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# Laplacians of matroid complexes

### Graham Denham

University of Michigan

###
January 28, 1999

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
A matroid is a generalization of the (in)dependence properties shared
by a finite set of points in a vector space and sets of edges in a
graph. One can study some matroid properties by looking at several
topological spaces that are defined purely by combinatorial data. A
(combinatorial) Laplacian is a linear self-map of a chain complex
that reveals homology and some additional structure.

This talk
will introduce the ideas above and attempt to show how an explicit
description of a certain Laplacian's eigenspaces relates to
enumerative questions and applies to the theory of hyperplane
arrangements.

This talk will be accessible to graduate students.