fbpx
Wikipedia

Richard Thomas (mathematician)

May 08, 2024

Richard Paul Winsley Thomas FRS is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.[3]

Richard Thomas
Born
Richard Paul Winsley Thomas
Alma materUniversity of Oxford
Known for
AwardsWhitehead Prize[1] (2004)
Scientific career
FieldsMathematics
InstitutionsImperial College London
ThesisGauge Theory on Calabi-Yau Manifolds (1997[2])
Doctoral advisorSimon Donaldson
Websitewww2.imperial.ac.uk/~rpwt

Education edit

Thomas obtained his PhD on gauge theory on Calabi–Yau manifolds in 1997 under the supervision of Simon Donaldson at the University of Oxford. In his dissertation research with Donaldson, he defined the Donaldson–Thomas invariants of Calabi–Yau 3-folds, a major topic in geometry and the mathematics of string theory.

Career and research edit

Before joining Imperial College, he was member of the Institute for Advanced Study in Princeton, New Jersey,[4] and affiliated with Harvard University and the University of Oxford. He was made professor of pure mathematics in 2005.[5]

Thomas has made contributions to algebraic geometry, differential Geometry, and symplectic geometry. His doctoral thesis, which introduced the invariants that later became known as Donaldson–Thomas invariants, was published in the Journal of Differential Geometry as `A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations'.[6] Motivated by homological mirror symmetry, he produced braid group actions on derived categories of coherent sheaves in joint work with Paul Seidel.[7] With Shing-Tung Yau he formulated a conjecture (now known as the Thomas–Yau conjecture) concerning the existence of a special Lagrangian in the Hamiltonian deformation class of a fixed Lagrangian submanifold of a Calabi–Yau manifold.[8] Together with Rahul Pandharipande he formulated a refinement of the Donaldson–Thomas invariants for the special case of curve counting, the Pandharipande–Thomas (PT) stable pair invariants.[9] With Martijn Kool and Vivek Shende, he used the PT invariants to prove the Göttsche conjecture—a classical algebro-geometric problem going back more than a century.[10] With Davesh Maulik and Pandharipande he proved the Katz–Klemm–Vafa (KKV) conjecture,[11] establishing links between the Gromov–Witten theory of K3 surfaces and modular forms. His collaboration with Daniel Huybrechts led to contributions to the deformation theory of complexes.[12] With Nick Addington he established a compatibility result for two rationality conjectures on cubic fourfolds.[13]

He coauthored a book on mirror symmetry.[14] Thomas also wrote expository notes on derived categories,[15] curve counting,[16] and homological projective duality.[17] He appeared in the documentary film 'Thinking space' by Heidi Morstang.[18] Thomas has played an important part in promoting geometry in the UK, encouraging younger mathematicians,[19] and in bringing more geometry to Imperial college: "[...] There was little geometry in Imperial then, but now, thanks largely to the drive of my colleague Richard Thomas, we have one of the main centres for research in this area." - Simon Donaldson[20]

Awards and honours edit

In 2004, Thomas was awarded the London Mathematical Society's Whitehead Prize and the Philip Leverhulme Prize, in 2010 the Royal Society Wolfson Research Merit Award. From the Whitehead prize citation:

"Thomas has made seminal contributions across an unusually broad range of topics. Much of his work is related to mirror symmetry and Calabi–Yau geometry, and thus has an important bearing on exciting contemporary interactions with mathematical physics. [...] This involved the combination of deep, original insights and sophisticated technical proofs that is characteristic of Thomas’s work."[21]

In 2010 he also was invited speaker for the algebraic geometry section at the International Congress of Mathematicians in Hyderabad, where he delivered a lecture on mirror symmetry.[22] Thomas was elected a Fellow of the Royal Society (FRS) in 2015.[23][24] His contributions to algebraic geometry led to his election to the 2018 class of fellows of the American Mathematical Society.[25]

