3. Name of the Seminar: Analysis Seminar
Time, Day and Date: 2:30 p.m., Tuesday, 13 August 2024.
Venue: Ramanujan hall
Host: Anandavardhanan
Speaker: Debanjan Nandi
Affiliation: IISc Bangalore
Title: Martin boundaries of groups hyperbolic to nilpotent subgroups
Abstract: The Martin boundary of a simple random walk on a finitely
generated group hyperbolic relative to nilpotent subgroups is not known in
general. For any such group one can however construct a 'natural' class of
random walks whose Martin boundary (probability-theoretic object) is
homeomorphic to the Bowditch boundary of the group (geometric object), and
the existence of such random walks characterizes these groups among
relatively hyperbolic groups. This is the main result I will discuss.
In the talk I plan to emphasize on giving an overview of this problem,
relations to more classical objects like the Brownian motion in manifolds
of negative curvature, and spend some time recalling the definitions of the
above class of groups, and the Martin boundary as a probabilistic and
potential-theoretic notion. I would also like to talk about further
questions that naturally arise, if time permits.