# Differential Geometry Seminar on Generalized Complex Geometry

## Managers

• Casey Blacker
• Sylvain Lavau

## Differential Geometry Seminar on Generalized Complex Geometry

 venue SPbU, Dept. of Mathematics & Computer Science time Fridays, 11am organizer Casey Blacker (cblacker271@gmail.com) PDMI coordinator Sylvain Lavau (lavau@math.univ-lyon1.fr) telegram https://t.me/joinchat/57dz7gWZz9UwOTU0 zoom 409 987 5545 (9D3ZyM)

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 Kähler structures
• T-duality

This seminar should appeal to students and researchers with interests in differential geometry and mathematical physics.

Mathematical references:

Physical references:

• 13 Apr