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Postgraduate Study in Mathematics

Before applying to the DPMMS three year PhD, you are encouraged to discuss informally with possible supervisors. It will help our consideration of your application to know with whom you are interested in working and in what fields. This does not necessarily have to be narrowed down to a single supervisor or research area. 

Potential supervisors for the four year PhD, Cambridge Mathematics of Information (CMI), can be found here

Contact details may be found on each supervisor's webpage. You are encouraged to make initial contact by email, and to provide a CV and brief explanation of your areas of interest.

Algebra
Algebraic Geometry
Analysis and Partial Differential Equations
Combinatorics
Differential Geometry and Topology
Information and Finance
Number Theory
Probability
Statistics

Algebra

Supervisor Interests
Stuart Martin Representation theory of finite and algebraic groups. In particular the representation theory of the symmetric groups, Schur algebras, Hecke algebras and other diagram algebras, together with the associated algebraic combinatorics
Simon Wadsley p-adic representation theory of p-adic groups via algebra, geometric representation theory and p-adic analysis
Gareth Wilkes Geometric group theory, with a particular focus on the interactions of this field with profinite groups. This includes both applying profinite methods to the classical objects of geometric group theory and studying how the techniques of GGT may be applied to profinite groups

Algebraic Geometry

Supervisor Interests
Caucher Birkar Algebraic Geometry
Ian Grojnowski Representation theory, reductive groups, algebraic geometry
Mark Gross Algebraic Geometry, Differential Geometry
Dhruv Ranganathan Algebraic geometry and combinatorics

Analysis and Partial Differential Equations

Supervisor Interests
Mihalis Dafermos Partial Differential Equations, General Relativity
Clement Mouhot Analysis (partial differential equations, functional inequalities, stochastic processes), foundation of statistical mechanics, kinetic theory
Pierre Raphael Non-linear waves, fluid mechanics and singularity formation
Peter Varju Analysis, Combinatorics, Number Theory
Claude Warnick PDE analysis, in particular hyperbolic PDE. Classical general relativity
Neshan Wickramasekera Geometric measure theory, partial differential equations, differential geometry
Andras Zsak Analysis

Combinatorics

Supervisor Interests Taking students for 2022
Bela Bollobas Graph Theory, Combinatorics, Additive Combinatorics, Combinatorial Geometry Yes
Tim Gowers Combinatorics, Additive Combinatorics Yes
Imre Leader Extremal Combinatorics, Ramsey Theory Yes
Julian Sahasrabudhe Extremal and Probabilistic Combinatorics, Discrete Analysis No
Julia Wolf Arithmetic Combinatorics, Connections with Model Theory No

Differential Geometry and Topology

Supervisor Interests Taking students for 2022
Jack Button Geometric and combinatorial group theory, especially word hyperbolic groups, acylindrically hyperbolic groups, fundamental groups of 3-manifolds Yes
Ailsa Keating Symplectic topology, singularity theory and mirror symmetry Unlikely
Alexei Kovalev Riemannian geometry, especially exceptional holonomy and special geometric structures Yes
Gabriel Paternain Differential geometry, geometric analysis, and inverse problems Possibly via CMI
Oscar Randal-Williams Algebraic topology, including high-dimensional manifolds, diffeomorphism groups, and homological stability phenomena Unlikely
Jake Rasmussen Low-dimensional topology, gauge theoretic and Khovanov-type invariants of knots, 3- and 4-manifolds Possibly
Ivan Smith Symplectic topology and low-dimensional topology Unlikely
Gareth Wilkes Geometric group theory, profinite groups, and geometric topology Yes
Henry Wilton Geometric group theory, hyperbolic groups and decision problems Yes

Information and Finance

Supervisor Interests
Varun Jog Information theory, machine learning, and convex geometry
Ioannis Kontoyiannis Information theory, applied probability, statistics
Mike Tehranchi Mathematical finance, stochastic control, applied probability

Number Theory

Supervisors who are willing to consider new students in Number Theory for October 2022 admission:

Supervisor Interests
Tom Fisher Computational number theory and arithmetical algebraic geometry, with a particular interest in elliptic curves
Holly Krieger Arithmetic and Complex Dynamics
Jack Thorne Number theory and arithmetic geometry
Peter Varju Analysis, Combinatorics, Number Theory
Rong Zhou Arithmetic geometry, representation theory, geometry of Shimura varieties

Probability

Supervisor Interests
Roland Bauerschmidt Probability theory and analysis, in particular in their applications to statistical mechanics; particularly interested in spin systems and phase transitions, self-avoiding walks, random matrices, renormalization, stochastic dynamics, and supersymmetry in probability theory
Ioannis Kontoyiannis Information theory, applied probability, and statistics, including their applications in neuroscience, bioinformatics, and the development of machine learning algorithms
James Norris Topics in Probability with an orientation to models from Mathematical Physics. Examples are models of particles under elastic and inelastic collision, and large-scale structures formed by random aggregation
Jason Miller Probability, in particular stochastic interface models (random surfaces and SLE), random walks, mixing times for Markov chains, and interacting particle systems
Sourav Sarkar Probability theory, particularly interested in the random growth models that belong to the so-called KPZ universality class, geometric properties of the KPZ fixed point and the relevant processes, last passage percolation, exclusion processes, competitive erosion, stable random fields, percolation theory, Coulomb gas and random walks on graphs
Perla Sousi Random walks, Brownian motion, mixing times of Markov chains, Poisson Brownian motions, rearrangement inequalities, dynamical percolation

Statistics

PhDs in Statistics within the Statistical Laboratory cover a wide range of contemporary challenges in the subject, from theoretical and methodological innovations, to computational developments and applications in many different domains. Prospective applicants are encouraged to make contact with a potential supervisor or supervisors prior to submitting their documents. List of PhD supervisors in Statistics who are willing to consider new students for October 2022 admission:

Supervisor Interests
John Aston Statistics: in particular Functional / Object Data Analysis, Time Series Analysis, Official and Public Policy Statistics, Statistical Neuroimaging, Statistical Linguistics, Seasonal Adjustment and other Applied Statistics
Sergio Bacallado

Bayesian methods and Bayesian nonparametrics, analysis of Markov models, and applications to biology and biophysics

Po-Ling Loh high-dimensional statistics, optimization,  network inference,  robust statistics, differential privacy and statistical applications to medical imaging and epidemiology
Kaisey Mandel Astrostatistics and astroinformatics, Applications in time-domain astronomy and cosmology, Bayesian modeling and inference, Statistical computation
Richard Nickl Mathematical Statistics; specifically high-dimensional inference, Bayesian nonparametrics, statistics for PDEs and inverse problems, empirical process theory
Richard Samworth

Nonparametric and high-dimensional statistics

Rajen Shah

High-dimensional statistics, causal inference, methodology for large-scale data analysis

Qingyuan Zhao Causal Inference, Methodology for Large-Scale Problems, Applications in Genetics, Epidemiology, and Social Sciences