Vorlesungen
course plan:
| week | content | references |
| 01 | Geometric structures I | |
| 02 | Geometric structures II | |
| 03 | Linear algebra of V + V* |
gualtieri2004 Chapter 2: Linear Algebra of V + V* marcut2016 An introduction to Dirac Geometry |
| 04 | Spinors for V + V* |
gualtieri2004 Chapter 2: Linear Algebra of V + V* korman2016 Spin Geometry meinrenken2013 Clifford Algebras and Lie Theory picard2022 Notes on Spinors and Non-Kahler Threefolds
|
| 05 | Linear generalized complex structures |
cavalcanti2007 Introduction to generalized complex geometry gualtieri2004 Chapter 2, 4: Generalized complex structures |
| 06 | Courant bracket, twists and symmetries |
gualtieri2004 Chapter 3: The Courant bracket |
| 07 | Generalized complex structures |
cavalcanti2006 The decomposition of forms and cohomology of generalized complex manifolds gualtieri2004 Chapter 4: Generalized complex structures
|
| 08 | Deformation of generalized complex structures | |
| 09 | Deformations and symmetries | |
| 10 | Branes |
gualtieri2010 Branes on Poisson Varieties bailey2017 The local structure of generalized complex branes martucci2006 D-branes on general N=1 backgrounds: superpotentials and D-terms |
| 11 | Reduction I |
Figueroa-O'Farrill2006 Lecture 2: Symplectic reduction fine2011 The Hamiltonian Geometry of the space of unitary connections with sympletic curvature bursztynCavalcantiGualtieri2006 Reduction of Courant algebroids and generalized complex structures |
| 12 | Reduction | |
| 13 | ||
| 14 |
evaluation:
The evaluation is based on attendence and a written exposition on a topic or paper in the field. Some example articles and notes are listed below. This may include filling in details and example calculations that are often omitted in research papers. It may also involve looking up references and putting the work of a particular paper into perspective of other papers.
Draft submission deadline: 31. December 2022*
Final submission deadline: 31. January 2023*
*submission before midnight means at the latest 11:59pm
articles:
- Leibniz algebroids, twistings and exceptional generalized geometry, Baraglia
- T-DUALITY AND GENERALIZED GEOMETRY WITH 3-FORM FLUX, Cavalcanti and Gualtieri
- Reduction of Courant algebroids and generalized complex structures, Bursztyn, Cavalcanti and Gualtieri
- Generalized Kaehler geometry of instanton moduli spaces, Bursztyn, Cavalcant and Gualtieri
- A SURGERY FOR GENERALIZED COMPLEX STRUCTURES ON 4-MANIFOLDS, Cavalcanti and Gualtieri
- Branes on Poisson Varieties, Gualtieri
- Generalized Kahler Geometry, Gualtieri
- Brackets, forms and invariant functionals, Hitchin
- GENERALIZED CALABI–YAU STRUCTURES, K3 SURFACES, AND B-FIELDS, Huybrechts
- Hyperkähler manifolds, Hitchin
- Low-dimensional geometry—a variational approach, Hitchin
- New aspects of the ddc-lemma, Cavalcanti
- Generalized K ̈ahler metrics from Hamiltonian deformations, Gualtieri
- Goto's generalized K ̈ahler stability theorem, Cavalcanti
- Morita equivalence and the generalized Kahler potential, Bischoff, Gualtieri and Zabzine
- The nondegenerate generalized Kahler Calabi-Yau problem, Apostolov and Streets
- PURE SPINORS ON LIE GROUPS, Alekseev, Bursztyn and Meinrenken
The design of this course is inspired by the course on generalized complex geometry taught by Marco Gualtieri in 2015 at the University of Toronto.