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• PhD & research …
• MPhil in Financ…
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Students on the MPhil in Finance programme choose 3 electives from a number of modules offered by Cambridge Judge Business School, the Faculty of Economics, and the Faculty of Mathematics.

The electives offered may vary from year to year. The list below should therefore be regarded as illustrative:

How to Do Finance

The How to Do Finance course introduces you to the methods, approaches, and strategies of research through a few recent and promising research topics in financial economics, providing a broad overview of the key theoretical and empirical methodological issues in each topic, as well as details related to the practical skills of organising, structuring, writing, and publishing research. The course is run by the consortium of Finance faculty members of the Cambridge Judge Business School. Experienced faculty members also share their insights on their current research and research papers.

Advanced Financial Models

Taught by the Faculty of Mathematics (part of the Maths Part III degree).

This module is an introduction to financial mathematics, with a focus on the pricing and hedging of contingent claims. It complements the material in Advanced Probability and Stochastic Calculus & Applications.

The course covers a selection of topics including:

• Discrete-time models. Arbitrage, martingale deflators, the fundamental theorem of asset pricing. Numeraires, equivalent martingale measures. Forwards, options, futures, bonds, interest rates. Attainable claims, market completeness. The Breeden-Litzenberger formula. Fourier pricing. American claims.
• Continuous-time models. Admissible strategies. Absolute and relative arbitrage. Existence of replicating strategies. Pricing and hedging via partial differential equations. The implied volatility surface. Dupire’s formula. Stochastic volatility models. The HJM approach to term structure. Merton’s problem.

Advanced Probability

Taught by the Faculty of Mathematics.

The Advanced Probability course introduces you to advanced topics in modern probability theory. The emphasis is on tools required in the rigorous analysis of stochastic processes, such as Brownian motion, and in applications where probability theory plays an important role.

A basic familiarity with measure theory and the measure-theoretic formulation of probability theory is very helpful. These foundational topics are at the beginning of the course, but student unfamiliar with them are expected to consult the literature to strengthen their understanding (for instance, Probability with Martingales by D. Williams, 1991).

Behavioural Economics

Taught by the Faculty of Economics.

This course offers an introduction to the behavioural approach to economics. Among the topic covered are behavioural game theory, intertemporal decision making, neuroeconomics, cognitive biases, decision-making heuristics and addiction. The course includes both theoretical and empirical material, but a recurring theme is the importance of experimental findings both in the laboratory and in the field.

Continuous Time Finance

The Continuous Time Finance course provides you with an overview of continuous-time finance methods and their applications to corporate finance and financial economics.

The course is taught primarily on the basis of journal articles, supplemented with the lecturer’s own teaching notes. Throughout the course you should also learn critically to assess and evaluate papers.

Important note: This course is offered biennially. If you wish to continue onto the PhD at Cambridge Judge, this course is mandatory if it’s running during your MPhil year.

Economics of Networks

The course introduces you to the economics of networks. This area of research has emerged in the last 2 decades and it has introduced a set of tools for economists to incorporate network structure in the analysis of individual behaviour and economic outcomes.

Topics covered include the formation of networks, the provision of local public goods, coordination, learning, trading, and financial networks. A central focus of the course is the interplay between theory and experiments.

Further Econometrics: Time Series

In a large number of empirical contexts in finance and management, data are temporarily ordered in the form of time series. The Time Series Econometrics module introduces you to concepts and methods that are appropriate for empirical research in such settings, covering methods for exploratory time series analysis, estimation of dynamic causal effects and forecasting.

Industrial Organisation

The Industrial Organisation course provides a rigorous treatment of the main concepts in industrial organisation. The course covers both theory and applications.

Development Economics

This course is on development economics and deals with the economic problems of poor countries. It considers some of the main theoretical and analytical issues in development economics as well as the historical development process of now-developed countries. The topics covered are growth, development, poverty, inequality, education, technology, innovation, mutual insurance, finance, savings, weather, climate, health, pandemics, representative democracy, religion, social capital and conflict.

Numerical Solution of Differential Equations

The goal of this module is to present and analyse efficient numerical methods for ordinary and partial differential equations. The exposition is based on few basic ideas from approximation theory, complex analysis, theory of differential equations and linear algebra, leading in a natural way to a wide range of numerical methods and computational strategies. The emphasis is on algorithms and their mathematical analysis, rather than on applications.

