ICTS

Due to the ongoing COVID pandemic,  the meeting will be conducted through Online Lectures. 

The second in a series of meetings focussing on the interface between hyperbolic geometry, probability and ergodic theory, this meeting will be on two topics.

1. Percolation on general background geometries
2. Invariant Random Subgroups

Bernoulli percolation is a canonical model of random geometry. Although a lot of the attention has been devoted to percolation on Euclidean lattices, starting with the work  of Benjamini, Schramm and co-authors in the 1990s, tremendous progress has also been made in understanding percolation in different and more general background geometries. Following the new results uncovered by Hutchcroft and coauthors, there has been a revived interest on the subject in the recent years. Also, moving away from independence, level set percolation of the Gaussian free field has emerged as a particularly important and useful model of study. 

An invariant random subgroup (IRS) of a locally compact group, is a random subgroup whose distribution is invariant under conjugation. In recent years, the theory of IRS has played an important role in different parts of geometry, dynamics and group theory (e.g. the solution of a longstanding problem on girth of Ramanujan graphs by Abert,  Glasner and Virag). The notion of IRS has also emerged as a natural generalization of lattices, and much interesting mathematics has been developed focussing on the interplay between IRS and lattices in the famous ‘seven samurai’ paper and its follow-up work.

This program will have seven mini-courses, each comprising of 2-4 lectures on topics related to the themes mentioned above by the following speakers;

1. Miklos Abert (Renyi Institute, Hungary)
2. Itai Benjamini (Weizmann Institute, Israel)
3. Ian Biringer (Boston College, USA)
4. Remi Coulon (Universite de Rennes, France)
5. Barbara Dembin (ETH Zurich, Switzerland)
6. Subhajit Goswami (TIFR, Mumbai, India)
7. Tom Hutchcroft (Cambridge University, UK)
8. Gourab Ray (University of Victoria, Canada)
 

Eligibility Criteria:

The program is aimed at active researchers working in the field of probability, ergodic theory and hyperbolic geometry, with an emphasis on their interactions. Since the program is relatively advanced, primary focus of selection will be on young faculty members and postdocs. However, PhD students with demonstrable expertise in these areas are also encouraged to apply.