Tutte polynomials of graphs and symplectic duality

Abstract: The Tutte polynomial of a graph is a two-variable polynomial, which is the universal polynomial satisfying the deletion contraction recursion. In this talk I will explain how this polynomial arises as a special case of a bicharacteristic polynomial defined for pairs of symplectic dual conical resolutions of singularities. More precisely, the Tutte polynomial records the dimensions of the graded pieces of the cohomology of hypertoric varieties (which I’ll introduce) along with the two filtrations by cohomological degree, coming from symplectic duality and Maulik-Okounkov stable envelopes (which I will also introduce). As well as recovering Tutte polynomials, there are other bicharacteristic polynomials of symplectic resolutions to explore, which I will describe if there is time. These results produce new inequalities of coefficients of Tutte polynomials of matroids. This talk is based on joint work with Michael McBreen.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

Geometry, Algebra and Physics at KIAS