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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.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20210118-C-Bla
 gojevic.html
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