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Tim Hosgood (Oct 21 2021 at 16:52):(sorry, forgot to post this one here — but it's starting in 10 minutes!)
Tim Hosgood (Oct 21 2021 at 16:52):Abstract:
Discrete homotopy theory, developed by H. Barcelo and collaborators, is a homotopy theory of (simple) graphs. Homotopy invariants of graphs have found numerous applications, for instance, in the theory of matroids, hyperplane arrangements, and time series analysis. Discrete homotopy theory is also a special instance of a homotopy theory of simplicial complexes, developed by R. Atkin, to study social and technological networks.
In the talk, I will introduce the main concepts and open problems of discrete homotopy theory. I will also report on the joint work with D. Carranza on developing a new foundation for discrete homotopy theory in the category of cubical sets, which offers solutions to a number of long standing open problems in the field.
Tim Hosgood (Oct 21 2021 at 16:52):https://www.youtube.com/watch?v=x6d391cUNT0