Research

Research interests

Mathematical structures of quantum field theory and string theory

• Mirror symmetry, Bridgeland stability conditions, D-brane dynamics

• Hall algebras and Donaldson-Thomas theory

• Topological field and string theory, geometrical aspects of string dualities

• Black hole microstates enumeration, localisation in AdS/CFT

• Relations to integrable systems

Complex algebraic geometry and applications

• Enumerative invariants; moduli spaces of curves, and allied enumerative theories

• Homological algebra, geometry and K-theory of singularities

• Derived categories and Grothendieck ring of varieties

• Noncommutative crepant resolutions, matrix factorisations 

• Relations to combinatorics

Recent research grants (2010--)

Engineering and Physical Sciences Research Council

• EPSRC Standard Grant Geometry from Donaldson-Thomas invariants, 2022-26 (PI: Tom Bridgeland, total value £615,457)

• EPSRC Programme Grant Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations,  2018-25 (PI: Iain Gordon (Edinburgh); Sheffield co-I: Tom Bridgeland; total value £2,716,102)

• EPSRC Fellowship Grant Mirror symmetry, quantum curves, and integrable systems, 2018-24 (PI: Andrea Brini; total value £975,192)

• EPSRC Standard Grant Derived categories and K-theory of singularities, 2020-23 (PI: Evgeny Shinder, total value £332,778)

• EPSRC Programme Grant Motivic invariants and categorification, 2011-18 (PI: Dominic Joyce (Oxford); Sheffield co-I: Tom Bridgeland; total value £1,859,687)

• EPSRC Postdoctoral Fellowship Interactions between Moduli Spaces, Non-Commutative Algebra, and Deformation Theory, 2015-18 (PI: Joe Karmazyn, total value £222,476)

• EPSRC Standard Grant Stability conditions and hypermultiplet space, 2010-13 (PI: Tom Bridgeland, total value £252,146)

European Commission

• ERC Consolidator Grant Motivic invariants in birational geometry, 2024-29 (PI: Evgeny Shinder, total value €1,999,340)

• ERC Advanced Grant Stability conditions, Donaldson-Thomas invariants and cluster varieties, 2015-21 (PI: Tom Bridgeland, total value €1,556,550)

Royal Society

• RS Research Professorship Geometry from Donaldson-Thomas invariants, 2021-26, PI: Tom Bridgeland

• RS Dorothy Hodgkin Fellowship Virtual calculus, 2014-2022, PI: Cristina Manolache