School on Disordered media
Description
The School on Disordered media (2025 January 20-24) will be held at the main lecture hall of Rényi Institute, Budapest, Hungary. The school is part of the Semester on Probability and Statistical Physics hosted by Erdős Center. The programme of the school consists of five minicourses given by distinguished researchers of the field, short presentations by participants of the school and an open problem session. Note that one week after the school, a Workshop on Disordered Media will also be held at Rényi Institute / Erdős Center.
Minicourses:
- David Belius: INTRODUCTION TO SPIN GLASSES,
- Nathanael Berestycki: LIOUVILLE QUANTUM GRAVITY AND ITS SPECTRAL GEOMETRY,
- Marek Biskup: EXTREMAL PROPERTIES OF THE RANDOM WALK LOCAL TIME,
- Ron Peled: DISORDERED SPIN SYSTEMS, FIRST-PASSAGE PERCOLATION AND MINIMAL SURFACES IN RANDOM ENVIRONMENT,
- Sergio Simonella: KINETIC LIMITS FOR THE DILUTE CLASSICAL GAS.
Details of Minicourses:
This minicourse will start with a discussion of the history and motivation of spin glass models in physics, and then move on to calculations and proofs in some of the (few) settings where these can be done by simple means (Curie-Weiss model, free energy at high enough temperature using second moment method). We will finish with a high-level discussion, with little or no proof, of the recently reinvigorated geometric Thouless-Andersson-Palmer (TAP) approach to these models.
I will explain the construction, which is closely related to the theory of Gaussian multiplicative chaos and the Gaussian free field, to which a brief introduction will also be presented. I will also discuss Liouville Brownian motion, the canonical diffusion in this random geometry. In particular I will present some recent results on the spectral geometry of LQG, showing that the eigenvalues satisfy a Weyl law, and discussing a number of conjectures which aim to relate LQG to "quantum chaos".
Lecturer: SERGIO SIMONELLA (Sapienza Università di Roma)
Title: KINETIC LIMITS FOR THE DILUTE CLASSICAL GAS
Abstract: We will review the state of the art in the validity problem for a mathematical justification of fluid equations based on fundamental laws of classical mechanics. With the techniques currently available, such problems can be faced in some simple cases, using kinetic theory as an intermediate step. In particular, we will study deterministic, time-reversible dynamics with random initial data, in a low-density scaling. Under suitable assumptions on the initial measure, a strong chaos property is propagated in time, which also encodes the transition to irreversibility. This result is complemented by large deviation estimates and by a theory of small fluctuations, allowing to establish the connection between microscopic and hydrodynamic scales. Many of the open problems left require a deeper understanding of the coupling mechanisms between deterministic and stochastic dynamics.
Tutor: RAPHAEL WINTER
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Application Information:
Application is now closed. Application deadline was: 2024 October 31.
The school covers full lodging for all accepted international participants (junior participants might share a room with another participant). There is very limited funding for travel support. Applicants are asked to send their application to the e-mail address probstatphys25@renyi.hu .The subject of the application e-mail should be: "School on Disordered media application". Your application e-mail should contain your name, affiliation and CV (which includes your list of publications). Please indicate in your application if you wish to apply for lodging in Budapest. In case you want apply for travel support, please write a short explanation why you lack travel funding and how participation in this school would be beneficial for you.
MSc and PhD students applying for the school should also ask their supervisor to send a short recommendation email (typically a few informal sentences) to the contact e-mail address probstatphys25@renyi.hu
A limited number of participants will also get a chance to give a short talk about their work. If you would like to give a short talk, please provide the proposed title and abstract in your application e-mail.