# space

Friday, October 24, 2014 - 9:00am - 9:45am

Franco Brezzi (Istituto Universitario di Studi Superiori)

The talk will review the Virtual Element spaces, recently introduced by the speaker and co-authors in order to approximate spaces of the type H(div) or H(curl) on polygonal and polyhedral decompositions. As is well known, these spaces are needed in the approximation of boundary value problems for (systems of) Partial Differential Equations in mixed form. The Virtual Element spaces are defined locally as solutions of systems of PDE's, that however don't need to be solved (not even in an approximate way).

Wednesday, September 10, 2014 - 9:00am - 9:50am

János Pach (École Polytechnique Fédérale de Lausanne (EPFL))

A set system is a k-fold covering of space if every point is contained in at least k sets. A 1-fold covering is called simply a covering. In 1980, motivated by a question of Laszlo Fejes Toth, I raised the following question. Given a plane convex set C, does there exist an integer k=k(C) such that every k-fold covering of the plane splits into 2 coverings? The same question makes sense in higher dimension. This problem has turned out to be relevant in sensor network scheduling and has generated a lot of research during the past 3 and a half decades.

Wednesday, March 5, 2014 - 11:30am - 12:20pm

Michael Farber (University of Warwick)

I will discuss several probabilistic models producing simplicial complexes, manifolds and discrete

groups. Random simplicial complexes are high dimensional analogues of random graphs and can be

used for studying the behaviour of large systems or networks depending on many random

parameters. We are interested in properties of random spaces which are satisfies with probability

tending to one. Using probabilistic models one may also test probabilistically the validity of open

groups. Random simplicial complexes are high dimensional analogues of random graphs and can be

used for studying the behaviour of large systems or networks depending on many random

parameters. We are interested in properties of random spaces which are satisfies with probability

tending to one. Using probabilistic models one may also test probabilistically the validity of open