RESEARCH PROFILE
- RAE: According to the RAE assessment over 65 per cent of the research in the Department is internationally excellent or world-leading in terms of originality, significance and rigour. This puts the Department in the top quarter of all UK Mathematics Departments and near the top in London.
- Research income: Approximately £2m per annum.
- Current number of academic staff: 40 permanent, 10 fixed-term
- Current number of research students: Approximately 40.
- Research grants: Researchers from our department currently hold research grants from BBSRC, EPSRC, STFC, Royal Society, Leverhulme Trust, London Mathematical Society and the European Comission. Our grants include studentships for postgraduate research students.
- Joint PhDs available: Exciting opportunities to gain a joint PhD with the University of Hong Kong and the Humboldt University of Berlin.
KEY FACTS
Student destinations
Our former PhD students have gone on to work in Universities, Industry, Government, Banking and Insurance.
Head of group/division
Professor Jürgen Berndt
Duration
Full-time: 3-4 years; Part-time: 6-8 years.
Location
Strand Campus.
Year of entry 2013
Offered by
School of Natural and Mathematical Sciences
Department of Mathematics
Closing date
No deadline for applications. Students interested in applying to funding should be aware that deadlines for this differ, therefore applicants should view the Graduate Funding Pages at
http://www.kcl.ac.uk/study/pg/funding/sources/index.aspx for more information.
PhD: 8-15 FT, 2-5 PT per year; MPhil: 5-10 FT, 1-5 PT per year.
Fees
CONTACTS
Contact information
Postgraduate Officer, Centre for Arts & Sciences Admissions (CASA)
tel: +44 (0) 20 7848 2555 / 7208
fax: +44 (0) 20 7848 7200
Email
Website
RESEARCH DESCRIPTION
Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The research groups organise regular seminars, where top-ranking scientists from around the world present new results, which our research students can witness firsthand. The students also organise their own informal seminars and discussion groups. The lively environment and the exceptionally friendly atmosphere at our department contribute to the high success rate of our students. You can apply for supervision in all fields of interest of our staff members. The department provides funding for PhD students to attend suitable schools and conferences during their studies.
Joint PhD programme
Exciting opportunities are now available to undertake a joint PhD programme with the University of Hong Kong or the Humboldt University of Berlin.
Staff interests associated with the research programme and its research groups
Analysis
Interests:
Analysis in a broad sense (with emphasis on Partial Differential Equations and Dynamical Systems) and Fluid Mechanics.
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Interests:
Spectral theory of PDEs; Schrodinger operators; scattering theory.
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020 7848 1167
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020 7848 2017
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Analysis: Partial differential and integral equations, microlocal analysis, global analysis, complex variables, spectral theory, functional analysis. Applications: Fluid dynamics, elasticity theory.
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020 7848 1379
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020 7848 2017
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Geometric index theory of elliptic operators; applications to quantum field theory.
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020 7848 2778
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My mathematical interests lie between spectral theory and geometry. I have studied spectral and other properties of differential operators on manifolds in connection with geometric properties of the manifolds. Some of my recent work is connected with convex analysis, the abstract theory of operators on a Hilbert space and their applications to problems of spectral theory.
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020 7848 2215
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02088482017
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Disordered Systems
Interests:
- Theory of spin glasses, complexity and structure of metastable states
- Out of equilibrium dynamics, fluctuation dissipation relations, effective temperatures interpretation
- Spin models on finitely connected random graphs
- Cellular signaling networks, proteomics, gene regulatory networks
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Theory of disordered systems; processes on complex networks; non-equilibrium statistical mechanics; econophysics
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020 7848 2235
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Applications of Statistical Mechanics in a broad range of fields including Soft Condensed Matter (fracture, friction), Packing Problems, Random Matrix Theory and methods in Statistical Mechanics (the Self-Consistent Expansion).
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080 7848 2864
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Statistical mechanics of disordered systems; theory of minority games; metabolic networks; quantam integrable models.
