## Speaker:

Giovanni Mongardi

## Title:

Automorphisms of holomorphic symplectic manifolds

## Abstract:

We will give an overview of known results on automorphisms of irreducible symplectic manifolds, focusing on deformations of Hilbert schemes of points on $K3$ surfaces. In particular, we will explain the technical tools that can lead to a classification and we will describe deformations of pairs (manifold, automorphisms) in the symplectic and nonsymplectic cases.