Institut für Mathematik


HS 07
Generalized complex geometry
Dr. Lennart Döppenschmitt


13:00 - 14:45
Y27H12 Plätze: 50

Video Streams

This lecture offers a video stream

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  




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.

VVZ Link