Workshop on scaling limits: from statistical mechanics to manifolds

This is an application for partial funding for a 3-day workshop in probability entitled ''Scaling limits: from statistical mechanics to manifolds'', to take place in Cambridge 7th-9th September 2020. The workshop is loosely timed to coincide with the 60th birthday of James Norris, who is professor of stochastic analysis at the University of Cambridge and one of the UK's most senior probabilists. The goal of the workshop is not to simply look back at his career, but instead take his work as a jumping-off point for an exploration of future research directions in probability. The meeting will benefit UK mathematics and reinforce the UK's position as a leading centre for probability research by providing an opportunity to learn about the latest developments and identify future directions. There is a particular emphasis on the representation of female academics -- 3 out of 4 organisers are female and 5 out of 16 speakers are female.

The meeting will be centred around five themes that all display beautifully the interplay between probability and analysis. We have invited experts working on 1) random growth processes and SPDEs, 2) Yang-Mills measure, 3) limits of random graphs, random planar maps and fragmentation processes, 4) Markov chains, interacting particle systems and fluid limits and 5) diffusion processes and heat kernels. Many of these areas have arisen out of a need for sophisticated models involving random mathematical structures which go well beyond the classical topics of real-valued random variables and processes. This workshop will play a role in keeping the UK at the forefront of new developments.

The impacts of the workshop are rather wide-ranging, but also difficult to predict accurately as is usually the case with fundamental research. In each of the five themes of the workshop there are applied motivations for looking at the specific objects, mostly coming from real world problems. We aim to reinforce the theoretical underpinnings of applied work in these areas. The pathways to impact that we envisage are standard for mathematical research, namely bringing our work to the attention of people working more directly in applications, via publications and research talks. We also have one participant who works extensively in chemical engineering and another who works for the National Security Agency. Such links will also facilitate the transfer of knowledge out of the theoretical arena and into application areas. A key impact that we anticipate is in the development of the skills of the participants, specially early-career researchers in probability and stochastic analysis, in cutting edge techniques and methodologies. There is not only the need to train the next generation of academics, but also to train people who will eventually pursue the bulk of their careers outside academia, in the public sector or in industry. Such people act as a crucial pathway to societal and economic impact, and are an important component of the UK's ability to be an effective player in a data-driven economy.