Speaker : Udit Mavinkure (University of Western Ontario)
Date: 25 March 2025, 3:00-4:00 PM
Location: Room 113
Title: Seifert-van Kampen theorems in discrete homotopy theory
Abstract:
Discrete homotopy theory is a homotopy theory designed for studying simple graphs, detecting combinatorial, rather than topological, "holes." Central to this theory are the discrete homotopy groups which, just like their continuous counterparts, are easy to define but generally hard to compute. A discrete analogue of the Seifert-van Kampen theorem is thus a crucial tool to have in our computational toolbox. However, the version found in literature turns out to be too restrictive and is not applicable to several examples of interest. In this talk, we will state and sketch a proof of a new version that applies to a wider range of examples, and along the way, introduce some techniques with broader applicability. This talk is based on joint work with C. Kapulkin (arxiv:2303.06029).