## Entropy, Algebraic Integers and Moduli of Surfaces

Curtis McMullen

Harvard University

December 7, 2010

Curtis McMullen

Harvard University

December 7, 2010

Assaf Naor

Institute for Advanced Study

December 6, 2010

The classical Dvoretzky theorem asserts that for every integer k>1 and every target distortion D>1 there exists an integer n=n(k,D) such that any

Tom Haines

University of Maryland; von Neumann Fellow, School of Mathematics

December 6, 2010

Institute for Advanced Study

December 3, 2010

David Huse

Princeton University; Member, School of Mathematics

December 3, 2010

**ANALYSIS/MATHEMATICAL PHYSICS SEMINAR**

Jonathan Williams

University of California, Berkeley

December 3, 2010

There is a way to specify any smooth, closed oriented four-manifold using a surface decorated with simple closed curves, something I call a surface diagram. In this talk I will describe three moves on these objects, two of which are reminiscent of Heegaard diagrams for three-manifolds. These may form part of a uniqueness theorem for such diagrams that is likely to be useful for understanding Floer theories for non-symplectic four-manifolds.

Ruochuan Liu

Institute for Advanced Study

December 2, 2010

December 1, 2010

Eric Babson

University of California at Davis

December 1, 2010

Paul Beame

University of Washington; Member, School of Mathematics

November 30, 2010