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Mathematics - Research

School Description:

Postgraduate study in the School of Mathematics offers students a range of subjects in pure mathematics, theoretical physics, and interdisciplinary subjects such as bioinformatics and neuroscience. 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 (www.hamilton.tcd.ie) 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.

Postgraduate students in the School may read for a Ph.D. or M.Sc. degree by research. They may also pursue a one-year, full-time taught course in High-Performance Computing. 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 possess a good honours degree (i.e. an upper second class at least) and to have the necessary background to pursue advanced study in their chosen field of research.

Entry requirements

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 appropriate School with your research proposal and arrange a suitable supervisor before submitting your application. You should initially consult the School website for further information.

Research students are placed either directly on the Ph.D. register or on the Masters register. Research students on the Masters register 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.

Further enquiries

Head of School: Sinead Ryan
Director of Teaching & Learning (Postgraduate):
Prof. John G. Stalker

Telephone:+353-1-896 1889
Fax:+353-1-896 2282
Email:mathdep@maths.tcd.ie

Application date

Research Applications

No closing dates apply for application for higher degrees by research but there are only two registration periods (September and March). Applicants are advised to apply as early as possible prior to their chosen registration period as supervisory capacity may be limited.

In exceptional circumstances it may be possible to register retrospectively. Applicants wishing to be considered for retrospective admission should contact the Graduate Studies Office by emailing research.admissions@tcd.ie

Research areas

Research Programmes

The School has two broad research groups in Pure Mathematics and Theoretical Physics areas.

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

Partial Differential Equations
Nonlinear partial differential equations, dynamical systems;

Paschalis Karageorgis: Hyperbolic nonlinear partial differential equations, especially nonlinear wave and Schrodinger equations. Problems of existence and qualitative properties of solutions;

John Stalker: Hyperbolic partial differential equations, especially those systems which are of particular physical interest. Mostly these are the Einstein equations of general relativity, but also the Euler equations of fluid mechanics and the equations governing nonlinear elasticity.

Functional analysis
Richard M. Timoney: Operator spaces, complex analysis. Complex analysis and geometry;

Complex Analysis and Geometry
Dmitri Zaitsev has interests including several complex variables (CR geometry), real and complex algebraic geometry, symplectic geometry and Lie group actions.

Algebra and Number Theory
Vladimir Dotsenko works on homological and homotopical algebra, combinatorics, representation theory, Grbner bases.

Algorithms
Colm O Dunlaing works on the theory of computation, algorithm design, computational complexity, and computational geometry.

History of Mathematics
David Wilkins works on the history of mathematics, concentrating on the work of Hamilton and contemporaries of the 19th century.

Theoretical Physics research groups focus on String Theory, Lattice Quantum Chromodynamics, and Mathematical Neuroscience.

String Theory: This is one of the most active areas of research in physics and mathematics, lying at the frontier of both sciences. Briefly, it is an attempt to find a unified theory of fundamental interactions, including gravity.

The group's research concentrates on mathematical aspects of string theory with special emphasis on geometric problems and methods.

Anton Gerasimov (HMI Senior Research Fellow): conformal and topological field theory, special geometry, integrable systems;

Sergey Frolov: string theory, gauge theory/string theory correspondence, integrable systems;

Samson Shatashvili: supersymmetric gauge theories, Donaldson and Seiberg-Witten theory, integrable systems, topological strings, string field theory;

Tristan McLoughlin: Quantum field theory, quantum gravity, string theory, gauge/gravity correspondence.

Lattice Quantum Chromodynamics: By discretising QCD onto a space time lattice one can make the analytically insoluble equations governing the dynamics of gluons and quarks susceptible to numerical investigation and obtain results that are of direct relevance to tests of the Standard Model of elementary particle physics. The group is a member of the FP7 Marie Curie Initial Training Network iSTRONGneti funded by the European Union.

Mike Peardon: Monte Carlo techniques, algorithms for simulating quantum field theories, anisotropic lattices, glueballs, hybrids and exotics, strong decays;

Stefan Sint: Non-perturbative renormalisation techniques, determination of quark masses and the strong coupling constant, CKM and Standard Model phenomenology;

Sinead Ryan: heavy quark physics, strong and weak decays, CKM and Standard Model phenomenology, novel lattice discretisations.

Enrolment and start dates

March 2017 Entry

Doctor in Philosophy, Mathematics (Part-Time)
Doctor in Philosophy, Mathematics (Full-Time)
Master in Science in School of Mathematics (Part-Time)
Master in Science in School of Mathematics (Full-Time)

September 2017 Entry

Doctor in Philosophy, Mathematics (Part-Time)
Doctor in Philosophy, Mathematics (Full-Time)
Master in Science in School of Mathematics (Part-Time)
Master in Science in School of Mathematics (Full-Time)

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