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The representation theory of algebras associated to hyperplane arrangements, oriented matroids and CAT(0) cube complexes

Algebra & Discrete Mathematics

Speaker: Ben Steinberg, CUNY
Location: 1147 MSB
Start time: Mon, Apr 25 2016, 4:10PM

The face poset of cell complexes associated to real and complex hyperplane arrangements, oriented matroids and finite CAT(0) cube complexes can be endowed with a semigroup structure. The

representation theory of these semigroups, in the case of hyperplane arrangements and oriented matroids, was used by Bidigare, Hanlon and Rockmore and by Brown and Diaconis to analyze a number of
natural Markov chains. In joint work with Margolis and Saliola, we have given a fairly complete picture of the representation theory of these algebras using the topology of the underlying cell
structures.