[Facets-of-complexity] Invitation to Monday Lecture & Colloquium - May 20th 2019

["Ita Brunke" <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our next Monday Lecture & Colloquium on May
20th at 14:15 h & 16:00 h at TU Berlin.

Location:
Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Time: Monday, May 20th - 14:15 h

Lecture: Matthew Kahle (Ohio State University)

Title: Configuration spaces of hard disks in an infinite strip
Abstract:
This is joint work with Bob MacPherson. We study the configuration space
config(n,w) of n non-overlapping disks of unit diameter in an infinite
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,
unstable, and trivial homology for every n ≥ 3.

Coffee & Tea Break :

Room MA 316 - Third Floor [British Reading]

Time: Monday, May 20th - 16:00 h s.t.

Colloquium: Davide Lofano (Technische Universität Berlin)

Title: Collapsible vs Contractible
Abstract:
Probably the most studied invariant in Topological Data Analysis is the
homology of a space. The usual approach is to triangulate the space and
try to reduce it in order to make the computations more feasible. A common
reduction technique is that of collapsing. In a collapsing process we
perform a sequence of elementary collapses, where at each step we delete a
free face and the unique facet containing it. If we are able to reduce a
complex to one of its vertices then we say it is collapsible and its
homology is trivial. Collapsibility implies that the space is contractible
but the converse is not always true, probably the best known example is
the Dunce Hat.
We are going to explore the difference between these two concepts and look
for minimal examples of contractible non collapsible complexes in each
dimension and how often they arise.