In these lectures we review Generalized Complex Geometry and discuss two main
applications to string theory: the description of supersymmetric flux compactifications and the …

We describe how generalized complex geometry, which interpolates between complex and
symplectic geometry, is compatible with T-duality, a relation between quantum field theories …

Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of
Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently …

Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of
generalized complex geometry. Just as we may require a complex structure to be …

A bstract We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral
Model with a Wess-Zumino term. For arbitrary groups, the one-loop β-functions are …

We recall fundamental aspects of the pluriclosed flow equation and survey various existence
and convergence results, and the various analytic techniques used to establish them …

We study left-invariant generalized Kähler structures on almost abelian Lie groups, ie, on
solvable Lie groups with a codimension-one abelian normal subgroup. In particular, we …

We review some constructions and properties of complex manifolds admitting pluriclosed
and balanced metrics. We prove that for a 6-dimensional solvmanifold endowed with an …

Symplectic forms taming complex structures on compact manifolds are strictly related to
Hermitian metrics having the fundamental form ∂̄∂-closed, ie, to strong Kähler with …

A Hermitian-symplectic metric is a Hermitian metric whose K\" ahler form is given by the $(1,
1) $-part of a closed $2 $-form. Streets-Tian Conjecture states that a compact complex …