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. Additionally, he contributes to departmental leadership as the Foundation Year Programme Leader for the Department of Mathematics, Physics, and Electrical Engineering.
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). His work has attracted over 2,700 citations, and his h-index is 29, according to Google Scholar.
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.
Joris Labarbe Radiative and diffusive instabilities in moving fluids Start Date: 01/10/2018 End Date: 26/10/2021
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