The module consists of 3 parts: methods for ordinary differential equations (with an emphasis on initial-value problems and a thorough treatment of stiff equations), numerical schemes for partial differential equations (both boundary and initial-boundary value problems, featuring finite differences and, time allowing, finite element methods) and numerical algebra of sparse systems (inclusive of fast Poisson solvers, sparse Gaussian elimination and iterative methods). We start from the very basics, analysing approximation of differential operators in a finite-dimensional framework, and proceed to the design of state-of-the-art numerical algorithms.

Stochastic Calculus

This course introduces you to Itô calculus.

• Brownian motion. Existence and sample path properties.
• Stochastic calculus for continuous processes. Martingales, local martingales, semi-martingales, quadratic variation and cross-variation, Itô’s isometry, definition of the stochastic integral, Kunita-Watanabe theorem, and Itô’s formula.
• Applications to Brownian motion and martingales. Levy characterization of Brownian motion, Dubins-Schwartz theorem, martingale representation, Girsanov theorem, conformal invariance of planar Brownian motion, and Dirichlet problems.
• Stochastic differential equations. Strong and weak solutions, notions of existence and uniqueness, Yamada-Watanabe theorem, strong Markov property, and relation to second order partial differential equations.
• Stroock-Varadhan theory. Diffusions, martingale problems, equivalence with SDEs, approximations of diffusions by Markov chains.

Prerequisites: We assume knowledge of measure theoretic probability as taught in Part III Advanced Probability. In particular we assume familiarity with discrete-time martingales and Brownian motion.

Topics in Accounting

This course offers training in the basic techniques of financial accounting and then introduces you to select applied settings that use financial reporting information for valuation and investment decisions.

The course first focuses on building a foundation of knowledge for understanding accounting measurement and reporting. Accounting is in essence a model for recording and presenting economic information, and the starting point is to grasp how this model works and understanding its strengths and limitations.

The second part of the course focuses on applying accounting knowledge to assess and evaluate companies through case studies.

The following 2 modules can also be taken as electives, provided you’ve not already taken them as a core course:

Asset Pricing II

This course builds upon Asset Pricing I. Asset Pricing II examines how assets are priced in practice and how pricing models are implemented via basic trading strategies.

The course is delivered using lecture slides, Jupyter notebooks, and a free online platform for building and backtesting algorithmic strategies (Quantopian). Some knowledge of Python would be helpful (although not a prerequisite).

Topics covered include:

• Asset pricing: foundations and quantitative implementation
• Valuing risk
• Estimation techniques and model selection
• Hypothesis testing
• Small sample inference
• Modelling, estimating and forecasting volatility
• Introduction to machine learning

Corporate Finance II

This course follows on Corporate Finance I that is taught in Michaelmas term. It introduces students who would like an academic career to fundamental empirical research in corporate finance.

Important to note: This course is heavily research-based. It is not suited and not recommended for you if you wish to enter a non-academic career. It has a very heavy reading load of original research papers that you’re required to be familiar with before you enter the class. There is no textbook for the course.

By the end of the course, you should be able to:

• appreciate the theoretical foundations of and empirical evidence on capital raising, internal capital market and control, and corporate governance
• assess critically the theoretical and empirical debates in the corporate finance literature

Please note that if you’re planning on continuing on to a PhD at the School, you will need to choose particular electives.

Find out more about our PhD pathways

Learn more about the application process and deadlines

Explore fees and funding options

Contact the admissions team

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The Centre for Financial Research (CFR) is based at the Centre for Mathematical Sciences of the University of Cambridge .  It is a centre of academic excellence with interests in mathematical and computational finance (including derivatives, risk management, trading systems, real options, foreign exchange, stock and commodity markets, fund management and hedge funds). It has recently amalgamated with the Centre for Research in Quantitative Finance (CRQF).

The Centre's research is primarily in the formulation, analysis and estimation of advanced models of financial markets, and the interests of its members include econometrics, option pricing, computational finance, market microstructure modelling, information effects and other forms of interaction.

Go to the CFR website.

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Statistical Aspects of Non-Linear Inverse Problems Workshop 17-19 September 2024

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Congratulations to  L. Heeney-Brockett (Trinity Hall)  awarded the Thomas Bond Sprague Prize for distinguished performance in the area of probability.

