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 |