Bath-Mannheim workshop on self-similarity
University of Bath, 13th December 2019
More details to be announced in due course.
Random structures: from the discrete to the continuous
University of Bath, 1st - 5th July 2019
An LMS Research school; more details to be announced in due course.
Scaling limits, rough paths, quantum field theory
Isaac Newton Institute programme, 3rd Sept - 21st Dec 2018
The goal of statistical mechanics is to calculate the properties, at macroscopic length scales, of a system composed of a large number of interacting microscopic subsystems. To formalise having a large ratio between largest and the smallest length scales, limits such as infinite volume limits, hydrodynamic limits and scaling limits are studied. These limits are random fields or, in cases where there is dynamics, solutions of nonlinear partial differential equations driven by white noise. Such limits can have symmetries that are not present before taking the limit; for example infinite volume limits may be translation invariant and scaling limits by construction are scale invariant. Increased symmetry leads to very special, beautiful, objects such as euclidean quantum field theories and specific partial differential equations driven by white noise. Then statistical mechanical models can be classified into universality classes characterised by these limits. We think of this as a search for far reaching extensions of the central limit theorem and the theory of large deviations. The possible limits are characterised by very few parameters. A new feature of these extensions is that limits have to be expressed in the correct variables because divergences are inherent in limits that have enhanced symmetries. This is the famous problem of renormalisation in quantum field theory. Divergences arise from the volume of non-compact symmetry groups of translations and dilations. Likewise for partial differential equations driven by white noise divergences appear in naive attempts to define the nonlinear terms in the equations. The solutions are too rough to permit ordinary pointwise multiplication. In the last few years, the theory of rough paths, existence, uniqueness and large deviations for singular partial differential equations has been making very rapid progress. Our four month program has been designed to foster a natural alliance with mathematical quantum field theory, specifically the theory of the renormalisation group, continuation in dimension, operator product expansions and conformally invariant quantum field theory. We aim for progress in global existence of solutions of stochastic pde, dynamical critical exponents, equilibrium critical exponents, bosonisation in two dimensions, better and more complete constructions of euclidean quantum fields.
For more information, visit the event website.
Bath-Beijing-Paris Meeting on Branching Structures
Peking University, 14th - 18th May 2018
The Bath-Beijing-Paris branching structures meeting in Beijing follows four successful workshops in Bath and Paris. It will be another opportunity to discuss a broad family of stochastic models which exhibit branching phenomena, including Galton-Watson trees, branching random walks and branching diffusions, the Gaussian free field, loop ensembles, fragmentation and coalescent processes, continuous state branching processes and superprocesses, search trees, and many more. Part of the meeting will be set aside for discussing open problems and beginning new collaborations. For more information, visit the event website.