A Kleinian eye on mapping class groups and higher-rank Lie groups

Organizers: Sami Douba, Theodore Weisman, Brandis Whitfield

Scientific committee: Kenneth Bromberg, Sara Maloni, Jing Tao

Sponsor: National Science Foundation grant DMS-1848346 (NSF CAREER - Maloni)

This workshop, in the tradition of the GEAR log cabin workshops, will be a week-long retreat themed around the exploration of subgroups of mapping class groups and higher-rank Lie groups via analogies with, and techniques from, Kleinian groups and hyperbolic geometry.

This is a satellite event for the SLMath programs Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups and Topological and Geometric Structures in Low Dimensions, and in particular the Pathways Workshop and Introductory Workshop that link the two programs and take place the following weeks.

There have been recent attempts to leverage the existing theory of Kleinian groups in non-hyperbolic settings by examining groups that are embedded in "hyperbolic directions." The aim of this workshop will be to survey some cutting-edge advances in this pursuit, which on occasions has even led to new insights on Kleinian groups themselves.

Participants will be divided into pairs/small groups, each of which will contribute a minicourse whose ultimate goal is to present recent work within one (or more) relevant subtopics, including (but not limited to):

• notions of geometric finiteness in the mapping class group;

• convex projective geometry beyond ellipsoids;

• combination theorems in mapping class groups, convergence groups, and higher-rank Lie groups;

• hyperconvex representations;

• surface subgroups of lattices and mapping class groups.

Each participant will be asked to contribute a lecture. If you are interested in participating, please apply by September 19, 2025.