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Intersections of finite sets: geometry and topology

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 09, 2017 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Florian Frick (Cornell University)
Tags/Keywords
  • Kneser hypergraph

  • chromatic number

  • geometric transversality

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

4-Frick

Abstract

Given a collection of finite sets, Kneser-type problems aim to partition the collection into parts with well-understood intersection pattern, such as in each part any two sets intersect. Since Lovász' solution of Kneser's conjecture, concerning intersections of all k-subsets of an n-set, topological methods have been a central tool in understanding intersection patterns of finite sets. We will develop a method that in addition to using topological machinery takes the topology of the collection of finite sets into account via a translation to a problem in Euclidean geometry. This leads to simple proofs of old and new results.

Supplements
29702?type=thumb Frick Notes 255 KB application/pdf Download
Video/Audio Files

4-Frick

H.264 Video 4-Frick.mp4 164 MB video/mp4 rtsp://videos.msri.org/data/000/029/569/original/4-Frick.mp4 Download
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