The Mirror Clemens-Schmid Sequence

Explore a 58-minute lecture by Charles Doran from the University of Alberta on the Mirror Clemens-Schmid Sequence. Delve into a four-term exact sequence connecting fibration cohomology to the cohomology of an open set, formed by removing the preimage of a general linear section of the base. Examine how this sequence respects Hodge, weight, and perverse Leray filtrations, forming an exact sequence of mixed Hodge structures on the graded pieces of the perverse Leray filtration. Consider the proposed mirror relationship to the Clemens-Schmid sequence, which describes degeneration structure, and investigate the "mirror P=W" conjecture linking filtrations. Analyze supporting evidence from the K3 surface setting, based on joint work with Alan Thompson.