Department of Complex Analysis and Potential Theory

Sergiy Plaksa

Professor, Doctor of Sciences

Head of Department of Complex Analysis and Potential Theory, Institute of Mathematics
of the National Academy of Sciences of Ukraine

ORCID: 0000-0002-2828-0329
  • 2017 - present - Head of Department of Complex Analysis and Potential Theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 2022 - 2024 - Research Fellow, Department of Mathematics "Tullio Levi-Civita", University of Padova, Padova, Italy
  • 2006 - 2017 - Leading Research Fellow , Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 2007 - 2012 - Professor of Department of Mathematical Analysis, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
  • 1999 - 2006 - Senior Research Fellow, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1992 - 1999 - Research Fellow, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1989 - 1992 - Junior Research Fellow, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1984 - 1989 - Postgraduate student, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 2012 - The Attestation Board of Ministry of Education and Science of Ukraine has given the title of Professor in Mathematical Analysis.
  • 2006 - Doctor of Sciences (in Physics and Mathematics, Mathematical Analysis). Dissertation Title: Monogenic functions in boundary problems for elliptic type equations with a degeneration on an axis , Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1989 - Ph.D. (in Physics and Mathematics, Mathematical Analysis). Theses: Riemann boundary problem and singular integral equations, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1984 - 1989 - Post-graduate studies under the guidance of Professor P.M. Tamrazov, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
  • 1979 - 1984 - Master of science, diploma with honors, Faculty of Physics and Mathematics, Zhytomyr Ivan Franko State Pedagogical Institute, Zhytomyr, Ukraine
  • Complex and Hypercomplex Analysis
  • Analytic Function Theory of Complex Variable
  • Monogenic Function Theory in Banach Algebras
  • Boundary Value Problems for Monogenic Functions
  • Boundary Value Problems of Mathematical Physics
  • Singular Integral Equations and Operators
  • Perturbation Theory of Noetherian and Semi-Noetherian Operators
  • 1. Problem posed by M.A. Lavrentiev: to develop methods for investigation of spatial potential solenoid fields analogous to analytic function methods in the complex plane for plane potential fields. We constructed analytic functions of vector variable with values in an infinite-dimensional commutative Banach algebra and proved that components of these functions generate axial-symmetric potential functions and Stokes flow functions. In such a way new integral expressions for these functions were obtained and new method for investigation of spatial axial-symmetric potential solenoid fields was found. The suggested method is analogous to analytic function method in the complex plane and is the solution of the Lavrentiev problem for spatial axial-symmetric potential fields. Using new integral expressions for axial-symmetric potential functions and Stokes flow functions, we developed a functional-analytic method for effective solving boundary problems for axial-symmetric potential solenoid fields.
  • 2. We developed an algebraic-analytic approach to classic equations of mathematical physics. An idea of such an approach means a finding of commutative Banach algebras such that monogenic functions defined on them form an algebra and have components satisfying to beforehand given equations with partial derivatives. We obtained constructive descriptions of monogenic functions taking values in commutative algebras associated with the two-dimensional biharmonic equation and the three-dimensional Laplace equation by means of analytic functions of the complex variable. For the mentioned monogenic functions we established basic properties analogous to properties of analytic functions of the complex variable: the Cauchy integral theorem and integral formula, the Morera theorem, the uniqueness theorem, the Taylor and Laurent expansions.
  • 3. We developed a hypercomplex methods for solving the principal biharmonic problem and boundary value problems of the plane elasticity theory. We proved that the mentioned problems are associated with Schwarz type boundary value problems for monogenic functions in a two-dimensional biharmonic algebra. Using a hypercomplex analog of the Cauchy type integral in the biharmonic algebra, we develop a scheme of its reduction to systems of integral equations. We established sufficient conditions under which these systems have the Fredholm property. It was made for the case where the boundary of domain belongs to a class being wider than the class of Lyapunov curves that was usually required in the plane elasticity theory.
  • 4. The classical theorems on stability of the Noetherian properties of operators in complete spaces are well-known. However, attempts to eliminate the requirement of completeness of spaces from theorems on stability of the Noetherian property faced essential difficulties of topological nature. To overcome these difficulties we developed algebraic methods for proving theorems on stability of Noetherian and semi-Noetherian properties of operators in incomplete vector spaces. These algebraic methods are indifferent with respect to topological properties of the given spaces and operators. Noether operators in incomplete spaces appear in the theory of singular integral equations on curves in the complex plane for extended classes of equation coefficients and curves. We studied the Noetherian property for singular integral Cauchy operators in incomplete spaces of quickly oscillating functions on closed Jordan regular rectifiable curves by the mentioned methods of algebraic nature.
  • 5. Solvability of boundary problems for analytic functions theory in domains with boundary not being piece-wise smooth rectifiable depends on combined properties both of the given functions and the boundary. Difficulties increase if the index of a boundary problem is infinite. To overcome these difficulties we developed methods for constructing asymptotic expansions for the Cauchy-type integrals on non-regular rectifiable curves (in particular, on spiral-form curves). Using these asymptotic expansions, we have solved explicitly some boundary problems for analytic functions with infinite index in domains with both regular and non-regular rectifiable boundary. We have also solved explicitly some Riemann boundary problems with quickly oscillating coefficients on Jordan rectifiable curves.
  • Books:
  • 2008 - Mel'nichenko I.P. and Plaksa S.A. Commutative algebras and spatial potential fields. Kyiv, Institute of Mathematics of the National Academy of Sciences of Ukraine (in Russian).
  • 2023 - Plaksa S.A. and Shpakivskyi V.S. Monogenic functions in spaces with commutative multiplication and applications. Frontiers in Mathematics, Birkhäuser Cham.
    DOI: 10.1007/978-3-031-32254-9
  • Edited volumes:
  • 2010 - Zelinskii Yu.B., Limarchenko O.S., Plaksa S.A., Tamrazov P.M., Trokhimchuk Yu.Yu. (eds). Complex Analysis and Free Boundary Flows. Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 7, No. 2.
  • 2012 - Zelinskii Yu.B., Gerasymenko V.I., Trokhimchuk Yu.Yu., Bakhtin O.K., Plaksa S.A. (eds). Analysis and Applications. Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 9, No. 2.
  • 2013 - Zelinskii Yu.B., Plaksa S.A. (eds). Complex Analysis, Potential Theory and Applications. Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 10, No. 4-5.
  • 2014 - Complex Analysis and Potential Theory, in memory of Promarz M. Tamrazov (Editor: M. Lanza de Cristoforis, Associated editor: S. Plaksa). Complex Variables and Elliptic Equations, 59, No. 1.
    DOI: 10.1080/17476933.2013.859254
  • 2022 - Plaksa S.A., Denega I.V. (eds). Complex Analysis and Applications. Transactions of the Institute of Mathematics of the National Academy of Sciences of Ukraine, 19, No. 1.
  • Chapters in books or edited volumes:
  • 2000 - Plaksa S. Boundary properties of axial-symmetrical potential and Stokes flow function. In: Joji Kajiwara, Zong Li, Kwang Ho Shon (eds). Finite or Infinite Dimensional Complex Analysis. Lecture Notes in Pure and Applied Mathematics. Marcel Dekker Inc., 214, 443-455.
  • 2012 - Plaksa S.A. Commutative algebras associated with classic equations of mathematical physics. In: Rogosin S., Koroleva A. (eds). Advances in Applied Analysis. Trends in Mathematics. Birkhäuser, Basel, 177-223.
    DOI: 10.1007/978-3-0348-0417-2_5
  • 2014 - Plaksa S. A. and Pukhtaievych R. P. Monogenic functions in a three-dimensional harmonic comutative algebras, In: T. Aliev, A. Golberg, and S. V. Rogosin (eds). Complex Analysis and Potential Theory with Applications, Proceedings of the 9th ISAAC Congress, Krakow, Poland, 5-9 August, 2013, Cambridge Scientific Publishers, Cottenham, UK, 148-155.
  • 2019 - Gryshchuk S.V. and Plaksa S.A. Biharmonic monogenic functions and biharmonic boundary value problems, In: Lindahl K., Lindström T., Rodino L., Toft J., Wahlberg P. (eds). Analysis, Probability, Applications, and Computation. Trends in Mathematics. Birkhäuser, Cham, 153-160.
    DOI: 10.1007/978-3-030-04459-6_14
  • 2019 - Gryshchuk S.V. and Plaksa S.A. Schwartz-type boundary value problems for monogenic functions in a biharmonic algebra, In: Rogosin S., Çelebi A. (eds). Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham, 193-211.
