School of Mathematics
- Head of School:Dr Dónal O' Donovan
- Director of Teaching & Learning (Postgraduate):Prof. John G. Stalker
- Telephone:+353-1-896 1889
- Fax:+353-1-896 2282
- Email:mathdep@maths.tcd.ie
- Url:www.maths.tcd.ie
- How to apply: Please see links below
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.
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 Schrödinger 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
- Donal P. O’Donovan: C*-algebras, especially K –theory;
- 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.
Algorithms
- Colm Ó Dúnlaing 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;
- Calin Lazaroiu: Calabi-Yau compactifications, homological mirror symmetry, topological string field theory, algebraic geometry;
- Samson Shatashvili: supersymmetric gauge theories, Donaldson and Seiberg-Witten theory, integrable systems, topological strings, string field theory.
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 ìSTRONGnetî 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.
Mathematical Neuroscience
- Conor Houghton: coding in spike trains, with a particular interest in primary auditory processing.