Title	On a topological version of Pach's overlap theorem
Creator	Bukh, Boris
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-02-05T10:34
Description	Pach showed that every d+1 sets of points Q_1,..,Q_{d+1} in R^d contain linearly-sized subsets P_i in Q_i such that all the transversal simplices that they span intersect. We show, by means of an example, that a topological extension of Pach's theorem does not hold with subsets of size C(log n)^{1/(d-1)}. We show that this is tight in dimension 2, for all surfaces other than S^2. Surprisingly, the optimal bound for S^2 is (log n)^{1/2}. This improves upon results of Barany, Meshulam, Nevo, Tancer. Joint work with Alfredo Hubard.
Extent	33 minutes
Subject	Mathematics; Convex and discrete geometry; Combinatorics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Carnegie Mellon University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-08-05
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0369710
URI	http://hdl.handle.net/2429/66666
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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