Serena An

Research Experience

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
[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!