The main aim of the paper is to develop the" Floer theory" associated to Calabi-Yau 3-folds,
exending the analogy of Thomas'" holomorphic Casson invariant". The treatment in the body …

We survey the metric aspects of the Strominger–Yau–Zaslow conjecture on the existence of
special Lagrangian fibrations on Calabi–Yau manifolds near the large complex structure …

Let (M, ω) be a compact symplectic manifold, and L a compact embedded Lagrangian
submanifold in M. Fukaya, Oh, Ohta and Ono [8] construct Lagrangian Floer cohomology …

We describe a new algorithm that solves a classical geometric problem: Find a surface of
minimal area bordered by an arbitrarily prescribed boundary curve. Existing numerical …

Let. M; J; g;/be a Calabi–Yau m-fold, and consider compact, graded Lagrangians L in M.
Thomas and Yau [81, 82] conjectured that there should be a notion of 'stability'for such L …

We give a new construction of compact Riemannian $7 $-manifolds with holonomy $ G_2 $.
Let $ M $ be a torsion-free $ G_2 $-manifold (which can have holonomy a proper subgroup …

We study the relation between supersymmetry and geometric flows driven by the Bianchi
identity for the three-form flux H in heterotic supergravity. We describe how the flow …

A bstract Brane brick models are Type IIA brane configurations that encode the 2d\(\mathcal
{N}=\left (0, 2\right)\) gauge theories on the worldvolume of D1-branes probing toric Calabi …

Adopting an elegant geometrical approach, this advanced pedagogical text describes deep
and intuitive methods for understanding the subtle logic of supersymmetry while avoiding …

We develop an abstract theory of flows of geometric 𝐻-structures, ie, flows of tensor fields
defining 𝐻-reductions of the frame bundle, for a closed and connected subgroup H⊂ …