Tom Bridgeland

Thomas Andrew Bridgeland FRS[3] (born 1973) is a Professor of Mathematics at the University of Sheffield.[2][4][5][6][7][8][1] He is most well-known for defining Bridgeland stability conditions on triangulated categories.

Tom Bridgeland

FRS
Born
Thomas Andrew Bridgeland[1]

1973 (age 47–48)
EducationShelley High School[1]
Alma mater
Awards
Scientific career
Institutions
ThesisFourier-Mukai transforms for surfaces and moduli spaces of stable sheaves (2002)
Doctoral advisorAntony Maciocia[2]
Websitetom-bridgeland.staff.shef.ac.uk

Education

Bridgeland was educated at Shelley High School[7] in Huddersfield and Christ's College, Cambridge where he studied the Cambridge Mathematical Tripos graduating with first class Bachelor of Arts degree with honours in Mathematics in 1995. He completed his PhD[9] at the University of Edinburgh, where he also stayed for a postdoctoral research position.

Research and career

Bridgeland's research interest is in algebraic geometry, focusing on properties of derived categories of coherent sheaves on algebraic varieties.[10][11] His most-cited papers are on stability conditions, on triangulated categories[12] and K3 surfaces;[13] in the first he defines the idea of a stability condition on a triangulated category, and demonstrates that the set of all stability conditions on a fixed category form a manifold, whilst in the second he describes one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.

Bridgeland's work helped to establish the coherent derived category as a key invariant of algebraic varieties and stimulated world-wide enthusiasm for what had previously been a technical backwater.[3] His results on Fourier-Mukai transforms solve many problems within algebraic geometry, and have been influential in homological and commutative algebra, the theory of moduli spaces, representation theory and combinatorics.[3] Bridgeland's 2002 Annals paper introduced spaces of stability conditions on triangulated categories, replacing the traditional rational slope of moduli problems by a complex phase. This far-reaching innovation gives a rigorous mathematical language for describing D-branes and creates a new area of deep interaction between theoretical physics and algebraic geometry. It has been a central component of subsequent work on homological mirror symmetry.[3]

Bridgeland's research has been funded by the Engineering and Physical Sciences Research Council (EPSRC).[14]

Awards and honours

Bridgeland won the Adams Prize in 2007 and was elected a Fellow of the Royal Society (FRS) in 2014.[3]

References
  1. Anon (2017). "Bridgeland, Prof. Tom Andrew". Who's Who. ukwhoswho.com (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.U281971. (subscription or UK public library membership required) (subscription required)
  2. Tom Bridgeland at the Mathematics Genealogy Project
  3. Anon (2014). "Professor Tom Bridgeland FRS". Royal Society. Retrieved 2 May 2014. One or more of the preceding sentences incorporates text from the royalsociety.org website where:
    “All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License.” --Royal Society Terms, conditions and policies at the Wayback Machine (archived 2016-11-11)
  4. Tom Bridgeland publications indexed by Google Scholar
  5. Tom Bridgeland publications indexed by the Scopus bibliographic database. (subscription required)
  6. Bridgeland, T. (2002). "Flops and derived categories". Inventiones Mathematicae. 147 (3): 613–632. arXiv:math/0009053. Bibcode:2002InMat.147..613B. doi:10.1007/s002220100185. S2CID 53059980.
  7. Bridgeland, Tom (2017). "Tom Bridgeland CV" (PDF). tom-bridgeland.staff.shef.ac.uk. Archived from the original (PDF) on 4 March 2016.
  8. "Tom Bridgeland publications". front.math.ucdavis.edu.
  9. Bridgeland, Thomas Andrew (1998). Fourier-Mukai Transforms for Surfaces and Moduli Spaces of Stable Sheaves (PhD thesis). University of Edinburgh. hdl:1842/12070. OCLC 606214894. EThOS uk.bl.ethos.641936.
  10. Bridgeland, T.; King, A.; Reid, M. (2001). "The McKay correspondence as an equivalence of derived categories" (PDF). Journal of the American Mathematical Society. 14 (3): 535. doi:10.1090/S0894-0347-01-00368-X. S2CID 15808151.
  11. Bridgeland, T. (2005). "T-structures on some local Calabi–Yau varieties". Journal of Algebra. 289 (2): 453–483. arXiv:math/0502050. Bibcode:2005math......2050B. doi:10.1016/j.jalgebra.2005.03.016. S2CID 14101159.
  12. Bridgeland, Tom (2002). "Stability conditions on triangulated categories". arXiv:math/0212237v3.
  13. Bridgeland, T. (2008). "Stability conditions on K3 surfaces". Duke Mathematical Journal. 141 (2): 241–291. arXiv:math/0212237. doi:10.1215/S0012-7094-08-14122-5. S2CID 16083703.
  14. "UK Government Grants awarded to Tom Bridgeland". gtr.rcuk.ac.uk. Swindon: Research Councils UK.

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