March 27, 2014

Mathematics Colloquium lecture today

By Reta McDermott

Alexander Polishchuk, University of Oregon, will present "Analogs of the j-invariant for Higher Genus Curves" as part of the mathematics department Colloquium lecture series at 2:30 p.m. Thursday, March 27, in 102 Cardwell Hall.

The abstract for the lecture is: The j-invariant of an elliptic curve plays a central role in the classical theory of elliptic curves and modular functions. In the first part of the talk I will present an analogous construction for higher genus curves that uses only elementary algebraic geometry of curves. Then I will discuss how the j-invariant and its higher genus analogs appear in the study of certain A-infinity algebras associated with algebraic curves. A-infinity algebras are generalizations of usual algebras - in addition to double products they are equipped with n-tuple products satisfying appropriate higher associativity constraints. The homological mirror symmetry conjecture of Kontsevich relates some natural A-infinity algebras appearing in symplectic geometry with those appearing in algebraic geometry. The A-infinity algebras discussed in my talk are expected to appear on algebro-geometic side of this picture in the case of genus 1 the mirror symmetry equivalence has been established.