| Résume | [L'exposé aura lieu en hybride, dans la salle 1016 et sur zoom : https://u-paris.zoom.us/j/89901122981?pwd=T1ltN2pDTTJoUVI2eTIwRmpNZU94QT09]
Examples of 2CY categories include the category of coherent sheaves on a K3 surface, the category of Higgs bundles, and the category of modules over preprojective algebras or fundamental group algebras of compact Riemann surfaces. Let p:M->N be the morphism from the stack of semistable objects in a 2CY category to the coarse moduli space. I'll explain, using cohomological DT theory, formality in 2CY categories, and structure theorems for good moduli stacks, how to prove a version of the BBDG decomposition theorem for the exceptional direct image of the constant sheaf along p, even though none of the usual conditions for the decomposition theorem apply: p isn't projective or representable, M isn't smooth, the constant mixed Hodge module complex Q_M isn't pure... As an application, I'll explain how this allows us to extend nonabelian Hodge theory to Betti/Dolbeault stacks. |
