Our research covers a broad spectrum from harmonic analysis and probability theory to pure and applied PDEs.

Harmonic Analysis

Interactions with number theory, combinatorics, discrete and integral geometry, geometric measure theory and PDEs, applications to elliptic BVPs and semilinear and linear PDEs with rough coefficients and/or domains; applications to nonlinear hyperbolic, dispersive and transport equations.

ODEs, PDEs and dynamical systems

Spectral theory of nonlinear (p-Laplacian-type) ODEs with jumping nonlinearities, nonlinear eigenvalue problems for ODEs and PDEs; spectral analysis of linear self-adjoint and non-self-adjoint operators and applications to mathematical physics.

Nonlinear PDEs and Applications

Free-boundary problems,  PDEs and variational methods in nonlinear elasticity and other continuum theories, nonlinear dissipative equations including Navier-Stokes and reaction-diffusion equations, transport equations arising in mathematical biology (e.g. chemotaxis), mathematical general relativity, optimal transport theory, nonlocal PDEs, dispersive equations, and stochastic PDEs.

Development of new probabilistic methods and approaches to stability, performance and rare events analysis of complex stochastic processes.

Limiting behaviour of stochastic models for queueing systems and networks, and of objects from stochastic geometry and percolation theory; probabilistic analysis of algorithms and communication protocols; rare events analysis for stochastic models with heavy-tailed inputs; applications to (tele)communication and power systems, transport and risk.

Theoretical & Numerical Stochastic Analysis

Analysis of Markovian models; construction of Markovian projections of non-Markovian models; ordinary and partial stochastic differential equations; nonlinear filtering and stochastic control; development of efficient solvers for SDEs

There are additional strong synergies with other groups, for example Applied & Computational Mathematics for numerical analysis.

STAFF

Assiotis, Theo
University of Edinburgh
Azzam, Jonas
University of Edinburgh
Ball, John
Heriot-Watt University
Blue, Pieter
University of Edinburgh
Boulton, Lyonell
Heriot-Watt University
Bournaveas, Nikolaos
University of Edinburgh
Bourne, David
Heriot-Watt University
Bruned, Yvain
University of Edinburgh
Capoferri, Matteo
Heriot-Watt University
Carbery, Tony
University of Edinburgh
Chevyrev, Ilya
University of Edinburgh
Coutand, Daniel
Heriot-Watt University
Dindos, Martin
University of Edinburgh
Dominic Breit
Heriot-Watt University
dos Reis, Goncalo
University of Edinburgh
Foss, Sergey
Heriot-Watt University
Gyongy, Istvan
University of Edinburgh
Hickman, Jonathan
University of Edinburgh
Karakhanyan, Aram
University of Edinburgh
Lord, Gabriel
Heriot-Watt University
Majka, Mateusz
Heriot-Watt University
Malham, Simon
Heriot-Watt University
Ottobre, Michela
Heriot-Watt University
Pelloni, Beatrice