Quantization and Gromov-Witten theory -- Tom Coates, 
September 26, 2003

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We describe a new point of view on Gromov-Witten theory, due to
Givental, which reveals surprising connections with symplectic
linear algebra, quantization and the theory of loop groups.  We
then explain how to use this to prove the Mirror Conjecture of
Candelas, de la Ossa, Green and Parkes, which predicts the
"virtual number" of holomorphic spheres of all degrees lying
on a quintic threefold.  This is joint work with Alexander
Givental.