
Center for Mathematical Sciences Lectures & The
Lewiner Institute for Theoretical Physics
Program of Lectures:

Physics Colloquium (11.3):
Classical
models of Quantum localization
After reviewing some mathematical aspects of quantum localization, I shall discuss
3 classical models which are closely
related to localization: The first is
the motion of a classical particle on the
Physics Seminar (14.3):
A Phase transition for a supersymmetric hyperbolic sigma model.
Spectral properties of random band matrices
and other disordered quantum systems can be expressed in terms of SUSY
statistical mechanics models. This talk will discuss a simplified version of
these models due to Zirnbauer. The
advantage of this model is that after integrating out the fermions, the action
is real so that probabilistic methods can be applied. Correlations can be
expressed as a random walk in a random environment. In 3D this model is shown
to have an
Mathematics Colloquium (15.3):
Central
Limit theorems for Statistical Mechanics
This talk will review some results and conjectures about the role of central limit theorems in statistical mechanics. In one dimension, fluctuations in statistical mechanics are described via the usual central limit theorem. In two dimensions, central limit theorems which arise in the study of anharmonic membranes, coulomb gases, and dimers are more difficult to establish due to strong correlations. We shall describe a strong version of the central limit theorem which is valid in two dimensions but which is false for sums of independent random variables. Central limit theorems for the selfavoiding walk and the Ising model in 4 or more dimensions will also be discussed.
Probability Seminar (16.3):
Central
Limit theorems for Random Surfaces
This talk will review principles of optimal
transportation and its relation to the integration by parts formula of Helffer,
Sjöstrand and