Geometry & Physics Seminar

For a hyper-kähler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse t-structure. We will discuss the role played by this filtration in the study of the topology and geometry of hyper-kähler varieties, as well as the connection to curve counting invariants of Calabi-Yau 3-folds. In particular, we will discuss recent progress on the P=W conjecture for Hitchin systems, and its compact analog for Lagrangian fibrations. Based on joint work with Qizheng Yin and Zili Zhang.
Speaker(s): Junliang Shen (MIT)