Richard Thomas

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We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The derivation involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R → 1/R duality and dynamical generation of superpotential by(More)
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)
Worm-like snakes (scolecophidians) are small, burrowing species with reduced vision. Although largely neglected in vertebrate research, knowledge of their biogeographical history is crucial for evaluating hypotheses of snake origins. We constructed a molecular dataset for scolecophidians with detailed sampling within the largest family, Typhlopidae(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 Kand 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)
Calabi–Yau m-folds are compact Ricci-flat Kähler manifolds (M,J, g) of complex dimension m, with trivial canonical bundle KM . Taken together, the complex structure J , Kähler metric g, and a holomorphic section Ω of KM make up a rich, fairly rigid geometrical structure with very interesting properties — for instance, Calabi–Yau m-folds occur in smooth,(More)
It is becoming feasible and practical to monitor the generic computer usage of students for extended periods, recording low level actions such as mouse clicks, typing and window changes. This paper presents a case study on the deployment of GRUMPS technology during a period of six weeks when 4.7 million such actions were collected from 141 first year(More)
The watersheds in which we live are comprised of a complex set of physical and social systems that interact over a range of spatial and temporal scales. These systems are continually evolving in response to changing climatic patterns, land use practices and the increasing intervention of humans. Management of these watersheds benefits from the development(More)
This paper describes the evolution of the design and implementation of a distributed run-time system that itself is designed to support the evolution of the topology and implementation of an executing, distributed system. The three different versions of the run-time architecture that have been designed and implemented are presented, together with how each(More)
What is the core of Computing? This paper defines the discipline of computing as centered around the notion of modeling, especially those models that are automatable and automatically manipulable. We argue that this central idea crucially connects models with languages and machines rather than focusing on and around computational artifacts, and that it(More)