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020 7848 2853
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Statistical mechanics of disordered systems (soft materials; rheology, polydispersity effects on phase behaviour; glassy dynamics), statistical inference and learning processes including Gaussian processes, support vector machines, non-parametric Bayesian inference
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020 7848 2875
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020 7848 2017
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Physics of glassy systems, neural networks and risk modelling.
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020 7848 1035
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020 7848 2017
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Financial Mathematics
Interests:
- Credit risk and pricing of credit derivatives
- Information-based modelling of asset prices
- Models for inflation and of inflation-linked securities
- Hybrid products
- Interest rate modelling
- Insurance reserving
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Portfolio management in markets with "friction factors" (taxes and transaction costs), utility maximisation, optimal stopping and stochastic control problems, numerical methods for free-boundary problems.
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Pricing, risk measurement, credit, counterparty risk, and stochastic models for commodities and inflation
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Asymptotics for stochastic volatility models and Lévy processes with an emphasis on large deviations theory, and diffusion-type processes.
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020 7848 2774
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Financial risk management, financial econometrics, mathematical finance and the development of computational techniques for risk management.
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Interests:
• Econophysics
• Application of methods from Statistical Physics to Finance
• Complex Systems
• Science of Networks
Others:
• Granular materials
• Numerical simulations of diffusive processes for the analysis of the magnetic properties in new materials
• Strongly Correlated Electronic Systems and High-Tc Superconductivity
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020 7848 2223
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Geometry
Interests:
Infinite dimensional Lie groups and algebras; quantum groups.
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Complex, differential, and symplectic geometry.
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My main research interest is geometric analysis with emphasis currently on the theory of minimal and constant mean curvature surfaces.
Minimal surfaces are defined as surfaces which are critical points for the area functional. The mean curvature of a minimal surface, the average of the two principal curvatures, is identically zero. Surfaces which are critical points for the area functional under a volume constraint are instead called constant mean curvature (CMC) surfaces and in fact the average of the two principal curvatures is constant. Not only are there plenty of mathematical examples for both of these surfaces (for instance planes, helicoids and catenoids are minimal surfaces while spheres, cylinders and Delaunay surfaces are non zero CMC surfaces), but they overtly present themselves in the real world. In nature, the shape of a soap film approximates with great accuracy that of a minimal surface while soap bubbles provide the analogous approximation for CMC surfaces. In other words, a soap bubble is the least-area surface that encloses the fixed volume inside.
The results in my papers and my recent interests can be divided into the following areas:
- Curvature estimates for nonzero CMC disks embedded in locally homogeneous manifolds.
- The asymptotic geometric structure of nonzero CMC surfaces properly embedded in locally homogeneous manifolds.
- The rigidity of CMC surfaces immersed in locally homogeneous manifolds.
- The geometry of surfaces embedded in Euclidean space with integral bounds for the mean curvature.
- Problems and results on the number, genus, shape and other geometric properties of compact CMC surfaces from the geometry of their boundary.
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020 7848 2981
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My own research is in geometry, but not restricted to it, and I often deal with problems and methods that are related to other areas. Geometry is one of the traditional areas of mathematics. In ancient civilizations geometry was used for solving practical problems. This changed drastically with the ancient Greeks, where geometry became the center of mathematics. Its axiomatic foundation and the theory based on propositions that were logically deducted from it influenced enormously our way of thinking and lead over the last 2000 years to many fundamental developments and discoveries in mathematics and the sciences. For instance, during the Renaissance, geometry influenced strongly the development of astronomy, geodesy, cartography, mechanics, optics and arts. Geometry nowadays has great impact on our lives through many applications, for example in medicine (diagnosis of cancer, brain imaging), building and construction industry (computer aided design), and manufacturing (robotics). This shows the potential for geometry to get involved in collaborative projects with partners from industry. On the theoretical side, there is a fundamental interaction between geometry and physics, for instance between Euclidean geometry and Newtonian mechanics, or Riemannian geometry and relativity theory, which represent remarkable scientific achievements. Currently there is an intense interaction between geometry and modern physical theories (string theories, supergravity theories, M-theory). Because of all these applications and its particular feature of visualization, geometry is also an extremely attractive area of mathematics for teaching at all levels in higher education.
