Papers and preprints

• M. Kool, J. Oh, J. V. Rennemo and R. P. Thomas, A Hopf index for isotropic sections of orthogonal bundles, preprint.
  
• R. P. Thomas, Refined sheaf counting on local K3 surfaces, preprint.
  
• J. Oh and R. P. Thomas, Quantum Lefschetz without curves, IMRN 2024, 12136-12149, 2024.
  
• J. Oh and R. P. Thomas, Complex Kuranishi structures and counting sheaves on Calabi-Yau 4-folds, II, preprint.
  
• S. Feyzbakhsh and R. P. Thomas, Rank r DT theory from rank 1, JAMS 36, 795-826, 2023.
  
• S. Feyzbakhsh and R. P. Thomas, Rank r DT theory from rank 0, Duke Math Jour. 173, 2063-2116, 2024.
  
• J. Oh and R. P. Thomas, Counting sheaves on Calabi-Yau 4-folds, I, Duke Math Jour. 172, 1333-1409, 2023.
  
• S. Feyzbakhsh and R. P. Thomas, Curve counting and S-duality, Épijournal de Géométrie Algébrique 7, 2023.
  
• S. Feyzbakhsh and R. P. Thomas, with an appendix by C. Voisin, An application of wall-crossing to Noether-Lefschetz loci, Quarterly Journal of Math. 72, 51-70, 2021. Issue dedicated to the memory of Sir Michael Atiyah.
  
• A. Gholampour and R. P. Thomas, Degeneracy loci, virtual cycles and nested Hilbert schemes II, Compositio 156, 1623-1663, 2020.
  
• R. P. Thomas, A K-theoretic Fulton class, in volume 2 of "Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday", LMS Lecture Note Series 473, 367-379, 2022.
  
• R. P. Thomas, Equivariant K-theory and refined Vafa-Witten invariants, Comm. Math. Phys. 378, 1451-1500, 2020.
  
• V. Muñoz, I. Smith and R. P. Thomas, Eds. Modern Geometry: A Celebration of the Work of Simon Donaldson, AMS 2018.
  
• T. de Fernex, B. Hassett, M. Mustaţă, M. Olsson, M. Popa and R. P. Thomas, Eds. Algebraic Geometry: Salt Lake City 2015, AMS 2018.
  
• D. Maulik and R. P. Thomas, Sheaf counting on local K3 surfaces, Pure Appl. Math. Quart. 14, 419-441, 2018.
  
• A. Gholampour and R. P. Thomas, Degeneracy loci, virtual cycles and nested Hilbert schemes I, Tunisian Jour. Math. 2, 633-665, 2020.
  
• Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces II: semistable case, Pure Appl. Math. Quart. 13, 517-562, 2017. Volume in honour of Simon Donaldson's 60th birthday.
  
• Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: stable case, Jour. Alg. Geom. 29, 603-668, 2020.
  
• M. Kool and R. P. Thomas, Stable pairs with descendents on local surfaces I: the vertical component, Pure Appl. Math. Quart. 13, 581-638, 2017.
  
• R. P. Thomas, Notes on HPD, in "Algebraic Geometry: Salt Lake City 2015", AMS, 2018.
  
• R. Pandharipande and R. P. Thomas, Notes on the proof of the KKV conjecture, Surveys in Differential Geometry 21, 289-311, ed. S.-T. Yau. International Press, 2016.
  
• E. Segal and R. P. Thomas, Quintic threefolds and Fano elevenfolds, J. reine angew. Math. 243, 245-259, 2018.
  
• J. Calabrese and R. P. Thomas, Derived equivalent Calabi-Yau 3-folds from cubic 4-folds. Math. Ann. 365, 155-172, 2016.
  
• Y. Jiang and R. P. Thomas, Virtual signed Euler characteristics, Jour. Alg. Geom. 26, 379-397, 2017.
  
