Geometric Analysis and Topology Seminar

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Rainbow matchings

Speaker: Krzysztof Ciosmak, University of Toronto

Location: Warren Weaver Hall 512

Date: Friday, December 13, 2024, 11 a.m.

Synopsis:

At the 1990 ICM Alon posed the following problem: suppose that X_1,...,X_n in R^n are sets, each containing precisely k points, such that their union is in general position. Does there exist an efficient algorithm to find pairwise k disjoint simplices, each of dimension n-1, such that each simplex has exactly one vertex in X_i for every i=1,...,n? The existence of such simplices has been established by Akiyama and Alon through the Borsuk--Ulam theorem. This talk will present a recent progress on the problem.