The Mathematics Area works across pure and applied mathematics. Its main fields are:
- Geometry: algebraic, differential and noncommutative geometry, with applications to quantum field theory and string theory.
- Mathematical physics: integrable systems and their applications, nonlinear partial differential equations, mathematical aspects of quantum physics.
- Mathematical analysis: partial differential equations, variational and topological methods, dynamical systems, conservation laws, transport, geometric measure theory, calculus of variations, control theory, stochastic analysis.
- Mathematical modelling: mechanics of solids, fluids and new materials, complex and biological systems, multiscale analysis.
- Numerical analysis and scientific computing: innovative algorithms and reduced order methods for computational mechanics, design, optimisation and uncertainty quantification.
The Mathematics Area is also home to two interdisciplinary laboratories: MathLab, dedicated to mathematical modelling and numerical simulation, and to their applications; and SAMBA, an experimental laboratory focusing on microscale motility, bio-inspired shape morphing, and tactile perception, in collaboration with the Cognitive Neuroscience Group.