## Spectral geometry on metric graphs

Lior Alon

Member, School of Mathematics

September 22, 2020

Lior Alon

Member, School of Mathematics

September 22, 2020

Pablo Boixeda Alvarez

Member, School of Mathematics

September 22, 2020

Elia Bruè

Member, School of Mathematics

September 22, 2020

Laurent Côté

Member, School of Mathematics

September 22, 2020

Cheol-Hyun Cho

Seoul National University

September 21, 2020

For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in singularity theory. As an application, we formulate a complete version of Berglund-Hübsch homological mirror symmetry and prove it for two variable cases.

Daniel Juteau

Centre National de la Recherche Scientifique/Université Paris Diderot; Member, School of Mathematics

September 17, 2020

In this second talk about Broué’s Abelian Defect Group Conjecture, we will explain its geometric version in the case of finite groups of Lie type: the equivalence should be induced by the cohomology complex of Deligne-Lusztig varieties. This was actually the main motivation for the conjecture in the first place. We will illustrate those ideas with the case of SL(2,q).

Sanmi Koyejo

September 15, 2020

Mark Davenport

September 11, 2020

Laura Balzano

September 11, 2020

Vincent Colin

Université de Nantes

September 11, 2020

In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate Reeb vector field has either 2 or infinitely periodic orbits and that on a closed 3-manifold that is not graphed, every nondegenerate Reeb vector field has positive topological entropy.