Embeddings of maximal tori in orthogonal groups
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic to contain a maximal torus of a given type.
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
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.
Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen.