Upcoming Events

Monday, February 1, 2010 at 3:00 PM in SAS 4201
Robert Pego, Carnegie Mellon
Self-similarity and eternal solutions for a model of min-driven clustering
Joint seminar between probability seminar and differential equations seminar.

A simple model of 1D coarsening dynamics in the Allen-Cahn equation is a 'one-dimensional bubble bath' which coarsens by two simple rules: (i) The two nearest domain walls 'pop', annihilating each other. (ii) Repeat indefinitely. We study mean-field models for a class of 'min-drive' clustering processes of this kind. By extending a remarkable solution procedure found by Gallay and Mielke, and using the sharp exponential Tauberian theorem of de Haan, we establish: a well-posedness theorem for measure-valued size distributions; necessary and sufficient conditions for approach to self-similar form; and a Levy-Khintchine representation formula for eternal solutions. This is joint work with Govind Menon and Barbara Niethammer.

Monday, February 15, 2010 at 3:00 PM in SAS 4201
Boris Gershgorin, New York University
Climate response and fluctuation-dissipation theorem
The fluctuation-dissipation theorem (FDT) provides an attractive
perspective to address climate change in an atmosphere-ocean system
(AOS).

The theorem states that in order to predict the linear response of a
dynamical system in equilibrium to a small perturbation in external
forcing, it is sufficient to find the appropriate correlation function

in equilibrium without the need for perturbing the system.
An attractive feature of applying the FDT to low-frequency climate
variables of an AOS is that the linear response operator computed by
the theorem can then be utilized for multiple climate change scenarios

without the need of running the complex climate model in each
individual case.
In this talk, we focus on the performance of FDT and its
approximations in predicting climate change in idealized models. On
the one hand these models are simple enough to be solved either
analytically or numerically and on the other hand they mimic some of
the key properties of a complex AOS. In particular, we consider three
different nonlinear test models that allow us to investigate such
important practical issues of assessing climate change via FDT as the
performance of linear regressions, the subtle departures from
Gaussianity and the time-dependent statistics in the model.

The results of our study should provide useful guidelines for applying

the FDT to more complex realistic systems.

Monday, March 8, 2010 at 3:00 PM in SAS 4201
Peter Kramer, Rensselaer Polytechnic Institute
TBA

Monday, March 22, 2010 at 3:00 PM in SAS 4201
Carl Mueller, University of Rochester
Nonuniqueness for some stochastic PDE
The superprocess is one of the most widely studied models in
probability. It arises as a limit of population processes which
depend on space as well as time. One long-standing question involves
the uniqueness of the stochastic PDE which describes the superprocess.
Due to randomness, standard results about uniqueness of PDE do not
apply. We will describe joint work with Barlow, Mytnik, and Perkins,
in which we prove nonuniqueness for the equation describing the
superprocess. Our results generalize to several related equations.

Monday, April 12, 2010 at 3:00 PM in SAS 4201
Leonid Bunimovich, Georgia Institute of Technology
TBA

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Seminar Organizer: Min Kang