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The tropical vertex

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Mirror symmetry is a phenomenon discovered by string theorists around 1989, positing that Calabi-Yau manifolds (conjecturally the three complex-dimensional manifolds used to compactify space-time in superstring theory) come in “mirror” pairs. Miraculously, in 1990 Candelas, de la Ossa, Green, and Parkes showed that certain traditionally very hard-to-compute data on one manifold (counting holomorphic maps from the Riemann sphere into the Calabi-Yau manifold) could be computed via certain integrals on the other manifold. There is now a huge industry devoted to understanding why this happens.

In joint work with Rahul Pandharipande and Bernd Siebert, I will explain a new example of mirror symmetry, which has the advantage of being easy to explain and at the same time is believed to lie at the heart of an explanation of mirror symmetry in general.

This talk is part of the Kuwait Foundation Lectures series.

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