    DOI: 10.1007/978-3-030-02650-9_10
  • 2019 - Plaksa S.A. Axial-symmetric potential flows, In: Flaut C., Hošková-Mayerová Š., Flaut D. (eds). Models and Theories in Social Systems, Studies in Systems, Decision and Control, 179, Springer, Cham, 165-195.
    DOI: 10.1007/978-3-030-00084-4_9
  • 2021 - Gryshchuk S.V. and Plaksa S.A. A hypercomplex method for solving boundary value problems for biharmonic functions, In: Hošková-Mayerová Š., Flaut C., Maturo F. (eds). Algorithms as a Basis of Modern Applied Mathematics. Studies in Fuzziness and Soft Computing, 404, Springer, Cham, 231-255.
    DOI: 10.1007/978-3-030-61334-1_12
  • 2023 - Tkachuk M.V. and Plaksa S.A. Menchov–Trokhimchuk theorem generalized for monogenic functions in a three-dimensional algebra, In: Kähler, U., Reissig, M., Sabadini, I., Vin-das, J. (eds) Analysis, Applications, and Computations. ISAAC 2021. Trends in Mathematics. Birkhäuser, Cham, 333-342.
    DOI: 10.1007/978-3-031-36375-7_25
  • 2025 - Gryshchuk S. and Plaksa S. A piecewise continuous Schwarz-type boundary-value problem in an angle for monogenic functions in a commutative biharmonic algebra, In: Ebert, M.R., Kähler, U., Sabadini, I., Toft, J. (eds) New Tools in Mathematical Analysis and Applications. ISAAC 2023. Trends in Mathematics. Birkhäuser, Cham, 121-132.
    DOI: 10.1007/978-3-031-77050-0_11
  • Publications in scientific journals:
  • 1989 - Plaksa S.A. Riemann boundary-value problem with an oscillating coefficient and singular integral equations on a rectifiable curve, Ukr. Math. J., 41(1), 107-112.
    DOI: 10.1007/BF01060659
  • 1990 - Plaksa S.A. Riemann boundary problem with index plus-infinity on a rectifiable curve, Ukr. Math. J., 42(9), 1070-1077.
    DOI: 10.1007/BF01056599
  • 1990 - Plaksa S.A. Riemann boundary-value problem with index minus infinity on a rectifiable curve, Ukr. Math. J., 42(10), 1199-1204.
    DOI: 10.1007/BF01057389
  • 1990 - Plaksa S.A. Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I, Ukr. Math. J., 42(11), 1351-1358.
    DOI: 10.1007/BF01066191
  • 1990 - Plaksa S.A. Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. II, Ukr. Math. J., 42(12), 1507-1515.
    DOI: 10.1007/BF01060822
  • 1993 - Plaksa S.A. On perturbation of semi-Noether operators in incomplete spaces. I, Ukr. Math. J., 45(2), 290-298.
    DOI: 10.1007/BF01060986
  • 1993 - Plaksa S.A. On perturbation of semi-Noether operators in incomplete spaces. II, Ukr. Math. J., 45(3), 424-429.
    DOI: 10.1007/BF01061015
  • 1993 - Plaksa S.A. On the composition of operators in vector spaces and their Noether property, Ukr. Math. J., 45(8), 1316-1320.
    DOI: 10.1007/BF01070982
  • 1993 - Plaksa S.A. On the Noether property of singular integral equations with Cauchy kernels on a rectifiable curve, Ukr. Math. J., 45(10), 1548-1559.
    DOI: 10.1007/BF01571089
  • 1995 - Mel'nichenko I.P. and Plaksa S.A. Reduction of the principal biharmonic problem for a quadrant to nonsingular integral equations, Ukr. Math. J., 47(6), 892–903.
    DOI: 10.1007/BF01058780
  • 1996 - Mel'nichenko I.P. and Plaksa S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I, Ukr. Math. J., 48(11), 1717-1730.
    DOI: 10.1007/BF02529493
  • 1996 - Mel'nichenko I.P. and Plaksa S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. II, Ukr. Math. J., 48(12), 1916-1926.
    DOI: 10.1007/BF02375377
  • 1997 - Mel'nichenko I.P. and Plaksa S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. III, Ukr. Math. J., 49(2), 253-268.
    DOI: 10.1007/BF02486440
  • 2000 - Plaksa S.A. Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. I, Ukr. Math. J., 52(4), 564–585.
