JCAS Lecture Series

• Generalized Geometry - Prof. Nigel Hitchin
  
  
• Gluing Asymptotically Cylindrical Associatives - Dr. Johannes Nordstrom
  
  
• Landau-Ginzburg B-models - Dr. Edward Segal

Generalized Geometry

by

Professor Nigel Hitchin,
Department of Mathematics
University of Oxford

Abstract:

Generalized geometry is an approach to differential geometry initiated by the Lecturer which incorporates in classical terms some of the features of supersymmetric theories in physics such as the B-field and T-duality. A particularly important case is that of a generalized complex structure which is a common framework for both complex and symplectic geometry and for the physicists is the structure on the target space in the sigma-model in order to have N=2 supersymmetry. This subject was developed by Gualtieri and Cavalcanti and recent results have provided existence theorems and examples for a number of associated objects, generalizing complex submanifolds and holomorphic vector bundles. Poisson geometry, both real and complex, plays an important role. The lectures will introduce and develop the subject and emphasize the geometry associated with holomorphic Poisson manifolds.

Gluing Asymptotically Cylindrical Associatives

by

Dr. Johannes Nordstrom,
Department of Mathematics
Imperial College London

Landau-Ginzburg B-models

by

Dr. Edward Segal,
Department of Mathematics
Imperial College London

Abstract:

A Landau-Ginzburg model is a Kahler manifold X together with a holomorphic function W. Physicists have predicted the existence of a topological field theory, called the B-model, arising from the algebraic geometry of any Landau-Ginsburg model (X,W). This theory is a generalization of the derived category of coherent sheaves, and also of the theory of matrix factorizations. I’ll describe this theory, starting from an introductory level, and go on to discuss two further topics: the proof that the full TFT structure exists when X is affine, and the existence of interesting equivalences between LG B-models.