Thin Parts of Arithmetic Locally Symmetric Spaces

by Prof. Jean Raimbault (Aix-Marseille Université)

Monday Dec 12, 2022, 2:00 PM → 3:15 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

The well-known collar or Margulis lemma describes the structure of negatively curved manifolds at mesoscopic scale, in particular it allows to describe these manifolds globally through the "thick-thin decomposition". This is not sufficient, however, to completely understand the homotopy type of the manifold, even roughly. In this talk I will describe an "arithmetic Margulis lemma" (essentially a consequence of work of E. Breuillard) which allows to describe thin parts at a macroscopic scale in certain circumstances, and how to use it to obtain sharp bounds on the volume of thin parts of arithmetic locally symmetric spaces. This is joint work with M. Frączyk and S. Hurtado.