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School of Mathematics

You are here Courses > Postgraduate > MSc and PhD by research

Postgraduate study in the School of Mathematics

The School is small and the setting is informal which encourages close contact with staff, postdoctoral fellows, visiting scholars and fellow postgraduate students. The workshops and guests of the School's Hamilton Mathematics Institute, TCD in addition to its joint seminars with the School of Theoretical Physics of the Dublin Institute for Advanced Studies and TCD's three neighbouring universities provide a stimulating intellectual backdrop to a student's stay at TCD.

There are no formal course requirements for those pursuing a degree by research, but research students are expected to participate fully in appropriate seminars. Prospective students are expected to have achieved at least a II.1 degree and to have the necessary background to pursue advanced study in their chosen field of research. For an M.Sc. candidate the focus is on writing a substantial thesis that takes account of previously published results but which falls short of the originality expected of a Ph.D. thesis. Following evidence of initial work on a thesis topic an M.Sc. candidate may apply to transfer to the Ph.D. register after the first year. For research degrees, the range of topics is limited by the expertise and availability of supervisors within the School. See the topics below.

The college handbook on postgraduate research can be found here and provides many details regarding research masters and PhD programmes. The regulations governing postgraduate studies are found in Part III of the College Calendar .

Entry Requirements

Postgraduate work in Trinity College Dublin is very academically challenging and as a result the University has high academic entry requirements.

Applicants will need to hold:

  • at least a 2.1 honors degree from an Irish university or equivalent result from a university in another country
  • a fluent command of the English language

Some courses may require higher standards or require you to take further tests or attend an interview.

Postgraduate Research Degrees

All students undertaking a research degree are assigned to a single principal supervisor. The supervisor’s role is essentially that of an academic guide and mentor.

If you plan to carry out your degree by research, you are advised to contact the School of Mathematics with your research proposal and arrange a suitable supervisor before submitting your application. You should initially consult the School website for further information.

Virtually all research students are initially placed on the Masters register. They may then transfer to the Ph.D. register if their progress has been satisfactory. Such transfers usually occur during the second year of full-time study.

Confirmation to the PhD registry

The confirmation to the PhD registry should occur within the first 18 months from a student's first enrolment, namely, by the end of September for students who started in March, and by the end of February for those who started in September.

The confirmation procedure serves to ensure that you are making sufficient progress on your PhD research and to give you a head start in writing your thesis.

For confirmation to the PhD registry, students are required to:

  • Write a 20-page report on their work. Students are advised to discuss their report with their supervisor before submitting it to the director of postgraduate studies. Their report should be finalised approximately one month before the 18-month period, at the very latest.
  • Give a short (approximately 20-minute) talk on their research, after submitting their report to their supervisor, another academic (the reader) and the director of postgraduate studies.
  • Complete the 5-credit Blackboard module on Research Integrity and Impact, ideally within the first 6 months.

Viva-voce presentations

Here is the list of steps that PhD students and their supervisors are required to follow as they organise the viva-voce.

  • Complete the "Intention to submit" form at least 1 month (and preferably 7 weeks) prior to the submission date for the thesis (which is listed below).
  • Submit the "external examiner application form" 10 weeks before the viva voce.
  • Submit the thesis to the Academic Registry at least 9 weeks before the viva voce.
  • If electronic submission is chosen, as recommended, the thesis will be sent directly from the Academic Registry to the external examiner.
  • Internal and External examiners should receive guidelines for filling in the relevant forms: a pre-viva form (one for each examiner) and a post viva form, which one of the examiners (usually the internal examiner) completes and sends to the Academic Registry.

Research Topics

Pure mathematics.

The main thrust is in analysis, especially partial differential equations, and also operator algebras, operator theory and complex analysis.

  • Partial Differential Equations
  • Functional analysis
  • Complex analysis and geometry
  • History of Mathematics

Theoretical Physics

  • String Theory
  • Lattice Quantum Chromodynamics
  • Quantum Field Theory
  • Research in High-Performance Computing

Further Details

  • Postgraduate Awards
  • Practical Information

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