Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Nov 27, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Mark Shoemaker
University of Michigan
Title |
A Mirror Theorem for the Mirror Quintic (Joint w/ Y.P. Lee) |
Abstract |
The celebrated Mirror Theorem of Givental and Lian-Liu-Yau states that the A model (quantum cohomology, rational curve counting) of the Fermat quintic threefold is equivalent to the B model (complex deformations, period integrals) of its mirror dual, the mirror quintic orbifold. In order for mirror symmetry to be a true duality however, one must also show that the B model of the Fermat quintic is equivalent to the A model of the mirror quintic. We prove such an equivalence by relating the orbifold Gromov-Witten theory of the mirror quintic to period integrals over a one parameter deformation of the Fermat quintic. This involves new calculations in orbifold Gromov-Witten theory. |
Algebraic Geometry