The Analysis group at Durham studies a broad range of problems using analytic methods and their interactions with other areas of mathematics. Research topics include analytic number theory (e.g., distribution of primes, Diophantine equations, modular forms, and L-functions); ergodic theory and dynamical systems, which examine the statistical behaviour of evolving systems and their connections with geometry, group theory, and number theory; partial differential equations, modelling complex phenomena with interests including fluid mechanics, kinetic theory, mean field games, and optimal transport; and spectral theory, which studies operators on infinite-dimensional spaces and their links with PDEs, geometry, probability, and mathematical physics.
Amit’s research focuses on investigating many element systems using the method of mean field limits, as well as studying long time behaviour of so-called kinetic equations using entropy functionals.
Gabriel works in abstract topological dynamics and ergodic theory, with a focus on self-maps of the Cantor set and the interval.
Katie investigates the interplay between the analysis of partial differential equations and the geometry of the underlying set. She studies problems in the field of Spectral Geometry and asymptotic formulae related to solutions of the heat equation.
Dynamics, Number Theory, Spectral Theory
Additive combinatorics, Analytic Number Theory, Modular forms, Probability Theory
Optimal transport theory; Mean Field Games; Calculus of Variations; Deterministic and Stochastic Control Theory.
Spectral theory, Geometry, Mathematical Physics
Analytic Number Theory, Homogeneous Dynamics
Partial differential equations, Dynamical systems, Numerical analysis, Fluid mechanics
The Durham Symposium on Mathematical Biology brought together around 100 researchers from the UK, Europe and North America to explore mathematical approaches to biological problems. As part of the programme, Professor Philip Maini FRS delivered the Pascal Public Lecture, demonstrating how mathematics can generate insights into biology, ecology and medicine.
Find out more about our research, research areas, other members of staff and more.
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