![A perspective projection of a dodecahedral tessellation in H3. Four dodecahedra meet at each edge, and eight meet at each vertex, like the cubes of a cubic tessellation in E3.](/ImageCropToolT4/imageTool/uploaded-images/algebra-geometry-vector-269401_1706103833621_eventportrait2018_x1.jpg)
Title: Refined Harder-Narasimhan filtrations in moduli theory
Speaker: Andrés Ibáñez Núñez
Abstract: We introduce a notion of refined Harder-Narasimhan 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 K-semistable Fano varieties, moduli of principal bundles on a curve, and quotient stacks. We will explain how refined Harder-Narasimhan filtrations are closely related both to stratifications and to the asymptotics of certain analytic flows, relating and expanding work of Kirwan and Haiden-Katzarkov-Kontsevich-Pandit, respectively. In the case of quotient stacks by the action of a torus, the refined Harder-Narasimhan filtration can be computed in terms of convex geometry.
Some snacks will be provided before and after the talk.