Abstract Matt Kerr

Matt Kerr will speak on

Hodge theory of degenerations

Abstract: The asymptotics and monodromy of periods in degenerating families of algebraic varieties are encountered in many settings — for example, in comparing various compactifications of moduli, in computing limits of invariants of algebraic cycles, and in applications to physics (Feynman amplitudes, topological string theory, etc.). In this talk, based on joint work with Radu Laza and Morihiko Saito, we shall describe several tools (building on classical work of Milnor, Deligne, Clemens, Steenbrink and Saito) for comparing the Hodge theory of singular fibers to that of their nearby fibers. After touching on some relations to birational geometry, we will explain how the theory works for several (non-semistable) degenerations of K3 surfaces arising in MMP and GIT compactifications of moduli.