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This talk will try to introduce non-specialists to some key concepts in mirror symmetry, by considering some of the simplest examples (such as cylinders or pairs of pants). These examples will be a pretext to discuss the Strominger-Yau-Zaslow picture of mirror symmetry (according to which mirror pairs carry dual torus fibrations), as well as Kontsevich's homological mirror symmetry conjecture (according to which mirror symmetry is an equivalence between two derived categories). I will also try to motivate the appearance of "wrapped" Fukaya categories in the case of open manifolds. The less introductory parts of the talk are based on joint work with Mohammed Abouzaid, Alexander Efimov, Dmitri Orlov, and Ludmil Katzarkov.

There will be a dinner for the speaker.