Abstracts
for the Seminar

Fall 2016

**Speaker: **Ghodrat Aalipour, University of Colorado Denver

**Title: **A weighted version of matrix-tree theorem and its applications to simplicial complexes

**Time:** 2:30 PM, Monday, November 28, 2016

**Place:** Malott 206

**Abstract:** The well-known Kirchhoff matrix-tree theorem counts the number of spanning trees of a graph in terms of its non-zero Laplacian eigenvalues. By assigning a weight to each edge of the graph, the new weighted Laplacian matrix contributes well to find the corresponding vertex-degree generating function for the number of spanning trees of the graph. This powerful technique has been extended to simplicial and cellular complexes by Duval, Klivans and Martin. In this talk, we present a slight improvement of their generalized matrix-tree theorem. As an application, we obtain the weighted count for spanning trees in several families of simplicial and cellular complexes. This is joint work with Art Duval and Jeremy Martin.

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