Back to Departmental Colloquium: Spring 2012
Departmental Colloquium
Date: Thursday, Feb 23, 2012
Time: 4:15PM
Location: JWB 335
Kay Magaard
University of Birmingham, England
Title |
Generating Systems for Finite Groups with a View towards Geometry |
Abstract |
When, back in 1832, Galois proved that it is impossible to solve the general quintic by radicals he invented group theory and modern algebra. Crucial to Galois proof was the knowledge that a certain pair of permutations of degree 5 forms a generating set for S_5, the symmetric group of degree 5. For this he needed to discover the maximal subgroups of S_5, and was thus lead to two fundamental problems of group theory. I will show how the classification of the finite simple groups provides new insight into both the maximal subgroup problem and the generation problem for finite groups and how this serves as a catalyst for ongoing developments in the theory of algebraic curves and surfaces. |
Number Theory
Geometric Group Theory
Geometry and Topology