Pallav Goyal

I am broadly interested in geometric representation theory and combinatorics. Some specific interests include:

Quantum groups
Hall algebras
Non-commutative geometry
Representation theory over positive characteristic
Rational Cherednik algebras
Commuting schemes of Lie algebras

Professional links

     MathSciNet  arXiv  Google Scholar

Publications

Cherednik algebras over curves with a Z/2-action - P. Goyal
(in preparation)
talk
Representation theory of mirabolic quantum sl_n - P. Goyal, D. Rosso
(Pre-print)
arXiv poster
Hall algebras and shifted quantum affine algebras - P. Goyal, P. Samuelson
(Pre-print)
arXiv talk
Almost commuting scheme of symplectic matrices and quantum Hamiltonian reduction - P. Goyal
Algebras and Representation Theory, Volume 27 - 2024, pp 1645-1669
doi arXiv
Invariant theory of general linear groups modulo Frobenius powers - P. Goyal
Communications in Algebra, Volume 46 - 2018, Issue 10, pp 4511-4529
doi arXiv
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
doi pdf

Seminars and conferences organized

Special session on Noncommutative Algebras in Representation Theory and Topology at the AMS Fall Western Sectional meeting (October 2024) at University of California, Riverside - with Peter Samuelson and Boris Tsvelikhovskiy
Student representation theory seminar (Fall 2019, Winter 2020, Fall 2020) at UChicago - with Ignacio Darago

Conferences and meetings attended

Geometric and Category-Theoretic approaches to Conformal Field Theory (January 2026), Chennai Mathematical Institute
New perspectives in quantum representation theory (November 2025), International Center for Mathematical Sciences
AMS Fall Western Sectional Meeting (August 2025), University of Denver
7th Canada-Mexico-US Meeting on Representation Theory, Noncommutative Algebra, and Categorification (July 2025), University of Southern California
Gone Fishing 2025 (March 2025), Washington University in St. Louis
Representation Theory Days (November 2024), MIT
AMS Fall Western Sectional Meeting (October 2024), University of California, Riverside
Quantum Groups and Representation Theory (October 2024), North Carolina State University
Representation Theory and Related Geometry: Progress and Prospects (May 2024), University of Georgia, Athens
AMS Spring Central Sectional Meeting (April 2024), University of Wisconsin, Milwaukee
Gone Fishing 2024 (April 2024), Northwestern University
89th Annual Conference of The Indian Mathematical Society (December 2023), BITS Pilani, Hyderabad campus
Quantized symplectic singularities and applications to Lie theory (June 2022), MIT
On the crossroads of algebra, geometry and physics (May 2022), Yale University
Lie Theory and Poisson Geometry (January 2022), CIRM
Compactifications, configurations, and cohomology (October 2021), Northeastern University
Summer School in Algebraic Combinatorics (June 2021) (via Zoom)
DG Methods in Commutative Algebra and Representation Theory (May 2020) (via Zoom)
Midwestern Algebraic Geometry Graduate Conference (May 2020) (via Zoom)
Quantum Structures in Algebra and Geometry (August 2019), Northeastern University
Graduate Summer School on the Geometry and Modular Representation Theory of Algebraic Groups (August 2019), Stony Brook University
Arithmetic and Algebraic Geometry (August 2019), University of Michigan, Ann Arbor

Expository notes and other writing

Notes from a talk I gave on the role of Hamiltonian reduction in mechanics - pdf
PhD thesis - Almost commuting scheme of symplectic matrices and quantum Hamiltonian reduction - pdf
Notes from a talk I gave on the mathematics of shoelacing - pdf
Notes from a talk I gave on the Chevalley restriction theorem and its generalizations - pdf
A computation of Catalan numbers using the Weyl integration formula - pdf
Topic proposal - Kac's conjecture on absolutely indecomposable representations of quivers - pdf