Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics

Tatiana Bandman 1 , Shelly Garion 2 ,  and Boris Kunyavskiĭ 1
  • 1 Department of Mathematics, Bar-Ilan University, Ramat Gan, 5290002, Israel
  • 2 Fachbereich Mathematik und Informatik, Universität Münster, Einsteinstrasse 62, Münster, 48149, Germany

Abstract

We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.

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