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Geometry-Topology Seminar

Tuesday, February 27, 2018 - 4:30pm

Robin Pemantle



University of Pennsylvania

DRL 4N30

This is a continuation of our experimental Geometry-Topology "Show and Tell" Seminar, in which faculty report on projects of current interest to them.

A fundamental problem in combinatorics is to extract the power series coefficients of a generating function, or to estimate them asymptotically.  For d-variable generating functions, the Cauchy integral formula gives the coefficient as an integral of a d-form over a small d-torus.  Successful estimation of this integral depends crucially on representing this d-cycle in a homology basis forced upon us by Morse theory.  The talk concerns progress and problems in effective computation in the relevant homology group.