This will be a follow-up of the March 2019 workshop and the 2021 online workshop. As before, the program lies at the juncture of three areas:
(1) Probability theory of random processes on negatively curved spaces.
(2) Ergodic theory and hyperbolic dynamics
(3) hyperbolic geometry.
The 2019 workshop laid stress on random walks, while the 2021 workshop emphasized Bernoulli percolation among topics allied with probability. While random walks on hyperbolic groups have received some attention, other random processes, such as first and last passage percolation, are in a barely nascent state. This is not due to a dearth of problems but rather that people with a dual expertise in both the relevant probabilistic methods and a feel for the geometry of negatively curved spaces, are rare.
The 2021 workshop addressed this lacuna by having a set of talks on Bernoulli percolation. The 2023 workshop will deal with more advanced themes like Liouville quantum gravity.
2. Ergodic theory: Invariant Random Subgroups:
The 2021 program brought the topic of IRS (Invariant Random Subgroups) to the attention of Indian mathematicians. The subject is in its infancy, and draws from a large number of themes:
(1) ergodic theory of lattices in Lie groups.
(2) Spectral geometry.
(3) Geometric or Gromov-Hausdorff limits
(4) representation theory of Lie groups
Each of these aspects has a sizeable Indian presence. Thus, the 2023 program will have a follow-up component on IRS emphasizing these interactions.
3. Hyperbolic Geometry:
The 2019 program involved random walks on hyperbolic spaces in the sense of Gromov, while the 2021 workshop stressed Patterson-Sullivan theory. A number of other aspects of hyperbolic geometry, including symbolic dynamics, circle packing and other random processes have become important across disciplines. We hope to cover some of these topics in the 2023 workshop.
Eligibility criteria: Research interests at the interface of geometry, dynamics, and probability demonstrable by research output (for faculty/postdocs) or topics studied (for PhD students).
ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.