SGGTC this Friday: Abigail Ward and Yingdi Qin
Oleg Lazarev
Dear all,
This Friday we have two speakers. Abigail Ward from Harvard will give a talk at 10:30 am in Math 520. Yingdi Qin from Harvard will give a talk at 1:00 pm in Math 407. We will meet at 11:35 in the lobby and go out for lunch.
Best, Oleg
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Abigail Ward: Homological mirror symmetry for elliptic Hopf surfaces
Abstract: We show that homological mirror symmetry is a phenomenon that exists beyond the world of Kähler manifolds by exhibiting HMS-type results for a family of complex surfaces which includes the classical Hopf surface (S^1 x S^3). Each surface S we consider can be obtained by performing logarithmic transformations to the product of P^1 with an elliptic curve. We use this fact to associate to each S a mirror "non-algebraic Landau-Ginzburg model" and an associated Fukaya category, and then relate this Fukaya category and the derived category of coherent analytic sheaves on S.
Yingdi Qin: Coisotropic branes on symplectic tori
Abstract: We show that homological mirror symmetry is a phenomenon that exists beyond the world of Kähler manifolds by exhibiting HMS-type results for a family of complex surfaces which includes the classical Hopf surface (S^1 x S^3). Each surface S we consider can be obtained by performing logarithmic transformations to the product of P^1 with an elliptic curve. We use this fact to associate to each S a mirror "non-algebraic Landau-Ginzburg model" and an associated Fukaya category, and then relate this Fukaya category and the derived category of coherent analytic sheaves on S.
Yingdi Qin: Coisotropic branes on symplectic tori
Abstract: Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapstin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori the version of Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it.
Abstract: Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapstin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori the version of Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it.