Related papers: Special Lagrangian conifolds, I: Moduli spaces (ex…

This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…

In this paper, we make progress on understanding the collapsing behavior of Calabi-Yau metrics on a degenerating family of polarized Calabi-Yau manifolds. In the case of a family of smooth Calabi-Yau hypersurfaces in projective space…

Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of…

Moduli spaces of stably irreducible sheaves on Kodaira surfaces belong to the short list of examples of smooth and compact holomorphic symplectic manifolds, and it is not yet known how they fit into the classification of holomorphic…

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be…

In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop…

Generalizing the work of Sen, we analyze special points in the moduli space of the compactification of the F-theory on elliptically fibered Calabi-Yau threefolds where the coupling remains constant. These contain points where they can be…

We study compactifications of type IIB supergravity on Calabi-Yau threefolds. The resulting low energy effective Lagrangian is displayed in the large volume limit and its symmetry properties - with specific emphasis on the SL(2,Z) - are…

The moduli space of N=1 type II warped compactions to flat space with generic internal fluxes is studied. Using the underlying integrable generalized complex structure that characterizes these vacua, the different deformations are…

In a recent preprint, Chi Li proved that aymptotically conical complex manifolds with regular tangent cone at infinity admit holomorphic compactifications (his result easily extends to the quasiregular case). In this short note, we show…

We study different phenomenological aspects of compact, D=4, N=1 Type IIB orientifolds considered as models for unification of the standard model and gravity. We discuss the structure of the compactification, string and unification scales…

In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by…

A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of these abelian varieties, and thus give a description of…

Coassociative 4-folds are a particular class of 4-dimensional submanifolds which are defined in a 7-dimensional manifold M with a G_2 structure given by a `positive' differential 3-form, sometimes called G_2-form. Assuming that a G_2-form…

This article is a continuation of the work "Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerated Calabi-Yau surfaces". We generalize the notion of tropical Lagrangian multi-sections to any dimensions.…

The moduli space of nonlinear $\sigma$-models on a Calabi--Yau manifold contains a complexification of the K\"ahler cone of the manifold. We describe a physically natural analytic continuation process which links the complexified K\"ahler…

Given a compact oriented manifold of dimension $n$ with a conically smooth stratification, we show that the moduli of $\mathcal{D}(k)$-valued constructible sheaves and the moduli of perverse sheaves are $(2-n)$-shifted Lagrangian. The…

We study the existence of special Lagrangian submanifolds of log Calabi-Yau manifolds equipped with the complete Ricci-flat K\"ahler metric constructed by Tian-Yau. We prove that if $X$ is a Tian-Yau manifold, and if the compact Calabi-Yau…

A primitive Calabi-Yau threefold is a non-singular Calabi-Yau threefold which cannot be written as a crepant resolution of a singular fibre of a degeneration of Calabi-Yau threefolds. These should be thought as the most basic Calabi-Yau…

Let $M_1$ and $M_2$ be special Lagrangian submanifolds of a compact Calabi-Yau manifold $X$ that intersect transversely at a single point. We can then think of $M_1\cup M_2$ as a singular special Lagrangian submanifold of $X$ with a single…