The school will be held on 07-11 July 2025 at the University of Warwick (Coventry)

Lecturers

• Martin HairerLink opens in a new window, EPFL (Switzerland) and ICL (UK)
• Nina HoldenLink opens in a new window, NYU Courant (US)
• Hubert LacoinLink opens in a new window, IMPA (Brazil)
• Richard NicklLink opens in a new window, University of Cambridge (UK)

Abstracts

• TBA (Martin Hairer)

• Scaling limits of random planar maps (Nina Holden)

  Planar maps are graphs embedded in the sphere such that no two edges cross, where we view two planar maps as equivalent if we can get one from the other via a continuous deformation of the sphere. Planar maps are studied in several different branches of mathematics and physics. In particular, in probability theory and theoretical physics random planar maps are used as natural models for discrete random surfaces. In this mini-course we will present scaling limit results for random planar maps and we will focus in particular on a notion of convergence known as convergence under conformal embedding. The limiting surface is a highly fractal surface called a Liouville quantum gravity (LQG) surface, which has its origin in string theory and conformal field theory.

• Localization transition for directed polymers in a random environment (in dimension larger than 3) (Hubert Lacoin)

  The Directed Polymer in a Random Environment (DPRE) is obtained by reweighting the trajectories of finite length simple random walk using an i.i.d. random environment. It is one of the simplest disordered models in statistical mechanics, and one for which the disorder-induced phase transition has been intensively studied. When the intensity of the disorder increases, the systems behavior changes drastically: at high temperature (low disorder intensity) the trajectories of the polymer are diffusive with a behavior which is very similar to that of the simple random walk, at low temperature, the trajectories of the polymer are conjecture to concentrate on a narrow space-time corridor, and its end-point distribution is localized.
  In this course, we will present the state of the art for the study of this transition in dimension larger than 3, and expose simple proof of some well established localization and delocalization results.

• Infinite-dimensional Bayesian inference for time evolution PDEs (Richard Nickl)

  We will discuss recent progress in our understanding of Gaussian process based inference methods for parameters or states of time evolution phenomena modelled by non-linear partial differential equations (PDEs) such as Navier Stokes, McKean Vlasov, and reaction diffusion systems. We will show that posteriors can deliver consistent solutions in the `informative’ large data/small noise limit, discuss probabilistic approximations to the fluctuations of such posterior measures in infinite dimensions, and how such results can be used to show that the non-convex problem of computation of the associated `filtering’ distributions are polynomial time problems.

Registration

Please use the link below to access the pre-registration form. Your registration will then be confirmed via email.

REGISTRATION PAGE

Registration closes on Sunday 19^th April 2025

All talks take place in Zeeman Buildig room B3.02Link opens in a new window at the University of Warwick, and refreshments in the common room.

Schedule: TBA

Useful Information

Accommodation

We are unable to cover the accommodation costs for participants, but there are several affordable options on campus or nearby.

• Maths Houses, small houses on campus managed by the Mathematics department and comprising 3 separate bedrooms, kitchen and living room. In case you are interested, you need to indicate it (and who you would want to share it with) in the registration page and we will make the necessary arrangements. The accommodation in the Maths Houses is allocated on a first-come-first-served basis.
• Student Housing (students only), these are on campus accommodation that are available off term. As for Maths houses, please specify in the registration form if you are interested to be considered.
• ScarmanLink opens in a new window and RadcliffeLink opens in a new window, hotels on campus.

For alternative off-campus accommodation, please check online travel platforms. For example, Kenilworth, Leamington Spa and Coventry are well-connected to the University using public transport and offer a good range of accommodation.

Travel to Campus

The School venue is the Zeeman BuildingLink opens in a new window at the University of Warwick which can be reached from

• Coventry, Leamington Spa or Kenilworth, there are buses running from these destinations to the University of Warwick. Details can be found using this link.Link opens in a new window
• Birmingham International (BHX) is the closest airport to the University. There is a train station within the airport from which regular trains to Coventry depart.
• London, for anyone arriving to London by plane or train, we recommend the following train routes:
  • London Euston to Coventry with Avanti Westcoast
  • London Euston to Canley with London Northwestern Railway 
  • London Marylebone to Leamington Spa with CrossCountry

For more information, check this linkLink opens in a new window.