SLMath summer graduate School
Every summer, the Simons Laufer Mathematical Sciences Institute (SLMath) organizes several summer graduate schools some of which are held at partner institutions around the world. In 2025, the FMJH is partnering one of these summer schools. Entitled “Local Limits of Random Graphs”, it will take place from June 2 to 13 at the Institut de Mathématique d'Orsay, Université Paris-Saclay. The audience will be made up partly of international PhD students supported by SLMath and partly of students invited by the FMJH.
Financial support provided by the US National Science Foundation and the academic sponsoring institutions of the Simons Laufer Mathematical Sciences Institute, Berkeley, CA.
Overview
Random graphs are a cornerstone of modern probability theory, celebrated not only for their mathematical elegance but also for their applications in modeling complex networks. In the early 2000s, I. Benjamini and O. Schramm introduced a groundbreaking framework that endowed the set of locally finite rooted connected graphs with the structure of a Polish space, known as the local topology. This summer school aims to explore the framework of local limits of random graphs, focusing on key concepts such as Benjamini-Schramm (or unbiased) limits, unimodularity, and their most significant applications.
The program will feature lectures by Nicolas Curien (Professor at Paris-Saclay University) and Justin Salez (Professor at Université Paris-Dauphine), complemented by interactive problem sessions. Students will work in small groups under the guidance of teaching assistants, who are active researchers in the field. The school will also include daily evening sessions for informal discussions, research talks by senior researchers, and opportunities to network over food and drinks.
School structure
Each day will consist of :
- Two lectures delivered by leading experts
- Two problem sessions where students will collaborate in small groups
- Evening sessions featuring research talks and informal discussions
Prerequisites
To fully benefit from the program, students should have a solid foundation in probability theory, including:
- Convergence of measures (convergence in law in Polish spaces).
- Poisson processes, countable Markov chains, and martingales (convergence theorems).
- Basic notions in statistics.
References
Recommended references include:
- Jean-François Le Gall's Measure Theory, Probability, and Stochastic Processes.
- Chapter 1 of Patrick Billingsley's Convergence of Probability Measures.
- Rick Durrett's Probability: Theory and Examples.
Familiarity with graph theory, discrete potential theory (random walks on graphs), and ergodic theory is advantageous but not mandatory. Key results from these areas will be reviewed during the lectures.
Lecturers
- Nicolas Curien (Professor at Paris-Saclay University)
- Justin Salez (Professor at Université Paris-Dauphine)
Teaching assistants
- Thomas Budzinski (CNRS, Lyon)
- Alice Contat (Post-Doc, P13)
- Alessandra Caraceni (Researcher, SNS Pisa)
- Olivier Hénard (McF, Orsay)
- Guillaume Blanc (Post-Doc, EPFL)
- Brune Massoulié (PhD, Dauphine)
- Delphin Sénizergues (McF, Nanterre)
Local organizers
- Ainhoa Aparicio-Monforte, Université Paris-Saclay
- Alexandra Genesco, Fondation Mathématique Jacques Hadamard
- Lead organizer : Pascal Massart, Fondation Mathématiques Jacques Hadamard
Practical information
Application procedure for international students
International students interested in applying should visit the Summer Graduate Schools homepage. Upon acceptance, an invitation letter will be sent to you.
Application Deadline: March 14, 2025
Application procedure for local students
Local students (those not requiring accommodation) who wish to receive an invitation to attend are requested to send an email to contact@fondation-hadamard.fr.
Application Deadline: April 11, 2025.
Limited spots remain open for local students to enroll—don't miss out !
Venue
The summer school will take place at the Orsay Mathematics Institute, located on the campus of Paris-Saclay University, approximately 35km south of Paris.
Accomodation
Non local students will be housed in single-occupancy rooms at the Crous Residence Les Rives de L'Yvette either at Buildings 231/232 voie de la Faculté or Building 233 rue Pierre de Coubertin
- Check-in: Sunday, June 1, 2025, between 3:00 PM and 7:00 PM at Building 233 rue Pierre de Courbertin 91 440 Bures-sur-Yvette
- Check-out: Saturday, June 14, 2025, by 10:00 AM.
Meals
On weekdays breakfast, lunch, and dinner will be provided. On weekends only breakfast and dinner will be provided.