Tom Bridgeland  

Born  Thomas Andrew Bridgeland^{ [1] } 1973 (age 49–50) 
Education  Shelley High School ^{ [1] } 
Alma mater  
Awards 

Scientific career  
Institutions  
Thesis  FourierMukai transforms for surfaces and moduli spaces of stable sheaves (2002) 
Doctoral advisor  Antony Maciocia^{ [2] } 
Website  tombridgeland 
Thomas Andrew Bridgeland FRS ^{ [3] } (born 1973) is a Professor of Mathematics at the University of Sheffield.^{ [2] }^{ [4] }^{ [5] }^{ [6] }^{ [7] }^{ [1] } He was a senior research fellow in 2011–2013 at All Souls College, Oxford and, since 2013, remains as a Quondam Fellow. He is most wellknown for defining Bridgeland stability conditions on triangulated categories.
Bridgeland was educated at Shelley High School ^{ [7] } in Huddersfield and Christ's College, Cambridge, where he studied the Mathematical Tripos in the University of Cambridge, graduating with a first class degree in mathematics in 1994 and a distinction in Part III the following year. He completed his PhD^{ [8] } at the University of Edinburgh, where he also stayed for a postdoctoral research position.^{[ citation needed ]}
Bridgeland's research interest is in algebraic geometry, focusing on properties of derived categories of coherent sheaves on algebraic varieties.^{ [9] }^{ [10] } His mostcited papers are on stability conditions, on triangulated categories^{ [11] } and K3 surfaces;^{ [12] } 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 worldwide 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 farreaching innovation gives a rigorous mathematical language for describing Dbranes 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).^{ [13] }
Bridgeland won the Berwick Prize in 2003, the Adams Prize in 2007 and was elected a Fellow of the Royal Society (FRS) in 2014.^{ [3] } He was an invited speaker at the International Congress of Mathematicians, Madrid in 2006.
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
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Richard Paul Winsley Thomas 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.
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Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras, simplicial commutative rings or ring spectra from algebraic topology, whose higher homotopy groups account for the nondiscreteness of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements. Derived algebraic geometry can be thought of as an extension of this idea, and provides natural settings for intersection theory of singular algebraic varieties and cotangent complexes in deformation theory, among the other applications.
The article "Sur quelques points d'algèbre homologique" by Alexander Grothendieck, now often referred to as the Tôhoku paper, was published in 1957 in the Tôhoku Mathematical Journal. It revolutionized the subject of homological algebra, a purely algebraic aspect of algebraic topology. It removed the need to distinguish the cases of modules over a ring and sheaves of abelian groups over a topological space.
Daniel Huybrechts is a German mathematician, specializing in algebraic geometry.
Mark William Gross is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry.
In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves on a smooth variety, , called its derived category, or the derived category of perfect complexes on an algebraic variety, denoted . For instance, the derived category of coherent sheaves on a smooth projective variety can be used as an invariant of the underlying variety for many cases. Unfortunately, studying derived categories as geometric objects of themselves does not have a standardized name.
In mathematics, and especially algebraic geometry, a Bridgeland stability condition, defined by Tom Bridgeland, is an algebrogeometric stability condition defined on elements of a triangulated category. The case of original interest and particular importance is when this derived category is the derived category of coherent sheaves on a Calabi–Yau manifold, and this situation has fundamental links to string theory and the study of Dbranes.
Denis Auroux is a French mathematician working in geometry and topology.
Dmitri Olegovich Orlov, is a Russian mathematician, specializing in algebraic geometry. He is known for the BondalOrlov reconstruction theorem (2001).
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