**UM Math Graduate Student Seminar**

James McKeown

* University of Miami *

**will present**

**An Introduction to Hyperplane Arrangements**

Friday, November 4, 2016, 5:00pm

Ungar Building Room 402

**Abstract: **

A hyperplane is an n-1 dimensional subspace of an n dimensional vector space. When the vector space is R^n, the complement of the hyperplanes is a collection of polyhedral regions. It is natural to ask how many of these polyhedral regions there are, and how many of them are bounded. This turns out to be a purely combinatorial problem and has a nice answer in terms of the Characteristic Polynomial of the arrangement. We will define this polynomial, and see that it generalizes the classical chromatic polynomial of a graph. Time permitting, we will introduce "the finite field method" as a computational tool for finding characteristic polynomials of arrangements.

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