Colloquium-Jacek Brodzki

On Friday Sept. 20, 2013 Prof. Jacek Brodzki of U. Southampton will give a colloquium lecture titled Subspaces of Groups and C^* Algebra Extensions.

The colloquium will take place at 3:30pm in Keller 401

Brodzki_9182013_smallest

While a great deal of information about the representation theory of a group is contained in its reduced C*-algebra, this is a very challenging object to study. One way to understand the structure of an operator algebra is to construct a C*-algebra extension, that is an exact sequence connecting the algebra under consideration to other algebras, the properties of which might already be known. In the case of groups, an ingenious way of constructing such extensions was proposed in the 1980s by Pimnser and Voiculescu, first for free groups, and then for groups acting on trees. This was a breakthrough result with many important consequences.

In this talk I will present a geometric picture that explains how extensions of this type arise, and how this unifying approach connects a number of important results of Lance, Pimsner and Voiculescu and others. A main ingredient in our construction is an operator algebra associated with a metric subspace of a discrete group, which plays the role of the reduced C*-algebra of a group. I will present several examples of how the interaction between the geometry of a subspace with that of the ambient group leads to interesting C*-algebra extensions. The talk will be aimed at non-specialists.

Colloquium-Daisuke Takagi

On Friday Sept. 13th, Prof. Daisuke Takagi (U. Hawai`i) will give a colloquium titled “Capturing stealthy swimmers and other adventures in fluid dynamics.” It will be held at 3:30pm in 401 Keller Hall.
Takagi_9132013

Fluid dynamics is a branch of applied mathematics concerned with fluids in motion. When a solid body propels itself through fluids the resultant motion is generally difficult to predict. Laboratory experiments reveal how microscopic particles can stealthily swim on surfaces, slide along walls, and slalom through obstacles. These observations are explained using a simple model that accounts for the fluid flow around each swimmer. I will discuss some broader implications of this work and possible directions for future research.

 

Marriott’s doctoral defense

O1_to_O2
John Marriott, a student of Prof. Monique Chyba, will defend his doctoral dissertation on September 5.

Abstract

This work addresses the contrast problem in nuclear magnetic resonance as a Mayer problem in
optimal control. This is a problem motivated by improving the visible contrast in magnetic resonance
imaging, in which the magnetization of the nuclei of the substances imaged are first prepared by
being set to a particular con figuration by an external magnetic field, the control. In particular we
examine the contrast problem by saturation, wherein the magnetization of the first substance is
set to zero. This system is modeled by a pair of Bloch equations representing the evolution of the
magnetization vectors of the nuclei of two di fferent substances, both influenced by the same control
field.
More…