An Introduction to the Classification of Finite Simple Groups (4/8/24)
Hi everyone, long time no see! This video comes from a talk I gave at the Johns Hopkins undergraduate math club Ex Numera. The gory details of some of the lemmas/theorems I did not prove, (as well as the relevant background theory), can be found in Isaacs' Character Theory of Finite Groups. Also, see this wonderful blog post by Terry Tao: https://terrytao.wordpress.com/tag/br....
Abstract: With a proof spanning thousands of pages across hundreds of journal articles, the classification of finite simple groups is a monumental achievement of 20th-century mathematics. In my talk, we will explore how finite simple groups act as the building blocks for all finite groups, and discuss the general strategy of classifying such simple groups. We will introduce Feit and Thompson’s odd-order solvability theorem, and show how this theorem, along with the Brauer-Fowler theorem, provides a possible attack strategy on the classification theorem.