Analysis and PDE Seminar Homepage, Winter 2010

Location: Room 383N.

Time: Wednesdays, 3-4pm, or 4-5pm if the geometry seminar does not meet.

• Wednesday, January 6, 3-4pm, Room 383N (joint with Applied Math):

  Alex Kiselev -- cancelled

  Cancelled!

• Tuesday, January 19, 1-2pm, Room 383N (joint with Geometry):

  Igor Rodnianski (Princeton)

  ``Focusing and formation of trapped surfaces in General Relativity''

• Wednesday, January 27, 4-5pm, Room 383N (joint with Geometry):

  Richard Melrose (MIT)

  ``Resolution and Compactification of Moduli and configuration spaces''

  Abstract: In this talk I will describe some of the significant properties of three compact manfolds with corners obtained, respectively, as the resolution of a group action (joint work with Pierre Albin), the asymptotic configuration space for a vector space and the compactified moduli space of magnetic monopoles (joint work with Michael Singer). I will not have time to discuss these constructions in any detail but intend instead to emphasize their common, particularly their iterative, features and how these can be expected to appear elsewhere.

• Wednesday, February 17, 3-4pm, Room 383N:

  Neil Trudinger (ANU)

  ``On weak solutions of Monge-Ampere type problems and their regularity''

• Wednesday, March 10, 2-3pm and 4-5pm, Bay Area Microlocal Analysis Seminar

  • Galina Perelman (École Polytechnique and CNRS)

    ``Vey theorem in infinite dimensions and its application to the KdV equation''

    Abstract. We develop an infinite dimensional version of the Vey theorem and apply it to construct the Birkhoff coordinates for the KdV equation in the vicinity of the origin in L_0^2(S^1). The obtained integrating transformation has the form "identity plus a 1-smoothing map". This is a joint work with S.Kuksin.

  and

  • Andrew Hassell (ANU)

    ``Quasi-orthogonality of boundary values of eigenfunctions''

    Abstract: Consider Dirichlet eigenfunctions for a smooth bounded plane domain. The normal derivatives of these eigenfunctions are known, at least heuristically, to be "quasi-orthogonal" when the eigenvalues are sufficiently close. I will discuss a new result -- with a remarkably simple proof -- expressing this quasi-orthogonality, and apply it to give sharp theoretical bounds on the accuracy of the "method of particular solutions" for numerically computing such eigenfunctions and eigenvalues. This is joint work with Alex Barnett (Dartmouth).

• Wednesday, March 31, 3:15-4:15pm, Room 380W:

  Simeon Reich (Technion)

  ``Integral solutions to a class of nonlocal evolution equations''

  Here is a link to the abstract.

• Monday, May 24, Bay Area Microlocal Analysis Seminar at Berkeley, in Evans 740

  At 1:10pm:

  • André Martinez (Bologna)

    ``Some new results on the width of quantum resonances''

  at 2:10pm:

  • Andras Vasy (Stanford)

    ``Wave propagation on asymptotically De Sitter and Anti-de Sitter spaces''

    Abstract: In this talk I describe the asymptotics of solutions of the wave equation on asymptotically De Sitter and Anti-de Sitter spaces. This is part of a larger program to analyze hyperbolic equations on non-product, non-compact manifolds, similarly to how various types of `ends' have been studied for the Laplacian and other elliptic operators on Riemannian manifolds. The AdS setting is particularly interesting from the point of view of propagation phenomena, since for the conformally related incomplete metric, there are null-geodesics which are tangent to the boundary.

  and, at 4:10pm:

  • Alexander Gamburd (UC Santa Cruz)

    ``Infinite volume generalization of Selberg's 3/16 Theorem''

• Schedule for Autumn 2009.
• Schedule for Spring 2009.
• Schedule for Winter 2009.
• Schedule for Spring 2008.
• Schedule for Winter 2008.
• Schedule for Autumn 2007.