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PhD in Pure Mathematics and Mathematical Statistics

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• Postgraduate Study

This is a three year research programme culminating in submission and examination of a single research thesis.  Students joining the course will often have completed prior study at a level comparable to our Part III (MMath/MASt) course and many have postgraduate experience.  Our students therefore begin their PhD research with a good understanding of advanced material, which they build on in various ways throughout the course of their PhD studies. Our PhD students might have written several papers before they submit their dissertation, and can go on to win academic positions at leading institutions around the world.

Structure of the PhD

Students are required to undertake a minimum of nine terms of research (i.e. three years). Students are not registered for the PhD in the first instance but are instead admitted on a probationary basis. All students are assessed for registration towards the end of their first year of full-time study (usually June). This assessment is based on a short written report submitted by the candidate for review by two assessors. In the fifth term there might also be a further assessment of progress, for which students submit a longer piece of written work and receive an oral assessment.

Research areas

The topic of the research thesis may be chosen from the wide range of subjects studied within the Department. It is expected that applicants to the PhD course will investigate the research interests and expertise of academic staff within DPMMS prior to making a formal application. This should be done by consulting the dedicated page on finding a supervisor , as well as  research pages of our website , and  individual profiles of our academic staff .

Additional training and opportunities

Whilst there are no mandatory taught components to the PhD degree, students may wish to undertake specific courses or further training to expand their knowledge, either for personal interest or to directly assist with their PhD research. All students are encouraged to participate and attend the wide range of lectures, seminars and events on offer within DPMMS and the Centre for Mathematical Sciences.

Many students submit a prize essay at the beginning of their fifth term. The best essays each year are of a scale and quality already adequate for a PhD dissertation, incorporating work already, or about to be, published. We intend that our students publish their work in leading journals. Our PhD students might have written several papers before they submit their dissertation, and can go on to win academic positions at leading institutions around the world.

DPMMS also promotes and encourages researcher development and transferable skills training. This can take the form of assisting with Part III catch-up lectures, attendance at skills based training sessions, or presenting their work at seminars and conferences. The University also offers training via the Researcher Development Programme .

There is no requirement for PhD students to teach but there are plenty of opportunities to do so, such as offering supervisions for third year undergraduates (this involves the supervisor sitting with a pair of students for an hour, discussing their work). PhD students might help too with running examples classes for Part III students.

Academic entry requirements

The usual minimum entry requirement is a first class honours degree, awarded after a four-year course in mathematics or mathematics/statistics, or a three-year degree together with a one-year postgraduate course in those areas. Part III (MMath/MASt) of the Mathemtical Tripos provides such a course and most of the PhD students in DPMMS have come through this route. The others have usually completed at least a comparable four-year undergraduate course, and many have postgraduate experience. Entry is competitive and a higher level of preparation may be required.

Funding opportunities

Applicants will be considered for Department funding. This may include a Research Council or  Heilbronn Doctoral Partnership  award. Receipt of this funding is not guaranteed and all applicants, irrespective of fee-status, are expected to apply to other funding schemes for which they are eligible. Applicants are advised to investigate potential sources of funding as early as possible.

Students should consult the Postgraduate Admissions website for details of the University Postgraduate Funding Competition. Other University wide funding opportunities can be found via the Funding Search Tool .

All applications for postgraduate study must be made via the University’s Postgraduate Admissions Office and details on the process for application and the supporting documentation required is provided on their website . It is important that applicants read all the relevant information and collate the necessary supporting documents prior to starting the application process. If you are an MMath student (i.e., Cambridge Part III student) you should include one reference from your College Director of Studies.

The University values diversity and is committed to equality of opportunity. The Department would particularly welcome applications from women, since women are, and have historically been, underrepresented in our student cohorts.

Please ensure that you use the correct course code when making your application: MAPM21

Finding a supervisor 

The topic of the research thesis may be chosen from the wide range of subjects studied within the Department. It is expected that applicants to the PhD course will investigate the research interests and expertise of academic staff within DPMMS prior to making a formal application. This should be done by consulting the  dedicated page on finding a supervisor , as well as  research pages of our website , and  individual profiles of our academic staff .

Applicants are encouraged to make informal contact with  potential supervisors  prior to making an application. Applicants should clearly state in the 'Proposed supervisor' field of the application form the name(s) of those member(s) of academic staff with whom they wish to work, and provide a clear indication of the areas or topics in which they intend to undertake research in the 'Research Summary' field. We do not currently require submission of a separate detailed research proposal.

