Conjugation-invariant norms on arithmetic groups

Abstract: A classical theorem of Ostrowski says that every absolute value on the field of rational numbers, or equivalently on the ring of integers, is equivalent to either the standard (real) absolute value, or a $p$-adic absolute value, for which the closure of the integers is compact. In this talk we will see a non-abelian analogue of this result for $SL(n\ge3,\Z)$, and related groups of arithmetic type. We will see a relation to the celebrated Margulis' normal subgroup theorem, and derive rigidity results for homomorphisms into certain non-locally compact groups -- those endowed with a bi-invariant metric. We will also discuss a relation to the deep work of Nikolov-Segal on profinite groups. This is a joint work with Leonid Polterovich and Yehuda Shalom.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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