Special Colloquium
Yanki Lekili
King's College
An arithmetic refinement of homological mirror symmetry for the 2-torus
Abstract: We explore a refinement of homological mirror symmetry which relates exact symplectic
opology 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 of coherent sheaves on the Tate curve over the "formal disc" Spec Z[[q]]. It
specializes over the "punctured disc" Spec 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 joint
work with Tim Perutz.
Tea at 4:15
Thursday January 31, 2013 at 3:00 PM in SEO 636