Theory HEP Seminar

Enumerative geometry, mirror symmetry, and algebraic cycles

Johannes Walcher

CERN Theory Division

In this talk, I will review the solution of the (genus 0) Gromov-Witten theory of a Calabi-Yau threefold via the variation of Hodge structure of the mirror manifold. I will then describe a recently discovered extension of this correspondence, which connects real enumerative geometry with the normal function (ie, the image under the Abel-Jacobi map) of a particular algebraic cycle of the mirror manifold. The results on both sides of this correspondence are new, and are suggestive of further generalizations.