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020 7848 2814
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My main work is on geometry of flag varieties, particularly in relation to Gromov-Witten theory and mirror symmetry. I also have a related interest in total positivity, a theory that allows many geometric objects occuring in Lie theory to be defined, in some sense, over the positive real numbers.
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I am interested in understanding modular forms and their generalizations. I take a particular interest in studying congruences between these objects modulo primes numbers. The general way to approach this problem is to study various cohomology groups that naturally arise, and I mostly study those cohomolgy groups which arise over certain algebraic varieties called Shimura varieties.
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These are mainly in the field of differential geometry and centred around the study of manifolds (typically Riemannian or complex ones) defined with reference to the action of a Lie group.
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020 7848 1222
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My research work utilizes concepts from pseudodifferential operators, index theory and non-commutative geometry in the construction of representations of geometric semigroups and categories whose characters define invariants of the background manifold. The character of the index bundle associated to a family of Dirac operators over a Riemann suraface, for example, can be used to enumerate holomorphic maps from the surface into complex projective space, while for manifolds with boundary the characters are connected to gauge groups reoresentations constructed using Grassmannians of elliptic boundary conditions for Dirac operators; this is closely tied in with ideas from quantum and conformal field theory.
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020 7848 2778
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Number Theory Group
Interests:
The representation theory of reductive p-adic groups, the Langlands correspondence and applications to local arithmetic.
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+44 020 7848 2488
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Number theory: Galois module structure, arithmetic algebraic geometry.
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Number theory, especially modular forms and Galois representations.
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020 7848 2107
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020 7848 2017
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Number theory and Arithmetic geometry with a special interest in Iwasawa theory.
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Interests:
I am interested in understanding modular forms and their generalizations. I take a particular interest in studying congruences between these objects modulo primes numbers. The general way to approach this problem is to study various cohomology groups that naturally arise, and I mostly study those cohomolgy groups which arise over certain algebraic varieties called Shimura varieties.
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Theoretical Physics (Mathematics Department)
Interests:
Supermanifold theory; applications to supersymmetry; supergravity, BRST theory and geometry.
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020 7848 2107
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020 7848 2017
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Conformal field theory; strings; branes.
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020 7848 2244
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My research interest is in quantum field theory, in particular the integrable or conformal kind. I'm quite interested in looking at QFT as a powerful theory for emergent fluctuations (collective behaviours) in many-body systems. This point of view connects it to condensed matter and statistical systems, but also provides a fundamental understanding of renormalisation group and an alternative view on the fundamental particles of physics. One of my present research paths is to develop the connection between mathematical measures (conformal loop ensembles) describing emergent fluctuations for a large class of statistical models, and the algebraic construction of conformal field theory based on the usual tools and ideas of QFT.
Other research paths include: the physics and mathematical formulation of quantum impurities out of equilibrium; the entanglement entropy in extended quantum systems; the relation between classical integrability and twist fields in quantum field theory models of free particles; as well as various fundamental aspects of relativistic integrable quantum field theory and conformal field theory, including the study of form factors and of vertex operator algebras.
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020 7848 5854
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String Theory, Supergravity, Supersymmetric Gauge Theories, AdS/CFT Correspondence, Geometry.
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020 7848 2153
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My main interests are in string theory, supergravity and M-theory. I currently work on the classification of supersymmetric supergravity backgrounds.
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Two-dimensional quantum field theory, in particular conformal field theory and integrable field theories.
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020 7848 1013, 020 7848 2107
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020 7848 2017
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String theory, supersymmetric field theories and exactly soluble models.
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020 7848 1119
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Supersymmetry; string theory and M-theory.
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020 7848 1222
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020 7848 2017
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020 7848 2149
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Field theories, supersymmetry, string theories and the underlying symmetries of nature
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Supersymmetric Gauge theory, String theory, String/SUSY phenomenology, N=4 Super-Yang Mills, Integrability.
