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Seminar

Cubical Sets: Discrete homotopy theory and cubical sets May 22, 2020 (02:00 PM PDT - 03:00 PM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Bob Lutz (University of Michigan)
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Video

Discrete Homotopy Theory And Cubical Sets

Abstract/Media

Zoom Link:

https://msri.zoom.us/s/93059090699

In this talk, we will introduce the main ideas of discrete homotopy theory (or A-theory), introduced by Barcelo et al. This theory assigns a bigraded sequence of groups to any simplicial complex by replacing continuous maps on spheres with graph homomorphisms on cubical grids. Originally studied as a qualitative measure of complex systems and their dynamics, discrete homotopy theory has grown into a topic of independent interest, with applications to hyperplane arrangements and group theory. We discuss these applications and describe a way to compute discrete homotopy groups of graphs in terms of topological data on certain cubical sets.

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Discrete Homotopy Theory And Cubical Sets

H.264 Video 25049_28438_8361_Discrete_Homotopy_Theory_and_Cubical_Sets.mp4