Summer Graduate School
| Parent Program: | -- |
|---|---|
| Location: | Columbia University |
Show List of Lecturers
- Roland Bauerschmidt (New York University, Courant Institute)
- Tom Hutchcroft (California Institute of Technology)
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.
percolation
spin models
phase transition
correlation inequalities
critical phenomena