| Citation | Professor of Pure Mathematics, School of Mathematics and Statistics, University of Sheffield
Tom Bridgeland has established the coherent derived category as a key invariant of algebraic varieties and stimulated world-wide enthusiasm for what had previously been a technical backwater. His results on Fourier-Mukai transforms solve many problems within algebraic geometry, and have been influential in homological and commutative algebra, orbifold and quantum cohomology, minimal model program, classification of Fano varieties, moduli constructions, representation theory and combinatorics. 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 rigorous mathematical content to work on 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.
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