This is a joint summer school organized by Columbia University and SLMath. The SLMath website can be found here. This website you are on will contain the most up to date information and materials.

School description: 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.

Funding acknowledgements:

• 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