Room P3.10, Mathematics Building

Luca Migliorini, University of Bologna
Topological properties of a class of algebraically completely integrable systems with $C^*$ action

I will discuss two examples, one arising from non-abelian Hodge theory, the other from Hilbert schemes of surfaces, of algebraically completely integrable systems with $C^*$ action, showing an as yet not understood behaviour. In both cases there exists another holomorphic symplectic variety whose Hodge theory reflects some topological properties of the integrable systems, more precisely, the weight filtration on the cohomology of this latter variety coincides up to a trivial renumbering with a topological filtration associated with the “integrable system map” (a variant of the Leray filtration, called the perverse Leray filtration). Joint work with M. de Cataldo, T. Hausel.