I am interested in algebraic combinatorics, and particularly combinatorial problems that arise from and have connections with problems in representation theory. Here's a growing list of math phrases that would get my attention if overheard at a party — Coxeter groups, reflection groups, Hecke algebras, representation theory of semisimple Lie algebras, BGG category O, crystal bases, symmetric functions, representation theory of finite groups, Young tableaux, (superspace) coinvariant ring, orbit harmonics, link homology.
Superspace coinvariants and wreath products (with Brendon Rhoades, preprint)
The superspace coinvariant ring of type B (accepted to appear in Algebraic Combinatorics)
The lattice of nil-Hecke algebras over real and complex reflection groups (with Apoorva Khare, preprint, in revision)
An interesting spin-off (with Prithwijit De), The Mathematical Gazette, Cambridge University Press
Coinvariants in Superspace, Algebra Seminar, University of Virginia
Coinvariants in Superspace, Advancement to Candidacy, University of California San Diego
The type B Superspace Coinvariant Ring, GSCC 2025, University of Southern California
Hilbert Series of the type B Superspace Coinvariant Ring, UCSD Combinatorics Seminar, University of California San Diego
Is the Set of All Binary Trees Equal to a Complex Number? Food for Thought, University of California San Diego
The lattice of nil-Hecke algebras over reflection groups, IISc Algebra and Combinatorics Seminar, Indian Institute of Science
Two Solutions to a Tiling Problem, Food for Thought, University of California San Diego
Here's a list of all the classes that I have TA'd for at UC San Diego, and some of the worksheets that I wrote for them. If you are looking for materials related to Olympiad training, you'll find them on a different page.
Linear Algebra (MATH 18) at UCSD: Fall 2022, Winter 2023, Winter 2025
Precalculus (MATH 3C) at UCSD: Spring 2023
Calculus I (MATH 10A) at UCSD: Fall 2023
Calculus II (MATH 10B) at UCSD: Winter 2024
Calculus and Analytic Geometry for Science and Engineering (MATH 20C) at UCSD: Spring 2024
Vector Calculus (MATH 20E) at UCSD: Spring 2024
Mathematical Reasoning (MATH 109) at UCSD: Fall 2024, Spring 2026
Enumerative Combinatorics (MATH 184) at UCSD: Spring 2025, Winter 2026
Differential Equations and Dynamical Systems (MATH 130) at UCSD: Winter 2026
Modern Algebra I (MATH 103A) at UCSD: Fall 2026
Outside of this, I've worked as
Faculty at BEAM Summer Away (New York): Summer 2026
Tutor Training TA (planning and running a training program for tutors in the Math department) at UCSD: Fall 2024 to Spring 2025
Resource Person at the International Mathematical Olympiad Training Camp (Homi Bhabha Centre for Science Education, TIFR, India): 2018 to 2024
Mentor in Math Summer Program for High School Students at UCSD: Summer 2023
Trainer with the International Olympiad Foundation (Dubai): Summer 2023
Grader and Office Hours Staff at Art of Problem Solving: Nov 2019 to Aug 2022
Trainer at the Monsoon Math Camp: Summer 2021
Trainer at the CAMP for Advanced Mathematical Preparation: Summer 2021
Trainer at the Indian National Mathematical Olympiad Training Camp at ISI Bangalore: Summer 2019 and 2020