Related papers: Moment maps, monodromy and mirror manifolds
In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading.…
This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds,…
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi-Yau manifolds have mirror partners.…
We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…
We describe mirror symmetry in N=2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane. We show that the topological symmetries of Calabi-Yau…
In this paper, we prove a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds in a 6-dimensional manifold equipped with a generalization of a Calabi-Yau structure. These perturbed special Lagrangian…
Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a…
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer…
We consider a Hamiltonian torus action on a compact connected symplectic manifold M. For a certain class of Lagrangian submanifolds Q of M we show that the image of Q under the momentum map is convex. As an application we complete the…
We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of…
A Lagrangian submanifold in an almost Calabi-Yau manifold is called positive if the real part of the holomorphic volume form restricted to it is positive. An exact isotopy class of positive Lagrangian submanifolds admits a natural…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
In some previous papers, a geometric description of Lagrangian Mechanics on Lie algebroids has been developed. In the present paper, we give a Hamiltonian description of Mechanics on Lie algebroids. In addition, we introduce the notion of a…
Let ({\Sigma}, {\omega}) be a compact Riemann surface with constant curvature c. In this work, we proved that the mean curvature flow of a given Hamiltonian diffeomorphism on {\Sigma} provides a smooth path in Ham({\Sigma}), the group of…
It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…
Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror…
This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special…
In this article we discuss the geometry of moduli spaces of (1) flat bundles over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills bundles over complex submanifolds in Calabi-Yau manifolds. These moduli spaces reflect…
In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds,…
We construct a family of non-geometric Bridgeland stability conditions on certain wrapped Fukaya categories, using homological mirror symmetry and categorical K\"unneth formulae. These stability conditions correspond to certain holomorphic…