3:45PM  6:00PM: Moduli spaces of curves with nonspecial divisors and Ainfinity algebrasAlexander PolishchukIn the first hour I will give an introduction to Ainfinity algebras and will explain how studying certain Ainfinity algebras associated with curves one gets an isomorphism between a moduli space of Ainfinity algebras and the moduli space of pointed curves (with possibly nonnodal singularities) such that the marked points form a nonspecial ample divisor. In the second hour I will discuss geometry of the latter moduli spaces. I will show that such curves have natural projective embeddings, with a canonical choice of homogenous coordinates up to rescaling. Using Groebner bases technique this leads to the identification of the moduli with the quotient of an affine scheme by the torus action. In the genus 1 case I will describe explicitly the corresponding GIT stability conditions. In characteristic zero this picture is complemented by canonical choices of formal parameters at marked points, leading to an interpretation of the moduli spaces in terms of the Krichever map.
