Discrete Math Seminar: James Wilson

  • Date: 03/10/2015
  • Time: 16:00
Lecturer(s):
James Wilson, Colorado State University
Location: 

University of British Columbia

Topic: 

Nilpotence, Simplicity, and Exotic Geometries

Description: 

In a quantifiable way most groups, rings, and Lie algebras are nilpotent. In fact even the extension of two abelian groups, or two trivial algebras, has enough variation to match the total quantity of all finite groups, resp. finite-dimensional algebras. However, our most developed theories concern groups, rings, and algebras that are simple, semisimple, or highly related to simplicity.

 

In this talk I will demonstrate a simple way to convert questions about nilpotence into questions about simple and semisimple groups and nonassociative rings. The process is recursive and captures new structure in a positive proportion of all products. In fact 4/5 of the 11 million groups of size at most 1000 are explained by this mechanism. I will close with a a surprising characterization of the base case of these recursive techniques: they are products without zero-divisors and thus have storied histories in discrete and differential geometry.

Other Information: 

Location: ESB 4127