PhD Public Lecture (Math) - Udit Mavinkurve

"The Fundamental Groupoid in Discrete Homotopy Theory"

A commonly used method in combinatorics involves constructing a simplicial complex using the data of a combinatorial object (such as a matroid or a graph) and studying its homotopy invariants. Discrete homotopy theory aims to develop the machinery to study some of these invariants in the native combinatorial setting. In this talk, we introduce the discrete fundamental groupoid of a graph and develop basic techniques (universal covers, van Kampen theorem) that will allow us to compute some nontrivial examples.