MFRS Lecture Series

Topological methods for discrete geometry

Xavier Goaoc

Université Paris-Est Marne-la-Vallée, France

Université Paris-Est Marne-la-Vallée, France

2016/11/04 Fri 5PM-6PM (Lecture 1)

2016/11/07 Mon 4PM-5PM (Lecture 2)

2016/11/07 Mon 4PM-5PM (Lecture 2)

Helly’s theorem, a classical result in discrete geometry, asserts that if n>d convex subsets of R^d have empty intersection, some d+1 of them must already have empty intersection. I will discuss some topological generalizations of Helly’s theorem, where convexity is replaced by connectivity assumptions on the nonempty intersections, that lead to non-embeddability results of Borsuk-Ulam type and to variations on Leray’s acyclic cover theorem (or the Nerve theorem).

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