Math Union Colloquium

Finite (algebraic) topology is a branch of topology that deals with finite spaces. Due to a correspondence between finite $T_0$ spaces and finite posets, finite spaces are naturally combinatorial objects, allowing for concrete models of concepts in (algebraic) topology besides having interesting theory of their own.

The first half of the talk will cover some foundational results, tools, and applications of finite topology. In the second half I’ll build up to a method, inspired by Morse theory, for using computer algebra to approximate the homotopy groups of spheres.