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Graduate Seminar

Adam Gutter
Carnegie Mellon University
Title: The Classification of Irreducible Root Systems

Abstract: In mathematics, it is not uncommon for difficult and highly abstract problems to be unexpectedly reduced to comparatively elementary and concrete problems. One such problem is the classification of complex simple Lie algebras. This classification problem ends being equivalent to the classification of irreducible root systems (a root system can be viewed as simply a finite subset of $\mathbb{R}^n$ satisfying a short list of unusual properties). Moreover, it turns out that the classification of irreducible root systems reduces one step further to the classification of a very special kind of directed graph, requiring no more than elementary linear algebra.

In this talk, I will define and develop the theory of root systems, following which I will state and (time permitting) prove the classification theorem for the "very special" graphs associated to root systems. Only knowledge of elementary linear algebra and graph theory will be assumed.

Date: Thursday, December 5, 2013
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell