Fri, 23 Oct 2009
16:30
L2

*My Nonlinear Odyssey : Analytics*, * Simulation & Visualization *

Professor Norm Zabusky
(Weizmann Institute)
Abstract

An overview of the early history of the soliton (1960-1970) and equipartition in nonlinear 1D lattices : From Fermi-Pasta-Ulam to Korteweg de Vries, to Nonlinear Schrodinger*…., and recent developments .

Fri, 29 May 2009
16:30
L2

Classifying spaces and cohomology of finite groups

Professor Dave Benson
Abstract

I shall give a gentle introduction to the cohomology of finite groups from the point of view of algebra, topology, group actions and number theory

Fri, 08 May 2009
16:30
L2

Eigenvalues of large random trees

Professor Steven N. Evans
(Berkeley)
Abstract

A common question in evolutionary biology is whether evolutionary processes leave some sort of signature in the shape of the phylogenetic tree of a collection of present day species.

Similarly, computer scientists wonder if the current structure of a network that has grown over time reveals something about the dynamics of that growth.

Motivated by such questions, it is natural to seek to construct``statistics'' that somehow summarise the shape of trees and more general graphs, and to determine the behaviour of these quantities when the graphs are generated by specific mechanisms.

The eigenvalues of the adjacency and Laplacian matrices of a graph are obvious candidates for such descriptors.

I will discuss how relatively simple techniques from linear algebra and probability may be used to understand the eigenvalues of a very broad class of large random trees. These methods differ from those that have been used thusfar to study other classes of large random matrices such as those appearing in compact Lie groups, operator algebras, physics, number theory, and communications engineering.

This is joint work with Shankar Bhamidi (U. of British Columbia) and Arnab Sen (U.C. Berkeley).

 

Tue, 05 May 2009

17:00 - 18:00
L2

Representation growth of finitely generated nilpotent groups

Christopher Voll
(Southampton)
Abstract

The study of representation growth of infinite groups asks how the

numbers of (suitable equivalence classes of) irreducible n-dimensional

representations of a given group behave as n tends to infinity. Recent

works in this young subject area have exhibited interesting arithmetic

and analytical properties of these sequences, often in the context of

semi-simple arithmetic groups.

In my talk I will present results on the representation growth of some

classes of finitely generated nilpotent groups. They draw on methods

from the theory of zeta functions of groups, the (Kirillov-Howe)

coadjoint orbit formalism for nilpotent groups, and the combinatorics

of (finite) Coxeter groups.

Wed, 03 Jun 2009

09:00 - 18:00
L2

Multiscale Models in Solid Mechanics

M. Ortiz, M. Luskin, F.Legoll, O. Pierre-Louis, A.Raoult
Abstract

Macroscopic properties of solids are inherently connected to their micro- and nano-scale details. For example, the microstructure and defect distribution influence the elastic and plastic properties of a crystal while the details of a defect are determined by its elastic far-field. The goal of multi-scale modelling is to understand such connections between microscopic and macroscopic material behaviour. This workshop brings together researchers working on different aspects of multi-scale modelling of solids: mathematical modelling, analysis, numerical computations, and engineering applications.

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