UCL Geometry & Topology

The UCL Geometry and Topology Group is part of the UCL Mathematics Department. We have nine 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 program spanning UCL, King's College and Imperial.

News
  • For the latest, check out our group blog.
  • Lagrangian Mean Curvature Flow: Progress and Problems will be held 4–5 Jan 2017 at UCL, organised by Jason Lotay and Felix Schulze.
Upcoming conferences
  • Lagrangian Mean Curvature Flow: Progress and Problems (4–5 Jan 2017)

Contact us:

Department of Mathematics, UCL,
Gower Street, London,
WC1E 6BT

UCL/KCL Geometry Seminar Schedule 2016–17

Autumn Term: Wednesday 15:00 at KCL.

Spring/Summer Terms: Wednesday 15:00 at UCL.

Click on the name of the speaker in the calendar to find out the day, time, room and to read the abstract. Subscribe to the seminar mailing list or contact the organisers, Jason Lotay and Yankı Lekili.

For the UCL/KCL Junior Geometry Seminar, see here.

Faculty

NameEmail @ ucl.ac.ukOfficeTelephone
Bellettini, Costantec.bellettini710+44 (0)20 7679 2863 (Internal: 32863)

Homepage | arXiv

I work 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. I am particularly interested in the impact of such regularity results on questions arising in differential geometry.

Casals, Rogerr.gutierrez703

Homepage | arXiv | MathSciNet

Evans, Jonnyj.d.evans802a+44 (0)20 7679 2272 (Internal: 32272)

Homepage | Blog | arXiv | MathSciNet

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

Johnson, F E Af.johnson705+44 (0)20 7679 2845 (Internal: 32845)

UCL Discovery | MathSciNet

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.

Lotay, Jasonj.lotay605+44 (0)20 7679 2836 (Internal: 32836)

Homepage | arXiv | MathSciNet

I work on differential geometry, with a particular focus on manifolds with special holonomy, their calibrated submanifolds, and related geometries. I am also interested in high-dimensional gauge theory, Lagrangian mean curvature flow and the Laplacian flow in G2 geometry. I mainly use methods from geometric analysis and exterior differential systems, which have applications throughout geometry and other areas in mathematics.

Louder, Larsl.louder609

Homepage | arXiv | MathSciNet

My work is in geometric group theory and low dimensional topology, primarily free groups and limit groups.
Schulze, Felixf.schulze607+44 (0)20 7679 2973 (Internal: 32973)

Homepage | arXiv | MathSciNet

My work is in Differential Geometry, Partial Differential Equations and Geometric Analysis. I am especially interested in geometric flows (mean curvature flow, Ricci flow, Willmore flow etc), minimal surfaces and Willmore surfaces.

Segal, Ede.segal605+44 (0)20 7679 3190 (Internal: 33190)

Homepage | arXiv | MathSciNet

My work involves algebraic geometry and homological algebra, with a lot of input from theoretical physics. My interests include derived categories, matrix factorizations, non-commutative resolutions, and topological field theories (mainly the B-model).

Singer, Michaelmichael.singer807a+44 (0)20 7679 3190 (Internal: 33190)

Homepage | MathSciNet

I have a number of interests in the differential geometry of special metrics and related geometric analysis. These include the study of Kähler metrics of constant scalar curvature and related questions about Bergman kernels and density functions; the geometry of self-dual and self-dual Einstein metrics in dimension 4; and also the application of analysis on manifolds with corners to geometric problems on singular and non-compact spaces. I am also interested in the geometry and topology of moduli spaces (for example of euclidean monopoles).

Postdocs

NameEmail @ ucl.ac.ukOfficeTelephone
Lambert, Benb.lambert600+44 (0)20 7679 3935 (Internal: 33935)

arXiv

Moore, Kimkim.moore600+44 (0)20 7679 3935 (Internal: 33935)

Homepage

Smith, Jackjack.smith602+44 (0)20 7679 2840 (Internal: 32840)

Homepage

PhD students

NameEmail @ ucl.ac.uk
Cioba, Alexa.cioba.12

I am a student of Dr. Wendl. My interests revolve around low dimensional topology, more specifically symplectic and contact structures in dimensions 4 and 3. I currently work on understanding what the structure of moduli spaces of pseudo-holomorphic curves has to say about the global properties of these manifolds.

Di Giovanni, Francescoucahdig

Evans, Christopherchristopher.evans.13

Evans, Johnjohn.evans.09

I am a student of Prof Johnson. I am interested in stable and unstable algebraic K-Theory.

Fowdar, Udhavudhav.fowdar.12

Habermann, Matthew

Konstantinov, Momchilmomchil.konstantinov.14

Homepage

My work is in the area of symplectic topology and my advisor is Dr. Jonny Evans. I am particularly interested in the topology of Lagrangian submanifolds. To study them I rely mostly on techniques from the theory of pseudoholomorphic curves.