    DOI: 10.1007/BF02515397
  • 2000 - Plaksa S.A. Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. II, Ukr. Math. J., 52(6), 856–867.
    DOI: 10.1007/BF02591780
  • 2001 - Plaksa S.A. On integral representations of an axisymmetric potential and the Stokes flow function in domains of the meridian plane. I, Ukr. Math. J., 53(5), 726-743.
    DOI: 10.1023/A:1012578200291
  • 2001 - Plaksa S.A. On integral representations of an axisymmetric potential and the Stokes flow function in domains of the meridian plane. II, Ukr. Math. J., 53(6), 938-950.
    DOI: 10.1023/A:1013351918523
  • 2001 - Plaksa S.A. Dirichlet problem for an axisymmetric potential in a simply connected domain of the meridian plane, Ukr. Math. J., 53(12), 1976-1997.
    DOI: 10.1023/A:1015486805984
  • 2002 - Plaksa S.A. On the solution of the exterior Dirichlet problem for an axisymmetric potential, Ukr. Math. J., 54(12), 1982–1991.
    DOI: 10.1023/A:1024073231378
  • 2003 - Plaksa S.A. Dirichlet problem for the Stokes flow function in a simply connected domain of the meridian plane, Ukr. Math. J., 55(2), 241-281.
    DOI: 10.1023/A:1025464312591
  • 2003 - Plaksa S.A. Singular integral operators in spaces of oscillating functions on a rectifiable curve, Ukr. Math. J., 55(9), 1457-1471.
    DOI: 10.1023/B:UKMA.0000018007.04762.eb
  • 2005 - Plaksa S.A. Differentiation of singular integrals with piecewise-continuous density and boundary values of derivatives of a Cauchy-type integral, Ukr. Math. J., 57(2), 261-270.
    DOI: 10.1007/s11253-005-0186-7
  • 2006 - Vasil'eva Yu.V. and Plaksa S.A. Piecewise-continuous Riemann boundary value problem on a rectifiable curve, Ukr. Math. J., 58(5), 616-628.
    DOI: 10.1007/s11253-006-0095-4
  • 2009 - Grishchuk S.V. and Plaksa S.A. Integral representations of generalized axially symmetric potentials in a simply connected domain, Ukr. Math. J., 61(2), 195-213.
    DOI: 10.1007/s11253-009-0209-x
  • 2009 - Grishchuk S.V. and Plaksa S.A. Monogenic functions in a biharmonic algebra, Ukr. Math. J., 61(12), 1865-1876.
    DOI: 10.1007/s11253-010-0319-5
  • 2010 - Shpakivskyi V.S. and Plaksa S.A. Integral theorems and a Cauchy formula in a commutative three-dimensional harmonic algebra, Bulletin de la Societe des Sciences et des Lettres de Lodz, 60(2), 47-54
  • 2011 - Plaksa S.A. and Shpakivskyi V.S. Constructive description of monogenic functions in a harmonic algebra of the third rank, Ukr. Math. J., 62(8), 1078-1091.
    DOI: 10.1007/s11253-011-0427-x
  • 2011 - Plaksa S.A., Gryshchuk S.V. and Shpakivskyi V.S. Commutative algebras of monogenic functions associated with classic equations of mathematical physics, Contemporary Mathematics, 553, Amer. Math. Soc., Providence, 245-258.
    DOI: 10.1090/conm/553
  • 2011 - Plaksa S.A. and Kudjavina Yu.V. Riemann boundary value problem on an open Jordan rectifiable curve. I, Ukr. Math. J., 62(11), 1511-1522.
    DOI: 10.1007/s11253-011-0465-4
  • 2011 - Plaksa S.A. and Kudjavina Yu.V. Riemann boundary value problem on an open Jordan rectifiable curve. II, Ukr. Math. J., 62(12), 1659-1671.
    DOI: 10.1007/s11253-011-0480-5
  • 2012 - Plaksa S.A. and Shpakivskyi V.S. Limiting values of Cauchy type integral in a three-dimensional harmonic algebra, Eurasian Math. J., 3(2), 120-128
  • 2012 - Plaksa S.A. and Shpakivskyi V.S. A description of spatial potential fields by means of monogenic functions in infinite-dimensional spaces with a commutative multiplication, Bulletin de la Societe des Sciences et des Lettres de Lodz, 62(2), 55-65
  • 2013 - Plaksa S.A. and Pukhtaievych R.P. Constructive description of monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical, Ukr. Math. J., 65(5), 740-751.
