Roman Matsyuk

Roman Matsyuk is a Senior Research Associate at the Department of Differential Equations and Function Theory, Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, with additional affiliation at the Lepage Research Institute in Slovakia. His research spans mathematical physics, differential geometry, and theoretical mechanics with a focus on geometric foundations of physical theories.

Matsyuk completed his education at Ivan Franko L'viv State University, studying in the Faculty of Physics from 1966 to 1971. He earned his MSc in 1971 with a thesis on "Some generalizations of the concepts of special theory of relativity on the basis of n-point geometry" and received his PhD in 1985 with a dissertation on "Poincaré-invariant equations of motion in Lagrangian mechanics with higher derivatives."

His primary research interests include physical geometry, differential-geometric structure of variational calculus with higher derivatives, Ostrohradskyj mechanics, and symmetries in the inverse problems of the calculus of variations. Matsyuk has made significant contributions to understanding variational principles for geodesic circles, uniformly accelerated motion, and relativistic spinning particles. His work consistently explores the geometric interpretation of mechanical systems, particularly those with higher derivatives.

An analysis of Matsyuk's publication record from 1981 to 2020 reveals a sustained focus on the geometric aspects of mechanics, especially in relativistic contexts. He has developed Lagrangian and Hamiltonian formulations for higher-order mechanical systems, investigated variational origins of particle dynamics, and explored connections between geometric structures and physical phenomena like Zitterbewegung. His research demonstrates a consistent mathematical rigor while maintaining relevance to physical theories, particularly in general relativity and classical field theory.

Matsyuk has maintained extensive international collaborations with researchers from the Union of Czech Mathematicians and Physicists, University of Prešov, Eötvös Loránd University, Italian Society for General Relativity and Gravitation, Transilvania University of Brasov, VŠB-TU Ostrava, and Lodz University of Technology, reflecting his standing in the global mathematical physics community.