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Differential Geometry Seminar on Generalized Complex Geometry
by Egor Pifagorov - Monday, 12 April 2021, 05:26 PM
Differential Geometry Seminar on
Generalized Complex Geometry

venue SPbU, Dept. of Mathematics & Computer Science
time TBD
organizer Casey Blacker (cblacker271@gmail.com)
PDMI coordinator Sylvain Lavau (lavau@math.univ.lyon1.fr)

A generalized complex structure \mathcal J on a smooth manifold M is an assignment to each fiber of the
extended tangent bundle  TM\oplus T^*M of a linear complex structure in a locally compatible manner. The
resulting formalism extends both complex and symplectic geometry, and was introduced in 2003 by
Nigel Hitchin with an eye to string theory.
The aim of this learning seminar is first to review the foundational material, and then to acquaint
ourselves with the state of the art and open questions.
Related constructions include,
• Lie algebroids
• Dirac structures
• Courant brackets
• moment maps
• generalized K ̈ahler structures
• T-duality
This seminar should appeal to students and researchers with interests in differential geometry and
mathematical physics.

Mathematical references:
• Gil Cavalcanti. Introduction to generalized complex geometry. Publica ̧c ̃oes Matem ́aticas do IMPA.
Instituto Nacional de Matem ́atica Pura e Aplicada (IMPA), Rio de Janeiro, 2007. 26o Col ́oquio
Brasileiro de Matem ́atica, https://impa.br/wp-content/uploads/2017/04/26CBM_05.pdf
• Marco Gualtieri. Generalized complex geometry. PhD thesis, University of Oxford, November
2003, https://arxiv.org/abs/math/0401221
• Nigel Hitchin. Lectures on generalized geometry. In Surveys in differential geometry. Volume
XVI. Geometry of special holonomy and related topics, volume 16 of Surv. Differ. Geom., pages
79–124. Int. Press, Somerville, MA, 2011
• Nigel Hitchin. Generalized Calabi-Yau manifolds. Q. J. Math., 54(3):281–308, 2003,
Physical references:
• Paul Koerber. Lectures on generalized complex geometry for physicists. Fortschr. Phys., 59(3-
4):169–242, 2011, https://proxy.library.spbu.ru:2150/doi/abs/10.1002/prop.201000083
• Maxim Zabzine. Lectures on generalized complex geometry and supersymmetry. Arch. Math.
(Brno), 42(suppl.):119–146, 2006, https://www.emis.de/journals/AM/06-S/zabzine.pdf