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ACADEMIC ENTRY REQUIREMENTS
General entry advice
Financial Maths: first class or 2:1 first degree. Those applying for the joint degree are encouraged to contact an academic at King's to develop research links with the partner institution. Candidates may also be interviewed.
Disordered Systems: first class or 2:1 first degree. Those applying for the joint degree are encouraged to contact an academic at King's to develop research links with the partner institution.
Theoretical Physics: first class or 2:1 first degree. A good MMath, MSci or master's
degree with high grades in modules that relate to the chosen research area will strengthen the application. Candidates may also be interviewed at the Department's open day or afterwards.
Pure Maths: a good MMath, MSci or master's degree with high grades in modules that relate to the chosen research area. Candidates may also be interviewed.
APPLYING TO KING'S
To apply for graduate study at King's you will need to complete our graduate online application form. Applying online makes applying easier and quicker for you, and means we can receive your application faster and more securely.
King's does not normally accept paper copies of the graduate application form as applications must be made online. However, if you are unable to access the online graduate application form, please contact the relevant admissions/School Office at King's for advice.
APPLICATION PROCEDURE
You can apply for supervision in all fields of interest of our staff members. Your application is considered and processed by the relevant admissions officers. We aim to reply within six weeks. To suitably qualified applicants, we offer opportunities to meet with prospective supervisors. Each February we hold an open day which provides information about our research activities and an opportunity to meet with relevant members of the department.
September, January, and April start dates are available. Applicants are strongly encouraged to start their degree at beginning of the academic year in September, when the College offers a full induction programme.
PERSONAL STATEMENT & SUPPORTING INFORMATION
Please include a personal statement summarising those aspects of your background that support your application. In particular please give your mathematical qualifications and reasons for pursuing a PhD. This statement can cover both sections 6 and 8 of the application form.
FUNDING
MPhil: students are self-funded. PhD: usually BBSRC, EPSRC, STFC and self-funded. The School offers a number of Graduate Teaching Assistantships. The Graduate School of King�s College London offers a variety of funding opportunities which are listed at
http://www.kcl.ac.uk/study/pg/funding/sources/index.aspx
Student profiles
Mathematics Research MPhil/PhD (Applied Mathematics, Pure Mathematics), option of joint PhD with HKUI graduated in Physics in Rome in 2007 working on a project on metabolic networks. For my PhD I wanted to research something similar and as exciting, so when my former supervisor recommended me to the Disordered Systems Group at King's I knew that was the best choice I could make. In fact there were very few places in Europe offering a comparable level of expertise and research quality.
Another great opportunity I enjoyed a lot at King's was giving tutorials to undergraduate students. This really helps you get used to teaching and enhances your knowledge transfer skills.
There are different funding opportunities in the Mathematics Department: my scholarship covers tuition fees and provides a good monthly stipend.
Staff profiles
Mathematics Research MPhil/PhD (Applied Mathematics, Pure Mathematics), option of joint PhD with HKUMathematics has been studied at King's throughout its history and the first Professor of Mathematics was appointed in 1830. Since then the Department has established a record of accomplishments in central areas of pure mathematics and applied mathematics. I have been Head of the Department since August 2009.
A key feature of the undergraduate experience at King's for Mathematics students is automatic membership to the King's College London Mathematics Society (KCL MathSoc). The KCL MathSoc is over 50 years old and has over 500 members who appreciate the beauty of mathematics and share a common passion for it. Over the years it has organised countless events and excursions including an annual trip to Cumberland Lodge, talks with financial and banking firms, and other social activities.
King's graduates are highly sought after both nationally and internationally in a wide range of professions. A degree in mathematics is one of the most flexible qualifications you can obtain, and as a result graduates are among the best paid and the least likely to be unemployed. Six months after graduating, 86% of 2009 Mathematics graduates were in full time employment. Recent King's graduates have found employment as tax consultants, financial analysts, traders, office managers, management consultants and secondary school teachers.