Intersections of finite sets: geometry and topology
Geometric and topological combinatorics: Modern techniques and methods October 09, 2017  October 13, 2017
Kneser hypergraph
chromatic number
geometric transversality
06XX  Order, lattices, ordered algebraic structures [See also 18B35]
49J50  Fréchet and Gateaux differentiability in optimization [See also 46G05, 58C20]
4Frick
Given a collection of finite sets, Knesertype problems aim to partition the collection into parts with wellunderstood intersection pattern, such as in each part any two sets intersect. Since Lovász' solution of Kneser's conjecture, concerning intersections of all ksubsets of an nset, 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.
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