• S. Katz, A. Klemm and R. Pandharipande, with an Appendix by R. P. Thomas, On the motivic stable pairs invariants of K3 surfaces, in K3 surfaces and their moduli, eds. C. Faber, G. Farkas, and G. van der Geer, Birkhauser Prog. in Math. 315, 111-146, 2016.
  
• R. Pandharipande and R. P. Thomas, The Katz-Klemm-Vafa conjecture for K3 surfaces, Forum of Math, Pi 4, 1-111, 2016.
  
• A. Gholampour, A. Sheshmani and R. P. Thomas, Counting curves on surfaces in Calabi-Yau 3-folds, Math. Annalen. 360, 67-78, 2014.
  
• Y. Odaka and R. P. Thomas, Separatedness of moduli of K-stable varieties, withdrawn due to flatness mistake.
  
• N. Addington and R. P. Thomas, Hodge theory and derived categories of cubic fourfolds, Duke Math Jour. 163, 1885-1927, 2014.
  
• R. Pandharipande and R. P. Thomas, Almost closed 1-forms, Glasgow Math. Jour. 56, 169-182, 2014.
  
• M. Kool and R. P. Thomas, Reduced classes and curve counting on surfaces II: calculations, Algebraic Geometry 1, 384-399, 2014.
  
• M. Kool and R. P. Thomas, Reduced classes and curve counting on surfaces I: theory, Algebraic Geometry 1, 334-383, 2014.
  
• L. Brambila-Paz, P. Newstead, O. Garcia-Prada, R. P. Thomas, Eds. Moduli spaces. Cambridge University Press, 2014.
  
• R. Pandharipande and R. P. Thomas, 13/2 ways of counting curves, in Moduli spaces, eds L. Brambila-Paz, P. Newstead, O. Garcia-Prada, R. P. Thomas. CUP, 2014.
  