References edit

  1. ^ . Imperial College London. Archived from the original on 27 January 2020. Retrieved 22 January 2013.
  2. ^ Richard Thomas at the Mathematics Genealogy Project
  3. ^ Richard Thomas FRS Biography
  4. ^ "Richard Thomas - Scholars | Institute for Advanced Study". 9 December 2019.
  5. ^ (PDF). Imperial College London. Archived from the original (PDF) on 2 October 2018.
  6. ^ Thomas, R. P. (2000). "A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on $K3$ fibrations". Journal of Differential Geometry. 54 (2). arXiv:math/9806111. doi:10.4310/jdg/1214341649. S2CID 119163745.
  7. ^ Seidel, Paul; Thomas, Richard (2001). "Braid group actions on derived categories of coherent sheaves". Duke Mathematical Journal. 108. doi:10.1215/S0012-7094-01-10812-0. hdl:10044/1/220. S2CID 458756.
  8. ^ Thomas, R. P.; Yau, S.-T. (2002). "Special Lagrangians, stable bundles and mean curvature flow". Communications in Analysis and Geometry. 10 (5): 1075–1113. arXiv:math/0104197. doi:10.4310/CAG.2002.v10.n5.a8. MR 1957663.
  9. ^ Pandharipande, R; Thomas, R. P (2009). "Curve counting via stable pairs in the derived category". Inventiones Mathematicae. 178 (2): 407–447. arXiv:0707.2348. Bibcode:2009InMat.178..407P. doi:10.1007/s00222-009-0203-9. S2CID 14113803.
  10. ^ A short proof of the Göttsche conjecture
  11. ^ Maulik, D; Pandharipande, R; Thomas, R. P (2010). "Curves on K 3 surfaces and modular forms". Journal of Topology. 3 (4): 937–996. CiteSeerX 10.1.1.756.7349. doi:10.1112/jtopol/jtq030. S2CID 54186798.
  12. ^ Huybrechts, Daniel; Thomas, Richard P (2009). "Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes". Mathematische Annalen. 346 (3): 545–569. arXiv:0805.3527. doi:10.1007/s00208-009-0397-6. S2CID 115164648.
  13. ^ Addington, Nicolas; Thomas, Richard (2014). "Hodge theory and derived categories of cubic fourfolds". Duke Mathematical Journal. 163 (10). arXiv:1211.3758. doi:10.1215/00127094-2738639. S2CID 119147791.
  14. ^ Hori, Kentaro; Katz, Sheldon; Klemm, Albrecht; Pandharipande, Rahul; Thomas, Richard; Vafa, Cumrun; Vakil, Ravi; Zaslow, Eric (2003). Mirror symmetry (PDF). Clay Mathematics Monographs. Vol. 1. Cambridge, MA: Clay Mathematics Institute. ISBN 0-8218-2955-6. MR 2003030.
  15. ^ Thomas, R. P (2000). "Derived categories for the working mathematician". Proceedings of the Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Cycles, Harvard, January. 1999 (2001). arXiv:math/0001045. Bibcode:2000math......1045T.
  16. ^ Thomas, R. P (2011). Moduli Spaces. pp. 282–333. arXiv:1111.1552. doi:10.1017/CBO9781107279544.007. ISBN 9781107279544. S2CID 117183792.
  17. ^ Thomas, R. P (2015). "Notes on HPD". arXiv:1512.08985 [math.AG].
  18. ^ "Frames of Mind | London Mathematical Society".
  19. ^ "Prizewinners 2004". Bulletin of the London Mathematical Society. 37 (3): 468–476. 2005. doi:10.1112/S0024609305004431.
  20. ^ . Archived from the original on 17 March 2018. Retrieved 8 April 2018.
  21. ^ "Prizewinners 2004". Bulletin of the London Mathematical Society. 37 (3): 468–476. 2005. doi:10.1112/S0024609305004431.
  22. ^ "ICM Plenary and Invited Speakers | International Mathematical Union (IMU)".
  23. ^ FRS announcement
  24. ^ Professors in Mathematics and Chemistry honoured with Royal Society Fellowships
  25. ^ 2018 Class of the Fellows of the AMS, American Mathematical Society, retrieved 3 November 2017

