Tonight at 5pm in LGRT 1528, I’ll tell you about homology. Not all about it. A bit like a “Homology for anybody” talk, in the spirit of UMass math program alum Dan Briggs. Come get pizza, and learn about one of the fundamental constructions within modern mathematics. Here’s an abstract:
When studying classification problems, mathematicians need invariants. Originating in algebraic topology, homology is an invariant that involves associating sequences of Abelian groups to mathematical objects. In the last 120 years, it has become an indispensable tool in several areas of mathematics. We’ll discuss simplicial homology for a few example spaces, showing how it is computable from triangulations. We’ll also discuss how integral simplicial homology of a surface connects to the classical invariant called the Euler characteristic. We’ll then conclude by discussing what is meant by “a homology theory”.