Refined HarderNarasimhan filtrations in moduli theory
Refined HarderNarasimhan filtrations in moduli theory

Andrés Ibáñez Núñez, Columbia University
Fine Hall 322
We introduce a notion of refined HarderNarasimhan filtration, defined abstractly for algebraic stacks satisfying natural conditions. Examples include moduli stacks of objects at the heart of a Bridgeland stability condition, moduli stacks of Ksemistable Fano varieties, moduli of principal bundles on a curve, and quotient stacks. We will explain how refined HarderNarasimhan filtrations are closely related both to stratifications and to the asymptotics of certain analytic flows, relating and expanding work of Kirwan and HaidenKatzarkovKontsevichPandit, respectively. In the case of quotient stacks by the action of a torus, the refined HarderNarasimhan filtration can be computed in terms of convex geometry.