|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 Special DPMMS Colloquium 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 listsFriday Morning Seminars, Dept of Veterinary Medicine Ancient India and Iran Trust Institution of Engineering and Technology Public Lectures
Other talksMetabolomics 2016 Pregnancy and Childbirth: Discussing current academic research and clinical expertise to ensure a healthy pregnancy. The mechanics of internal wave generation by volcanic eruptions Helminth-induced suppression of inflammation – a role for the gut microbiota? Molecular and cellular studies of membrane perforation in the arms race between host and pathogen Design for Security Test against Fault Injection Attack, and Fast Test with Compressive Sensing