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.