# Mathematics

Find a programmeRun by | Faculty of Science |
---|---|

Awards available | PhD, MSc by research |

Programme length |
PhD: Three to four years full-time, or part-time equivalent
MScR: One year full-time, or part-time equivalent |

Location of programme | Clifton campus |

Part-time study available | Yes |

Start date | Usually September 2019, but flexible if funding allows. |

## Programme overview

The School of Mathematics is one of the largest schools in the Faculty of Science, with about 120 members of academic staff and research assistants and 70 postgraduate students. Our staff and students are engaged in research across a wide range of areas in applied mathematics, probability, pure mathematics and statistics. We are proud of our world-class reputation for research excellence and our commitment to provide the highest-quality training for our postgraduate students.

#### World-class research

The school’s successes have been formally recognised in the latest Research Excellence Framework (2014), in which 87 per cent of the school’s research was rated as world-leading or internationally excellent. According to the *Times Higher Education* analysis of these results, Bristol is in the top five UK mathematics departments, along with Cambridge, Imperial, Oxford and Warwick. Eight members of the school hold the prestigious position of being a Fellow of the Royal Society, which means they are among the most eminent scientists, engineers and technologists from the UK and the Commonwealth. In recent years the quality of our research has attracted a number of distinguished prizes and substantial external grants.

#### Our postgraduates

The success of our school is based on attracting not only the best available staff, but also by recruiting the best possible postgraduate students. The school offers cutting-edge PhD and taught master's programmes, and we welcome applications from national and international students all year round. Postgraduate students in Bristol enjoy a friendly and stimulating environment. During your programme you will have the opportunity to develop your mathematical skills, collaborate with leading researchers and apply your expertise across a range of academic disciplines.

#### Our partnerships

The school has collaborative research programmes with other departments, such as biological sciences, chemistry, earth sciences, engineering mathematics, aerospace engineering, electrical and electronic engineering, computer science, physics and medical sciences. It is involved with University research centres in behavioural biology, complexity sciences, environmental and geophysical flows, and nanoscience and quantum information. It has strong links to the Centres for Doctoral Training in Communications and Quantum Engineering.

The school also has well-established connections with a number of external research institutions, such as Hewlett-Packard, QinetiQ, Unilever, Barclays Bank, Toshiba and National Air Traffic Services.

The Heilbronn Institute for Mathematical Research is an exciting partnership between the University of Bristol and the Government Communications Headquarters (GCHQ). Established in 2005, the Heilbronn Institute brings together high-calibre mathematicians to conduct research across several areas of interest, including number theory, quantum information and computational statistics. In collaboration with the school, it organises an annual conference and several workshops and weekly seminars, which further enhances the research environment for our postgraduate students.

## Fees for 2019/20

We charge an annual tuition fee. Fees for 2019/20 are as follows:

- UK/EU: full-time
- £4,300
- UK/EU: part-time
- £2,150
- Overseas: full-time
- £21,700
- Channel Islands/Isle of Man: full-time
- £9,300

**Bench fees:** For postgraduate research students who are not funded by UK Research Councils or (specific) UK charities, it is usual to charge a bench fee. A bench fee covers the costs of laboratory consumables, specialist equipment and other relevant costs (e.g. training) for the duration of the programme. The bench fee charged can vary considerably depending on the nature of the programme being undertaken. Details of specific bench fee charges can be provided on request and will made clear in the offer letter sent to applicants.

*Fees are subject to an annual review. For programmes that last longer than one year, please budget for up to a five per cent increase in fees each year. Find out more about tuition fees.*

### Alumni scholarship

University of Bristol students and graduates can benefit from a ten per cent reduction in tuition fees for postgraduate study. Check your eligibility for an alumni scholarship.

### Funding for 2019/20

UK/EU students may be eligible to apply for EPSRC funding for PhD study. To be considered for EPSRC funding, applications should be submitted before **Monday 7 January 2019.**

The school provides financial support for PhD students from a number of sources, including research councils, industry and scholarships. For further details, see the School of Mathematics website.

Further information on funding for prospective UK, EU and international postgraduate students.

## Entry requirements

A first-class or upper second-class honours degree (or international equivalent) in mathematics or a closely related subject. Selection is competitive, based on academic achievement and research potential.

See international equivalent qualifications on the International Office website.

