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, Theodoros
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
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
Heriot-Watt University
Penrose, Oliver
Heriot-Watt University
Pocovnicu, Oana
Heriot-Watt University
Rynne, Bryan
Heriot-Watt University
Sabanis, Sotirios
University of Edinburgh
Scardia, Lucia
Heriot-Watt University
Siska, David
University of Edinburgh
Szpruch, Lukasz
University of Edinburgh
Tadahiro (Choonghong) Oh
University of Edinburgh
Wright, Jim
University of Edinburgh
Youngson, Martin
Heriot-Watt University

Postdocs

Lim, Dongyoung
University of Edinburgh
Lo, Hugo
University of Edinburgh
Roos, Joris
University of Edinburgh

PhD students

Adams, Daniel
University of Edinburgh
Baker, Katie
Heriot-Watt University
Burnazyan, Jean
University of Edinburgh
Chapouto, Andreia
University of Edinburgh
Chen, Xingyuan
University of Edinburgh
De Roubin, Pierre
University of Edinburgh
Dimoudis, Spyros
Heriot-Watt University
Dupree Mcintyre, Finlay
University of Edinburgh
Egamberganov, Khakim
University of Edinburgh
Egan, Charlie
Heriot-Watt University
Espin, Tim
University of Edinburgh
Farmakis, George
Heriot-Watt University
Forlano, Justin
Heriot-Watt University
Georgios Farmakis
Heriot-Watt University
Germ, Fabian
University of Edinburgh
Gierjatowicz, Patryk
University of Edinburgh
Govindan Sheri, Aswin
University of Edinburgh
Green, John
University of Edinburgh
Haig, Alastair
Heriot-Watt University
Hammersley, William
University of Edinburgh
Holden, Matthew
Heriot-Watt University
Horner, Chris
University of Edinburgh
Hyde, Matthew
University of Edinburgh
James-Kahn, Felix
University of Edinburgh
Johnston, Tim
University of Edinburgh
Katsetsiadis, Foivos
University of Edinburgh
Kerimkulov, Bekzhan
University of Edinburgh
Kolodziejczyk, Martin
Heriot-Watt University
Lazaridou, Christina
Heriot-Watt University
Lefter, Maria
University of Edinburgh
Li, Guopeng
University of Edinburgh
Lisai, Stefania
Heriot-Watt University
Louca, Nikoletta
Heriot-Watt University
Lytras, Iosif
University of Edinburgh
Moyo, Thamsanqa Castern
Heriot-Watt University
Nadeem, Muhammad Usama
University of Edinburgh
O'Neill, Xander
Heriot-Watt University
Platonov, Vadim
University of Edinburgh
Sätterqvist, Erik
University of Edinburgh
Slade, Andrew
Heriot-Watt University
Spence, Jonny
Heriot-Watt University
Spoitu, Marius
University of Edinburgh
Stewart, John
Heriot-Watt University
Stoček, Jakub
Heriot-Watt University
Strange, Calum
University of Edinburgh
Tang, Michael
University of Edinburgh
Torkington, David
Heriot-Watt University
Ulmer, Martin
University of Edinburgh
Wheeler, Reuben
University of Edinburgh
Wu, Sizhou
University of Edinburgh
Zhang, Ying
University of Edinburgh
Zine, Younes
University of Edinburgh