Speaker:T. Kuna, Universitaet Bielefeld/Rutgers
University
Time/Place:Thursday, 12/1/05,
12-1:00PM, Room 705
Title: "Reliability of Point
Processes (A Truncated Moment Problem)"
Abstract:
Point processes are describing random distributions of points.
Correlation functions are characteristics of these processes. They are
moments w.r.t. to a class of polynomials. The question of
realizability is to find criteria to single out functions which could
appear as correlation functions of a point process. This is an
infinite dimensional truncated moment problem. One can see it also as
a first step of a more general inverse problem, i.e. to find further
properties of the point process like Gibbsian structure, form of the
interaction etc. The latter is part of the theory of classical
fluids. The question of realizability was raised as an isolated
problem in context of heterogeneous materials by S. Torquato and
F. H. Stillinger. General and special necessary and general sufficient
conditions are discussed. Detailed result for a one dimensional
lattice case are given. An interesting question the maximal realizable
density for a given pair correlation. General considerations for low
densities are presented.
Speaker: B. Schlein, Harvard University
Time/Place:Thursday, 12/8/05, 12-1:00PM, Room 705
Title: " Derivation of the cubic nonlinear Schroedinger
equation from many-body quantum dynamics"
Abstract:
We consider a system of N bosons, interacting through a repulsive
short range mean field potential. In the limit of large N, we prove
that the macroscopic dynamics of the system can be described by
the one-particle nonlinear Schroedinger equation. This is a joint
work with L. Erdoes and H.-T. Yau.
THERE WILL BE A BROWN BAG LUNCH FROM 1:00-2:00PM. PLEASE JOIN US
Speaker:J. Kahn, Rutgers University
Time/Place:Thursday, 12/8/05, 2-3:00PM, Room 705
Title: "Some correlation inequalities"
Abstract: We show positive association (positive
correlation of increasing events) for some families of random
variables arising in percolation, the random cluster model and the
"fractional fuzzy Potts model," and mention a few open problems.
Speaker: O. Costin, Ohio State University
Time/Place:Thursday, 12/15/05 12-1:00PM, Room 705
Title: "Time Evolution and Ionization of Quantum Systems
Under Time Periodic Forcing"
Abstract:We analyze the
time evolution of one particle quantum systems with attractive binding
potential, including the Coulombic one, subjected to a time periodic
external field. We show that in many cases such systems, started in a
bound state will get fully ionized at $t \to \infty$. This is
irrespective of the magnitude or frequency of the external field.
Some exceptional, non-generic systems may evolve to a localized
stationary state, corresponding to
eigenfunctions of the Floquet operator.
Speaker: P. Contucci, University of Bologna
Time/Place:Thursday, 12/15/05 2-3:00PM, Room 705
Title: "Stochastic Stability and the Ghirlanda-Guerra
identities"
Abstract:The talk will review the method
of stochastic stability to obtain the factorization properties of the
overlap distribution in spin glass models. In addition it will be
shown a martingale bound for the energy fluctuations which, together
with stochastic stability, implies the whole class of Ghirlanda-Guerra
identities.