Serena An

Research Experience

This summer, I will be participating in the Imperial College London summer research exchange.

Last summer, I participated in the UMN Combinatorics and Algebra REU.

  • Equality and saturated Newton polytopes of Postnikov-Stanley polynomials
    [arXiv] [pdf] [slides] with Katherine Tung and Yuchong Zhang under mentor Shiyun Wang and TA Meagan Kenney
  • Mixed dimer model for exceptional type quiver representations and cluster algebras
    [pdf] [slides] with Casey Appleton and Sogol Cyrusian under mentor Kayla Wright and TA Elise Catania

In summer 2023, I participated in the MIT math department's SPUR program.

In high school, I participated in the MIT PRIMES-USA program.

  • The Stembridge equality for skew stable Grothendieck polynomials and skew dual stable Grothendieck polynomials
    [journal] with Fiona Abney-McPeek and Jakin Ng under mentor Adela Zhang
    Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 187-208.

Other Writing and Presentations

  • Homotopy groups of spheres
    [pdf] Final paper for MATH 231BR Algebraic Topology II.
  • Faithful specializations of the Burau representation
    [pdf] Final paper for 18.704 Seminar in Topology.
  • Dyson Brownian motion
    [pdf] Final paper for 18.676 Stochastic Calculus.
  • Projective modules
    [pdf] [slides] Final paper for 18.704 Seminar in Algebra.
  • How to get good at SET
    [slides] Presentation for HMMT Education in November 2023.

Math Contests

I participated extensively in math contests in high school and enjoy remaining involved!

  • TA for the Math Olympiad Program 2022-2025
  • Deputy leader of the USA EGMO team
  • Proposer of 2024 USAJMO Problem 2 (with Claire Zhang)
  • AoPS username: anser