Poincar\'e profiles of groups and spaces

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Tim\'{a}r. In this paper we focus on properties of the Poincar\'{e} profiles of groups with polynomial growth, and of hyperbolic spaces, where we deduce a connection between these profiles and conformal dimension. As applications, we use these invariants to show the non-existence of coarse embeddings in a variety of examples.Comment: 55 pages. To appear in Revista Matem\'atica Iberoamerican

Arithmetic Groups vs. Mapping Class Groups: Similarities, Analogies and Differences

Arithmetic groups arise naturally in many fields such as number theory, algebraic geometry, and analysis. Mapping class groups arise in both low dimensional topology and geometric group theory. They have been studied intensively by different groups of people. The purpose of this workshop is to bring experts and aspiring young mathematicians together to interact and develop further exchanges and new collaboration

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum