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Number Theory Lunch Seminar
Number Theory Lunch Seminar
Counting bundles with extra structures over curves II
Counting bundles with extra structures over curves II
Organizers
Speaker
Time
Thursday, May 14, 2026 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
In this talk I will discuss a counting problem for vector bundles over a smooth projective curve defined over a finite field. We consider bundles equipped with parabolic structures at finitely many points and a nilpotent endomorphism, and study the corresponding generating functions.
A theorem of Anton Mellit shows that this counting problem admits a striking factorization: each marked point contributes independently, and the contribution is given by a modified Macdonald polynomial. As a consequence, these polynomials admit a geometric interpretation as weighted point counts on affine Springer fibers associated to constant nilpotent matrices.
If time permits, I will briefly explain how this perspective leads to a proof of the conjectural formula of Hausel--Letellier--Rodriguez-Villegas for the Poincaré polynomials of character varieties of punctured Riemann surfaces.
A theorem of Anton Mellit shows that this counting problem admits a striking factorization: each marked point contributes independently, and the contribution is given by a modified Macdonald polynomial. As a consequence, these polynomials admit a geometric interpretation as weighted point counts on affine Springer fibers associated to constant nilpotent matrices.
If time permits, I will briefly explain how this perspective leads to a proof of the conjectural formula of Hausel--Letellier--Rodriguez-Villegas for the Poincaré polynomials of character varieties of punctured Riemann surfaces.
Speaker Intro
Tao Su obtained his Ph.D. degree from UC Berkeley in 2018. He joined BIMSA in 2024. His current research interests include interactions between algebraic analysis, algebraic geometry and symplectic geometry.