Speaker: Daisuke Takagi (U. Hawaii, Manoa)

Title: Capturing stealthy swimmers and other adventures in fluid dynamics

Abstract: 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.

Speaker: Thomas Hangelbroek

Title: A Gentle Introduction to Frames

SPEAKER: Jacek Brodzki (U. of Southampton, UK)

TITLE: Subspaces of groups and C*-algebra extensions

ABSTRACT: 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.

SPEAKER: Yuriy Milenko (U. Hawai`i)

TITLE:TBA

SPEAKER: Yuriy Milenko (U. Hawai`i)

TITLE:TBA

SPEAKER: Dennis Dreesen (University of Southampton, UK.)

TITLE: LOCALLY COMPACT HYPERBOLIC GROUPS

Abstract: The common convention when dealing with hyperbolic groups is that such groups are ﬁnitely generated and equipped with the word length metric relative to a ﬁnite symmetric generating subset. Gromov’s work already contained ideas which encompass locally compact hyperbolic groups. We study this class of groups and elaborate on the similarities and differences between the discrete and non-discrete setting.

The Department of Mathematics & Manoa Math Ohana Invite you to Luana in the Afternoon Refreshments provided. All students and faculty welcome.

luana. Hawaiian. v. To be at leisure, enjoy pleasant surroundings and associates, enjoy oneself, relax, be content.