Richard Thomas (mathematician)

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Richard Paul Winsley Thomas is a British mathematician who deals with geometry (algebraic geometry, differential geometry, symplectic geometry) and their application in mathematical physics ( Calabi-Yau manifolds , mirror symmetry, gauge field theories ). He is a professor at Imperial College London .

Thomas received his PhD in 1997 from the University of Oxford under Simon Donaldson ( Gauge theory on Calabi-Yau Manifolds ). The Donaldson-Thomas invariants of Calabi-Yau varieties are named after him and Donaldson, and the Pandharipande-Thomas invariants are named after him and Rahul Pandharipande .

With Pandharipande in 2014, he proved the Katz-Klemm-Vafa conjectures, which combine the Gromow-Witten theory of K3 surfaces with modular shapes. With M. Kool and V. Shende he proved the Göttsche conjecture of algebraic geometry (named after Lothar Göttsche , but with roots in the 19th century).

In 2004 he received the Whitehead Prize and the Leverhulme Prize and in 2010 a Wolfson Research Merit Award from the Royal Society . In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad (India) ( Exercises in Mirror Symmetry ). In 2015 he was elected to the Royal Society and in 2019 to the Academia Europaea . He is a Fellow of the American Mathematical Society .

Fonts (selection)

  • A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 vibrations. J. Differential Geom. 54 (2000), no. 2, 367-438.
  • with P. Seidel: Braid group actions on derived categories of coherent sheaves. Duke Math. J. 108 (2001), no. 1, 37-108.
  • with R. Pandharipande: Curve counting via stable pairs in the derived category. Invent. Math. 178 (2009), no. 2, 407-447.
  • Moment maps, monodromy and mirror manifolds , in Fukaya, Oh, Ono, Tian (editor) Symplectic geometry and mirror symmetry (Seoul, 2000) , World Scientific, 2002, pp. 467-498, online
  • Mirror Symmetry: a geometric survey , in Naber u. a. (Ed.) Encyclopedia of Mathematical Physics , Elsevier 2006
  • with Rahul Pandharipande, Cumrun Vafa, Ravi Vakil, Eric Zaslow, Sheldon Katz, Kentaro Hori, Albrecht Klemm Mirror Symmetry , Clay Mathematics Monographs, Volume 1, 2003
  • with Pandharipande: Notes on the proof of the KKV conjecture, Surveys in Differential Geometry, Arxiv

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Pandharipande, Thomas, The Katz-Klemm-Vafa-conjecture for K3 surfaces, 2014, Arxiv
  3. ↑ M. Kool, V. Shende, RP Thomas, A short proof of the Göttsche conjecture, Geom. Top., Volume 15, 2011, pp. 397-406, Arxiv
personal data
SURNAME Thomas, Richard
ALTERNATIVE NAMES Thomas, Richard Paul; Thomas, Richard Paul Winsley
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH 20th century