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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