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Topics in Mirror Symmetry

Course Type: 
PhD Course
Academic Year: 
20 h

Mirror symmetry is a mysterious duality discovered by string theorists in the 80-s. Mirror symmetry has attracted a lot of attention in mathematics since the beginning of the 90-s when a group of string theorists used it to make astonishing predictions in enumerative geometry. In this course we will focus on a conjectural formulation of Mirror Symmetry called Homological Mirror Symmetry (HMS) which is due to Kontsevich. HMS is formulated in terms of two subtle invariants, the derived category and the Fukaya category.  The topics that we will cover in this course might vary depending on the audience interest: they might include the proof of HMS in some fundamental example (e.g. the elliptic curve), and the recent  sheaf-theoretic models of the Fukaya category. The course will be based on frontal lectures and seminars given by the participants to the course. The final mark will be based on seminars given by the students.

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