Interplay
between the probability theory and geometric group theory yielded many
spectacular results enriching both areas. Asymptotic properties of various
models coming from statistical physics and probabilities were connected to the
geometry and combinatorics of the underlying discrete algebraic structure (for
instance a group, a graph, a group action). The study started with simple
random walks and their boundary theory and then extended to other models, such
as percolation or the Ising model. Substantial progress was achieved on many
different fronts, and several applications to group theoretical problems were
found outside of probability. The goal of this program is to gather experts
from different areas (ranging from group theory to probability) in order to
tackle some important challenges using the cutting-edge techniques that
surfaced in recent years.
The program of the semester is structured around one Summer School and two
Conferences. Two or three colloquium-style Bernoulli lectures will take place
during the semester. In between the conferences, a small number of scientists
will be in residence at the CIB, thus providing the opportunity for
collaborations between experts in different fields.
03 July - 07 August 2015
01 October 2015
05 - 09 October 2015
03 December 2015
07 - 11 December 2015
24 December 2015