Nikon Kurnosov (Moscow) will speak in the geometry seminar on 10th November. The talk will be at 2pm in O8.08, 8th floor of building NO. Nikon’s title is *Betti numbers of hyperkahler manifolds* and his abstract follows.

Let M be a simple hyperkahler manifold, that is, a compact Riemannian manifold with holonomy equal to Sp(n). There are two known families of such manifolds and two sporadic examples; the quest to find more (or to prove that none other exist) is still ongoing. It is known that there are only finitely many families with a given second cohomology lattice, hence the bounds on second Betti number provide restrictions on the number of deformation classes of hyperkahler manifolds. I will explain boundary conditions for the second Betti number which follow from Rozansky-Witten invariants and so(4, b_2-2)-action on cohomology.