We review recently introduced geometric tools used to characterize supersymmetric flux backgrounds, with special emphasis on Generalised Complex Geometry as developed by Hitchin. We then proceed to describe Exceptional Generalised Geometry, an extension of the latter formalism based on the...

The Chern-Simons path integral is one of the most interesting examples for the usefulness of heuristic path integral expressions. In a famous paper Edward Witten was able to compute the so-called "Wilson loop observables" of Chern-Simons theory explicitly at a heuristic level.
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We will discuss Poisson quasi-Nijenhuis structures on manifolds and on Lie algebroids. We will show that a Lie algebroid with a Poisson quasi-Nijenhuis structure has an associated quasi-Lie bialgebroid and that a Courant algebroid morphism is involved.

We will describe the spin foam state sum models an their relation to BF theories. We will then explain how to construct spin foam perturbative expansions in 3 and 4 dimensions and how are these related to topological quantum field theories and to theories of quantum gravity.

We study Hamiltonian spaces associated with pairs $(E,A)$, where $E$ is a Courant algebroid and $A\subset E$ is a Dirac structure. These spaces are defined in terms of morphisms of Courant algebroids with suitable compatibility conditions. Several of their properties are discussed, including a...

Riemannian 4-manifolds obeying Einstein's equations play a significant role in attempts to understand quantum gravity, from black hole thermodynamics to string theory. I will describe how the Ricci flow provides a natural gradient flow for the Euclidean EinsteinHilbert action which in the context...

Abstract:
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