Pure Mathematics – (Ph.D.)

The Cardiff School of Mathematics offers an exceptionally wide range of opportunities for postgraduate studies in mathematics. The academic staff are engaged in research projects in fields that are as varied as number theory, functional analysis and spectral theory in pure mathematics, image processing, operational research, statistics and quantum field theory.
Many research projects undertaken by members of staff in the School are funded by the public and private sectors. The leader of the Operator Algebras and Non-Commutative Geometry group is the co-ordinator of the European Network on Non-Commutative Geometry funded by the EU TMR programme. Other sources of funding include EPSRC, Leverhulme Trust, NATO, INTAS, Ministry of Defence, Wellcome Trust, GlaxoSmithKline, Proctor and Gamble.
The School has close links with several universities and institutions abroad. These include the Institute of Advanced Study in Princeton, the Australian National University and the Australian Road Research Board in Melbourne, Ecole Superieure d'Electricite in Gif-Sur Yvette, ETH in Zurich and universities in Canada, the Czech Republic, France, Germany, Italy, Ireland, Norway, Saudi Arabia, Japan, Malaysia and USA.

The School provides training and a high level of support, and the postgraduate community contributes substantially to the University's international reputation for research. In their first and second year of study, research students follow a programme of lectures and reading courses agreed with their supervisors. These include formal assessment.

Moreover, research students benefit from a carefully developed graduate program including computational, presentational and subject-specific skills.

Students will also write a substantial end-of-year report and give a seminar in the department.

Available Research Areas:
Ordinary and partial differential equations, functional analysis, analytical and computational spectral theory, quantum mechanics, number theory and its applications, mathematical physics, operator algebras, quantum field theory, differential geometry and general relativity.

Special Features:
* Three research networks have been coordinated from Cardiff: the EU-TMR Network on Non-Commutative Geometry, the EPSRC Network on Algebraic Geometry, Boundary Conformal Field Theory and Non- Commutative Geometry, and the EPSRC Network on Spectral Theory (jointly with a group from the School of Computer Science).
* Colloquia are held regularly and each research group has a weekly research seminar.
* The School hosts and participates in frequent workshops organised by WIMSC research clusters, with which the research groups are associated.
* The many collaborative projects with groups in other institutions in the UK and abroad, bring a steady stream of distinguished visitors to the School.