Application and funding deadlines

We strongly encourage all applicants to apply by  12:00am (midnight) UK time on 4 January 2024.   Anyone wishing to apply after this date should contact the  DPMMS Course Administrator  before submitting an application. Students wishing to be considered for Departmental funding, or as part of the University  Postgraduate Funding Competition  must apply by this deadline. If you are a USA citizen, resident in the USA, and wish to be considered for  Gates funding,  please note the deadline for applications is in October.

Selection process

After the January closing date, we will review all the applications received and contact those who have been shortlisted to invite them for an interview. Space limitations may mean that late applications cannot be considered.

Interviews take place either in Cambridge or online. During the interview, the panel will try to ascertain the extent of the applicant's mathematical knowledge and experience. We aim to contact all interviewees within a week or two of the interview with a provisional outcome. It is important to note, however, that formal offers of admission can only be made by the University’s Postgraduate Admissions Office.

Applicants should expect to receive a decision within twelve weeks following the submission of their completed application and required supporting documents.  Applicants should check the Applicant Portal for formal notification of the outcome of their application.

Postgraduate open day

Click here for further information on the Postgraduate Open Day .

Please read our PhD applicant Frequently Asked Questions . For any enquiries not covered by the FAQs, you can email us on [email protected] .

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• Mathematical and Computational Finance @ Oxford
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DPhil (PhD) studies in Mathematical Finance @ Oxford

The Mathematical and Computational Finance Group (MCFG) at Oxford is one of the largest and most dynamic research environments in mathematical finance in the world.

We combine core mathematical expertise with interdisciplinary approach. We foster lively interactions between researchers coming from different backgrounds and a truly impressive seminar programme, all this within one of the world's top universities, singular through its tradition and unique environment.

If you are passionate about mathematics and research and want to pursue a DPhil in Financial Mathematics, Oxford simply offers one of the best and most exciting places to do it!

 Research Topic and Supervisor Allocation

We welcome students with their own particular ideas of research topic as well as students with a broad interest in the field of Mathematical Finance. You have an opportunity to tell us about your research passions, and indicate potential supervisors, in your application form. This will be followed up during the interview.

In light of this, if you are offered a place, an appropriate supervisor will be proposed prior to your arrival in Oxford. However, there can be some flexibility over this once you arrive.  Keeping with the Oxford tradition, we offer our students independence and respect as early researchers, and always aim to match students with the most appropriate supervisors.

Outstanding students with a strong background in analysis, probability and data science are welcome to apply for our DPhil program. Each year we receive a large number of excellent applications. The selection process is extremely competitive and we can only admit a handful of candidates each year.

In order to apply for DPhil studies in Mathematical & Computational Finance, please indicate your interest in Mathematical and Computational Finance on your application form. Selected applicants will be invited for an interview -- either in person or by video call.

For general information on DPhil please consult our  Doctor of Philosophy (DPhil) admissions pages .

For the CDT Mathematics of Random Systems please consult our  the CDT website .

Or please contact  @email .

Funding for DPhil students is available from a variety of sources. Please note that some funding opportunities have deadlines: it is advised to apply before the deadline in order to maximise your chances of receiving funding.

Funding is also available through the  Centre for Doctoral Training in Mathematics of Random Systems . To apply for this program please How to Apply .

Email:  @email Phone:  +44 (0)1865 615234

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DPhil Graduates

We have 29 financial mathematics PhD Projects, Programmes & Scholarships

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financial mathematics PhD Projects, Programmes & Scholarships

Phd mathematical sciences, funded phd programme (students worldwide).

Some or all of the PhD opportunities in this programme have funding attached. Applications for this programme are welcome from suitably qualified candidates worldwide. Funding may only be available to a limited set of nationalities and you should read the full programme details for further information.

China PhD Programme

A Chinese PhD usually takes 3-4 years and often involves following a formal teaching plan (set by your supervisor) as well as carrying out your own original research. Your PhD thesis will be publicly examined in front of a panel of expert. Some international programmes are offered in English, but others will be taught in Mandarin Chinese.

PhD Projects in Mathematics

Maths research programme.

PhD Research Programmes describe the opportunities for postgraduate research within a University department. You may often be asked to submit your own research project proposal as part of your application, although predefined research projects may also be available.

Fully funded PhD positions in Astronomy, Biology, Computer Science, Chemistry & Materials, Data Science & Scientific Computing, Earth Science, Mathematics, Neuroscience, and Physics

International phd programme.

