Mathematics
All Souls has for some years had a small number of Senior Research Fellows in mathematics. An earlier incumbent was Ronald Jensen, and Graeme Segal is now an Emeritus Fellow. Current Senior Research Fellows are Tom Bridgeland and Dan Segal.
Dan Segal works in algebra, mainly in group theory and related topics in Lie algebras, commutative algebra and Diophantine decision problems. His current interests centre on profinite groups, and on problems in finite group theory arising from profinite questions. One such family of problems concerns verbal width, the subject of a recent lecture notes volume.
Tom Bridgeland is an algebraic geometer whose research focuses on homological properties of complex varieties. The main objects of study in this field are derived categories of coherent sheaves, together with similar categories arising in the representation theory of quivers. Over the last twenty years this whole subject has been hugely influenced by the discovery of deep links with quantum field theory, and in particular by Kontsevich's homological mirror symmetry conjecture.
In recent years, Graeme Segal's main work has been in quantum field theory - its conceptual and mathematical structure, and its purely mathematical applications - but he is also interested in a chain of topics which interpolate between quantum field theory and geometry: the central theme is the structure of smooth manifolds, but it has led him from algebraic topology into global analysis - index theory and integrable systems - and also the geometry and representation theory of finite- and infinite-dimensional Lie groups.
The Post-Doctoral Fellowship is also open to mathematicians, previous incumbents being Simon Donaldson, Marcus du Sautoy and Michael McQuillan. Visiting Fellows in mathematics have included Jonathan Alperin, Samuel Gitler, Walter Feit, Tony Joseph, Leonard Scott, Avinoam Mann, Aner Shalev, Geoff Robinson, Graeme Wake, Yuri Berest, Martin Barlow, Gus Lehrer and Steve Smith.