I will discuss the existence of very stable Higgs bundles how it implies a precise formula for the multiplicity of the components of the nilpotent cone and its relationship to mirror symmetry. Joint project with Nigel Hitchin.

Tamas Hausel is currently professor at IST Austria. He was previously professor at Oxford and EPFL(Switzerland). Professor Hausel has made important contributions to geometry, topology, and arithmetic of moduli spaces arising in supersymmetric quantum field theories and representation theory of quivers, finite groups, Lie and Hecke algebras. He received several distinctions including Whitehead Prize in 2008 and an ERC advanced grant in 2013.