Geometry/Physics Seminar

Title: Homological Mirror Symmetry for a Calabi-Yau hypersurface in projective space
Speaker: Nick Sheridan
Speaker Info: MIT
Brief Description:
Special Note:

We prove homological mirror symmetry for a Calabi-Yau hypersurface in projective space. In the one-dimensional case, this is the elliptic curve, and our result is related to that of Polishchuk-Zaslow; in the two-dimensional case, it is the K3 quartic surface, and our result reproduces that of Seidel; and in the three-dimensional case, it is the quintic three-fold (also considered by Nohara-Ueda, using our work). After stating the result carefully, we will describe some of the techniques used in its proof. Namely, we will introduce equivariant versions of the affine and relative Fukaya categories, explain how they behave under ramified covers, and how to use a Morse-Bott model to make computations in them. We will go through the one-dimensional case with pictures. Finally, we will outline how to make computations in the derived category of coherent sheaves, via graded matrix factorizations.
Date: Thursday, September 22, 2011
Time: 4:00pm
Where: Lunt 107
Contact Person: Eric Zaslow
Contact email: zaslow@math.northwestern.edu
Contact Phone:
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