Richard Thomas

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We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes(More)
We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties (X, L); in particular for K-and Chow stability. For each type of stability this leads to a concept of slope µ for varieties and their subschemes; if (X, L) is semistable then µ(Z) ≤ µ(X) for all Z ⊂ X. We give examples such as(More)
1 Introduction Calabi–Yau m-folds are compact Ricci-flat Kähler manifolds (M, J, g) of complex dimension m, with trivial canonical bundle K M. Taken together, the complex structure J, Kähler metric g, and a holomorphic section Ω of K M make up a rich, fairly rigid geometrical structure with very interesting properties — for instance, Calabi–Yau m-folds(More)
We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on that of [Th]. We give new results about the stability condition, and propose a Jordan-Hölder-type decomposition of (special) Lagrangians. The main results are the uniqueness of special Lagrangians in hamiltonian deformation classes of Lagrangians,(More)
A detailed description of the skull and jaw of the gecko Sphaerodactylus roosevelti is presented. The bones are described articulated and isolated with special consideration given to the type of suture among joining elements. S. roosevelti was compared with 109 gekkotan species to evaluate the osteological variation and to find characters for cladistic(More)
We find stability conditions ([D2], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the(More)
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 sub-manifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case(More)