Seminar Algebra and Geometry: Nikon Kurnosov (University of Georgia, Athens, US)

Hyperkähler manifolds and their Betti numbers

Hyperkähler manifolds are higher-dimensional generalizations of K3 surfaces. The Beauville conjecture predicts that the number of deformation types of compact irreducible hyperkähler manifolds is finite in any dimension. In this talk I will briefly discuss some basic notions of the theory, explain why hyperkähler manifolds play a very important role in classification of complex manifolds, and then explain what are the evidences for Beauville's conjecture.

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