## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Surface subgroups from linear programming

**Speaker:** Danny Calegari

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**: **Please not the unusual time and place.**

**Abstract:**

A famous question of Gromov asks whether every (one-ended) 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 resolution of the virtual Haken conjecture. 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 an HNN extension of a free group associated to a ''random'' endomorphism contains
a surface subgroup with probability one. This is joint work with Alden Walker.

**Date:** Friday, February 08, 2013

**Time:** 1:00pm

**Where:** 102

**Contact Person:** Michael Couch

**Contact email:** mcouch@math.northwestern.edu

**Contact Phone:**

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