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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 果冻影院 Geometry and Topology Group is part of the 果冻影院 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 , a graduate programme spanning 果冻影院, King's College London and Imperial College London.
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.
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.
works in differential geometry and symplectic topology. He is particularly interested in the partial differential equations of gauge theory and their听relation to enumerative invariants of manifolds with special holonomy, such as Calabi-Yau manifolds.听
works in differential geometry. His current research interests focus on manifolds with special and exceptional holonomy, in particular G2 and hyperk盲hler metrics, and gauge theory, and are often directly inspired by theoretical physics.
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.
鈥檚 work is about deformation spaces of geometric structures on manifolds. More specifically, I have worked on moduli spaces of structures on surfaces, complex hyperbolic geometry and Lorentzian geometry. I also try to apply geometric techniques to rigidity questions in dynamical systems.
: 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.
works in geometric analysis. He is primarily interested in harmonic maps, minimal surfaces and their connection to optimisation problems for eigenvalues of elliptic operators.
works in geometric group theory and low dimensional topology, primarily free groups and limit groups.
works in geometric group theory and is especially interested in Coxeter groups, Chevalley groups and buildings. She also works in algebraic combinatorics.
听works in noncommutative ring theory, algebraic geometry, and their interactions. Recently her interests include the behaviour of idealizers, a subring of a noncommutative ring, which often exhibit interesting and pathological behaviour.听
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).
has various research interests in differential geometry.听 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
is an IMSS fellow working in Poisson geometry and related areas. His current research deals with deformation problems and rigidity phenomena in this context.
works in Harmonic analysis, geometrical analysis of PDEs, microlocal analysis, spectral analysis and scattering theory as well as quantum field theory and quantum mechanics.
works in differential geometry and geometric analysis including minimal submanifolds, calibrated geometry and manifolds of special holonomy.听
works in analysis and PDE on manifolds where global dyanimcs of geodesics quantitatively determine analytic properties of solutions.
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