All Souls College

Tom Bridgeland has been working with homological techniques in algebraic geometry. He has completed his project with Ivan Smith relating quadratic differentials to stability conditions on certain three-dimensional Calabi-Yau categories. He is now studying derived categories of complex symplectic manifolds.

Link to Website

Background

Quondam Fellow, All Souls College (from 2013)
Senior Research Fellow, All Souls College (from 2011 to 2013)
University Reader and Royal Society Research Fellow (until 2006), then Professor of Mathematics, Sheffield University (from 2004 to 2010)
EPSRC Research Assistant (to 2000), then EPSRC Research Fellow (to 2003) and, finally, Royal Society Research Fellow, University of Edinburgh (from 1998 to 2004)
Postgraduate, Edinburgh University (from 1995 to 1998)
Undergraduate, Christ’s College, Cambridge (from 1991 to 1995)

Research Interests

Algebraic geometry and its connections with string theory and mirror symmetry
Focussing more specifically on properties of derived categories of coherent sheaves on algebraic varieties

Selected publications

(with P. Aspinwall et al.), Dirichlet Branes and Mirror Symmetry, Clay Mathematics Monographs (2009), 684pp
'Stability Conditions and Kleinian Singularities', to appear, International Math. Research Notices (2009)
'Spaces of Stability Conditions', Algebraic Geometry–Seattle 2005. Part 1, 1–21, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI. (2009)
'Stability Conditions on K3 Surfaces', Duke Math. J., 141 (2008), no. 2, 241-91
'Stability Conditions on Triangulated Categories', Ann. of Math. (2) 166 (2007), no. 2, 317–45
Derived Categories of Coherent Sheaves, International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich (2006), 563-82
(with S. Iyengar), 'A Criterion for Regularity of Local Rings', C. R. Math. Acad. Sci., Paris 342 (2006), no. 10, 723-6
'Stability Conditions on a Non-Compact Calabi-Yau Threefold', Comm. Math. Phys., 266 (2006), no. 3, 715-33
'T-structures on Some Local Calabi-Yau Varieties', J. of Algebra, 289 (2005), 453-83
'Flops and Derived Categories', Invent. Math., 147 (2002), 613-32
(with Antony Maciocia), 'Fourier-Mukai Transforms for K3 and Elliptic Fibrations', J. Alg. Geom., 11 (2002), 629-57
(with Alastair King and Miles Reid), 'The McKay Correspondence as an Equivalence of Derived Categories', J. Amer. Math. Soc., 14 3 (2001) 535-54
(with Antony Maciocia), 'Complex Surfaces with Equivalent Derived Categories', Math. Zeit., 236 4 (2001), 677-97
'Equivalences of derived categories and Fourier-Mukai transforms', Bull. Lond. Math. Soc., 31 1 (1999), 25-34
'Fourier-Mukai Transforms for Ellptic Surfaces', J. reine ang. math. 498 (1998), 115-133

Research awards and grants

Cambridge University Adams Prize (2007).
Invited speaker at Inernational Congress of Mathematics (2006).
Whittemore Lecturer at Yale (2006).
Edinburgh Mathematical Society Whittaker Prize (2005).
London Mathematical Society Berwick Prize (2003).

Professor Tom Bridgeland

Professor Richard Ericson

Professor Sir Rees Davies

Professor Malcolm Bowie

Richard Harrison

The Revd. Professor John McManners

Professor Susan Hurley

Dr Simon Walker

Robert Shackleton

Francis Willis-Bund