Mathematical Physics
Seminar
February Schedule
Please join us for cookies and coffee in Hill 705
kitchen at 11:40am every Thursday before each seminar
Date: Thursday February 7, @ 12:00PM, Hill 705
Speaker: Thomas Chen, Princeton University
Title: On Quantum Charge Transport in Random Media
Abstract: In this
talk, we discuss some recent results addressing the long-time dynamics
of charged quantum mechanical particles in a weakly disordered random
medium. We especially focus on the derivation of Boltzmann equations
in a kinetic scaling limit of the quantum dynamics. This will be
addressed both in the one-particle, and in the fermionic manybody
framework. In connection with the latter, we report on a recent joint
work with I. Sasaki, and on a current collaboration with
I. Rodnianski.
There will be a
brown bag lunch from 1-2pm. Please join us.
Date: Thursday February 7, @ 2:00PM, Hill 705
Speaker: Roger Nussbaum, Rutgers University
Title: Inequivalent Measures of Noncompactness and
Generalizations of the Krein-Rutman Theorem
Abstract: The classical Krein-Rutman theorem considers a compact, bounded linear map L:X-->X, where X is a Banach space. Under the assumption that L(C) is contained in C, where C is a closed, total cone in X, the K-R theorem asserts that L has an eigenvector u in C with eigenvalue r equal to the spectral radius of L. We shall describe some generalizations of this theorem to the case of maps f:C-->C which may be nonlinear or noncompact. Even if f is linear, open questions remain when f is noncompact. Our work leads us to questions about "measures of noncompactness". The Kuratowski measure of noncompactness on a Banach space (X,|| . ||) assigns to each bounded subset S of X a nonnegative real number a(S) defined by a(S):={d>0: S can be covered by a finite number of subsets of diameter
Speaker: Jose A. Carrillo de la Plata, University of Barcelona, Spain
Date/Time/Place: Thursday, February 14, 2008 @ 12:00pm, Hill 705
Title: Contractive Probability Metrics for Dissipative Boltzmann
Equations
Abstract: We will discuss the contractivity for the inelastic
Boltzmann equation in the maxwellian approximation using Wassertein
and Fourier-based metrics.
As a consequence, we will discuss the nonlinear asymptotic stability
and decay rates for equilibria due to thermostats and homogeneous
cooling states.
and decay rates for equilibria due to thermostats and homogeneous
cooling states.
THERE WILL BE NO SEMINAR THURSDAY, FEBRUARY 21 AND 28, 2008