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

Expository notes and other writing

• Notes from a lecture series on quantized symplectic singularities and applications to Lie theory by Ivan Losev - pdf
• 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

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