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Mathematics Institute

SETSAC Warwick University

Mathematics Department:
  • Colm Connaughton

Use of SPDEs to study the statistical properties of interacting particle systems and related coalescence/growth processes which are popular testing-grounds for theories of non-equlibrium statistical mechanics. Physical implications of the so-called non-equilibrium fluctuation theorems like the Gallavotti-Cohen theorem, Jarzinski Inequality and related results.

  • K D Elworthy

Geometric stochastic analysis, Infinite dimensional stochastic analysis, especially geometric analysis on path spaces of Riemannian and more general manifolds, and thier interactions with SPDE theory.

PhD Students:

Patrick O'Callaghan

Yuxin Yang

Ergodic properties of stochastic PDE’s, especially fluid flow equations and equations drivin by non-markovian noises such as fractional Brownian Motions. Also joint work with Andrew Stuart et al.

PhD Students:

Charles Manson

Pavel Bubak

Probability Theory; Stochastic Analysis including:

Stochastic Differential Equations and Dynamical Systems, Analysis on Infinite Dimensional Spaces, Malliavin Calculus; Properties of Stochastic Processes; Geometric Properties of Stochastic Flows.

Probability theory, especially stochastic processes related to random matrices, combinatorics, reflection groups and representation theory.

  • James Robinson

Stochastic and ordinary partial differential equations as random dynamical systems especially fluid flow equations

PhD students:

Masoumeh Dashti

Eleonora Pinto de Moura

Sampling Function Space Using SPDEs

Many problems arising in applications can be formulated, using Bayesian statistics, in terms of a probability distribution on function space. Sampling such measures effectively is thus of some practical importance. SPDEs provide a unifying concept around which a number of sampling methods can be motivated or analyzed. This group is pursuing such ideas, especially in the context of MCMC methods. It includes Martin Hairer and Andrew Stuart with:

Post-doctoral Research Assistants: Alex Beskos, Jochen Voss

PhD Students

Simon Cotter

David White

  • R Tribe

Stochastic travelling waves. Coalescing particles, especially large time behaviour for spatial co-alescing systems and non-mean field behaviour. Joint work with Oleg Zaboronski.

PhD Students:

Tim Hobson

Stochastic travelling waves

Nick Woodward

Stochastic travelling waves

  • Oleg Zaboronski

Large time behaviour for spatial coalescing systems, and their non-mean field behaviour; use of group renormalisation methods and spde.

Statistics Department:

  • Sigurd Assing

Investigation of scaling limits of fluctuation fields of interacting particle systems and related SPDEs.

PhD Students:

James Bichard

Space evolution of solutions of SPDEs

 

 

Participating Groups: