Summer Graduate School

The Sherrington-Kirkpatrick model, aka the randomly-weighted complete graph. Edge weights are indicated using grayscale. Six distinguished vertices have been randomly chosen; edges between those vertices are shaded black to form a "hidden signal".

The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

The phrase "group dynamics" is used loosely here -- it may refer to species migration, the spread of a virus, or the propagation of electrons through an inhomogeneous medium, to name a few examples. Very commonly, such systems can be described via stochastic processes which approximately behave like the solution of an appropriate partial differential equation in the large-population limit.

School Structure

This summer school will take place over a four-week period in Montréal, hosted by the Centre de Recherches Mathématiques.  There will be two principal courses, each with 24 hours of lectures.  In addition, there will be 12 hours reserved for short presentations by participants.  Finally, there will be 3 shorter topics courses, of 3 hours each, to complement the main course. The housing of the participants in shared, apartment-style accommodation gives students mulitiple shared common areas, making it easy for participants to coordinate their own group-work and study sessions.  

Suggested Prerequisites

• A first year-long graduate course in probability, roughly covering the material of Billingsley's Probability and Measure, excuding Sections 9, 28 and 30.
• Rademacher theorem. 
• Some familiarity with basic properties of the Ising model and Hamilton-Jacobi equations would be a plus, but not strictly necessary.
  • For the Ising model, the first two chapters of this book: https://www.unige.ch/math/folks/velenik/smbook/
  • For Hamilton-Jacobi equations: Lawrence Evans, Partial Differential Equations, Sections III.10.1 and III.10.2.

For eligibility and how to apply, see the Summer Graduate Schools homepage

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.