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Geometry and Topology

Our research interests range from low-dimensional topology and geometric group theory, through algebraic geometry to symplectic geometry (and topology), gauge theory, differential geometry analysis.

The UCL Geometry and Topology Group is part of the UCL Mathematics Department. We have eight faculty members, five postdocs and 14 PhD students. Our research interests include differential geometry and geometric analysis, symplectic geometry, gauge theory, low-dimensional topology and geometric group theory. We are involved with the London School of Geometry and Number Theory (LSGNT), a graduate programme spanning UCL, King's College and Imperial.

Costante Bellettini works in geometric analysis, with special emphasis on regularity questions arising in the calculus of variations and in calibrated geometry, often using methods from geometric measure theory and partial differential equations. He is particularly interested in the impact of such regularity results on questions arising in differential geometry.

Jonny Evans I am interested in symplectic topology and Floer theory, particularly in questions about Lagrangian submanifolds.

Francis Johnson Topology of manifolds; low-dimensional topology; the D(2) problem, more generally problems involving the fundamental group; Lie groups and their discrete subgroups; homological algebra; geometric invariant theory.

Jason Lotay’s area of research is differential geometry.  He mainly studies manifolds with special holonomy, their calibrated submanifolds and related geometries.  He also works on geometric flows, including Lagrangian mean curvature flow and the G_2 Laplacian flow, and on gauge theory.  He primarily uses methods from geometric analysis and exterior differential systems

Lars Louder works in geometric group theory and low dimensional topology, primarily free groups and limit groups.

Felix Schulze works in Differential Geometry, Partial Differential Equations and Geometric Analysis. He is especially interested in geometric flows (mean curvature flow, Ricci flow, Willmore flow etc), minimal surfaces and Willmore surfaces.

Ed Segal works in algebraic geometry and homological algebra, with a lot of inspiration from theoretical physics. His interests include derived categories, matrix factorizations, non-commutative resolutions, and topological field theories (mainly the B-model).

Michael Singer has various research interests in differential geometry.  He is currently working on projects in Kaehler geometry, hyperKaehler and ant-self-dual Einstein metrics in four dimensions, and moduli spaces arising in mathematical physics (in particular euclidean monopoles).

List of Permanent Academic Staff 

Costante Bellettini
Jonny Evans

Francis Johnson
Jason Lotay
Lars Louder
Felix Schulze
Ed Segal
Michael Singer

Postdoctoral Research Associates

Ben Lambert
Andrew McLeod
Kim Moore
Jack Smith
Michael Wong