International PhD programs are often designed for international students. Your PhD will usually be delivered in English, though some opportunities to gain and use additional language skills might also be available. Students may propose their own PhD topics or apply for advertised projects.

Simulation-based inference for financial econometrics models

Phd research project.

PhD Research Projects are advertised opportunities to examine a pre-defined topic or answer a stated research question. Some projects may also provide scope for you to propose your own ideas and approaches.

Competition Funded PhD Project (Students Worldwide)

This project is in competition for funding with other projects. Usually the project which receives the best applicant will be successful. Unsuccessful projects may still go ahead as self-funded opportunities. Applications for the project are welcome from all suitably qualified candidates, but potential funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Empirical Modeling in Financial Engineering

Funded phd project (students worldwide).

This project has funding attached, subject to eligibility criteria. Applications for the project are welcome from all suitably qualified candidates, but its funding may be restricted to a limited set of nationalities. You should check the project and department details for more information.

Financial Engineering: Modelling and Methods

Phd programmes in education, social sciences research programme.

Social Sciences Research Programmes present a range of research opportunities, shaped by a university’s particular expertise, facilities and resources. You will usually identify a suitable topic for your PhD and propose your own project. Additional training and development opportunities may also be offered as part of your programme.

PhD programmes in Liberal Arts

Arts research programme.

Arts Research Programmes present a range of research opportunities, shaped by a university’s particular expertise, facilities and resources. You will usually identify a suitable topic for your PhD and propose your own project. Additional training and development opportunities may also be offered as part of your programme.

PhD Position in Machine Learning and Computer Vision

Design of net zero strategies and best practices for manufacturing and service organisations (research and experimentation in complex scenarios with competing priorities) phd, self-funded phd students only.

This project does not have funding attached. You will need to have your own means of paying fees and living costs and / or seek separate funding from student finance, charities or trusts.

Pre-emptive strategies for achieving positive restoration of supply networks PhD

Develop high-accuracy prediction models with small datasets and uncertainty of one-sided information in the free-market system phd, quality assurance framework for digital twins across product lifecycle phd, driving sustainability: myopic mean field games and marl for incentive mechanisms in manufacturing supply chains phd, early alzheimer's disease diagnosis using deep learning retinal image analysis phd.

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Primary tabs

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• Requirements
• How To Apply

The MPhil is offered by the Faculty of Mathematics as a full-time period of research and introduces students to research skills and specialist knowledge. Its main aims are:

• to give students with relevant experience at first-degree level the opportunity to carry out focused research in the discipline under supervision; and
• to give students the opportunity to acquire or develop skills and expertise relevant to their research interests. 

Programme Structure

The MPhil is a 12-month full-time programme and involves minimal formal teaching: students are integrated into the research culture of the Department of Pure Mathematics & Mathematical Statistics (DPMMS), or the Department of Applied Mathematics and Theoretical Physics (DAMTP), as appropriate. They may attend the Departments’ programmes of research seminars and other postgraduate courses, but most research training is overseen by their research supervisor, and, where appropriate, within a research group. 

Opportunities to develop research and transferable skills also exist through attendance at training sessions organised at Department, School or University level as part of the wider postgraduate programme, and informally through mentoring by fellow students and members of staff.

Partnership with St John's College

The Martingale Foundation, Faculty of Mathematics and St John's College  have partnered to ensure that students admitted via the Martingale Scholars Programme will typically be admitted as members of St John's College and become part of a Martingale Scholars Cohort.  If you would like more information on this partnership, please contact the Faculty directly.

Learning Outcomes

By the end of the programme, students will have:

• acquired a comprehensive understanding of techniques, and a thorough knowledge of the literature, applicable to their own research;
• demonstrated originality in the application of knowledge, together with a practical understanding of how research and enquiry are used to create and interpret knowledge in their field;
• shown abilities in the critical evaluation of current research and research techniques and methodologies;
• demonstrated some self-direction and originality in tackling and solving problems, and acted autonomously in the planning and implementation of research.

MPhil students wishing to apply for a PhD at Cambridge must apply via the Postgraduate Admissions Office for continuation by the relevant deadline.

The Postgraduate Virtual Open Day usually takes place at the beginning of November. It’s a great opportunity to ask questions to admissions staff and academics, explore the Colleges virtually, and to find out more about courses, the application process and funding opportunities. Visit the  Postgraduate Open Day  page for more details.

