Nikita Borisov

A beautiful image

I am a second-year PhD student at the University of Pennsylvania. My interests lie in algebraic combinatorics and related algorithms. My advisor is Jim Haglund

My undergraduate advisor at Cornell University was Martin Kassabov

Email: nborisov@sas.upenn.edu

Pronouns: He/him/his

Office: DRL 3C9

CV

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 extensions of representation stability for 0-Hecke algebras and various analogs of RSK correspondence, such as ones arising from 3+1-free posets.

Here is my thesis, "On Quiver Representations and Dynkin Diagrams", as part of the requirements for passing my qualifying exam.

In the works: Publications: Recent and Upcoming Conferences:

Teaching and Outreach

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

During 2023-2024 I co-organized Penn Graduate Pizza Seminar with Frenly Espino.

Courses taught and/ or graded:
  • Spring 2024: TA for Math 3610 Advanced Calculus
  • 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