I am a fifth-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
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.
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 representation stability over the symmetric group (Church, Ellenburg, Farb) and 0-Hecke algebras (Laudone) and applications to the combinatorics of MacDonald polynomials and LLT polynomials.
Here is my minor thesis, "On Quiver Representations and Dynkin Diagrams", as part of the requirements for passing my qualifying exam.
Some other fun stuff:
In the works: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: