M theory compactifications on G2 holonomy manifolds, whilst supersymmetric, require
singularities in order to obtain non-Abelian gauge groups, chiral fermions and other …

This is an introduction to a very active field of research, on the boundary between
mathematics and physics. It is aimed at graduate students and researchers in geometry and …

This graduate level text covers an exciting and active area of research at the crossroads of
several different fields in Mathematics and Physics. In Mathematics it involves Differential …

We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-
Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions …

We attempt to define a new invariant I of (almost) Calabi-Yau 3-folds M, by counting special
Lagrangian rational homology 3-spheres N in M in each 3-homology class, with a certain …

This is the last in a series of five papers studying compact special Lagrangian submanifolds
(SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x1,..., xn locally modelled …

There is a strong analogy between compact, torsion-free $ G_2 $-manifolds
$(X,\varphi,*\varphi) $ and Calabi-Yau 3-folds $(Y, J, g,\omega) $. We can also generalize …

The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M, M'in
terms of special Lagrangian fibrations f: M--> B and f': M'--> B over the same base B, whose …

We study special Lagrangian cones in [inline-graphic xmlns: xlink=" http://www. w3.
org/1999/xlink" xlink: href=" 01i"/] with isolated singularities especially the case n= 3. Our …

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 …