Speaker: Bratati Som
Date: December 04, 2025
Affiliation: TIFR, Mumbai

Abstract: An acylindrical action generalizes proper and cobounded actions on hyperbolic spaces. Non-elementary acylindrical actions provide acylindrically hyperbolic groups, which includes most mapping class groups of punctured surfaces, $3$-manifold groups, and $\mathrm{Out}(F_n)$ for $n > 1$. In this talk, we will explore how acylindricity of a group action on a tree can be preserved under quotients by certain subgroups and discuss the existence of the largest acylindrical action for some groups acting on trees. In addition, we will show when $\mathrm{Out}(\mathrm{BS}(p,q))$ is acylindrically hyperbolic for non-solvable Baumslag-Solitar groups, despite $\mathrm{BS}(p,q)$ itself not being acylindrically hyperbolic, and explore further applications of these acylindricity results. This is a joint work with Daxun Wang.