We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Stable commutator length in free groups

Presented by Danny Calegari, Cambridge University

5 December 2011 16:00 in CM221

Stable commutator length (scl) answers the question: 'what is the simplest surface in a given space with prescribed boundary?' where 'simplest' is interpreted in topological terms. This topological definition is complemented by several equivalent definitions - in group theory, as a measure of non-commutativity of a group; and in linear programming, as the solution of a certain linear optimization problem. On the topological side, scl is concerned with questions such as computing the genus of a knot, or finding the simplest 4-manifold that bounds a given 3-manifold. In free groups, stable commutator length turns out to be a rich and mysterious invariant, with connections to dynamics, hyperbolic surfaces, and the geometry of integral polyhedra. We will discuss some of the phenomena that arise, and the connections to various areas of mathematics.

Contact for more information