Dr Oleg Kirillov

Associate Professor

School: Engineering, Physics and Mathematics

Dr. Oleg Kirillov earned his PhD in Theoretical (Mathematical) Mechanics from the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University in 2000. He began his academic career in Russia, conducting research at Moscow State University and the Russian Academy of Sciences. In 2005, he moved to Europe as an Alexander von Humboldt Research Fellow at the University of Hannover and TU Darmstadt. His international research career also includes a JSPS fellowship at Kyushu University in Japan, as well as positions at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) and the University of Trento, with support from the German Research Foundation (DFG) and European Research Council (ERC).

In 2016, Dr. Kirillov joined Northumbria University as a Vice-Chancellor's Senior Research Fellow. He was nominated for the Student-Led Teaching Awards and became a Fellow of the Higher Education Academy. Promoted to Senior Lecturer in 2018 and Associate Professor in Mathematics in 2022, Dr. Kirillov has developed and taught a wide range of modules involving mathematical analysis, linear algebra, dynamics, and applied mathematics for students in both mathematics and engineering. He has successfully supervised PhD and MSc students at Northumbria, and co-supervised doctoral candidates in Germany and Italy. Contributing to departmental leadership he served as the Foundation Year Programme Leader for the Department of Mathematics, Physics, and Electrical Engineering (2022-2025).

Dr. Kirillov’s research portfolio includes 21 competitive fellowships and grants, 80 articles in top-tier peer-reviewed journals, and several major publications, including his monograph, Nonconservative Stability Problems of Modern Physics (De Gruyter, 2013, 2021), which is now a standard reference in the field. OK organized 10 international research workshops and symposia, including ones in BIRS (Canada) and CISM (Italy). He was a Chair of the Organising Committee of the 23rd International Couette-Taylor Workshop - ICTW2025. His work has attracted over 2,850 citations, and his h-index is 28, according to Google Scholar.

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
Radiation-induced instability of a finite-chord Nemtsov membrane, Labarbe, J., Kirillov, O. 7 Jan 2022, In: Physics of 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
Unification theory of instabilities of visco-diffusive swirling flows, Kirillov, O., Mutabazi, I. 20 Dec 2024, In: Physical Review Fluids
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

Professional Activity

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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
Oral presentation: The strongest stable massless column with a follower load and relocatable masses 2025
Organising a conference, workshop, ...: European Solid Mechanics Conference 2025
Oral presentation: Local stability analysis of spiral Poiseuille flow with radial temperature gradient 2025
Oral presentation: Stationary and oscillatory (McIntyre) instabilities of differentially heated swirling flows 2025
Oral presentation: Talk at the Newcastle Applied Seminar 2024
Oral presentation: Local instabilities of visco-diffusive swirling flows with a radial heating 2024