Tel Aviv University
Hello everyone,
The next colloquium talk will be held on:
Monday, 21/01/2013, 12:15, Schreiber 006, Tel Aviv University.
Speaker: Danny Calegari (University of Chicago)
Title: Surfaces From Linear Programming.
This talk is part of the Blumenthal Lectures in geometry 2013.
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloquia, see
A famous question of Gromov asks whether every hyperbolic
group contains a subgroup which is isomorphic to the fundamental group of
a closed surface. Surface subgroups play a very important role in many
areas of low-dimensional topology, for example in Agol's recent proof that
every hyperbolic 3-manifold has a finite cover which fibers over the circle.
I would like to describe several ways to build surface subgroups in certain
hyperbolic groups. The role of hyperbolicity is twofold here: first,
hyperbolic  geometry allows one to certify injectivity by *local* data;
second, hyperbolic dynamics allows one to use ergodic theory to
produce the pieces out of which an injective surface can be built. I would
like to sketch a proof  of the fact that the extension of a free group
associated to a ''random'' endomorphism contains a surface subgroup with
probability one. This is  joint work with Alden Walker.
Technion Math Net-2 (TECHMATH2)
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