Dr Oleg Kirillov is Associate Professor in Mathematics at Northumbria University, UK, working at the interface of applied mathematics, fluid dynamics, stability theory, magnetohydrodynamics, and mathematical physics. He received his Bachelor of Science in Applied Mathematics and Physics, with honours, and subsequently his Master of Science in Applied Mathematics and Physics, with honours, from the Faculty of Aerophysics and Space Research of the Moscow Institute of Physics and Technology. He then continued his academic formation at the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, where he completed his PhD in Theoretical (Mathematical) Mechanics in 2000, followed by research positions at Moscow State University and the Russian Academy of Sciences.

He has developed an international research career through fellowships and appointments in Germany, Italy, Japan, and the UK, including support from the Alexander von Humboldt Foundation, JSPS, DFG, and ERC-linked research environments. Since joining Northumbria University in 2016 as a Vice-Chancellor’s Senior Research Fellow, he has combined research leadership, postgraduate supervision, and academic service with the development of internationally connected research activity.

Dr Kirillov’s research focuses on the mathematical analysis and physically informed modelling of complex dynamical systems, with applications ranging from nonconservative mechanics and spectral stability to rotating and swirling flows, fluid-structure interactions, and magnetohydrodynamic instabilities. He is the author of the monograph Nonconservative Stability Problems of Modern Physics (De Gruyter, 2013; 2nd expanded edition 2021), widely used as a reference in the field. His work has resulted in around 80 peer-reviewed research articles, more than 3,000 citations, and an h-index of 30 (Google Scholar).

A significant part of his work has been devoted to building international and interdisciplinary research links across applied mathematics, mechanics, fluid dynamics, and space-related physical sciences. He has secured 21 competitive fellowships and grants and has organised 10 international workshops and symposia, including meetings at BIRS (Canada) and CISM (Italy). Most recently, he served as Lead Organiser and Chair of the Organising Committee of the 23rd International Couette–Taylor Workshop (ICTW2025).

Dr Kirillov has substantial experience in research coordination, postgraduate supervision, and academic leadership, including supervision of MSc and PhD students in the UK and co-supervision of doctoral researchers in Germany and Italy. His current work is increasingly directed towards the development of international collaborative programmes that connect mathematical theory, reduced modelling, instability analysis, and data-informed interpretation across disciplinary boundaries.

Oleg Kirillov's research focuses on the mathematics of nonconservative and non-Hermitian models in physics and engineering, where he has made key theoretical contributions. His work integrates perturbation methods for multiparameter matrix and non-self-adjoint differential operators with asymptotic methods for partial differential equations, singularity theory, and dynamical systems. He is particularly interested in non-Hermitian singularities and dissipation-induced instabilities, with applications in areas like magnetohydrodynamics (MHD), fluid dynamics, fluid-structure interactions, and solid mechanics.

A major focus of Oleg’s research in mathematical physics is the study of non-Hermitian eigenvalue crossings and their geometry. He and his co-authors developed the first analytical computation of geometric phase around exceptional points, validated by microwave cavity experiments. His work on differential operators in Krein spaces also contributed to magnetohydrodynamic dynamo theory.

In hydrodynamics and MHD, Oleg has studied fluid instabilities, including the McIntyre instability in stratified fluids and instabilities in swirling, rotating flows. His work provided proof of helical and azimuthal magnetorotational instabilities in electrically conducting Keplerian flows, enhancing our understanding of fluid behavior in non-homogeneous magnetic fields. He and his PhD student also developed new methods for solving coupled membrane-fluid problems using complex analysis.

In dynamical systems, Oleg and his co-authors contributed to the theory of ponderomotive magnetism on the example of a particle in a rotating saddle potential and to a theoretical framework to unfold parametric families of 4-dimensional dynamical systems in 1:1 semi-simple resonance, with important implications for understanding dissipation-enhanced modulation instability. His resolution of the Ziegler paradox due to vanishingly small damping in discrete and continuous Hamiltonian and reversible systems, and the theory of gyroscopic stabilization in the presence of dissipative and non-conservative positional forces, has been experimentally validated and applied to friction-induced vibrations in mechanical systems.

Oleg’s overarching goal is to bridge theory with practical applications, advancing the understanding of instability phenomena in complex systems. Through new mathematical approaches, he aims to address critical challenges in modern physics and engineering, particularly where nonconservative forces play a key role.