External links edit

May 08, 2024
richard, thomas, mathematician, richard, paul, winsley, thomas, british, mathematician, working, several, areas, geometry, professor, imperial, college, london, studies, moduli, problems, algebraic, geometry, mirror, symmetry, phenomenon, pure, mathematics, pr. Richard Paul Winsley Thomas FRS is a British mathematician working in several areas of geometry He is a professor at Imperial College London He studies moduli problems in algebraic geometry and mirror symmetry a phenomenon in pure mathematics predicted by string theory in theoretical physics 3 Richard ThomasBornRichard Paul Winsley ThomasAlma materUniversity of OxfordKnown forDonaldson Thomas theoryThomas Yau conjectureAwardsWhitehead Prize 1 2004 Scientific careerFieldsMathematicsInstitutionsImperial College LondonThesisGauge Theory on Calabi Yau Manifolds 1997 2 Doctoral advisorSimon DonaldsonWebsitewww2 wbr imperial wbr ac wbr uk wbr rpwt Contents 1 Education 2 Career and research 3 Awards and honours 4 References 5 External linksEducation editThomas obtained his PhD on gauge theory on Calabi Yau manifolds in 1997 under the supervision of Simon Donaldson at the University of Oxford In his dissertation research with Donaldson he defined the Donaldson Thomas invariants of Calabi Yau 3 folds a major topic in geometry and the mathematics of string theory Career and research editBefore joining Imperial College he was member of the Institute for Advanced Study in Princeton New Jersey 4 and affiliated with Harvard University and the University of Oxford He was made professor of pure mathematics in 2005 5 Thomas has made contributions to algebraic geometry differential Geometry and symplectic geometry His doctoral thesis which introduced the invariants that later became known as Donaldson Thomas invariants was published in the Journal of Differential Geometry as A holomorphic Casson invariant for Calabi Yau 3 folds and bundles on K3 fibrations 6 Motivated by homological mirror symmetry he produced braid group actions on derived categories of coherent sheaves in joint work with Paul Seidel 7 With Shing Tung Yau he formulated a conjecture now known as the Thomas Yau conjecture concerning the existence of a special Lagrangian in the Hamiltonian deformation class of a fixed Lagrangian submanifold of a Calabi Yau manifold 8 Together with Rahul Pandharipande he formulated a refinement of the Donaldson Thomas invariants for the special case of curve counting the Pandharipande Thomas PT stable pair invariants 9 With Martijn Kool and Vivek Shende he used the PT invariants to prove the Gottsche conjecture a classical algebro geometric problem going back more than a century 10 With Davesh Maulik and Pandharipande he proved the Katz Klemm Vafa KKV conjecture 11 establishing links between the Gromov Witten theory of K3 surfaces and modular forms His collaboration with Daniel Huybrechts led to contributions to the deformation theory of complexes 12 With Nick Addington he established a compatibility result for two rationality conjectures on cubic fourfolds 13 He coauthored a book on mirror symmetry 14 Thomas also wrote expository notes on derived categories 15 curve counting 16 and homological projective duality 17 He appeared in the documentary film Thinking space by Heidi Morstang 18 Thomas has played an important part in promoting geometry in the UK encouraging younger mathematicians 19 and in bringing more geometry to Imperial college There was little geometry in Imperial then but now thanks largely to the drive of my colleague Richard Thomas we have one of the main centres for research in this area Simon Donaldson 20 Awards and honours editIn 2004 Thomas was awarded the London Mathematical Society s Whitehead Prize and the Philip Leverhulme Prize in 2010 the Royal Society Wolfson Research Merit Award From the Whitehead prize citation Thomas has made seminal contributions across an unusually broad range of topics Much of his work is related to mirror symmetry