Polymath Jr.

I worked as an assistant mentor in the Polymath Jr. program in both 2021 and 2022. This is a program designed to give broad access to mathematical research experiences for undergraduates. Here is the program website.

  • 2022: Our project, involving 22 students, was on solvability criteria for lattice models. Work on this project is still ongoing.
  • 2021: Our project, involving 22 students, was on Gelfand-Tsetlin polytopes, lattice models, and formulas for Whittaker functions. Work on this project is still ongoing.

Algebra and Combinatorics REU

I worked as a TA for the UMN Combinatorics REU during the summers of 2018 and 2019, and a mentor in 2020. The REU brings together around 15 mathematically-inclined undergraduates for 8 weeks to work on research-level mathematics. For more information about this program, see here.

I have been a TA or mentor for the following projects. In several of them, the work is still ongoing.

  • Neelima Borade, Matthew Huynh, and Henry Twiss studied the alcove walks model and its relation to double coset decompositions and Whittaker functions. This work is still ongoing.
  • Jared Marx-Kuo, Vaughan McDonald, John O'Brien, and Alex Vetter studied the Renner monoids and Hecke algebras associated to reductive monoids. This work can be found here and here.
  • Johnny Gao and Vaughan McDonald studied f-vectors, h-vectors, and cd-indices of weight polytopes. Their work can be found here.
  • C.J. Dowd, Valerie Zhang, and Sylvester Zhang found a formula for the ratio of arborescence sums of a graph and its regular cover in terms of the voltage Laplacian. Their report can be found here.
  • Zack Stier, Julian Wellman, and Zixuan Xu worked on the dihedral sieving phenomenon and asociated polynomials. Their report can be found here.
  • Quang Dao, Julian Wellman, Calvin Yost-Wolff, and Sylvester Zhang worked from several different viewpoints on correspondences between order ideals, and more generally, P-partitions, of the rectangle and trapezoid posets. Their report can be found here.
  • Quang Dao, Nathan Kenshur, Feiyang Lin, Christina Meng, Zack Stier, and Calvin Yost-Wolff worked on the representation theory of the nontrivial Schur covers of finite untwisted groups of Lie type. Their report can be found here.