    DOI: 10.1007/s11253-013-0810-x
  • 2013 - Plaksa S.A. and Shpakivskyi V.S. On the logarithmic residues of monogenic functions in a three-dimensional harmonic algebra with two-dimensional radical, Ukr. Math. J., 65(7), 1079-1086.
    DOI: 10.1007/s11253-013-0843-1
  • 2013 - Gryshchuk S.V. and Plaksa S.A. Basic properties of monogenic functions in a biharmonic plane, Contemporary Mathematics, 591, Amer. Math. Soc., Providence, 127-134.
    DOI: 10.1090/conm/591
  • 2013 - Gryshchuk S.V. and Plaksa S.A. Schwartz-type integrals in a biharmonic plane, Intern. J. of Pure and Applied Math., 83(1), 193-211.
    DOI: 10.12732/ijpam.v83i1.13
  • 2013 - Plaksa S.A. and Shpakivskyi V.S. On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical, Annales Universitatis Mariae Curie-Sklodowska. Sectio A, 67(1), 57-64
  • 2014 - Plaksa S.A. and Shpakivskyi V.S. Cauchy theorem for a surface integral in commutative algebras, Complex Variables and Elliptic Equations, 59(1), 110-119.
    DOI: 10.1080/17476933.2013.845178
  • 2014 - Plaksa S.A. and Pukhtaievych R.P. Monogenic functions in a finite-dimensional semi-simple commutative algebra, An. St. Univ. Ovidius Constanta, 22(1): 221-235.
    DOI: 10.2478/auom-2014-0018
  • 2014 - Plaksa S.A. and Shpakivskyi V.S. Monogenic functions in a finite-dimensional algebra with unit and radical of maximal dimensionality, Journal of Algerian Mathematical Society, 1, 1-13.
  • 2015 - Пухтаєвич Р.П. і Плакса С.А. Інтергал типу Коші по прямій в тривимірній гармонічній алгебрі з одновимірним радикалом Зб. Пр. Інст. Мат. НАН Укр., 12(3), 212-219.
  • 2016 - Gryshchuk S.V. and Plaksa S.A. Monogenic functions in the biharmonic boundary value problem, Mathematical Methods in the Applied Sciences, 39(11), 2939-2952.
    DOI: 10.1002/mma.3741
  • 2017 - Plaksa S.A. and Shpakivskyi V.S. An extension of monogenic functions and spatial potentials, Lobachevskii Journal of Mathematics, 38(2), 330-337.
    DOI: 10.1134/S1995080217020160
  • 2017 - Gryshchuk S.V. and Plaksa S.A. A Schwartz-type boundary value problem in a biharmonic plane, Lobachevskii Journal of Mathematics, 38(3), 435-442.
    DOI: 10.1134/S199508021703012X
  • 2017 - Gryshchuk S.V. and Plaksa S.A. Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations, Open Mathematics, 15(1), 374-381.
    DOI: 10.1515/math-2017-0025
  • 2017 - Pukhtaievych R. and Plaksa S. On logarithmic residue of monogenic functions in a three-dimensional commutative algebra with one-dimensional radical, An. St. Univ. Ovidius Constanta, 25(3), 167-182.
    DOI: 10.1515/auom-2017-0043
  • 2018 - Plaksa S.A. and Shpakivskyi V.S. Integral theorems for monogenic functions in an infinite-dimensional space with a commutative multiplication, Bulletin de la Societe des Sciences et des Lettres de Lodz, 68(2), 25-36
  • 2019 - Plaksa S.A. A functionally-analytic method for modelling axial-symmetric flows of ideal fluid, Demonstratio Mathematica, 52(1), 213-224.
    DOI: 10.1515/dema-2019-0018
  • 2019 - Pukhtaievych R. and Plaksa S. Some properties of a Cauchy type integral in a three-dimensional commutative algebra with one-dimensional radical, Monatsh. Math, 189(3), 523-548.
    DOI: 10.1007/s00605-019-01288-4
  • 2019 - Plaksa S.A. Monogenic functions in commutative algebras associated with classical equations of mathematical physics, J. Math. Sci., 242(3), 432-456.