• M. Kool, V. Shende and R. P. Thomas, A short proof of the Göttsche conjecture, Geometry & Topology 15, 397-406, 2011.
• I. Smith and R. P. Thomas, Khovanov homology from ALE spaces, never-to-appear, unfinished preprint.
• R. P. Thomas, An exercise in mirror symmetry. Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010.
• D. Maulik, R. Pandharipande and R. P. Thomas, Curves on K3 surfaces and modular forms, with an Appendix by A. Pixton. Journal of Topology 3, 937-996, 2010.
• J. Ross and R. P. Thomas, Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metrics, Jour. Diff. Geom. 88, 109-160, 2011.
• J. Ross and R. P. Thomas, Weighted Bergman kernels on orbifolds, Jour. Diff. Geom. 88, 87-108, 2011.
• J. Stoppa and R. P. Thomas, Hilbert schemes and stable pairs: GIT and derived category wall crossings, Bull. SMF. 139, 297-339, 2011.
• S. Rollenske and R. P. Thomas, Smoothing nodal Calabi-Yau n-folds, Journal of Topology 2, 405-421, 2009.
• D. Huybrechts and R. P. Thomas, Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes, Math. Ann. 346, 545--569, 2010.
• R. Pandharipande and R. P. Thomas, Stable pairs and BPS invariants, Jour. AMS. 23, 267-297, 2010.
• R. Pandharipande and R. P. Thomas, The 3-fold vertex via stable pairs, Geometry & Topology 13, 1835-1876, 2009.
• R. Pandharipande and R. P. Thomas, Curve counting via stable pairs in the derived category, Inventiones 178, 407-447, 2009.
• M. Khovanov and R. P. Thomas, Braid cobordisms, triangulated categories, and flag varieties, Homology, Homotopy and Applications 9, 19-94, 2007.
• R. P. Thomas, Notes on GIT and symplectic reduction for bundles and varieties, Surveys in Differential Geometry 10, 221-273, ed. S.-T. Yau. International Press, 2006.
• D. Huybrechts and R. P. Thomas, P-objects and autoequivalences of derived categories, Math. Res. Lett. 13, 87-98, 2006.
• J. Ross and R. P. Thomas, A study of the Hilbert-Mumford criterion for the stability of projective varieties, Jour. Alg. Geom. 16, 201-255, 2007.
• J. Ross and R. P. Thomas, An obstruction to the existence of constant scalar curvature Kähler metrics, Jour. Diff. Geom. 72, 429-466, 2006.
• R. P. Thomas, The geometry of mirror symmetry, in Encyclopaedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006.
• B. Khesin, A. Rosly and R. P. Thomas, A Polar de Rham Theorem, Topology 43, 1231-1246, 2004.
• R. P. Thomas, Stability conditions and the braid group, Communications in Analysis and Geometry 14, 135-161, 2006.
• R. P. Thomas, Nodes and the Hodge conjecture, Jour. Alg. Geom. 14, 177-185, 2005.
• I. Smith and R. P. Thomas, Symplectic surgeries from singularities, Proceedings of Ninth Gökova Geometry/Topology Conference, 2002.
• H. Clemens, with appendices by R. P. Thomas and C. Voisin, Cohomology and obstructions II: curves on K-trivial threefolds. J. Algebraic Geom. 14, 705--739, 2005.
• I. Smith, R. P. Thomas and S.-T. Yau, Symplectic conifold transitions, Jour. Diff. Geom. 62, 209-242, 2002.
• R. P. Thomas and S.-T. Yau, Special Lagrangians, stable bundles and mean curvature flow , Communications in Analysis and Geometry 10, 1075-1113, 2002.
• R. P. Thomas, Moment maps, monodromy and mirror manifolds. In "Symplectic geometry and mirror symmetry" , eds K. Fukaya, Y.-G. Oh, K. Ono and G. Tian. World Scientific, 2001, 467-498.
• Hori, K., Katz, S., Klemm, A., Pandharipande, R., Thomas, R. P., Vafa, C., Vakil, R. and Zaslow, E. Mirror symmetry, Clay Mathematics Monographs 1, AMS, 2003.
• P. Seidel and R. P. Thomas, Braid group actions on derived categories of sheaves, Duke Math. Jour. 108, 37-108, 2001.
• R. P. Thomas, Examples of bundles on Calabi-Yau 3-folds for string theory compactifications, Adv. Theor. Math. Phys. 4, 231-247, 2000.
• R. P. Thomas, Mirror symmetry and actions of braid groups on derived categories. In "Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds", January 1999, eds C. Vafa and S.-T. Yau. AMS/IP Studies in Advanced Mathematics (International Press, Cambridge MA), 2001, 363-377.
• R. P. Thomas, Derived categories for the working mathematician. In "Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds", January 1999, eds C. Vafa and S.-T. Yau. AMS/IP Studies in Advanced Mathematics (International Press, Cambridge MA), 2001, 349-361.
• R. P. Thomas, An obstructed bundle on a Calabi-Yau 3-fold, Adv. Theor. Math. Phys. 3, 567-576, 1999.
• R. P. Thomas, A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, Jour. Diff. Geom. 54, 367-438, 2000.
• S. K. Donaldson and R. P. Thomas, Gauge theory in higher dimensions, in "The Geometric Universe; Science, Geometry, And The Work Of Roger Penrose", Oxford University Press, 1998. Why I love Steven Bradlow.
• R. P. Thomas, Gauge theories on Calabi-Yau manifolds, D. Phil. Thesis, University of Oxford, 1997.
• R. P. Thomas, Seiberg-Witten equations on complex 3-folds, First Year dissertation, large parts of which are wrong, 1995.
• Some LMS reports: Mary Cartwright Lecture 2002, Hodge Theory in a New Century 2003, Random Surfaces 2008 and The Work of Simon Donaldson 2018.
• MSRI newsletter: Enumerative geometry beyond numbers 2018.