MS Seminar (Mathematics - String Theory)

Speaker: David Morrison (UC Santa Barbara )
Title: Supersymmetric T^3 Fibrations
Date: Thu, Nov 18, 2010, 15:30 - 17:00
Place: Seminar Room A
Abstract: When mirror symmetry between Calabi-Yau threefolds was discovered around 1990, it looked completely mysterious, asserting connections between Hodge theory and curve-counting on pairs of Calabi-Yau threefolds which had no apparent geometric relationship. That situation changed somewhat in 1996, when Strominger, Yau, and Zaslow proposed that Calabi-Yau threefolds should generally admit fibrations by three-tori (singular fibers are allowed), with mirror pairs being obtained by dualizing the fibers in the fibrations. In the Strominger-Yau-Zaslow story, the three-tori should preserve half of the supersymmetry of the bulk theory, which is geometrically expressed by saying that they should be special Lagrangian submanifolds of the Calabi-Yau threefold.

The details of how this story works near singular fibers in the fibration are still somewhat elusive. There has been substantial work by Gross, Wilson, Ruan, Joyce and others to determine what those details should be; in this talk, I will synthesize those works and formulate some precise conjectures about the structure of supersymmetric T^3 fibrations which are consistent with the basic Strominger-Yau-Zaslow picture. Towards the end of the talk, I will speculate on some further extensions of these ideas and explain what they suggest about the structure of Calabi-Yau moduli space.
Remarks: As usual in this seminar, the first 25 minutes will provide a general introduction to the subject aimed at a broad audience.