Analysis and Partial Differential Equations


PhD Projects and Studentships

The Department of Mathematics offers the opportunity to study for a PhD in Mathematics, for which the normal duration of study is expected to be three years.

The format is almost exclusively research-based, although students may attend a number of taught modules in consultation with their supervisor.  EPSRC-funded research students at our department are required to undertake a minimum of 100 hours of mathematical broadening training during their PhD.


Our overall aim is to create an environment conducive to discussion and research collaboration at the highest level.

Research students have dedicated shared office space close to their supervisors' offices and are supplied with a desktop computer. The Department has its own computing research laboratory containing several workstations and PCs. As researchers, PhD students have full access to the University's high-performance computing facilities.

Interaction between research students is greatly supported by the provision of a dedicated communal space and kitchen.  Research students also use this space to give seminars to their peers.  Additionally, the facilities of the Sussex Research Hive are available to all doctoral researchers and research staff.


Student progress is reviewed annually by written report and interview to ensure timely completion of the PhD. In their first year, students will have an additional, shorter Interim Interview in December.

Funding for UK & EU students

We expect to have a number of EPSRC-funded studentships in the Department of Mathematics each year.  EU students should check their eligibility.  School-funded scholarships may also be available, for both UK and EU students.  All currently-available funded PhD opportunities are on the Searchable Funding database.

Funding for Overseas students

Funded PhDs are occasionally available.  Where a School-funded PhD is offered, which normally waives only the UK/EU fees, an overseas student can be considered providing there is a realistic plan for funding the additional fees incurred by overseas students.  All currently-available funded PhD opportunities are on the Searchable Funding database.


For practical questions about applications and/or funding please contact the Research & Enterprise Coordinator on .  For academic questions please contact the Mathematics Director of Doctoral Studies, Dr Dimitrios Tsagkarogiannis.

Application Process
How to Apply

Applications should be submitted through the University application pages.  For more general information on postgraduate studies at Sussex see the University Postgraduate Study page.

Deadlines for Applications

We welcome applications from potential PhD students at any time, but funded PhD positions may have a specific deadline. The normal expected start date is the third week of September, but students may also start in January or May.

Possible Projects and Supervisors

Students will be allocated a nominal project and main supervisor on accepting a PhD place. All students are allocated a second supervisor on arrival, whose share of supervision can amount from a nominal 5% (offers occasional advice) up to 45% (joint supervision).

We are also open to discussion of modifying these projects or developing ideas that candidates may have themselves. Please also feel free to contact any of the individual faculty members in relation to potential research projects with them.

Projects currently available

These are research areas currently available.  For funded PhD positions, check the Searchable Funding Database.

Feel free to contact any of the individual faculty members in relation to potential research projects with them.



Filippo Cagnetti Rigidity and stability in symmetrization inequalities
Gabriel Koch Regularity criteria for Navier-Stokes and related problems
Michael Melgaard

Nonlinear PDEs in Quantum Chemistry

Michael Melgaard

Resonances in Quantum Chemistry

Michael Melgaard

Phase space bounds and eigenvalue asymptotics for Schrödinger operators and Dirac operators

Michael Melgaard

Spectral and scattering properties near thresholds for scalar-valued and matrix-valued Schrödinger operators

Michael Melgaard

Spectral and scattering properties of quantum wires

Michael Melgaard

Spectral and scattering properties for Schrödinger and Dirac operators with a constant magnetic field.

Arghir Zarnescu Reduced models for complex materials
Analysis topics in low-regularity domains