Mathematical Physics Seminar
September Schedule




Unless otherwise indicated, all seminars take place in room 705 of Hill Center on Busch Campus, Rutgers University.
Organizer: Joel L. Lebowitz, lebowitz@math.rutgers.edu


COFFEE & COOKIES AVAILABLE IN ROOM 705 KITCHEN AT 11:45AM. PLEASE JOIN US.


Speaker: J. Lebowitz, Rutgers U.
Date/Time/Place: Thursday, September 4, 2008, 12:00pm, Room 705
Title: Elliptic Integrals and Phase Transitions in the ABC Model



Speaker: A. Shadi Tahvildar-Zadeh, Rutgers U.
Date/Time/Place: Thursday, September 11, 2008, 12:00pm, Room 705
Title: Naked, Hairy, Well-posed and Uncensored: Quantum Probing of Singular Spacetimes
Abstract: The classical way of probing a singularity of a spacetime is to throw a test particle at it and watch what happens. Classical particles have well-defined paths: they move along geodesics of spacetime, therefore this probing cannot be done when the singularity is due to geodesic incompleteness. Quantum probing on the other hand involves the study of the well-posedness and propagation of waves on a given background. This is tricky however, if the singularity in question is naked, i.e. can be seen from afar. Cosmic censorship is an attempt to banish naked singularities from the universe, claiming in effect that "if it can be seen, it doesn't exist." In this talk, after providing the necessary background on Einstein's theory of gravitation, we consider a simple model of a spherically symmetric spacetime with an eternal naked singularity, and study the propagation of scalar waves on it, finding sufficient conditions for the well-posedness of the Cauchy problem, and obtaining certain a-priori estimates for the solutions, which also give us some evidence against the censorship conjectures. Along the way, we'll learn how to measure the hairiness of a naked singularity.



Speaker: R. Frank. Princeton U.
Date/Time/Place: Thursday, September 18, 2008, 12:00pm, Room 705
Title: Lieb-Thirring and Hardy-Sobolev Inequalities
Abstract: Lieb-Thirring inequalities estimate moments of negative eigenvalues of Schroedinger operators T-V in terms of integral norms of the potential V. We prove that such inequalities for general operators of the form T-V are, under certain conditions on the `kinetic energy' T, equivalent to Sobolev-type inequalities. In particular, any improvement of Sobolev inequalities will lead to an improvement of Lieb-Thirring inequalities. As an application, we show that the classical Lieb-Thirring inequalities remain valid, with possibly different constants, when the critical Hardy-weight C/|x|^2 is subtracted from the Laplace operator -T. Similar results are true for fractional powers of the Laplacian, and also in the presence of a magnetic field.



Speaker:T. Bodineau, ENS, France
Date/Time/Place: Thursday, September 25, 2008, 12:00pm, Room 705
Title: Current large deviations in stochastic systems
Abstract:We will review the large deviations of the heat current through a diffusive system maintained off equilibrium. We will focus on the the long range correlations and show that they become singular when the system approaches the transition.