Scientific directions of the department:

• • “Theory of functions” (OD Trofimenko). Includes harmonic analysis and theory of approximation of functions by polynomials: Fourier series and integrals, positive definite functions and splines, direct theorems on approximation of functions by polynomials with various restrictions, the Pompey problem and its application to various problems of function theory and integral geometry
  • “Differential equations in partial derivatives” (K.O. Buryachenko, Y.S. Horban, M.O. Shan). Includes the study of boundary value problems for linear and nonlinear partial differential equations and variational inequalities. Special attention is paid to the theory of supersingular solutions and the problem of eliminating singularities.
  • “Theory of operators” (V.O. Derkach). Includes the theory of operator extensions, interpolation problems, the problem of moments, the spectral theory of differential operators: inverse problems, similarity of operators, the question of the completeness of the system of root vectors.
  • “Theory of invertible functions, quasigroups, Latin squares and functional equations” (F.M. Sokhatskyi). Includes decomposition of polynomial functions using superpositions, orthogonality of Latin squares, cubes, and hypercubes, classification of functional equations on quasigroups, and classification of corresponding identities and manifolds in algebra.
  • “Mechanics of thin-walled structures” (V.P. Shevchenko, Yu.M. Kononov, O.S. Vetrov). It includes the study of the elastic-deformed state of anisotropic plates and shells under the influence of static and dynamic loads of various nature; shell destruction mechanics; dynamics of systems of solid bodies with cavities containing liquid.

Competitive state budget research topics:

• • 2001-2002 – state budget project jointly with the Department of Nonlinear Analysis of the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine “Qualitative theory and averaging of nonlinear elliptic and parabolic boundary value problems” (leader – Academician of the National Academy of Sciences of Ukraine, Doctor of Physical and Mathematical Sciences, Academician I.V. Skrypnyk, subject code: 1.1.4.1, state registration number – 0101U001095);
  • 2010-2012 – “Investigation of the elastic-deformed state of anisotropic plates and shells with stress concentrators under the action of force and temperature fields” (state registration number: 0110U003461, supervisor – V.P. Shevchenko);
  • 01.2012-12.31.2012 – state budget project No. 10-1vv/19 “Qualitative properties of solutions of singular, spectral, non-classical problems for elliptic and evolutionary equations and variational inequalities”, manager – prof. A.E. Shishkov;
  • 04/01/2013-12/31/2014 – state budget project No. 12-1vv/19 “Harmonic and spectral analysis of functions and operators, convolution equations and approximation of functions”, manager – prof. R.M. Tryhub;
  • 2013-2015 – “Development of models and methods for researching the strength and stability of thin-walled structures under the influence of force and temperature fields” (state registration number 0113U001528, supervisor – doctor of physical and mathematical sciences, professor V.P. Shevchenko);
  • 01.2015-31.12.2017 – state budget project No. 15-1vv/19 “Metric spaces, harmonic analysis of functions and operators, spectral and non-classical problems for differential equations”, head – prof. A.E. Shishkov;
  • 2016-2018 – “Development of methods for researching the strength and stability of thin-walled structures under the action of various types of static and dynamic loads” (state registration number 0116U002522, supervisor – doctor of physical and mathematical sciences, professor V.P. Shevchenko);
  • 01.2018-31.12.2020 – state budget project No. 18-1vv/19 “Properties of singular solutions of differential equations, spectral analysis of difference systems and modeling of nonlinear processes” (state registration number 0118U003138, head – senior researcher Yu. V. Rassokhina);
  • 2019-2021 – “Development of methods for studying the strength and stability of thin-walled shells and elastic solid bodies with liquid under the action of various types of dynamic loads” (state registration number 0119U100042, supervisor – doctor of physical and mathematical sciences, professor V.P. Shevchenko) ;

The department holds a weekly scientific seminar: “General theory of invertible functions and their application” (leader – doctor of physical and mathematical sciences, professor F.M. Sokhatskyi).

Over the past 5 years, the department has held 3 international conferences:

• V International Conference of Young Scientists named after I WOULD. Lopatinsky “Differential equations and their applications” (November 9-11, 2016);
• VI International School-Seminar named after Y.B. Lopatinsky “Differential equations and their applications” (June 18-20, 2019);
• XII International Algebraic Conference in Ukraine, dedicated to the 215th anniversary of the birth of V. Bunyakovsky (July 02-06, 2019).

Teachers and students participate in grant competitions and programs and get the opportunity to attend foreign scientific events and undergo internships:

• International Mathematical Congress, Berlin, Germany, 2016 (participant – master’s degree holder Y. Pereverzev, leader – PhD in Physics, Associate Professor O.D. Trofymenko);
• World Congress of Mathematicians, Rio de Janeiro, Brazil, 2018 (Ph.D., Associate Professor O.D. Trofymenko, M.O. Shan);
• International Congress on Industrial Mathematics, Valencia, Spain, 2019 (Science of Physics, Associate Professor O.D. Trofimenko);
• International Mathematical Summer School “Applied Mathematical Problems in Geophysics”, July 1-05, 2019, Cetraro, Italy, (Ph.D., Associate Professor K.O. Buryachenko, M.O. Shan )
• Research internship at Humboldt University of Berlin, Berlin, Germany, 2020 (Shan M.O.);
• Leonard Euler scholarship program 2020-2021 (A. Solovyova, 2nd year master’s degree, specialty 111 Mathematics; A. Kostenko, 1st year master’s degree, specialty 111 Mathematics).