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Helly type theorems and topology | Prof. Roy Meshulam (Department of Mathematics Technion, Haifa, Israel)

Kurzbeschreibung:
Startdatum: 16.05.2017 - 16:00
Enddatum: 16.05.2017 - 17:30
Adresse: MZH 6210
Organisator/Ansprechpartner: Prof. Thorsten Dickhaus, Prof. Christine Knipping, (0421) 218-63651, (0421) 218-63721
Preis: 0€

Helly's theorem asserts that if a finite family of convex sets in d-space has an empty intersection, then there exists a subfamily of cardinality at most d+1 with an empty intersection.
Helly's theorem and its numerous extensions play a central role in discrete and computational geometry. It is of
considerable interest to understand the role of convexity in these results, and to find suitable topological extensions. The class of d-Leray complexes (introduced by Wegner in 1975) is a natural framework for formulating topological Helly type theorems. We will survey some old and new results on Leray complexes with geometrical and algebraic applications.
In particular, we'll discuss topological versions of the colorful Helly Theorem and of the Amenta-Morris theorem on Helly numbers of unions of convex sets, as well as some commutative algebra aspects of Leray complexes.

Einladung von Prof. Dmitry Feichtner-Kozlov (ALTA)