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Graduate Research Seminar in Applied Topology (GRST)

Thursday, April 22, 2021 - 3:00pm

Sanjeevi Krishnan

Ohio State University


University of Pennsylvania

via Zoom (link in abstract)

A dynamical system can often be formalized as some sort of diagram of phase spaces. The homotopy colimit of that diagram is interpretable as the state space of the system, on which simple, computable topological invariants then yield some properties of the system. Unfortunately, that homotopy colimit forgets directionality and hence important properties of the dynamical system. One way around this is to take a directed analogue of a homotopy colimit. This talk reports recent work developing the foundations for such directed homotopy colimits, which are not merely homotopy colimits in some model category of directed spaces. We will discuss some concrete applications, such as a homological algebra for monoids and state space verification, as well speculate on possible future applications in directed type theory. No familiarity with homotopy colimits or directed homotopy theory is assumed. Zoom link: