Dr Oleg Kirillov

Associate Professor

School: Engineering, Physics and Mathematics

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 2,900 citations, and an h-index of 29 (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.

Campus Address

City, Ellison Building
Room D210

Email Oleg

Research Themes and Scholarly Interests

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.

Key Publications

Please visit the Pure Research Information Portal for further information
Instabilities in visco-thermodiffusive swirling flows, Kirillov, O., Mutabazi, I. 10 Sep 2025, In: Journal of Fluid Mechanics
Geometrical Optics Stability Analysis of Rotating Visco-Diffusive Flows, Kirillov, O. 24 Jan 2025, In: Mathematics
Flutter instability in solids and structures, with a view on biomechanics and metamaterials, Bigoni, D., Dal Corso, F., Kirillov, O., Misseroni, D., Noselli, G., Piccolroaz, A. Nov 2023, In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Unification theory of instabilities of visco-diffusive swirling flows, Kirillov, O., Mutabazi, I. 20 Dec 2024, In: Physical Review Fluids
From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory, Kirillov, O., Verhulst, F. 1 Mar 2022, Novel Mathematics Inspired by Industrial Challenges, Cham, Springer

Professional Activity

Please visit the Pure Research Information Portal for further information
Participating in a conference, workshop, ...: Vortices and vorticity in geophysical flows, Apr 20 – 24, 2026, Institut Henri Poincaré, Paris 2026
Organising a conference, workshop, ...: Workshop on vortex phenomena in coupled layered atmosphere-ionosphere models. 2026
Hosting an academic visitor: Alexander Movchan 2026
Visiting an external academic institution: University of Liverpool 2026
Oral presentation: Talk at the Engineering Fluids Group Seminar (University of Cambridge) 2026
Visiting an external academic institution: University of Cambridge 2026
Publication Peer-review: Scientific Reports (Journal) 2025
Oral presentation: Local Short-Wavelength Analysis of Centrifugal and McIntyre Instabilities in Visco-Diffusive Swirling Flows 2025
Oral presentation: Local monotonic and oscillatory instabilities in differentially heated visco-diffusive swirling flows 2025
Organising a conference, workshop, ...: 23rd International Couette-Taylor Workshop - ICTW2025 2025