Mirror symmetry, elliptic fibrations, and Jacobi forms

Mirror symmetry, elliptic fibrations, and Jacobi forms

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Sheldon Katz, University of Illinois at Urbana-Champaign
Fine Hall 322

Please note special day (Wednesday).  We conjecture, with evidence, that the all-genus Gromov-Witten generating function of an elliptically fibered Calabi-Yau threefold is expressed as a quotient of weak Jacobi forms with a universal denominator. For the Calabi-Yau Weierstrass fibration over the projective plane, the conjecture allows the GW invariants for any curve class to be computed algorithmically up to genus 189, while the GW invariants for curve classes which project to a plane curve of degree at most 20 can be computed algorithmically to arbitrarily high genus. This talk is based on joint work with Min-xin Huang and Albrecht Klemm.