See further the  Postgraduate Admissions Events  pages for other events relating to Postgraduate study, including study fairs, visits and international events.

Departments

This course is advertised in the following departments:

• Faculty of Mathematics
• Department of Applied Mathematics and Theoretical Physics
• Department of Pure Mathematics and Mathematical Statistics

Key Information

12 months full-time, 2 years part-time, study mode : research, master of philosophy, department of applied mathematics and theoretical physics this course is advertised in multiple departments. please see the overview tab for more details., course - related enquiries, application - related enquiries, course on department website, dates and deadlines:, michaelmas 2025.

Some courses can close early. See the Deadlines page for guidance on when to apply.

Funding Deadlines

These deadlines apply to applications for courses starting in Michaelmas 2025, Lent 2026 and Easter 2026.

Similar Courses

• Applied Mathematics and Theoretical Physics PhD
• Pure Mathematics and Mathematical Statistics PhD
• Mathematics (Mathematical Statistics) MASt
• Mathematics (Pure Mathematics) MASt
• Mathematics (Theoretical Physics) MASt

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PhD Financial Mathematics / Overview

Year of entry: 2025

• View full page

The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Before applying we also recommend that you read the 'Advice to Applicants' section.

Programme options

Programme description

The Department of Mathematics has an outstanding research reputation and a thriving community of PhD students.

Opportunities for PhD research are available in a range of Financial Mathematicsresearch topics or Mathemathics research areas . For more information, please see advice on choosing a project or find out more about specific projects . Please contact the relevant individual members of staff for information about a specific project, or get in touch with the Postgraduate Admissions Tutor .

Students may enter our graduate programme in Mathematical Finance by initially taking our taught M.Sc. course over 1 year. This, subject to satisfactory progress, can lead to admission to the PhD programme.

Visit our Events and Opportunities page to find out about upcoming open days and webinars.

Fees for entry in 2025 have not yet been set. For reference, the fees for the academic year beginning September 2024 were as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

The programme fee will vary depending on the cost of running the project. Fees quoted are fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgradua t e fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

Scholarships/sponsorships

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page to search for scholarships, studentships and awards you may be eligible for.

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Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Programmes in related subject areas

Use the links below to view lists of programmes in related subject areas.

• Mathematics

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Barbara Prinari, co-founder and deputy editor, Cambridge Journal of Nonlinear Waves

Journal of Nonlinear Waves, poster courtesy of Cambridge Core, 2024. ISSN: 3033-4268 (Online) Frequency: 1 issue per year.

Published September 9, 2024

The UB Department of Mathematics is pleased to announce that Professor Barbara Prinari is co-founder and deputy editor of Cambridge Core's Journal of Nonlinear Waves. Prinari's research adds scope and depth to the journal's editorial board. Problems addressed by Prinari include the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc.  

Journal of Nonlinear Waves

Journal of Nonlinear Waves is the home for the field of nonlinear wave phenomena, broadly defined. It publishes authoritative articles on theoretical and computational aspects of nonlinear waves grounded in applications, as well as on experimental investigations that have direct connection to the mathematics of nonlinear waves. The journal invites papers on fundamental contributions to nonlinear waves and applications in many physical settings including optics, condensed matter, fluid dynamics, geophysics, material science, plasma physics, and biological systems.

Article topics include:

• Nonlinear waves in the physical and applied sciences (optics, condensed matter, fluid dynamics, solid state and materials science, and geophysics/atmospheric/plasma physics, and biology)
• Applied integrable and non-integrable systems
• Dispersive hydrodynamics
• Solitary waves and soliton theory
• Deterministic and random nonlinear wave phenomena (e.g., wave or soliton turbulence)
• Nonlinear waves in lattices
• Numerical methods (including ML/AI-based ones) for nonlinear waves models.
• Scientific computation and data-driven methods for nonlinear waves.
• Asymptotic and variational methods for nonlinear waves problems
• Modelling and experiments related to nonlinear waves
• Dynamical systems approaches to nonlinear waves problems
• Nonlinear wave modulation theory
• Nonlinear waves in dissipative systems
• Stability of nonlinear waves
• Lagrangian and Hamiltonian nonlinear wave mechanics

Learn more about the journals editorial board, here.

Cambridge Core

Cambridge Core is the home of academic content from Cambridge University Press. online platform has been designed to help readers and researchers to make fast and easy journeys to a vast range of valuable content. We consulted extensively with almost 10,000 users while developing Cambridge Core to make sure we are providing a platform that meets the needs of our researchers and customers.

