The homogeneous coordinate ring of a projective variety may be constructed by geometrically quantizing the multiples of a symplectic form, using the complex structure as a polarization. In this talk, I will explain how a holomorphic Poisson structure allows us to deform the complex polarization into a generalized complex structure, leading to a non-commutative deformation of the homogeneous coordinate ring. The main tool is a conjectural construction of a category of generalized complex branes, which makes use of the A-model of an associated symplectic groupoid. I will explain this in the example of toric Poisson varieties. This is joint work with Marco Gualtieri (arXiv:2108.01658).

TBA

The so called Drinfeld conjecture states that the complement to very stable bundles has pure codimension one in the moduli space of vector bundles. In this talk I will explain a constructive proof in rank three, and discuss if/how it generalises to wobbly fixed points of the nilpotent cone as defined by Hausel and Hitchin. This is joint work with Pauly (Nice).

The curve graph of a surface of finite type is a fundamental object in the study of its mapping class group both from the metric and the combinatorial point of view. I will discuss joint work with Valentina Disarlo and Thomas Koberda where we conduct a thorough study of curve graphs from the model theoretic point of view, with particular emphasis in the problem of interpretability between different curve graphs and other geometric complexes.   

In this talk I will review the “holomorphic modular bootstrap,” i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, Zn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.