## Finiteness results for hyperkaehler manifolds – Ljudmila Kamenova

In this talk we are going to show that there are finitely many deformation types of hyperkaehler manifolds with fixed topological invariants such as the Fujiki constant and the discriminant of the BBF form. For hyperkaehler manifolds that admit a fibration structure it is enough to fix the degree of the polarization on the general fiber in order to obtain a finiteness result. The subject of this talk is a class of codes based on combinatorial designs. These combinatorial codes possess remarkable error-correction properties, admit efficient decoding, and present a viable alternative to a subclass of Reed-Muller codes.