The School has two broad research groups in Pure Mathematics and Theoretical Physics areas. Research in the School is being funded by IRC, SFI, ERC, H2020, the Royal Society, and the Simons Foundation.
Pure Mathematics: The main research groups concentrate on partial differential equations, operator algebras, operator theory and complex analysis, several complex variables, real and complex algebraic geometry, algebra, algorithms, numerical analysis and scientific computing as well as history of mathematics.
Partial Differential Equations
• 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.
• Richard M. Timoney: Operator spaces, complex analysis.
Complex Analysis and Geometry
• Andreea Nicoara works in several complex variables, real and complex algebraic geometry, model theory.
• Dmitri Zaitsev has interests including several complex variables (CR geometry), real and complex algebraic geometry, symplectic geometry and Lie group actions as well as connections with Partial Differential Equations and Combinatorics. His other interests include applications of Category Theory to Functional Reactive Programming and Algorithmic Complexity.
Algebra, Algebraic Geometry, and Algebraic Topology
• Vladimir Dotsenko works on homological and homotopical algebra, combinatorics, representation theory, Gröbner bases.
• Sergey Mozgovoy: Moduli spaces of quiver representations, Nakajima quiver varieties, quivers with superpotentials, non-commutative crepant resolutions of 3-Calabi-Yau varieties, brane tilings and dimer models, enumerative problems in representation theory, refined Donaldson-Thomas invariants and BPS counting, wall-crossing formulas, moduli spaces of Higgs bundles, moduli spaces of vector bundles on surfaces, Hilbert schemes of surfaces and Hilbert schemes of plain curve singularities, Hall algebras of curves and quivers.
• Colm Ó Dúnlaing works on the theory of computation, algorithm design, computational complexity, and computational geometry.
Numerical Analysis and Scientific Computing
• Kirk Soodhalter : numerical linear algebra, ill-posed problems, Krylov subspace methods, data-driven iterative methods, high-performance computing applications.
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 and Lattice Quantum Chromodynamics.
String Theory: This is one of the most active areas of research in physics and mathematics, lying at the frontier of both. 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.
• Ruth Britto: Scattering amplitudes, perturbative gauge theory and quantum chromodynamics, quantum field theory, Feynman integrals;
• Sergey Frolov: string theory, gauge theory/string theory correspondence, integrable systems;
• Tristan McLoughlin: Quantum field theory, quantum gravity, string theory, gauge/gravity correspondence;
• Jan Manschot: Quantum field theory, gravity, string theory, number theory, geometry;
• Andrei Parnachev: Conformal field theory, holography, strongly coupled quantum field theories;
• Samson Shatashvili: supersymmetric gauge theories, Donaldson and Seiberg-Witten theory, integrable systems, topological strings, string field theory;
• Dmytro Volin: Integrable systems, gauge/gravity correspondence, representation theory, quantum spectral curve.
Lattice Quantum Chromodynamics: The discretisation of QCD on a space-time lattice allows the analytically insoluble equations governing the dynamics of quarks and gluons to be simulated numerically, providing results that are of direct relevance to elementary particle physics and which shed light on theories of strongly-interacting matter.
The group is a partner in the H2020 Program for European Joint Doctorates - HPC-LEAP.
• Marina Krstic Marinkovic: Standard Model phenomenology, muon g-2, heavy quark physics, Monte Carlo techniques, high performance computing;
• Mike Peardon: Monte Carlo techniques, algorithms for simulating quantum field theories, hadron spectroscopy and scattering;
• Alberto Ramos: Non-perturbative effects in quantum field theories, lattice field theory and its applications to understand the phenomenology of the strong interactions;
• Sinead Ryan: QCD at zero and finite temperature, heavy quark physics, spectroscopy of strong exotic matter;
• Stefan Sint: Non-perturbative renormalisation techniques, determination of quark masses and the strong coupling constant, CKM and Standard Model phenomenology.