|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
An arithmetic refinement of homological mirror symmetry for the 2-torus
If you have a question about this talk, please contact Julia Blackwell.
This talk has been canceled/deleted
We explore a refinement of homological mirror symmetry which relates exact symplectic topology to arithmetic algebraic geometry. We establish a derived equivalence of the Fukaya category of the 2- torus, relative to a basepoint, with the category of perfect complexes on the Tate curve over Z[[q]]. It specializes to an equivalence, over Z, of the Fukaya category of the punctured torus with perfect complexes on the nodal Weierstrass curve y2+xy=x3, and, over the punctured disc Z((q)), to an integral refinement of the known statement of homological mirror symmetry for the 2- torus. We will survey a general strategy of proof of homological mirror symmetry while carrying it out in the specific case of the 2-torus. In contrast to the abstract statement of our main result, the focus of the talk will be a concrete computation which we will express in more familiar terms. This is my joint work with Tim Perutz.
This talk is part of the DPMMS Presentations series.
This talk is included in these lists:
This talk is not included in any other list
Note that ex-directory lists are not shown.
Other listsPublic talk: Duncan Watts Sir David King's Surface Science Seminars Quastel Midgen LLP Presentation
Other talks“Leveraging social psychological theory to understand engagement with personalized genomic information in a genome sequencing trial” Title 'TBA' Manifold correspondence: a signal processing perspective The evolution of Business Models [Provisional - TBC] New Frontiers in Submillimetre-Wave and Far-Infrared Atmospheric Science Workshop Deadwood taxonomies: trees of nature before evolution