14:15

### Generalized Gelfand--Graev representations for finite groups of Lie type

## Abstract

16:30

### Linear equations in primes

## Abstract

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

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`

14:15