Dear colleagues and friends,
The schedule of the forthcoming short course Fluctuations in exclusion processes by Prof. Oriane Blondel (Lyon) has been modified.
The new schedule is 28/4 (Mon) 10:45-12:15 29/4 (Tue) 10:45-12:15 (changed) & 14:15-15:45 30/4 (Wed) 16:15-17:45
For more details, please see https://trimester2025.math.gssi.it/blondel/
With best wishes,
Lu Xu
Begin forwarded message:
From: Lu Xu xu.probability@outlook.com Subject: Mini-courses in GSSI trimester Date: 31 March 2025 at 14:35:37 CEST To: random@mail.dm.unipi.it
Dear colleagues and friends,
as part of the GSSI intensive trimester “Particles, Fluids and Patterns: analytical and computational challenges”, we are glad to announce 3 short courses in April:
April 14-17: Prof. Makiko Sasada (Tokyo) April 28-30: Prof. Oriane Blondel (Lyon) and Prof. Alessandro Giuliani (Rome)
Please see at the end of the email for the detailed place and time, titles and abstracts. Other courses hosted by the trimester can be found in https://trimester2025.math.gssi.it/all_courses/.
Registration is free through the web form: https://indico.gssi.it/event/745/.
We would be grateful if you could circulate the announcement among potentially interested students and researchers. For any information do not hesitate to contact us (patterns@gssi.it).
———————————————— Venue for all courses: Main Lecture Hall, Gran Sasso Science Institute (Viale F. Crispi 7, L’Aquila) ———————————————— Introduction to probabilistic aspects of integrable systems
Lecturer: Makiko Sasada (The University of Tokyo)
14/4 (Mon) 9:00-10:30 15/4 (Tue) 14:15-15:45 16/4 (Wed) 10:45-12:15 17/4 (Thu) 9:00-10:30
In recent years, there has been growing interest in the study of integrable systems from the perspectives of statistical mechanics and probability theory. The theory of generalized hydrodynamics, developed by mathematical physicists, suggests that the macroscopic behavior of integrable systems is highly universal. To mathematically substantiate such theories with concrete models, a type of cellular automaton called the box-ball system (BBS) has been extensively studied by probabilists in recent years. The BBS, which exhibits solitonic behavior, has been studied from various viewpoints, such as tropical geometry, combinatorics, and representation theory, over 30 years. However, research from the probabilistic perspective began only about 10 years ago. Recently, probabilistic approaches, including the application of the Pitman transform, analysis of invariant measures, and scaling limits, have rapidly expanded. These have revealed new connections between probability theory and classical integrable systems, showing that the macroscopic behavior of integrable systems exhibits a universality distinct from that of chaotic systems. In this lecture, I will introduce these new research topics, mainly focusing on the box-ball system, and present the rigorous results obtained in the past several years, starting from the basic concepts. ———————————————— Long range order in atomistic models for solids
Lecturer: Alessandro Giuliani (Rome Tre)
28/4 (Mon) 16:15-17:45 29/4 (Tue) 16:15-17:45 30/4 (Wed) 10:45-12:15 & 14:15-15:45
The emergence of long range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in physics. To address this challenge I will introduce a discrete microscopic model for an elastic crystal with dislocations in three dimensions, originally proposed by Ariza and Ortiz. The model is rich enough to support some realistic features of three-dimensional dislocation theory, most notably grains and the Read-Shockley law for grain boundaries, which I will review and show how to derive microscopically in the context of the Ariza-Ortiz model, at least in a simple, explicit geometry. I will also explain how to analyze the model at positive temperatures, in terms of a Gibbs distribution with energy function given by the Ariza–Ortiz Hamiltonian plus a contribution from the dislocation cores. The main result is that the model exhibits Long Range Positional Order (LRPO) at low temperatures. Its proof is based on the tools of discrete exterior calculus, together with cluster expansion techniques. In this mini-course I will introduce these methods and explain how to combine them in order to prove existence of LRPO. Time permitting, I will discuss some perspectives about the extension of these ideas and methods to two dimensions. Based on joint work with Florian Theil. ———————————————— Fluctuations in exclusion processes
Lecturer: Oriane Blondel (University of Lyon 1)
28/4 (Mon) 10:45-12:15 29/4 (Tue) 9:00-10:30 & 14:15-15:45 30/4 (Wed) 16:15-17:45
We will focus on weakly asymmetric exclusion processes on the line or half-line, and investigate their fluctuations out of equilibrium. We will review the various tools used in proving convergence to the KPZ equation in the strategy initiated in [Bertini-Giacomin ‘97] and discuss how they can be adapted to the singular initial condition that arises when one considers fluctuations of the facilitated exclusion process at the interface. ————————————————
With our best wishes,
Lu Xu Assistant Professor (RTDb) Gran Sasso Science Institute