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
School of Mathematics
ANALYSIS/MATHEMATICAL PHYSICS SEMINAR
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.
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.