NSCPHD1272 Homological Mirror Symmetry, Deformation Quantization and Noncommutative Geometry

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• Subject area

     Homological Mirror Symmetry

• Scientific content

     Homological mirror symmetry (HMS) is a conjecture made by Maxim Kontsevic during his address to the 1994 International Congresss of Mathematicians in order to elucidate a long standing mystery bewteen certain manifolds in Physics. HMS is expected to explain a phenomenon observed in string theory, called mirror symmetry. Ever since its formulation, several connections with active areas of mathematical research have been found, deformation theory and non-commutatiave geometry (NCG) to name af few. The goal of the masterclass is to introduce HMS and explore its connection with NCG, using deformation theory as a tool. Lars Halvard Halle (KU) will give lectures on algebraic geometric prerequisites of HMS, Yan Soibelman (KSU) will talk about HMS and Noncommutative geometry and how deformation quatization comes into the picture, Ryszard Nest (KU) will talk about the role played by deformation quantization in NCG, and Ludmil Katzarkov (UV) will talk about HMS and some of its applications.

• Learning outcome:

     Homological mirror symmetry is  a highly specialized area of math and we expct the participants to have varied mathematical backgrounds. For this reason, I propose a 7-day duration with some problem solving session facilitated by Clarisson Rizzie Canlubo (KU). In the end, we expect the participant to have not just an appreciation of the interplay between HMS and NCG but also a decent understanding of the technicalities involved therein.