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. There are no formal course requirements for those pursuing a degree by research. Prospective students are expected to possess a good honors 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.
The School has two research groups as listed below:
Pure Mathematics: The main thrust is in analysis, especially partial differential equations, and also operator algebras, operator theory and complex analysis.
Partial Differential Equations
Prof. Adrian Constantin: 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
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 focuses on the String Theory Lattice Quantum Chromodynamics and Bio-Mathematics.
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. The group is a member of the Marie Curie Forces Universe European network.
Sergey Cherkis: string theory, supersymmetric gauge theories, integrable systems, supergravity solutions, and quaternionoc geometry;
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;
Prof. Samson Shatashvili: Donaldson and Seiberg-Witten theory, special geometry, string field theory, topological strings.
Further information can be found on the group’s homepage:
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 particles. The group uses novel discretisation and algorthmic ideas to access a wide range of physics.
Dr Mike Peardon: Monte Carlo techniques, algorithms for simulating quantum field theories, anisotropic lattices, glueballs, hybrids and exotics, strong decays;
Dr Stefan Sint: Non-perturbative renormalization techniques, determination of quark masses and the strong coupling constant, CKM and Standard Model phenomenology;
Dr Sinead Ryan: heavy quark physics, strong and weak decays, CKM and Standard Model phenomenology, novel lattice discretisations.
Bio-Mathematics is represented by Dr Conor Houghton who is involved in mathematical neuroscience with a particular interest in primary auditory processing.