions for Schur-maximality with Stephanie van Willigenburg
  Electronic Journal of Combinatorics, Vol. 25, P2.30 (2018)

Refereed Conference

• On e-positivity of trees and connected partitions
  

• A signed e-expansion of the chromatic symmetric function and some new e-positive graphs
  Seminaire Loharingien de Combinatoire 91B.48 (2024)

• Horizontal-strip LLT polynomials
  Seminaire Loharingien de Combinatoire 89B.40 (2023)

• A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
  Seminaire Loharingien de Combinatoire 85B.18 (2021)

• Schur-positivity of equitable ribbons with Stephanie van Willigenburg
  Seminaire Loharingien de Combinatoire 80B.18 (2018)