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DESCRIPTION: Ten years ago\, in February 2011\, I joined the group of Günte
r M. Ziegler at Freie Universität Berlin. Now\, ten years later\, I will sh
ow you some of the problems in Geometric and Topological Combinatorics that
intrigued us\, some of which we managed to solve\, and sketch some of the
crucial ideas\, methods\, and the tools we had to develop in order to answe
r them. We will see how -- work on the Bárány-Larman conjecture on c
olored point sets in the plane gave birth to the Optimal colored Tverberg
theorem\, -- the constraint method collected all classical Tverberg typ
e results under one roof and opened a door towards counter-examples to t
he topological Tverberg conjecture. Furthermore\, we will illustrate how
the search for convex partitions of a polygon into pieces of equal area an
d equal perimeter forced us to -- study the topology of the classical co
nfiguration spaces\, -- construct equivariant cellular models for them\,
-- prove a new version of an equivariant Goresky-MacPherson formula for
complements of arrangements\, -- revisit a classical vanishing theorem
of Frederick Cohen\, and explain why these answers are related to the exist
ence of highly regular embeddings and periodic billiard trajectories. Fi
nally\, we will talk about -- equi-partitions of convex bodies by affine
hyperplanes\, and -- greedy convex partitions of many measures. These
results are joint work with\, in chronological order\, Günter M. Ziegler\,
Benjamin Matschke\, Florian Frick\, Albert Haase\, Nevena Palić\, Günter R
ote\, and Johanna K. Steinmeyer.
DTSTAMP:20210105T151600
DTSTART:20210118T160000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Pavle Blagojević (Freie Universität Berlin): Ten years in one lectu
re
UID:107739226@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210118-C-Blagojevic.html
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