Mykola Staryi

My doctoral research focuses on finite-dimensional Lie algebras—fundamental structures used for modeling symmetries within mathematical physics and non-linear dynamics.

As a PhD candidate at the Institute of Mathematics of the National Academy of Sciences of Ukraine, I work at the intersection of representation theory, mathematical physics, and the theory of differential equations. My current research centers on the classification of realizations and invariants of simple Lie algebras, such as the algebra $\mathfrak{sl}(2, \mathbb{C})$.

My methodology involves using symbolic computation methods via computer algebra systems such as Maple to execute complex algorithmic tasks in symmetry analysis. In particular, this computational approach allows to facilitate the complex calculations of differential invariants.

My primary objective is to bridge the gap between abstract Lie theory and its practical applications to differential equations modeling real physical systems. This involves the systematic study of invariant systems, and the derivation of exact solutions with prescribed properties. Beyond my core research, I am interested in the broader applications of symmetry methods in the theory of differential equations as well as their opportunities in addressing contemporary problems in mathematical physics.