Cambridge Core is the place to find valuable, useful and inspirational research and academic information. With over 1.8 million journal articles and 46,000+ books, Cambridge Core is the central destination for academic research.

Find out more about Cambridge University Press here .

Cambridge University Press publications are deposited in the following digital archives to guarantee long-term digital preservation:

• CLOCKSS (journals) 
• Portico (journals and books)

Digital archives are available for this journal, providing instant online access to a repository of high-quality digitised historical content. 

Faculty Profile

Barbara prinari.

Research Interests

Nonlinear waves; integrable systems; solitons; mathematical modeling in social and behavioral science.

Contact Information

314 Mathematics Building UB North Campus

Buffalo NY, 14260-2900

Phone: (716) 645-8799

[email protected]

PhD in Physics (1999), University of Lecce, Italy 

Research Summary

The study of wave phenomena by means of mathematical models often leads to a certain class of nonlinear partial differential equations referred to as integrable systems.

My main area of research deals with nonlinear waves and integrable systems, and has concerned both the study of the integrability of certain nonlinear partial differential equations and their discretizations (differential-difference equations), and of the properties of these equations and their solutions. Specific problems that I have addressed are: the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc. Other integrable systems I have studied over the years include: short-pulse systems, Maxwell-Bloch equations, the Kadomtsev-Petviashvili equations in 2 spatial dimensions, etc.

I have also been interested in mathematical models for social and behavioral sciences. We have applied generalized kinetic methods and artificial neural networks to analyze and control the quality of an existing neuropsychiatric ward. Recently, we also developed a dynamical systems model for triadic reciprocal determinism, to study how a person experiences stress or traumatic events, and the interplay among coping self-efficacy, behavior and the perception of external environment.

Selected Publications

• M.J. Ablowitz, B. Prinari, A.D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems, LMS Lecture Notes Series 302, Cambridge University Press (2004) 
• B. Prinari, “Inverse Scattering Transform for nonlinear Schrödinger system on a nontrivial background: a survey of classical results, new developments and future directions”, J. Nonlin. Math. Phys. 30, 317-383 (2023) [invited review article]
• B. Prinari, A.D. Trubatch, and B-Feng Feng, “Inverse scattering transform for the complex short-pulse equation by a Riemann-Hilbert approach”, Eur. Phys. J. Plus, 135, 716 (2020)
• M. Lo Schiavo, B. Prinari, I. Saito, K. Shoji, and C.C. Benight, “A deterministic dynamical system approach to triadic reciprocal determinism of social cognitive theory”, Math. Comp. Simul., 159, 18-38 (2019)
•  B. Prinari, F. Demontis, S. Li and T.P. Horikis, “Inverse scattering transform and soliton solutions for a square matrix nonlinear Schrödinger equation with nonzero boundary conditions, Physica D 368, pp 22-49 (2018)
• G. Biondini, D.K. Kraus, B. Prinari, “The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, Comm. Math. Phys. 348, pp. 475-533 (2016)
• B. Prinari, “Discrete solitons of the Ablowitz-Ladik equation with nonzero boundary conditions via inverse scattering”, J. Math. Phys. 57, 083510 (2016)
• B. Prinari, F. Vitale and G. Biondini, “Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, J. Math. Phys. 56, 071505 (2015) [selected as featured article for the July 2015 issue of JMP]
• M. Lo Schiavo, B. Prinari, J.A. Gronski and A.V. Serio, “An artificial neural network approach for modelling the ward atmosphere in a medical structure”,  Math. Comp. Simul.  116, pp. 44-58 (2015) 
• F. Demontis, B. Prinari, C. van der Mee, F. Vitale, “The inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, Stud. App. Math.  131, pp. 1-40 (2013)
• B. Prinari, G. Biondini and A.D. Trubatch, “Inverse scattering transform for the multicomponent nonlinear Schrödinger equation with nonzero boundary conditions at infinity”, Stud. App. Math. 126 (3), pp. 245-302 (2011)
• M. Lo Schiavo, B. Prinari and A.V. Serio, “Mathematical modeling of quality in a medical structure: A case study”,  Math. Comp. Mod.  54, pp. 2087-2103 (2011) 
• B. Prinari, M.J. Ablowitz and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrödinger equation with non-vanishing boundary conditions”, J. Math. Phys. 47, 063508, 33pp (2006)