Abstract: The P=W conjecture by de Cataldo, Hausel, and Migliorini suggests a surprising connection between the topology of Hitchin systems and Hodge theory of character varieties. In this talk, we will focus on interactions between Hilbert schemes, compact hyper-Kaehler geometries, and Hitchin systems. Such connections, together with symmetries coming from the moduli of compact hyper-Kaehler manifolds, lead to new progress on the P=W conjecture. I will discuss the results we obtained and the difficulties we met. Based on joint work with Mark de Cataldo and Davesh Maulik.

Please email Martijn Kool voor the Zoom link and password: M.Kool@uu.nl