In this talk, we will first provide a brief overview of the journey of amenability starting from the Banach-Tarski Paradox on a sphere all the way to topological amenability on a locally compact group. We will then move ahead to introduce and explore the concept of topological amenability in the broader category of (semi)-hypergroups, which are natural extensions to the category of locally compact (semi)groups. Finally in this broader setting, we will discuss certain stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as F-algebraic (certain kind of Banach algebras) properties of the associated measure algebras. We conclude by briefly discussing topological amenability of sub-semihypergroups, that in turn provides an affirmative answer to a long-standing open question on semigroups asked by J. Wong in 1980.

The video of this talk is available on the IISc Math Department channel.