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 NonKahler 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 Dbranes on general N=1 backgrounds: superpotentials and Dterms 
11  Reduction I 
FigueroaO'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 
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
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.