### English language requirements

If English is not your first language, you need to meet this profile level:

**Profile F**

Further information about English language requirements and profile levels.

### Admissions statement

Read the programme admissions statement for important information on entry requirements, the application process and supporting documents required.

## Research groups

**Research priorities**

The priorities of the school's research efforts are:

- execution of internationally recognised world-class mathematical and statistical research, resulting in key publications and presentations;
- research training of graduate students who show the highest potential;
- research development and career progression of post-doctoral research workers;
- interaction with external groups both within academia and beyond;
- commercialising opportunities combining research and enterprise.

**Research institutes**

There is a wide range of research conducted in the school, spanning many of the conventional boundaries between disciplines. Potential applicants are encouraged to consult the school's website for detailed accounts of the research themes, but broadly there are **five research institutes**:

Within the **Institute for Applied Mathematics**, research is concentrated in the areas of

- Applied Mathematics
- Dynamical Systems and Statistical Mechanics
- Fluid Dynamics
- Fluids and Materials
- Materials Science
- Scientific Computing
- Complex Systems

The **Institute for Mathematical Physics** concentrates on mathematical physics research themes:

The **Institute for Probability, Analysis and Dynamics** research themes are intricately intertwined:

- Analysis
- Analysis and Partial Differential Equations
- Applied Probability
- Behavioural Biology
- Dynamical Systems and Statistical Mechanics
- Ergodic Theory and Dynamical Systems
- Scaling Limits
- Statistical Physics

The **Institute for Pure Mathematics** is concerned with discovering, understanding and explaining abstract mathematical structures within the research themes of:

- Algebra
- Combinatorics
- Group Theory
- Mathematical Logic and Set Theory
- Number Theory
- Representation Theory
- Set Theory and Logic

The **Institute for Statistical Science** explores the whole spectrum of modern statistics under the research themes:

- Bayesian Modelling and Analysis
- Monte Carlo Computation
- Multiscale Methods
- Nonparametric Regression
- Optimisation Under Uncertainty
- Statistical Bioinformatics
- Statistical Signal Processing
- Statistics
- Time Series

**Collaboration**

Members of the school collaborate with colleagues from a variety of disciplines at Bristol, including physics, social sciences, biology and medicine, as well as with external organisations, such as Hewlett Packard, QinetiQ, Unilever, Barclays Bank, the Government Communications Headquarters and National Air Traffic Services.

## Careers

Graduates have gone on to on to work in industry, finance, consultancy and academia, including post-doctoral positions and lectureships.

## Staff profiles

## Institute for Applied Mathematics

**
Dr Isaac Chenchiah, (Senior Lecturer)**,
Applications of nonconvex calculus of variations and partial differential equations; growth of biological materials; solid mechanics and materials science; statics and dynamics of microstructures and phase transitions in solids.

**
Professor Jens Eggers, (Professor of Applied Mathematics)**,
Complex fluids; hydrodynamics; statistical mechanics.

**
Professor Andrew Hogg, (Professor of Fluid Mechanics)**,
Geophysical and environmental fluid mechanics; granular flows

**
Professor Tanniemola Liverpool, (Professor of Theoretical Physics)**,
Biological physics; systems biology; theoretical soft matter physics

**
Dr Richard Porter, (Senior Lecturer in Applied Mathematics)**,
Wave motion in fluids and elastic solids and the interaction of waves with structures.

**
Professor Jonathan Robbins, (Professor of Mathematics)**

**
Dr John Russo, (Lecturer in Applied Mathematics)**,
Complex fluids, soft condensed matter systems, statistical mechanics and molecular simulations

**
Dr Valeriy Slastikov, (Senior Lecturer in Applied Mathematics)**,
Applied analysis, calculus of variations and nonlinear partial differential equations; liquid crystals and micromagnetics; materials science.

**
Professor Stephen Wiggins, (Professor of Applied Mathematics)**,
Dynamical systems and applications

## Institute for Mathematical Physics

**
Dr Tamara Grava, (Senior Lecturer)**,
Long time behaviour of solutions to Hamiltonian PDEs; normal matrix models; study of solutions to Hamiltonian PDEs near critical points

**
Professor Noah Linden, (Professor of Theoretical Physics)**,
Quantum information and quantum computation

**
Professor Francesco Mezzadri, (Professor of Mathematical Physics)**,
Applications of random matrix theory to quantum chaos, statistical mechanics and quantum transport.

