Real Cubings and Large Scale Geometry of Hierarchically Hyperbolic Groups (24rit021)


Ilya Kazachkov (Ikerbasque - Basque Foundation for Science)


The Banff International Research Station will host the "Real Cubings and Large Scale Geometry of Hierarchically Hyperbolic Groups" Research in Teams workshop in Banff from May 19 - 26, 2024.

The philosophy of studying groups from far away can be dated back to Gromov. Finitely generated groups are discrete objects and so the traditional local geometric machinery cannot be used to study them. In his influential paper on asymptotic invariants, Gromov suggested that, in order to regain the geometric perspective, one should change the position and move up the observation point infinitely far away. By doing this, one obtains the \emph{asymptotic cone of the group}, a more continuous object that is amenable to study by topological, dynamical, and infinitesimal machinery, and which ``fills our geometer's heart with joy" (to quote Gromov). The aim of our project is to study asymptotic cones of hierarchically hyperbolic groups.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. BIRS is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Alberta Technology and Innovation.