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We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
The n-dimensional pair of pants is defined to be the complement of n + 2 generic hyperplanes in CPn. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism A∞ alg...
this paper we study Lagrangian Floer theory on toric manifolds from the point of view of mirror symmetry. We construct a natural isomorphism between the Frobenius manifold structures of the (big) quan...
We outline work in progress suggesting an algebro-geometric version of the Strominger-Yau-Zaslow conjecture. We define the notion of a toric degeneration, a special case of a maximally unipotent degen...
We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes...
Talk given at Harvard, January 1999, published in the Proceedings of the Harvard Winter School on mirror symmetry, vector bundles and lagrangian cycles, 1999, International Press. Surveys the joint wo...

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