Current Seminars
updated 9/20/01

September

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

 

Analysis Seminar

Topic: Asymptotic dynamics of nonlinear Schrodinger equations with multiple bound states

Presenter: Tai-Peng Tsai, Institute for Advanced Study

Date: Monday, September 24, 2001, Time; 4:00 p.m., Location: Fine Hall 314

 

PACM Colloquium

Topic: Language learning and evolution

Presenter:  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

 

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.

 

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

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