and Calabi Yau geometry and thus has an important bearing on exciting contemporary interactions with mathematical physics This involved the combination of deep original insights and sophisticated technical proofs that is characteristic of Thomas s work 21 In 2010 he also was invited speaker for the algebraic geometry section at the International Congress of Mathematicians in Hyderabad where he delivered a lecture on mirror symmetry 22 Thomas was elected a Fellow of the Royal Society FRS in 2015 23 24 His contributions to algebraic geometry led to his election to the 2018 class of fellows of the American Mathematical Society 25 References edit Department of Mathematics Prizes and Awards Imperial College London Archived from the original on 27 January 2020 Retrieved 22 January 2013 Richard Thomas at the Mathematics Genealogy Project Richard Thomas FRS Biography Richard Thomas Scholars Institute for Advanced Study 9 December 2019 Academic Promotions 2005 PDF Imperial College London Archived from the original PDF on 2 October 2018 Thomas R P 2000 A holomorphic Casson invariant for Calabi Yau 3 folds and bundles on K3 fibrations Journal of Differential Geometry 54 2 arXiv math 9806111 doi 10 4310 jdg 1214341649 S2CID 119163745 Seidel Paul Thomas Richard 2001 Braid group actions on derived categories of coherent sheaves Duke Mathematical Journal 108 doi 10 1215 S0012 7094 01 10812 0 hdl 10044 1 220 S2CID 458756 Thomas R P Yau S T 2002 Special Lagrangians stable bundles and mean curvature flow Communications in Analysis and Geometry 10 5 1075 1113 arXiv math 0104197 doi 10 4310 CAG 2002 v10 n5 a8 MR 1957663 Pandharipande R Thomas R P 2009 Curve counting via stable pairs in the derived category Inventiones Mathematicae 178 2 407 447 arXiv 0707 2348 Bibcode 2009InMat 178 407P doi 10 1007 s00222 009 0203 9 S2CID 14113803 A short proof of the Gottsche conjecture Maulik D Pandharipande R Thomas R P 2010 Curves on K 3 surfaces and modular forms Journal of Topology 3 4 937 996 CiteSeerX 10 1 1 756 7349 doi 10 1112 jtopol jtq030 S2CID 54186798 Huybrechts Daniel Thomas Richard P 2009 Deformation obstruction theory for complexes via Atiyah and Kodaira Spencer classes Mathematische Annalen 346 3 545 569 arXiv 0805 3527 doi 10 1007 s00208 009 0397 6 S2CID 115164648 Addington Nicolas Thomas Richard 2014 Hodge theory and derived categories of cubic fourfolds Duke Mathematical Journal 163 10 arXiv 1211 3758 doi 10 1215 00127094 2738639 S2CID 119147791 Hori Kentaro Katz Sheldon Klemm Albrecht Pandharipande Rahul Thomas Richard Vafa Cumrun Vakil Ravi Zaslow Eric 2003 Mirror symmetry PDF Clay Mathematics Monographs Vol 1 Cambridge MA Clay Mathematics Institute ISBN 0 8218 2955 6 MR 2003030 Thomas R P 2000 Derived categories for the working mathematician Proceedings of the Winter School on Mirror Symmetry Vector Bundles and Lagrangian Cycles Harvard January 1999 2001 arXiv math 0001045 Bibcode 2000math 1045T Thomas R P 2011 Moduli Spaces pp 282 333 arXiv 1111 1552 doi 10 1017 CBO9781107279544 007 ISBN 9781107279544 S2CID 117183792 Thomas R P 2015 Notes on HPD arXiv 1512 08985 math AG Frames of Mind London Mathematical Society Prizewinners 2004 Bulletin of the London Mathematical Society 37 3 468 476 2005 doi 10 1112 S0024609305004431 The Shaw Prize Top prizes for astronomy life science and mathematics Archived from the original on 17 March 2018 Retrieved 8 April 2018 Prizewinners 2004 Bulletin of the London Mathematical Society 37 3 468 476 2005 doi 10 1112 S0024609305004431 ICM Plenary and Invited Speakers International Mathematical Union IMU FRS announcement Professors in Mathematics and Chemistry honoured with Royal Society Fellowships 2018 Class of the Fellows of the AMS American Mathematical Society retrieved 3 November 2017External links editRichard Thomas publications indexed by Google Scholar Retrieved from https en wikipedia org w index php title Richard Thomas mathematician amp oldid 1220162394, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.