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Combinatorics Seminar

Matrix-tree theorems, higher determinants, and the Tutte-Bernardi polynomial
Friday, November 18, 2022
3:00-4:00 PM
4088 East Hall Map
The Matrix-Tree Theorem is a mid-19th century result by G. Kirchhoff, representing the minors of the Laplace matrix as sums of positive monomials of matrix elements indexed by directed rooted forests. We will present higher-degree generalizations of both notions appearing above: a minor and a forest. The theorem involves an analog, due to O. Bernardi, of the classical Tutte polynomial for directed graphs. Applications include a formula, due to B. Epstein and M. Polyak, for the Casson-Walker invariant of a rational homology 3-sphere. Speaker(s): Yurii Burman (Higher School of Economics, Moscow)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics