 
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 thennew
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 Hodgetheoretic terms: the predictions are encoded in a
powerseries expansion of a quantity which describes the variation of Hodge structures,
and in particular this powerseries expansion is calculated from the periods of the
holomorphic threeform 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
