Yalong Cao (Chinese Academy of Sciences)

Title: Critical pullback in K-theory

Abstract: Given a (-1)-shifted Lagrangian L on a derived critical locus Crit(f), under fairly general hypothesis, we construct a natural pullback map from the critical K-theory of f to the Grothendieck group of coherent sheaves on L, and show it satisfies natural functorial properties. Applied to the case of quasimaps to critical loci, it allows us to define quantum critical K-theory. Joint work with Yukinobu Toda and Gufang Zhao.

Andres Herrero (University of Pennsylvania)

Title: Decomposition theorem for the logarithmic Hitchin fibration

Abstract: This talk will focus on the intersection cohomology of the moduli space of semistable logarithmic G-Higgs bundles on a smooth curve, where G is a reductive group. I will explain a uniform description of the decomposition theorem for the corresponding Hitchin fibration, and how this can be used to understand the degree dependence of the intersection cohomology of the moduli space.  This is based on joint work with Mark Andrea de Cataldo, Roberto Fringuelli and Mirko Mauri.