Serena An

Course Notes

Thank you to Sanjana Das for the LaTeX template.

• 18.785 Number Theory I

  [notes] taught by Andrew Sutherland, fall 2025

• 18.965 Geometry of Manifolds I

  [notes] taught by William Minicozzi, fall 2025

Research Experience

I am currently doing research on chromatic quasisymmetric functions under Tatsuyuki Hikita at Kyoto University.

In summer 2025, I participated in the Imperial College London summer research exchange.

• Rank varieties for modules over quantum complete intersections

  [pdf] under mentor Benjamin Briggs

In summer 2024, I participated in the UMN Combinatorics and Algebra REU.

• Equality and saturated Newton polytopes of Postnikov–Stanley polynomials

  [pdf] [slides] with Katherine Tung and Yuchong Zhang under mentor Shiyun Wang and TA Meagan Kenney

• Newton polytopes of dual Schubert polynomials

  [arXiv] with Katherine Tung and Yuchong Zhang

• Postnikov–Stanley polynomials are Lorentzian

  [arXiv] with Katherine Tung and Yuchong Zhang

• 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.

• Flip graphs on self-complementary ideals of chain products

  [arXiv] [slides] with Holden Mui under mentor Elisabeth Bullock

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 18.904 Seminar in Topology.

• Dyson Brownian motion as noncolliding 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), 2026 USAMO Problem 5, and 2026 AMM Problem 1
• AoPS username: anser