MIT PDE/Analysis Seminar, Fall 2009

At MIT in Building 2
In Room 2-146 at 4:00 PM on Tuesdays, unless otherwise noted.

• September 29: Pierre Albin (Courant/IAS)
  "Equivariant cohomology and resolution"

  Abstract: The equivariant cohomology of a manifold with a group action is, in some sense, the cohomology of the space of orbits. I will describe joint work with Richard Melrose where we make this precise. In fact our method of lifting the group action and the equivariant cohomology to a manifold with corners and smooth orbit space also allows us to extend the `delocalized' equivariant cohomology of Baum, Brylinski, and MacPherson from actions of Abelian Lie groups to actions of arbitrary compact Lie groups.
  

• October 6: Hamid Hezari (MIT)
  "Complex zeros of eigenfunctions"

  Abstract: The distribution of nodal sets and the critical points of eigenfunctions are very hard to study. There is hope that by studying the complex nodal sets we can obtain some results about the real nodal sets. In this talk we will talk about the distribution of complex zeros of 1D Schrödinger operators and we show that as $h \to 0$ the complex zeros concentrate on some lines in the complex plane. We will describe these lines for some examples including the double well potentials.

• Special Friday seminar: October 9, 4PM, Room 2-143
  Gunther Uhlmann (U. Wash)
  "The Calderon problem with partial data"

• No seminar October 13

• October 20: Cedric Villani (ENS de Lyon and IHP)
  "Smoothness of optimal transport in curved geometry, and stability of the cut locus"

• November 17: Antti Knowles (Harvard)
  "Controlling quantum fluctuations in the mean-field limit"

  Abstract: It is well known that the mean-field time evolution of a quantum Bose gas is governed by the nonlinear Hartree equation. I will report on recent joint work with P. Pickl, in which we derive explicit bounds on the magnitude of the quantum fluctuations. Our approach applies to a large class of one-body Hamiltonians and interaction potentials. In particular, we control the quantum fluctuations in the mean-field approximation of a boson star, and provide a microscopic derivation of the nonrelativistic Hartree equation with a critical nonlinearity. We also show that in a scattering regime the quantum fluctuations are bounded uniformly in time.