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UNIVERSITY OF CALIFORNIA, SANTA BARBARA BERKELEY DAVIS IRVINE LOS ANGELES MERCED RIVERSIDE SAN DIEGO SAN FRANCISCO
 

Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
Normal functions and disk counting
Dave Morrison
UCSB
Friday, January 11, 2008, 4:00 p.m.
Room 6635 South Hall
Abstract: In 1990, Candelas, de la Ossa, Green, and Parkes used the then-new
technique of mirror symmetry to predict the number of rational curves of each
fixed degree on a quintic threefold. The techniques used in the prediction were
subsequently understood in Hodge-theoretic terms: the predictions are encoded in a
power-series expansion of a quantity which describes the variation of Hodge structures,
and in particular this power-series expansion is calculated from the periods of the
holomorphic three-form on the quintic, which satisfy the Picard­Fuchs differential
equation.
In 2006, Johannes Walcher made an analogous prediction for the number of
holomorphic disks on the complexification of a real quintic threefold whose boundaries
lie on the real quintic, in each fixed relative homology class. (The predictions were

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics