Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 21, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Michael Farber (University of Warwick)

Geometry and topology of random 2-dimensional complexes

In the talk I will discuss geometric and topological properties of random 2‐complexes. One of the central questions is whether one can generate randomly aspherical 2‐complexes (i.e. such that π₂(Y)=0) and whether random aspherical 2‐complexes satisfy the Whitehead Conjecture. This conjecture was proposed in 1941 by J.H.C. Whitehead; it states that any subcomplex of an aspherical 2‐complex is also aspherical.

A result presented in the talk states that (under certain assumptions) any aspherical subcomplex Y' \subset Y of a random 2‐complex Y satisfies the Whitehead conjecture, with probability tending to 1. The other results describe torsion in the fundamental groups of random 2‐complexes.

The proofs use Cheeger constants and systoles of simplicial surfaces as well as properties of Gromov hyperbolic groups.

The talk is based on a joint work with Armindo Costa.

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