14:15
14:15
14:15
Generalized Gelfand--Graev representations for finite groups of Lie type
Abstract
This talk is about the ordinary representation theory of finite groups of Lie type. I will begin by carefully reviewing algebraic groups and finite groups of Lie type and the construction and properties of (ordinary) Gelfand--Graev characters. I will then introduce generalized Gelfand--Graev characters, which are constructed using the Lie algebra of the ambient algebraic group. Towards the end I hope to give an idea of how generalized Gelfand--Graev characters can and have been used to attack Lusztig's conjecture and the role this plays in the determination of the character tables of finite groups of Lie type.
16:30
Linear equations in primes
Abstract
I shall report on a programme of research which is joint with Terence Tao. Our
goal is to count the number of solutions to a system of linear equations, in
which all variables are prime, in as much generality as possible. One success of
the programme so far has been an asymptotic for the number of four-term
arithmetic progressions p_1 < p_2 < p_3 < p_4 <= N of primes, defined by the
pair of linear equations p_1 + p_3 = 2p_2, p_2 + p_4 = 2p_3. The talk will be
accessible to a general audience.
15:45
Stochastic flows, panar aggregation and the Brownian web
Abstract
Diffusion limited aggregation (DLA) is a random growth model which was
originally introduced in 1981 by Witten and Sander. This model is prevalent in
nature and has many applications in the physical sciences as well as industrial
processes. Unfortunately it is notoriously difficult to understand, and only one
rigorous result has been proved in the last 25 years. We consider a simplified
version of DLA known as the Eden model which can be used to describe the growth
of cancer cells, and show that under certain scaling conditions this model gives
rise to a limit object known as the Brownian web.
14:15
Differential Equations Driven by Gaussian Signals
Abstract
We consider multi-dimensional Gaussian processes and give a novel, simple and
sharp condition on its covariance (finiteness of its two dimensional rho-variation,
for some rho <2) for the existence of "natural" Levy areas and higher iterated
integrals, and subsequently the existence of Gaussian rough paths. We prove a
variety of (weak and strong) approximation results, large deviations, and
support description.
Rough path theory then gives a theory of differential equations driven by
Gaussian signals with a variety of novel continuity properties, large deviation
estimates and support descriptions generalizing classical results of
Freidlin-Wentzell and Stroock-Varadhan respectively.
(Joint work with Nicolas Victoir.)
14:30
Volatile exsolution from volcanic craters and other fluid exchange problems
14:15
15:45
Pathwise stochastic optimal control
Abstract
/notices/events/abstracts/stochastic-analysis/mt06/rogers.shtml