In the solar system as elsewhere, we learn most from the unexpected. I will describe three recent observational projects challenging existing ideas about solar system objects, and provoking new ones. The freaks are an interstellar object (‘Oumuamua) and a long-period comet (C/2017 K2), active far beyond Uranus. The conundrum concerns the origin of the Trojans of Neptune in the context of planetary migration.
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.
In conformal field theory, in contrast to gapped theories, S-matrix is not well-defined. Similarly, various inclusive observables which make sense in a gapped theory, such as "energy squared" calorimeters, suffer from IR divergences in CFTs. Using the example of Wilson-Fisher theory, I will discuss how these observables can be renormalized and what is the physical meaning of their anomalous dimensions.
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).