Given a probability measure on $R^d$, what is the probability that the

simplex spanned by $d+1$ randomly selected points contains the origin

in its interior? To study this question and its relatives, we

introduce the following definition. The overlap number of a finite

$(d+1)$-uniform hypergraph $H$ is the largest constant $c(H)\in (0,1]$

such that no matter how we map the vertices of $H$ into $R^d$, there

is a point covered by at least a $c(H)$-fraction of the simplices

induced by the images of its hyperedges. We survey some old and new

results related to this concept. Joint work with J. Fox, M. Gromov, V.

Lafforgue, and A. Naor.

[Invited by Prof. Ruth Kellerhals]

When? | 08.03.2011 17:15 |
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Where? | PER 08 Phys 2.52 Chemin du Musée 3 1700 Fribourg |

Contact | Department of Mathematics isabella.schmutz@unifr.ch |