I am broadly interested in geometric representation theory. Recently, I have been working on the commuting schemes
of Lie algebras and other related objects. This has led me to the realm of non-commutative geometry, more specifically, to
the representation theory of rational Cherednik algebras. In the past, I have also thought about deformation quantizations
and applications to representation theory in positive characteristic.

Publications

Almost commuting scheme of symplectic matrices and quantum Hamiltonian reduction - P. Goyal
(preprint) arxiv

Invariant theory of general linear groups modulo Frobenius powers - P. Goyal
Communications in Algebra, Volume 46 - 2018, Issue 10, pp 4511-4529 doiarxiv

Projective normality of GIT quotient varieties modulo finite groups - P. Goyal, S. K. Pattanayak
Communications in Algebra, Volume 45 - 2017, Issue 7, pp 2996-3004 doipdf

Seminars

I co-organized the student representation theory seminar at UChicago in Fall 2019, Winter 2020 and Fall 2020.

Expository notes

Topic proposal on Kac's conjecture on absolutely indecomposable representations of quivers - pdf

A computation of Catalan numbers using the Weyl integration formula - pdf

Notes from a talk I gave on the Chevalley restriction theorem and its generalizations - pdf

Notes from a talk I gave on the mathematics of shoe-lacing - pdf