GAAG seminar - Classification problems for birational automorphisms of hyperkaehler manifolds

Hyperkaehler manifolds are one of the building blocks for compact Kaehler manifolds with trivial first Chern class. The question of understanding their symmetries comes up naturally. For instance, they can allow one to construct examples with interesting geometric features. Thanks to the existence of a (Strong) Torelli theorem, as for K3 surfaces, hyperkaehler manifolds and their birational automorphisms can be studied numerically through a distinguished quadratic form on their second integral cohomology. 
In this talk, I introduce the standard lattice theory used to study such symmetries of finite order, and I will present two of the main classification problems which arise in this context. We will also discuss recent approaches to work on these problems, both computationally and theoretically.