Models of polymer dynamics

Speaker: 

Professor Peter March

Institution: 

Ohio State University

Time: 

Tuesday, April 4, 2006 - 11:00am

Location: 

MSTB 254

There is a rich physical literature on polymer dynamics which presents a number of fascinating challenges for mathematicians. We model thermal fluctuation of a polymer in solvent as a curve or loop obeying a stochastic partial differential equation (SPDE). The simplest instance is the so-called Rouse model which is an infinite dimensional Ornstein-Uhlenbeck process satisfying a linear SPDE. We'll review the Rouse model and then describe recent results (a) of Seung Lee on an SPDE for the Rouse model in a half-space with reflecting boundary conditions; and (b) of Scott McKinley on an SPDE model of the hydrodynamic interaction.

A Coupling, and the Darling-Erdos Conjectures

Speaker: 

Professor Davar Khoshnevisan

Institution: 

University of Utah

Time: 

Tuesday, October 11, 2005 - 11:00am

Location: 

MSTB 254

We present a coupling of the 1-dimensional Ornstein-Uhlenbeck process with an i.i.d. sequence.
We then apply this coupling to resolve two conjectures of Darling and Erd\H{o}s (1956).
Interestingly enough, we prove one and disprove the other conjecture. [This is joint work with David Levin.]

Time-permitting, we may use the ideas of this talk to describe precisely the rate of convergence in the
classical law of the iterated logarithm of Khintchine for Brownian motion (1933).
[This portion is joint work with David Levin and Zhan Shi, and has recently appeared in
the Electr. Comm. of Probab. (2005)]

The asymptotic shift for the principal eigenvalue under small obstacles.

Speaker: 

Professor Iddo Ben-Ari

Institution: 

UCI

Time: 

Tuesday, October 4, 2005 - 11:00am

Location: 

MSTB 254

We study the asymptotic shift for principal eigenvalue for a
large class of second order elliptic operators on bounded domains subject
to perturbations known as obstacles. The results extend the well-studied
self-adjoint case. The approach is probabilistic.

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