ESI Program: minicourses

• Selected applications on the antifield-BRST (BV) formalism, by M. Henneaux:

Abstract:

• Principles of antifield formalism. Koszul-Tate resolution, longitudinal derivative.
• Computation of local cohomologies: selected examples
• Applications to the problem of consistent interactions for theories with a gauge freedom. First order deformations. Obstructions.
• Quantum Master Equation. Measure.


• (Proper) Lie groupoids and Poisson geometry, by R. L. Fernandes:

Abstract:

• Introduction to Lie groupoids and Lie algebroids. The integrability problem. Relationship with Poisson geometry and the Poisson sigma-model.
• Basic properties of proper groupoids. Linearization and slices. Stratifications. Morita equivalence and orbispaces.
• Groupoid versus algebroid cohomology. Van Est maps. Vanishing of cohomology.
• Symplectic groupoids. Monodromy lattice. Applications to Poisson topology.


• Poisson structure as a graph complex , by S. Merkulov:

  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.



• Low dimensional TFTs and sigma models , by M. Zabzine:

  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.



• Generalized complex geometry, by G. Cavalcanti :

  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.



• Generalized geometry and super-symmetric sigma models, U. Lindstrom:

  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.