UCL Geometry & Topology

The UCL Geometry and Topology Group is part of the UCL Mathematics Department. We have seven faculty members, two 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.
  • The 19th UK/Japan Winter School will be held 4–7 Jan 2017 at UCL. The theme for the conference is "Singularities, Symmetries and Submanifolds" and it will feature minicourses by D. Joyce, A. Keating and K. Ueda as well as research talks from a variety of exciting speakers spanning symplectic geometry and geometric analysis.
  • The 10th Brussels-London Geometry Seminar will be on Monday 23rd Jan 2017. The speakers are A. Juhasz, J. Rasmussen and A. Wand. The theme is low-dimensional topology.
  • The first British Isles Graduate Workshop on Higgs bundles: algebraic and differential geometric perspectives will be held 2–8 Apr 2017. The goal is to bring together a group of approximately 30 graduate students to work on a specific topic under the guidance of three senior mathematicians. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field.
  • The London Summer School and Workshop: the Sen conjecture and beyond will be held 19–23 Jun 2017 at UCL, organised by K. Fritzsch, C. Kottke and M. Singer. The purpose of the Summer School and Workshop is to introduce and disseminate new analytical methods for tackling the Sen conjecture (on L2-harmonic forms on monopole moduli spaces), while also surveying the recent developments on the geometry and physics of singular monopoles.

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.

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.schulze504b+44 (0)20 7679 7897 (Internal: 327897)

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.

Singer, Michaelmichael.singer807a+44 (0)207 679 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
Espina, Jacquij.espina600+44 (0)20 7679 3935 (Internal: 33935)

arXiv

Fritzsch, Karstenk.fritzsch600+44 (0)20 7679 3935 (Internal: 33935)

I'm interested in geometric analysis on manifolds with corners, in particular in singular pseudodifferential operator calculi adapted to the specific geometry of the manifold in question or cohomology theories for (non-compact) manifolds with corners and their relation to geometric PDE. I'm working with Michael Singer on improving the understanding of the geometry of compactifications (as manifolds with corners) of monopole moduli spaces.

PhD students

NameEmail @ ucl.ac.uk
Begley, Tomt.begley at maths.cam.ac.uk

Homepage

I am a PhD student at Cambridge working under the joint supervision of Dr Felix Schulze (UCL) and Neshan Wickramasekera (Cambridge). I am currently interested in variational problems in geometry, formulated in the languages of geometric measure theory and geometric PDE. Most recently I have been working on mean curvature flow where I am particularly interested in singularity formation and the existence and regularity of weak solutions. I am also interested in minimal surfaces and the structure of their singularities.

Brown, Sams.brown.12

I am studying with Dr Henry Wilton (now at Cambridge), researching geometric group theory with a particular interest in the links to the geometry and topology of 2- and 3-manifolds. I am currently looking into various properties of non-positively curved cube complexes.

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.

Evans, Johnjohn.evans.09

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

Fowdar, Udhav

Galan, Raulraul.galan.13

I am a student of Prof Michael Singer. I am interested in differential geometry and magnetic monopoles.

Hashimoto, Yoshiyoshinori.hashimoto.12

I am a PhD student of Prof Michael Singer and Dr Jason Lotay, and work in the field of complex Kähler geometry. More specifically, I am interested in the problems concerning the constant scalar curvature metrics on polarised Kähler manifolds and its connection to algebro-geometric stability. I am now particularly interested in the method called quantisation, in which a sequence of balanced metrics approximate the constant scalar curvature Kähler metric.

Konstantinov, Momchilmomchil.konstantinov.14

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.

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.

Moore, Kimk.moore at maths.cam.ac.uk

I am a PhD student at Cambridge working under the joint supervision of Dr Jason Lotay (UCL) and Dr Alexei Kovalev (Cambridge). I am working on calibrated submanifolds in Spin(7) manifolds and Lagrangian mean curvature flow.

Sodoge, Tobiastobias.sodoge.13

I am a student of Dr Jonny Evans. My interests in symplectic topology are manifold and include: Lagrangian and coisotropic submanifolds I am interested in studying the space of Lagrangians, which are Hamiltonian isotopic to a fixed Lagrangian and finding restrictions on the ambient topology of coisotropic submanifolds. Lagrangian Floer Theory. A long term project of mine is to think about possible extensions of the exisiting (Lagrangian) Floer Theory.

Sutton, Chrischristopher.sutton.10

Vittis, Jasonjason.vittis.11

General information on PhDs

SupervisorTaking students?StudentsExpectations
Costante Bellettini
Jonny EvansMaybe for 2017Tobias Sodoge (2013–)
Momchil Konstantinov (2014–)
Emily Maw (2015–)
Apart from hard work and enthusiasm, I would expect a masters project in a subject closely related to differential geometry or topology.
Jason LotayYesPast: Yoshi Hashimoto (with Michael Singer),
Goncalo Oliveira (with Simon Donaldson, Imperial).
Current: Udhav Fowdar,
Celso Viana (with André Neves, Imperial),
Kim Moore (with Alexei Kovalev, Cambridge)
I definitely expect you to know some differential geometry and some analysis. Preferably functional analysis and/or analysis of PDEs.
Lars LouderYes
Felix SchulzeYesPast (Free University Berlin):
Adrian Hammerschmidt
Felix Jachan
Current: Tom Begley (co-supervising with Neshan Wickramasekera, Cambridge),
Mattia Miglioranza.
Definitely differential geometry and analysis of PDEs. Preferably some Functional Analysis. It would be good to have an interest in Geometric Measure Theory.
Michael SingerYesYoshi Hashimoto,
Raul Galan

Recent preprints (2015–)

  • 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