Lehmann, Fabianfabian.lehmann.16

Maw, Emilyemily.maw.15

Homepage

I am interested in symplectic topology, particularly questions about Lagrangian submanifolds. My supervisor is Dr Jonny Evans.

Miglioranza, Mattiamattia.miglioranza.14

I am a PhD student of Dr Felix Schulze. I am working on the fields of mean curvature flow, Riemannian geometry and geometric measure theory.

Sutton, Chrischristopher.sutton.10

Vittis, Jasonjason.vittis.11

Wood, Albertalbert.wood.16

Past members

  • Tom Begley
  • Sam Brown
  • Jacqui Espina
  • Karsten Fritzsch
  • Raul Galan
  • Yoshi Hashimoto
  • Panagiotis Gianniotis
  • Tobias Sodoge

General information on PhDs

SupervisorTaking students?StudentsExpectations
Costante BellettiniYes
Roger Casals
Jonny EvansMaybe for 2018Momchil Konstantinov, Emily Maw

Past: Tobias Sodoge
Apart from hard work and enthusiasm, I would expect a masters project in a subject closely related to differential geometry or topology.
Jason LotayYes Francesco Di Giovanni, Chris Evans (with Felix Schulze, UCL), Udhav Fowdar, Matt Habermann (with Felix Schulze, UCL), Fabian Lehmann (with Mark Haskins, Imperial/Bath), Celso Viana (with André Neves, Imperial/Chicago)

Past: Kim Moore (with Alexei Kovalev, Cambridge), Yoshi Hashimoto (with Michael Singer), Goncalo Oliveira (with Simon Donaldson, Imperial).
I definitely expect you to know some differential geometry and some analysis. Preferably functional analysis and/or analysis of PDEs.
Lars LouderYes
Felix SchulzeMaybe for 2018Mattia Miglioranza, Albert Wood, Chris Evans (joint with Jason Lotay), Matthew Habermann (joint with Jason Lotay).

Past: Adrian Hammerschmidt, Felix Jachan, Tom Begley (joint with Neshan Wickramasekera).
Definitely differential geometry and analysis of PDEs. Preferably some Functional Analysis. It would be good to have an interest in Geometric Measure Theory.
Ed Segal
Michael SingerYesYoshi Hashimoto,
Raul Galan

Recent preprints (2015–)

  • J. Evans, I. Smith, Bounds on Wahl singularities from symplectic topology
        arXiv:1708.02268
  • J. Lotay, T. Pacini, Uniqueness and persistence of minimal Lagrangian submanifolds
        arXiv:1704.08226
  • M. Konstantinov, Higher rank local systems in Lagrangian Floer theory
        arXiv:1701.03624
  • C. Mantegazza, M. Novaga, A. Pluda, F. Schulze, Evolution of networks with multiple junctions
        arXiv:1611.08254
  • P. Gianniotis, F. Schulze, Ricci flow from spaces with isolated conical singularities
        arXiv:1610.09753
  • A. Cioba, C. Wendl, Unknotted Reeb orbits and nicely embedded holomorphic curves
        arXiv:1609.0166
  • J. Lotay, G. Oliveira, SU(2)2-invariant G2-instantons
        arXiv:1608.07789
  • J. Evans, I. Smith, Markov numbers and Lagrangian cell complexes in the complex projective plane
        arXiv:1606.08656
  • F. Schulze, B. White, A local regularity theorem for mean curvature flow with triple edges
        arXiv:1605.06592
  • J. Fine, J. Lotay, M. Singer, The space of hyperkähler metrics on a 4-manifold with boundary
        arXiv:1603.08170
  • J. Lotay, Y. Wei, Laplacian flow for closed G_2 structures: real analyticity
        arXiv:1601.04258
  • C. Kottke, M. Singer, Partial compactification of monopoles and metric asymptotics
        arXiv:1512.02979
  • L. Louder, D. B. McReynolds, P. Patel, Zariski closures and subgroup separability
        arXiv:1510.04144
  • C. Bellettini, G. Tian, Compactness results for triholomorphic maps
        arXiv:1507.06558
  • C. Bellettini, Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles
        arXiv:1507.06548
  • C. Bellettini, Semi-calibrated 2-currents are pseudo holomorphic, with applications
        arXiv:1507.06542
  • J. Evans, Y. Lekili, Generating the Fukaya categories of Hamiltonian G-manifolds
        arXiv:1507.05842
  • J. Lotay, T. Pacini, Complexified diffeomorphism groups, totally real submanifolds and Kähler-Einstein geometry
        arXiv:1506.04630
  • J. Lotay, Y. Wei, Stability of torsion-free G_2 structures along the Laplacian flow
        arXiv:1504.07771
  • J. Lotay, Y. Wei, Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness
        arXiv:1504.07367
  • T. Begley, K. Moore, On short time existence of Lagrangian mean curvature flow
        arXiv:1501.07823