**
Dr Ashley Montanaro, (Lecturer)**,
Quantum algorithms and computational complexity, quantum query and communication complexity, quantum walks.

**
Dr Sebastian Muller, (Senior Lecturer)**,
Quantum chaos and its relation to random matrix theory.

**
Professor Jon P Keating, (Henry Overton Wills Professor of Mathematics, Chair of the Heilbronn Institute for Mathematical Research, Director of Institute for Mathematical Physics)**,
Random matrix theory, quantum chaos, and connections with number theory

**
Dr Roman Schubert, (Lecturer in Mathematics)**,
Time dependent problems in quantum mechanics and their relation to classical mechanics, in particular quantum chaos.

**
Dr Martin Sieber, (Reader in Applied Mathematics)**,
Quantum chaos

**
Dr Nina Snaith, (Reader)**,
Connection between Random Matrix Theory and certain number theoretical functions.

**
Dr Yves Tourigny, (Senior Lecturer in Numerical Analysis)**,
Spectral properties of Schrodinger operators, diffusion processes and the Schrodinger equation, products of random matrices.

**
Dr Karoline Wiesner, (Reader in Complexity Sciences)**,
Information theory in the sciences

## Institute for Probability, Analysis and Dynamics

**
Professor Balint A Toth, (Professor of Probability and Director of Institute for Probability, Analysis and Dynamics)**,
Limit theorems; probability theory;random walks; randomness in space and time; statistical physics (classical and quantum); stochastic processes.

**
Dr Marton Balazs, (Senior Lecturer)**,
Interacting systems; stochastic processes

**
Professor Carl Dettmann, (Professor of Applied Mathematics and Deputy Director of Institute for Probability, Analysis and Dynamics)**,
Dynamical systems, statistical physics, wireless networks ; Nonlinear dynamics and mathematical physics.

**
Professor Alexander Gorodnik (Gorodnyk), (Professor of Pure Mathematics)**,
Ergodic theory and dynamical systems; number theory

**
Dr Asma Hassannezhad, (Lecturer)**,
Geometric analysis

**
Dr A J Ganesh, (Reader in Complexity Sciences)**,
Applied probability; Bayesian modelling and analysis; optimisation under uncertainty

**
Professor Oliver Johnson, (Professor of Information Theory)**,
Data compression; entropy theory; probabilistic limit theorems

**
Dr Thomas M Jordan
Senior Lecturer in Pure Mathematics**,
Connections between multifractal analysis, large deviations and the thermodynamic formalism, self-similar and self-affine sets, non-conformal dynamical systems and Fourier transforms for invariant measures.

**
Dr John M Mackay, (Lecturer in Pure Mathematics)**,
Geometric group theory, particularly hyperbolic and relatively hyperbolic groups. Analysis on metric spaces, especially questions related to Hausdorff dimension and quasisymmetric maps.

**
Professor Jens Marklof, (Professor of Mathematical Physics Head of School)**,
Number theory, quantum chaos, ergodic theory, dynamical systems

**
Dr Yuri Netrusov, (Senior Lecturer in Pure Mathematics)**,
Functional spaces; partial differential equations; spectral theory

**
Professor Corinna Ulcigrai, (Professor of Pure Mathematics)**,
Ergodic theory and Teichmueller dynamics

**
Dr Feng Yu, (Senior Lecturer in Statistics)**,
Applied probability; behavioural biology; statistical signal processing

## Institute for Pure Mathematics

**
Dr Andrew Booker, (Reader of Pure Mathematics)**,
L-functions and their applications to number theory and automorphic forms

**
Professor Tim Browning, (Professor in Number Theory Director of Institute for Pure Mathematics)**,
Analytic number theory and Diophantine geometry, interested in questions about rational points on algebraic varieties over non-closed fields

**
Dr Tim Burness, (Senior Lecturer in Pure Mathematics)**,
Group theory and representation theory

**
Professor Tim Dokchitser, (Professor in Algebraic/Arithmetic Geometry Deputy Director of Institute for Pure Mathematics)**,
Algebraic number theory and elliptic curves

