Speaker: Roy Meshulam (Technion)

Title: A Topological Colorful Helly Theorem

Abstract: 
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Let F_1,...,F_{d+1} be d+1 families of
convex sets in R^d.
The following colorful extension of the
classical Helly Theorem was proved by Lovasz:
If for every choice of A_1 \in F_1 ,..., A_{d+1} \in F_{d+1}
the intersection of the A_i's in non empty,
then one of the families F_i is intersecting.
Lovasz result and its Caratheodory type dual (due to Barany)
have several important applications in combinatorial geometry.
We'll describe a topological extension of the colorful Helly theorem.
Along the way we'll discuss Leray complexes - these are
topological abstractions of nerves of families
of convex sets and share many of their combinatorial
properties.

(Joint work with Gil Kalai)