Current Seminars
updated 9/19/01

September

Statistical Mechanics Seminar  *** Note special time
Topic:  Entropy production for quantum spin systems
Speaker:  David Ruelle, I.H.E.S., France
Date: Wednesday, September 19, 2001, Time: 3:45 p.m., Location: Jadwin 343
Abstract:  We consider a quantum spin system consisting of a finite subsystem connected to infinite reservoirs at different temperatures.  In this setup we define nonequilibrium steady states and prove that the rate of entropy production in such states is nonnegative.  This uses the thermodynamic definition in terms of energy flux and temperatures of the reservoirs.  If we try a precise physical discussion of entropy production, we see however that some questions of principle remain to be clarified.

Topic: Topological Degree for a Mean Field Equation with Boundary Conditions
Presenter: Chiun-Chuan Chen, N.T.U., Taiwan
Date:  Friday, September 21, 2001, Time: 3:00 p.m., Location: Fine Hall 401

 

PACM Colloquium

Topic: Language learning and evolution

Speaker:  Natalia Komarova, Institute for Advanced Study

Date: Monday, September 24, 2001, Time: 4:00 p.m., Location: Fine Hall 214

Abstract :Motivated by the paradox of natural language acquisition, we will explore the concept of individual learning.  One immediate result is the necessity of a finite search space, or Universal Grammar of Chomsky.  We will further talk about learning algorithms and calculate the rate of convergence of the so-called memoryless learner algotithm.  The resulting mathematical problem involves finding eigenvalues of a class of stochastic matrices and calculating the statistics of a harmonic mean.

Next, we will introduce the concept of population learning.  Using ideas of theoretical biology, a system of nonlinear ODE's can be derived which describes the learning and evolution of language.  A certain universality property of this system will be demonstrated which will enable us to link the results for individual learning with population dynamics and maintaining grammatical coherence by a population

 

Ergodic Theory and Statistical Mechanics

Topic: Quasi-linear approximations of Navier-Stokes system

Speaker: Yakov Sinai, Princeton University

Date: Thursday, September 27, 2001, Time: 2:00 p.m., Location: Fine Hall 401

Statistical Mechanics Seminar 
Topic:  Spectral Analysis of Stochastic Lattice Ginzburg-Landau Models
Speaker:  Emmanuel Pereira, Rutgers University
Date: Wednesday, September 26, 2001, Time: 2:00 p.m., Location: Jadwin 343
Abstract:  We consider the relaxation to equilibrium of solutions of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg-Landau interactions.  Using a Feynman-Kac formula we relate the stochastic problem to a quantum field theory, and then we study the low-lying spectrum of the generator of the dynamics.  We prove the existence (or absence) of bound states for d=1,2,3.  Furthermore, using a perturbative approximation, we describe the curves for the one-particle and two-particle bound state masses in terms of the noise strength and predict an interesting phenomenon: the crossover between the one-particle and the bound state masses for a certain noise intensity.

October

Department Colloquium
Topic: Hypersurfaces of prescribed curvature and energy inequalities in General Relativity
Presenter:  Gerhard Huisken, Universität Tübingen
Date:  Wednesday, October 17, 2001, Time: 4:00 p.m., Location: Fine Hall 314