Hierarchical hyperbolicity from a cubical perspective

G2T2 Seminar

Organizer：

G2T2 Group

Speaker：

Abdul ZALLOUM (Harbin Institute of Technology)

Time：

Fri., 10:00-11:30 am, Mar. 28, 2025

Venue：

Ningzhai 203

Title:

Hierarchical hyperbolicity from a cubical perspective

Abstract：

The theory of hierarchically hyperbolic spaces (HHSs) emerged from the observation that many cocompact CAT(0) cube complexes (CCCs) exhibit a structure analogous to that of mapping class groups and Teichmüller spaces. In particular, the powerful machinery of subsurface projections, which plays a fundamental role in the study of mapping class groups and Teichmüller spaces, extends to a broad class of CCCs. This insight not only led to the definition of HHSs but also raised the natural question of whether the reverse perspective holds: Can techniques from CCCs be leveraged to study mapping class groups, Teichmüller spaces, and HHSs more generally? In this talk, I will define these key objects and discuss recent developments that shed light on this question.