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DESCRIPTION: This is joint work with Bob MacPherson. We study the configura
tion space config(n\,w) of n non-overlapping disks of unit diameter in an i
nfinite strip of width w. Our main result establishes the rate of growth of
the Betti numbers for fixed j and w as n → ∞. We identify three regions in
the (j\,w) plane exhibiting qualitatively different topological behavior.
We describe these regions as (1) a “gas” regime where homology is stable\,
(2) a “liquid” regime where homology is unstable\, and (3) a “solid” regime
where homology is trivial. We describe the boundaries between stable\, uns
table\, and trivial homology for every n ≥ 3.
DTSTAMP:20190417T155700
DTSTART:20190520T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Matthew Kahle (Ohio State University): Configuration spaces of hard
disks in an infinite strip
UID:95690836@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190520-L-Kahle.html
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