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The fundamental group of random 2-dimensional simplicial complexes
Geometry/Topology| Speaker: | Matt Kahle, University of Washington |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 18 2006, 4:10PM |
Description
In 1959, Erdos and Renyi found a sharp threshold function for the
connectivity of the random graph. In other words, they gave a sharp
estimate for the number of edges one needs to randomly add to n isolated
points before the graph becomes connected. More recently, Nati Linial
and Roy Meshulam viewed this as a topological statement and gave a
homological analogue of the Erdos-Renyi theorem for random 2-dimensional
simplicial complexes.
In this talk, we'll prove some facts about the expected properties of
Linial-Meshulam complexes, and show in particular that the fundamental
group must have a different threshold for vanishing than the first
homology group. The main technique is a local-to-global theorem for
isoperimetric inequalities due to Gromov, and we will especially emphasize
connections to random groups and hyperbolicity. This is joint work with
Chris Hoffman.