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Abstract:
Abstract: We give an introduction to the theory of operads, props and wheeled props, explain how an arbitrary formal Poisson structure can be identified with a representation of a certain graph complex with surprisingly small cohomology ("genes"), and discuss applications of these results to deformation quantization.
Abstract: I will give an introduction to an important class of 2D and 3D topological field theories (TFTs). In particular I will consider the Poisson sigma model, A-model, B-model and their different generalizations. The construction of these models within BV-AKSZ formalism will be reviewed. I will finish with a brief review of the quantization of those models.
Abstract: In this course, I'll introduce generalized complex structures, generalized Kahler structures and their submanifolds. After going over the basics, we will discuss nontrivial examples of generalized complex structures in 4 dimensions constructed via surgeries and blow down. A second goal is to discuss a quotient procedure for these structures which includes both symplectic reduction and complex quotients.
Abstract: Supersymmetric non-linear sigma models have an intriguing relation to complex geometry. The subject has a history of almost thirty years. I will cover some of this starting from the first results by Zumino and Alvarez-Gaumé proceeding via the bi-hermitean geometry of Gates-Hull and Rocek and end up with the present understanding of Generalized Kähler Geometry gained from N=2 superspace formulations of sigma models.