Configuration spaces and Morse theory

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The configuration space of n points in the plane is well studied and
well loved in topology; for example, it's an Eilenberg-MacLane space.
There's been some interest in recent years in the topology of what one
might call "exotic configuration spaces". These might describe the
space of possible states for a robotic arm, for example, or the phase
space for a hard-spheres gas, where the particles have thickness and
the ambient region has boundary. So the topology of such spaces is of
interest in engineering applications, and also in physics.

Understanding the topology of these spaces seems hard, but people have
applied a few different kinds of Morse theory so far:
––computational Morse Theory and the nudged elastic band method
––min-type Morse theory, e.g. from distance functions on manifolds
––discrete Morse theory on regular CW complexes
––the PL Morse Theory of Bestvina & Brady

We will read and discuss several papers to get a sense of the
Morse-theory landscape. We can also discuss other techniques for
understanding the topology of these spaces. Not much is known, so
there are many attractive open questions. Anyone with an interest in
topology or computational topology is welcome.

Schedule:
August 28: Introduction (Matthew Kahle)
September 4: Labor Day, no meeting
September 11: "Finding topology in a factory: configuration spaces" (Érika Roldán Roa)
September 18: Introduction to Morse theory (Matthew Kahle)
September 25: "Configuration spaces of thick particles on a metric graph" (Jessica Zehel)
October 2: "Min-type Morse theory for configuration spaces of hard spheres" (Katie Ritchey)
October 9: "Computational topology for configuration spaces of hard spheres" (Jimin Kim)
October 16: "The twelve spheres problem" (Hannah Alpert)
October 23: TBD