Publications
64 results found
Stoppa J, Thomas RP, 2011, HILBERT SCHEMES AND STABLE PAIRS: GIT AND DERIVED CATEGORY WALL CROSSINGS, BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, Vol: 139, Pages: 297-339, ISSN: 0037-9484
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- Citations: 23
Kool M, Shende V, Thomas RP, 2011, A short proof of the Gottsche conjecture, GEOMETRY & TOPOLOGY, Vol: 15, Pages: 397-406, ISSN: 1465-3060
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- Citations: 46
Huybrechts D, Thomas RP, 2010, Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes, MATHEMATISCHE ANNALEN, Vol: 346, Pages: 545-569, ISSN: 0025-5831
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- Citations: 72
Pandharipande R, Thomas RP, 2010, STABLE PAIRS AND BPS INVARIANTS, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 23, Pages: 267-297, ISSN: 0894-0347
Thomas RP, 2010, An Exercise in Mirror Symmetry, International Congress of Mathematicians (ICM 2010), Publisher: HINDUSTAN BOOK AGENCY-INDIA, Pages: 624-651
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- Citations: 4
Maulik D, Pandharipande R, Thomas RP, 2010, Curves on <i>K</i>3 surfaces and modular forms, JOURNAL OF TOPOLOGY, Vol: 3, Pages: 937-996, ISSN: 1753-8416
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- Citations: 73
Pandharipande R, Thomas RP, 2009, Curve counting via stable pairs in the derived category, INVENTIONES MATHEMATICAE, Vol: 178, Pages: 407-447, ISSN: 0020-9910
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- Citations: 190
Pandharipande R, Thomas RP, 2009, The 3-fold vertex via stable pairs, GEOMETRY & TOPOLOGY, Vol: 13, Pages: 1835-1876, ISSN: 1465-3060
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- Citations: 44
Rollenske S, Thomas R, 2009, Smoothing nodal Calabi-Yau <i>n</i>-folds, JOURNAL OF TOPOLOGY, Vol: 2, Pages: 405-421, ISSN: 1753-8416
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- Citations: 1
Ross J, Thomas R, 2007, A study of the Hilbert-Mumford criterion for the stability of projective varieties, JOURNAL OF ALGEBRAIC GEOMETRY, Vol: 16, Pages: 201-255, ISSN: 1056-3911
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- Citations: 93
Khovanov M, Thomas R P, 2007, Braid cobordisms, triangulated categories, and flag varieties, Homology, homotopy and applications, Vol: 9, Pages: 19-94, ISSN: 1532-0073
Ross J, Thomas R, 2006, An obstruction to the existence of constant scalar curvature Kahler metrics, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 72, Pages: 429-466, ISSN: 0022-040X
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- Citations: 71
Huybrechts D, Thomas R, 2006, ℙ-objects and autoequivalences of derived categories, Mathematical Research Letters, Vol: 13, Pages: 87-98, ISSN: 1073-2780
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- Citations: 47
Thomas RP, 2006, Mirror Symmetry: A Geometric Survey, Encyclopedia of Mathematical Physics: Five-Volume Set, ISBN: 9780125126601
Huybrechts D, Thomas R, 2006, P-objects and autoequivalences of derived categories, MATHEMATICAL RESEARCH LETTERS, Vol: 13, Pages: 87-98, ISSN: 1073-2780
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- Citations: 47
Thomas RP, 2006, The geometry of mirror symmetry, Encylopedia of mathematical physics, Editors: Francoise, Naber, Tsou, Oxford, Publisher: Elsevier, Pages: 439-448, ISBN: 9780125126601
Thomas R P, 2006, Notes on GIT and symplectic reduction for bundles and varieties, JDG Conference on Geometry and Topology, Publisher: International Press
Thomas RP, 2006, Stability conditions and the braid group, Communications in Analysis and Geometry, Vol: 14, Pages: 135-161, ISSN: 1019-8385
Thomas RP, 2005, Nodes and the Hodge conjecture, JOURNAL OF ALGEBRAIC GEOMETRY, Vol: 14, Pages: 177-185, ISSN: 1056-3911
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- Citations: 6
Khesin B, Rosly A, Thomas R, 2004, A polar de Rham theorem, TOPOLOGY, Vol: 43, Pages: 1231-1246, ISSN: 0040-9383
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- Citations: 5
Thomas RP, 2004, Mirror Symmetry: A Geometric Survey, Encyclopedia of Mathematical Physics: Five-Volume Set, Pages: 439-448, ISBN: 9780125126663
Mirror symmetry was discovered in the late 1980s by physicists studying superconformal field theories (SCFTs). One way to produce SCFTs is from closed string theory; in the Riemannian (rather than Lorentzian) theory the string's world line gives a map of a Riemannian 2-manifold into the target with an action which is conformally invariant, so the 2-manifold can be thought of as a Riemann surface with a complex structure. Making sense of the infinities in the quantum theory (supersymmetry and anomaly cancelation) forces the target to be 10-dimensional - Minkowski space times by a 6-manifold X - and X to be (to first order) Ricci flat and so to have holonomy in SU(3). That is X is a Calabi-Yau 3-fold (Formula;). So SCFTs come from -models (mapping Riemann surfaces into Calabi-Yau 3-folds) but, it turns out, in two different ways - the A-model and the B-model. Deformations of the SCFT and either -model are isomorphic, so over an open set the two coincide. Thus, it was natural to conjecture that almost all of the relevant SCFTs came from geometry - from an A or B -model.
Smith I, Thomas R, 2003, Symplectic surgeries from singularities, Turkish Journal of Mathematics, Vol: 27, Pages: 231-250, ISSN: 1300-0098
Hori K, Katz S, Klemm A, et al., 2003, Mirror symmetry, Providence, RI, Publisher: American Mathematical Society, ISBN: 9780821829554
Thomas RP, Yau ST, 2002, Special Lagrangians, stable bundles and mean curvature flow, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, Vol: 10, Pages: 1075-1113, ISSN: 1019-8385
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- Citations: 83
Smith I, Thomas RP, Yau ST, 2002, Symplectic conifold transitions, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 62, Pages: 209-242, ISSN: 0022-040X
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- Citations: 49
Thomas RP, 2001, Mirror symmetry and actions of braid groups on derived categories, Providence, R.I, Mirror symmetry; winter school on mirror symmetry, vector bundles and Lagrangian submanifolds, Cambridge MA, January 1999, Publisher: American Mathematical Society, Pages: 363-377, ISSN: 1089-3288
Thomas RP, 2001, Moment maps, monodromy and mirror manifolds, Symplectic geometry and mirror symmetry, proceedings of the 4th KIAS annual international conference, Seoul, South Korea 14 - 18 August 2000, Editors: Fukaya, Oh, Ono, Tian, River Edge, NJ, Publisher: World Scientific Publishing, Pages: 467-498, ISBN: 9789810247140
Thomas RP, 2001, Derived categories for the working mathematician, Providence, R.I, Mirror symmetry; Winter school on mirror symmetry, vector bundles and Lagrangian submanifolds, Cambridge, MA, January 1999, Publisher: American Mathematical Society, Pages: 349-362
Seidel P, Thomas R, 2001, Braid group actions on derived categories of coherent sheaves, Duke Mathematical Journal, Vol: 108, Pages: 37-108, ISSN: 0012-7094
Thomas RP, 2000, A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on <i>K</i>3 fibrations, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 54, Pages: 367-438, ISSN: 0022-040X
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- Citations: 248
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