Intersections of Finite Sets: Geometry and Topology

Series: 
Combinatorics Seminar
Friday, April 27, 2018 - 3:00pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Cornell University
Organizer: 
Given a collection of finite sets, Kneser-type problems aim to partition this 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.