## Nonlinear Dvoretzky Theory

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

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

Scott Aaronson

Massachusetts Institute of Technology

November 29, 2010

In recent joint work with Alex Arkhipov, we proposed a quantum optics experiment, which would sample from a probability distribution that we believe cannot be sampled (even approximately) by any efficient classical algorithm, unless the polynomial hierarchy collapses. Several optics groups are already working toward doing our experiment.