Nikita Borisov

About me

I grew up in Brooklyn, NY, and attended Stuyvesant High School. I got my B.A. in mathematics from Cornell University in 2021. My hobbies include snowboarding, cycling, and rock climbing.

Research

I am mostly interested in algebraic combinatorics and representation theory. In particular, I like looking at how properties of various things (discrete objects, representations of the symmetric group, etc.) can be encoded algebraically. This allows us to use algebraic methods such as the theory of symmetric functions to prove surprising combinatorial identities. And in the other direction, combinatorial and algorithmic reasoning can be used to prove algebraic identities.

Currently, I am thinking about problems relating to MacDonald polynomials and LLT polynomials, particularly approaches using representation stability as defined by Farb, Church, and Ellenberg. I am also interested in various analogs of RSK correspondence, such as ones arising from 3+1-free posets.

In the works:

• Creating a package for Macaulay2 that computes A1-Brouwer degrees as part of the University of Minnesota workshop project led by Thomas Brazleton

Publications:

• On maps preserving square roots of idempotent and rank-one nilpotent matrices with H. Julius and M. Sikora in J. Algebra Appl., 2021. This was part of an REU project at Kent State with Mikhail Chebotar

Teaching and Outreach

I became a big fan of math pedagogy while tutoring at the Cornell Math Support Center.

Currently I am running the Penn Graduate Pizza Seminar with Frenly Espino.

Courses taught and/or graded:

• Fall 2023: Grader for Math 3200 Computation methods in mathematics and Math 4100 Complex Analysis
• Winter 2023: Grader for Math 533 at Drexel University
• Summer 2022: Teaching assistant for MIT Beaver Works Summer Institute (Quantum Software Group)
• Fall 2020: Grader at Cornell for Math 1105: Finite Mathematics for the Life and Social Sciences

Contact me