Seminar

For zoom details contact Christian Kaiser (kaiser@mpim...)

Miniseries abstract: The Fukaya category is an invariant of a symplectic manifold governing the intersection theory of its Lagrangian submanifolds, built from the pseudoholomorphic disks which bound these Lagrangians. One particularly important version for non-compact symplectic manifolds is the partially wrapped Fukaya category, which plays a prominent role in homological mirror symmetry. This miniseries will lead up to a toolbox for computing and studying structural properties of partially wrapped Fukaya categories. One of the key tools is a descent formula, i.e. a cosheaf property with respect to Weinstein sectorial coverings. We will emphasize concrete examples, and homological mirror symmetry will be a recurring point of reference.

Tensor-triangular geometry is a geometric approach to certain classification problems in a wide variety of contexts, ranging from topology to representation theory and algebraic geometry. In a series of three talks we will introduce the audience to this approach, particularly geared towards the study of cohomological (or, "motivic") aspects of algebraic varieties. In the last few years, this has unearthed interesting structures in categories of motives which we will report.