    DOI: 10.1007/s10958-019-04488-3
  • 2020 - Plaksa S.A. Schwarz boundary-value problems for solutions of a generalized Cauchy-Riemann system with a singular line, J. Math. Sci., 244(1), 36-46.
    DOI: 10.1007/s10958-019-04602-5
  • 2021 - Gryshchuk S.V. and Plaksa S.A. Schwartz-type boundary-value problems for canonical domains in a biharmonic plane, J. Math. Sci., 259(1), 37-52.
    DOI: 10.1007/s10958-021-05599-6
  • 2022 - Tkachuk M.V. and Plaksa S.A. An analog of the Menchov-Trokhimchuk theorem for monogenic functions in a three-dimensional commutative algebra, Ukr. Math. J., 73(8), 1299-1308.
    DOI: 10.1007/s11253-022-01991-w
  • 2023 - Gryshchuk, S.V. and Plaksa S.A. Biharmonic problem in an angle and monogenic functions, Ukr. Math. J., 74(11), 1686-1700.
    DOI: 10.1007/s11253-023-02164-z
  • 2023 - Plaksa S.A. Monogenic functions and harmonic vectors, Proceedings of the International Geometry Center, 16(1), 59-76.
    DOI: 10.15673/tmgc.v16i1.2385
  • 2024 - Plaksa S.A. On continuous extension of the Cauchy-type integral with parameter-dependent density to the boundary of the domain, Ukr. Math. J., 76(3), 522–527.
    DOI: 10.1007/s11253-024-02335-6
  • 2002 - Universities of Leiden, Amsterdam and Eindhoven, the Netherlands (May - June, 2002).
  • 2008 - Universities of Leeds, Cardiff, London and Nottingham, UK (May, 2008).
  • 2008 - University of Mostaganem, Algeria, (May, 2008).
  • 2009 - Bar-Ilan University and Holon Institute of Technology, Israel, (May, 2009).
  • 2011 - University of Padova, Italy, (June, 2011).
  • 2011 - Universities of Weimar and Freiberg, Germany, (July, 2011).
  • 2014 - University of Cuernavaca and CINVESTAV, Mexico, (November, 2014).
  • 2018 - University of Padova, Italy, (June - July, 2018).
  • 2022 - 2024 - Visiting Scholar at Department of Mathematics "Tullio Levi-Civita" of the University of Padova, Italy, (November 2022 - July 2024).
  • 1996 - 2nd European Congress of Mathematics, (Budapest, Hungary);
  • 1997 - Conference on Differential Equations and their Applications, (Brno, Czech Republic);
  • 1998 - XII International Conference on Analytic Functions, (Lublin, Poland);
  • 1999 - 7-th International Colloquium on Finite or Infinite Dimensional Complex Analysis, (Fukuoka, Japan);
  • 1999 - Second International ISAAC Congress, (Fukuoka, Japan);
  • 2000 - International Conference dedicated to M.A. Lavrentiev on the occasion of his birthday centenary, (Kyiv, Ukraine), Plenary lecture "On the Lavrentiev's problem: description of axial-symmetric potential fields by means of analytic functions";
  • 2001 - International Conference on Complex Analysis and Potential Theory, (Kyiv, Ukraine);
  • 2001 - Ukrainian Congress of Mathematics , (Kyiv, Ukraine);
  • 2002 - International Conference on Factorization, Singular Operators and Related Problems in Honour of Professor Georgii Litvinchuk , (Funchal, Madeira, 2002);
  • 2002 - International Workshop on Potential Flows and Complex Analysis , (Kyiv, Ukraine);
  • 2003 - International Conference "Complex Analysis and its Applications" , (Lviv, Ukraine);
  • 2003 - International Workshop "Potential Theory and Free Boundary Flows" , (Kyiv, Ukraine);
  • 2003 - International Conference "Analytic Methods of Analysis and Differential Equations" , (Minsk, Belarus);
  • 2005 - 5-th International ISAAC Congress, (Catania, Italy);
  • 2005 - International Workshop "Free boundary flows and related problem of analysis" , (Kyiv, Ukraine);
  • 2006 - International Conference on Complex Analysis and Potential Theory , (Gebze, Turkey);
  • 2007 - 6-th International ISAAC Congress, (Ankara, Turkey);
  • 2007 - International Conference "Complex analysis and wave processes in mechanics" within the framework of Bogolyubov Readings, (Zhytomir, Ukraine);
