Dipartimento di Matematica, Aula Magna.<\/p>\n
Irreducible holomorphic symplectic (IHS) varieties can be thought as a generalization of hyperk\u00e4hler manifolds allowing singularities. Among them we can find for example moduli spaces of sheaves on $K3$ and abelian surfaces, which have been recently shown to play a crucial role in nonabelian Hodge theory. After recalling the main features of IHS varieties, I will present several results concerning their intersection cohomology and the perverse filtration associated with a Lagrangian fibration, establishing a compact analogue of the celebrated $P=W$ conjecture by de Cataldo, Hausel and Migliorini for varieties which admit a symplectic resolution. The talk is based on joint works with Mirko Mauri, Junliang Shen and Qizheng Yin.<\/p>\n
Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" Irreducible holomorphic symplectic (IHS) varieties can be thought as a generalization of hyperk\u00e4hler manifolds allowing singularities. Among them we can find for example moduli spaces of sheaves on $K3$ and abelian surfaces, which have been recently…<\/p>\n