Mathematics

Hyperkahler (HK) manifolds appear in many fields of mathematics, suchas differential geometry, mathematical physics, representation theory,and algebraic geometry. Compact HK manifolds are one of the buildingblocks for algebraic varieties with trivial first Chern class andtheir role in algebraic geometry has grown immensely over the last 20year. In this talk I will give an overview of the theory of compact HKmanifolds and then focus on some of my work.