Pallav Goyal

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

• Commuting schemes of Lie algebrs
• Rational Cherednik algebras
• Deformation theory
• Reprsentation theory over positive characteristic
• Hall algebras
• Quantum groups

Publications

• Hall algebra of restricted representations and Shifted quantum loop algebras - P.Goyal, P. Samuelson
  (in preparation)
Talk
• Chevalley restriction theorem in Type C and Cherednik algebras over algebraic curves - P.Goyal
  (in preparation)
  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

• AMS Fall Western Sectional Meeting (August 2025), University of Denver
• 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