Discrete CATS Seminar
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U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2011 - 2012

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"Configuration spaces of hard spheres"

Matt Kahle

Ohio State University

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Monday, April 23, 2012

4:00 pm

845 Patterson Office Tower

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Abstract:

Configuration spaces of n points in a region of R^d are well studied
in algebraic topology, and their topology is well understood. But
much less seems to be known when the points actually have some
thickness. These kinds of spaces also have intrinsic interest in
physics, as the phase space for a hard spheres gas.

I will report on some preliminary progress on understanding the
topology of these spaces. In joint work with Baryshnikov and Bubenik,
we develop some theoretical tools, and in joint work with Carlsson,
Gorham, and Mason, we explore these spaces computationally and see
that they can be quite complicated. We see enough structure to make
rough conjectures about what happens for large numbers of particles.