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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, gauge theory, differential geometry and geometric analysis.

The UCL Geometry and Topology Group is part of the UCL Mathematics Department. We have eight faculty members, three 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 University College London, King's College London and Imperial College London.

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.

Dario Beraldo works in geometric representation theory, especially on the geometric Langlands program. His other interests include derived algebraic geometry, higher category theory, connections to number theory and to mathematical physics.

Lorenzo Foscolo works in differential geometry. His current research interests focus on manifolds with special and exceptional holonomy, in particular G2 and hyperkähler metrics, and gauge theory, and are often directly inspired by theoretical physics.

Jeffrey Galkowski works in microlocal analysis with an emphasis on high frequency spectral and scattering theory problems motivated by mathematical physics. Typically, these problems are posed on non-trivial manifolds where the underlying geometry plays a crucial role.

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.

Nikon Kurnosov works in algebraic geometry. His current research interests focus on holomorphically symplectic manifolds, in particular, hyperkähler manifolds.

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

Yusra Naqvi works in geometric group theory and is especially interested in Coxeter groups, Chevalley groups and buildings. She also works in algebraic combinatorics.

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).

Postdoctoral Research Associates

Damián Gvirtz is an EPSRC-funded fellow working on rational points on algebraic varieties. Among his research interests are the geometry and arithmetic of K3 surfaces.

Fritz Hiesmayr is an EPSRC-funded postdoc working with C. Bellettini. His research is in geometric analysis, with a focus on surfaces with prescribed mean curvature and the Allen-Cahn equation.

Massimo Pippi works in the area of (derived) algebraic geometry and noncommutative algebraic geometry. Among his interests there are categories of singularities, matrix factorizations and their connection with vanishing cycles.

Michael Wong is an ERC-funded postdoc working with Ed Segal. His research is primarily in noncommutative geometry. He is particularly interested in derived categories, matrix factorizations, deformation theory, and some noncommutative geometric aspects of mirror symmetry.

 

For more information on the activities of the group please click here.