Title: Hochschild homology and related generalities
Abstract: In this talk we will convey some ideas regarding trace methods in modern algebraic topology and why people care. We will cater this talk to someone who might not have seen much topology before. To that end, we will begin with a discussion on ordinary homology and cover an application which naturally leads into Hochschild homology. Next, we introduce some machinery and discuss why they might be natural to consider and give a conceptual picture of Hochschild homology. We will try to work in a setting that is as concrete as possible and do some examples that highlight an important property. Time permitting, we will quickly sketch how this should generalize to connect with various higher algebras and geometries. No knowledge of homology is necessary for this talk, although a familiarity with tensor products will be helpful.
