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