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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220516T163000
DTEND;TZID=Asia/Seoul:20220516T173000
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UID:5553-1652718600-1652722200@dimag.ibs.re.kr
SUMMARY:Andreas Holmsen\, A colorful version of the Goodman-Pollack-Wenger transversal theorem
DESCRIPTION:Hadwiger’s transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in $\mathbb{R}^d$ by Goodman\, Pollack\, and Wenger. Here we establish a colorful extension of their theorem\, which proves a conjecture of Arocha\, Bracho\, and Montejano. The proof uses topological methods\, in particular the Borsuk-Ulam theorem. The same methods also allow us to generalize some colorful transversal theorems of Montejano and Karasev.
URL:https://dimag.ibs.re.kr/event/2022-05-16/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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