The P=W Conjecture in Genus Two and the Hodge Numbers of O'Grady 10

Explore a lecture by Mark Andrea de Cataldo from SUNY Stony Brook on two projects involving moduli of sheaves of families of curves and resulting perverse filtrations on their singular cohomology. Delve into the determination of Betti and Hodge numbers of the irreducible holomorphic symplectic variety known as O'Grady 10. Examine the establishment of the P=W conjecture for the Non Abelian Hodge Theory in arbitrary rank of a curve of genus two, and discover the strong evidence provided for arbitrary rank and genus. Gain insights into these complex mathematical concepts through this hour-long presentation from the University of Miami.