JCAS Lecture Series

 

 

 

 

 

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.

 

 
Venue: Room 502A, Academic Building No. 1, CUHK, Hong Kong
March 14, 2010
(Wednesday)
2:00 pm - 3:00pm
Lecture 1: The Courant bracket, the B-field and skew torsion
3:30 pm - 4:30 pm
Lecture 2: Gerbes, spinors and twisted cohomology
March 23, 2010
(Tuesday)
2:00 pm - 3:00pm
Lecture 3: Generalized complex manifolds and Poisson structures
3:30 pm - 4:30 pm
Lecture 4: Goto's deformation theorem
March 24, 2010
(Wednesday)
2:00 pm - 3:00pm
Lecture 5: Generalized holomorphic bundles and Poisson modules
3:30 pm - 4:30 pm
Lecture 6: Generalized holomorphic bundles and the B-field action

 

   

Gluing Asymptotically Cylindrical Associatives

by

Dr. Johannes Nordstrom,
Department of Mathematics
Imperial College London

 

 
Venue: Room 502A, Academic Building No. 1, CUHK, Hong Kong
March 16, 2010
(Wednesday)
9:20 pm - 10:40pm
Gluing Asymptotically Cylindrical Associatives
March 18, 2010
(Thursday)
9:20 pm - 10:40pm
March 23, 2010
(Tuesday)
9:20 pm - 10:40pm
March 25, 2010
(Thursday)
9:20 pm - 10:40pm

 

   

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. Ill 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.

 

 
Venue: Room 502A, Academic Building No. 1, CUHK, Hong Kong
March 11, 2010
(Thursday)
9:30 pm - 11:00pm
Landau-Ginzburg B-models
March 12, 2010
(Friday)
9:30 pm - 11:00pm
March 13, 2010
(Saturday)
9:30 pm - 11:00pm