Mathematical physics

The Mathematics Physics research area encompasses applications to physics arising from diverse areas of mathematics. This includes applications to areas of physics such as:

• String Theory
• Quantum and Conformal Field Theory
• Integrable Models in Statistical Mechanics and Quantum Field Theory
• Gauge Theory

using and developing techniques from:

• Algebra (including Algebraic Topology and Algebraic Geometry)
• Representation Theory
• Differential Geometry
• Operator algebras

Capabilities

• Rowena Ball: dynamical systems, Indigenous and non-Western mathematics
• Qiuye Jia: partial differential equations, mathematical physics, and inverse problems via techniques and tools from microlocal analysis and harmonic analysis
• Ian Le: Representation theory and algebraic combinatorics. Cluster theory.
• Brett Parker: Symplectic geometry and Gromov-Witten and related invariants using exploded manifolds.
• Pierre Portal: Partial differential equations analysed using stochastic analysis to understand random dynamics at the microscopic level, and harmonic analysis to understand oscillatory patterns at the macroscopic level.
• Alex Rose: Harmonic analysis, Fourier analysis, additive combinatorics, mathematical physics, mathematical data science
• James Tener: Operator algebras, functional analysis, and representation theory. Mathematical foundations of quantum field theory.
• Bryan Wang: Geometric properties of moduli spaces in symplectic topology. Gauge theory.
• Xiaoxu Wu: Wave turbulence; mathematical problems in quantum computing; long-time behaviour of solutions to dispersive PDEs