Descendent series for Hilbert schemes of points on surfaces

Abstract: Structure often emerges from Hilbert schemes of points on surfaces when the underlying surface is fixed but the number of points parametrized is allowed to vary. One example of such structure comes from integrals of tautological bundles, which appear in physical and geometric computations. When compiled into generating series, these integrals display interesting functional properties.

I will focus on the example of K-theoretic descendent series, certain series formed from holomorphic Euler characteristics of tautological bundles. Namely, I will explain how to use a Macdonald polynomial symmetry of Mellit to deduce that the K-theoretic descendent series are expansions of rational functions.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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