**
Dr Viveka Erlandsson, (Lecturer in Mathematics)**,
Hyperbolic geomtery Low dimensional topology Teichmüller theory

**
Dr Kentaro Fujimoto, (Lecturer in Mathematical and Philosophical Logic)**,
Mathematical Logic and Proof Theory

**
Dr Mark Hagan, (Lecturer in Mathematics)**,
Group theory Topology Geometry Combinatorics Geometric group theory

**
Dr Min Lee, (Royal Society University Research Fellow)**,
Number Theory

**
Dr Fatemeh Mohammadi, (Lecturer in Pure Mathematics)**,
Algebra Combinatorics

**
Dr Fatemeh Mohammadi, (Lecturer in Pure Mathematics)**,
Commutative Algebra, Applied Algebraic Geometry and Combinatorics

**
Professor Jeremy Rickard, (Professor of Mathematics)**,
Modular representation theory of ﬁnite groups

**
Dr Misha Rudnev, (Senior Lecturer in Pure Mathematics)**,
Geometric and arithmetic combinatorics and geometric measure theory

**
Dr Lynne Walling, (Reader in Pure Mathematics)**,
Number theory

**
Professor Philip Welch, (Professor of Pure Mathematics)**,
Mathematical Logic and Set Theory

**
Dr Julia Wolf, (Heilbronn Reader in Combinatorics and Number Theory)**,
Combinatorics, number theory, harmonic analysis

**
Professor Trevor Wooley, (Professor of Pure Mathematics)**,
Analytic number theory, quantitative arithmetic geometry, arithmetic combinatorics

## Institute for Statistical Science

**
Professor Christophe Andrieu, (Professor in Statistics)**,
Signal processing

**
Dr Haeran Cho, (Lecturer)**,
Highdimensional statistical inference; multiscale modelling; time series analysis

**
Dr Mathieu Gerber, (Lecturer in Statistical Science)**

**
Dr Arne Kovac, (Senior Lecturer)**,
Nonparametric regression and image analysis

**
Dr Dan Lawson, (Sir Henry Dale Research Fellow)**,
Bayesian modelling Statistical Genetics Statistical analysis of Big Data Statistical methods for intractible models Dynamical systems and game theory Networks

**
Dr Anthony Lee, (Lecturer in Statistical Science)**,
Bayesian Modelling and Analysis Monte Carlo Computation Number Theory

**
Professor Guy P Nason, (Professor of Statistics and Director of Institute for Statistics)**,
Non-stationary time series. Multiscale methods in statistics. Variance stabilization. Computational statistics. Networks Official Statistics, Economics, Epidemiology, Energy

**
Dr Nick P Whiteley, (Lecturer in Statistics)**,
Bayesian modelling and analysis; Monte Carlo computation; statistical signal processing; time series.

**
Dr Patrick Rubin-Delanchy, (Lecturer in Statistical Science)**,
Networks, time series, and point processes Machine-learning

**
Professor Jonathan Rougier, (Professor of Statistical Science)**,
Bayesian modelling and analysis

**
Dr Vladislav Tadic, (Senior Lecturer in Statistics)**,
Monte Carlo computation; optimisation under uncertainty; statistical signal processing.

**
Professor Simon Wood, (Professor of Statistical Science)**,
Modern regression modelling, especially using smooth functions and random effects, and in statistics applied in ecology, especially to ecological dynamics

**
Dr Yi Yu, (Lecturer in Statistical Science)**,
High-dimensional statistics network studies survival analysis applications in brain imaging data.

**Application deadline:**

We welcome applications at any time of year. However, to be considered for school funding, applications should be submitted before **Monday 7 January 2019**.

## International students

Find out more about becoming a student at Bristol, applying for a visa and the support we offer to international students.

#### REF 2014 results

- Mathematical Sciences:
**43%**of research is*world-leading*(4*)**44%**of research is*internationally excellent*(3*)**12%**of research is*recognised internationally*(2*)**1%**of research is*recognised nationally*(1*)

Results are from the most recent UK-wide assessment of research quality, conducted by HEFCE. More about REF 2014 results.

## Bristol Doctoral College

The Bristol Doctoral College facilitates and supports doctoral training and researcher development across the University.

## Open days and visits

Find out more about opportunities to visit Bristol.

## Get in touch

Postgraduate Student Administrator Email: pgsec-maths@bristol.ac.uk

School of Mathematics

University of Bristol

University Walk

Bristol BS8 1TW
http://www.bristol.ac.uk/maths/

## Disclaimer

Important disclaimer information about our programmes.