David Baraglia

Leibniz algebroids, twistings and exceptional generalized geometry

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a construction starting from graded Lie algebras. In this case the Leibniz bracket is a derived bracket and there are higher derived brackets resulting in an L∞-structure. The algebroids can be twisted by a non-abelian cohomology class and we prove that the twisting class is described by a Maurer–Cartan equation. For compact manifolds we construct a Kuranishi moduli space of this equation which is shown to be affine algebraic. We explain how these results are related to exceptional generalized geometry.

Real structures on moduli spaces of Higgs bundles

We construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A) and (A, A, B). We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory.

Higgs Bundles and (A, B, A)-Branes

Through the action of anti-holomorphic involutions on a compact Riemann surface Σ we construct families of (A, B, A)-branes

Topological T-duality for torus bundles with monodromy

{\mathcal{L}_{G_{c}}}

CONFORMAL COURANT ALGEBROIDS AND ORIENTIFOLD T-DUALITY

LGc in the moduli spaces

Arithmetic of singular character varieties and their E-polynomials

{\mathcal{M}_{G_{c}}}