Summer Graduate School

<p>The five largest clusters in critical site percolation on a large three-dimensional box</p>

Percolation and spin models such as the Ising model have a history that goes back over 100 years. The subject has taken a central role in probability theory over the last few decades, in particular through interactions with various other areas of mathematics. These include graph theory, theoretical computer science, statistical physics, quantum field theory, complex analysis, partial differential equations, and geometric group theory. Through examples, the summer school aims to illustrate some of the successful techniques and ideas in the subject area.

The summer school will cover a sample of topics from this field, beginning with the proof of the existence of phase transitions and correlation inequalities, the critical phenomena associated with these models, the role of symmetry, and end with more specialized topics such as hierarchical percolation or the use of Grassmann variables.

School Structure

There will be two lectures each morning, and exercise sessions each afternoon.

Prerequisites

Most important is mathematical maturity ensured for example by course on real analysis or measure theoretic probability theory, and familiarity with standard probabilistic concepts, for example, at the level of Durrett’s book Probability: Theory and Examples or Varadhan’s book Probability Theory. Background in statistical physics or percolation will not be assumed.

Application Procedure

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

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

Venue

The summer school will take place at Columbia University. 

The summer school is additionally supported by:
Columbia University, Departments of Mathematics and Statistics
Princeton University, Department of Mathematics
National Science, Foundation DMS:1937254 (RTG: Research Training in Applied Mathematics at Columbia University)
Simons Foundation, Ivan Corwin's Investigator Award MPS-SIM-00929852