School of Mathematical Sciences
Monday, November 8, 2010
Schreiber 006, 12:15
Helly type theorems and topology
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 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 describe a result on
projections of d-Leray complexes with two applications:
1) A topological extension of Helly's theorem for unions.
2) A proof of Terai's conjecture on the Castelnuovo-Mumford regularity of
Joint work with Gil Kalai.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006