MATHEMATICAL PHYSICS SEMINAR

Department of Mathematics
Princeton University
Princeton University Department of Mathematics Seminars Spring 2011 Schedule


SPRING 2012 Lectures

**PLEASE NOTE SPECIAL DAY & TIME**

Regular meeting time: Tuesdays 3:30-4:30
Place: Jadwin A06

 

Date Speaker Title
Feb. 7, 4:30 p.m.
A06 - Jadwin
Jonathan Breuer, Hebrew University
Nonintersecting random walkers with a staircase initial condition
We study a model of one dimensional particles, performing geometrically weighted random walks that are conditioned not to intersect. The walkers start at equidistant points and end at consecutive integers. A naturally associated tiling model can be viewed as one of placing boxes on a staircase. For a particular value of the parameters we obtain a known model for the Schur measure, which has the sine kernel as a scaling limit. However, for other parameter values the process at the local scale, close to the starting points, does not fall in the universality class of the sine kernel. Instead, as the number of walkers tends to infinity we obtain a new family of kernels describing the local correlations. We shall describe these limits and some of their interesting features. This is joint work with Maurice Duits.

Feb. 28, 3:30 p.m.
A06 - Jadwin

Christian Hainzl,
University of Tuebingen

Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs
We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. This is joint work with Robert Seiringer.

Mar. 27, 3:30 p.m.
A06 - Jadwin

Sourav Chatterjee,
Courant Institute

Invariant measures and the soliton resolution conjecture
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. I will present a theorem that proves a "statistical version" of this conjecture at mass-subcritical nonlinearity. The proof involves a combination of techniques from large deviations, PDE, harmonic analysis and bare hands probability theory.

Thursday, Mar. 29 **, 3:00 p.m., A06 - Jadwin Jeff Schenker,
Courant Institute
Diffusion of wave packets for the Markov Schroedinger equation
The long time evolution of waves in a homogeneous random environment will be discussed. Proving that the wave amplitude evolves diffusively over any sufficiently long time scales remains an open problem. One obstacle that arises is recurrence -- return of portions of the wave packet to regions previously visited. However, if one removes recurrence by allowing the environment to evolve randomly in time, then diffusion of the wave amplitude can be proved in a relatively simple fashion.

 

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For more information about this seminar, contact Princeton University Department of Mathematics Seminar