| Abstract: |
In this talk I will summarize some of the techniques and applications appearing in my recent work with Vivek Shende, where we describe how to construct Calabi-Yau structures on categories that arise as global sections of (co)sheaves of categories. In our work, the main application of these techniques has been to understanding the duality structures appearing in infinitesimal and wrapped Fukaya categories of Weinstein manifolds, but we also describe how to get ertain Lagrangian correspondences on epresentation stacks. In the technical part of the talk, I plan on describing in more depth what is the role played by the diagonal and ualizing bimodules in this story and how hey interact with the sheaf structure. Time allowing, I will also talk about some more ecent research, also with Shende, where we propose to use similar methods in the context of stability conditions. |
