Peter Schupp: Geometry with fluxes

This short course provides an introduction to Generalized Geometry, which is a generalization of Riemannian geometry that naturally incorporates fluxes and symmetries of theories of extended objects (strings) and is a natural setting for the formulation of various gravity theories.

For supplemental background material on string compactifications, please see the very nice set of lectures by Mariana Grana and Hagen Triendl [2]. The intriguing relation of graded (super Poisson) geometry and generalized geometry is investigated in [3]. In [4] we review the emergence of non-associative structures in the presence of non-geometric background fluxes.

References:

[1] Hitchin, Lectures on generalized geometry, arXiv:1008.0973
[2] Lectures on string theory compactifications, fluxes and generalized geometry by Grana and Triendl at CEA/Saclay: http://ipht.cea.fr/Docspht//articles/t13/042/public/Notes.pdf
[3] Roytenberg, On the structure of graded symplectic supermanifolds and Courant algebroids, arXiv:math/0203110
[4] Mylonas, Schupp, Szabo, Nonassociative geometry and twist deformations in non-geometric string theory, arXiv:1402.7306 (and references therein)