Polytopes, Polynomials, and Picard-Fuchs Equations

12/07/2010 - 12:15pm
12/07/2010 - 1:10pm
Ursula Whitcher (Harvey Mudd College)

Mirror symmetry predicts that varying the complex structure of a family of Calabi-Yau varieties should correspond to varying the Kaehler structure of a mirror family. The variation of complex structure for a family of Calabi-Yau varieties is encoded in a differential equation called the Picard-Fuchs equation. We'll describe how to realize Calabi-Yau varieties as hypersurfaces in toric varieties using combinatorial objects called polytopes. Then we'll describe an algorithm for computing the Picard-Fuchs equations of families of hypersurfaces. We use our techniques to study symmetric families of complex surfaces. This talk describes joint work with Dagan Karp, Jacob Lewis, Daniel Moore (HMC '11), and Dmitri Skjorshammer (HMC '11).

Millikan 208 (Pomona College)