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.
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.
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.