Dr. Ryan Grady (Dept. of Mathematical Sciences, MSU)

10/11/21  4:10pm

Abstract:

The Euler characteristic is---a priori---a combinatorial quantity associated to a triangulated object, e.g., a graph or a simplicial complex. Basic properties of the Euler characteristic show that it is actually a topological invariant. In this talk, I will recall the Euler characteristic and show how it leads to an easy classification of Platonic solids. We will then jump forward a few hundred years and discuss the categorification of the Euler characteristic: homology. Finally, inspired by topological data analysis, we will tell a parallel story for Euler curves, persistence modules, and algebraic K-theory.

The latter part of the talk discusses work that is joint with Anna Schenfisch.