  • 2008 - 3-rd Schools on Abstract Differential Equations and OrdinaryDifferential Equations, (Mostaganem, Algeria);
  • 2009 - 4-th International Conference on Complex Analysis and Dynamical Systems, (Nahariya, Israel);
  • 2009 - International Workshop "Applied Nonlinear Analysis", (Holon, Israel);
  • 2009 - International Conference "Analytic methods of mechanics and complex analysis" dedicated to N.A. Kilchevskii and V.A. Zmorovich on the occasion of their birthday centenary , (Kyiv, Ukraine);
  • 2009 - 2nd Ukrainian Congress of Mathematics , (Kyiv, Ukraine);
  • 2010 - 3-rd International Workshop on Contemporary Problems of Mathematics and Mechanics , (Minsk, Belarus);
  • 2010 - 6-th International Conference "Finsler Extensions of Relativity Theory" , (Moscow, Russia);
  • 2011 - International Workshop "Mini-courses in Mathematical Analysis-2011" , (Padova, Italy);
  • 2011 - The 9-th International Conference on Clifford Algebras and their Applications , (Weimar, Germany);
  • 2011 - 8-th International ISAAC Congress , (Moscow, Russia);
  • 2012 - International Conference "Analytic Methods of Analysis and Differential Equations" , (Minsk, Belarus);
  • 2012 - International Conference dedicated to the 120th anniversary of Stefan Banach , (Lviv, Ukraine);
  • 2013 - International Workshop "A new approach in theoretical and applied methods in algebra and analysis" , (Constanta, Romania);
  • 2013 - 9-th International ISAAC Congress , (Krakow, Poland);
  • 2014 - International Workshop on Operator Theory and its Applications IWOTA-2014 , (Amsterdam, the Netherlands);
  • 2014 - The School "Festival de Matematicas" , (Cuernavaca, Mexico);
  • 2014 - The Annual Seminar "Analisis: Norte-Sur 2014" , (Mexico City, Mexico);
  • 2015 - International Conference "Analytic Methods of Analysis and Differential Equations" , (Minsk, Belarus);
  • 2017 - 11th International ISAAC Congress , (Vaxjo, Sweden);
  • 2018 - International Workshop "Mini-courses in Mathematical Analysis-2018" , (Padova, Italy);
  • 2018 - (Hyper)Complex Analysis in Differential Equations, Geometry and Physical Applications , (Bedlewo, Poland);
  • 2018 - IECMSA-2018: 7th International Eurasian Conference on Mathematical Sciences and Applications, (Kyiv, Ukraine), Invited Speaker.
  • 2019 - (Hyper)Complex Analysis in Differential Equations, Geometry and Physical Applications , (Bedlewo, Poland);
  • 2021 - International Online Conference Algebraic and Geometric Methods of Analysis dedicate to the memory of Yuriy Trokhymchuk , (Odesa, Ukraine); Invited Speaker.
  • 2021 - 13th International ISAAC Congress , (Ghent, Belgium);
  • 2021 - (Hyper)Complex Seminar 2021 , (Bedlewo, Poland); Invited Speaker.
  • 2023 - International Workshop "Mini-courses in Mathematical Analysis-2023" , (Padova, Italy);
  • 2023 - (Hyper)Complex Seminar 2023 , (Bedlewo, Poland); Invited Speaker.
  • 2023 - 14th International ISAAC Congress , (Sao Paulo, Brazil);
  • 2024 - International Workshop "Mini-courses in Mathematical Analysis-2024" , (Padova, Italy);
  • 2024 - (Hyper)Complex Seminar 2024 , (Lodz, Poland); Invited Speaker.
  • Training courses for masters and postgraduate students:
  • - Selected questions of the analytic function theory
  • - Selected qestions of complex analysis
  • - Elements of hypercomplex analysis
  • - Сomplex analysis
  • - Singular integral operators and boundary value problems for analytic functions
  • - Monogenic functions and basic elliptic equations of mathematical physics
  • Supervision of post-graduated studies:
  • - 5 PhD theses in Physics and Mathematics have been defended under my supervision
  • - 2 disirtations of Doctor of Sciences in Physics and Mathematics have been defended under my supervision
  • Membership in Scientific Societies:
  • - International Society for Analysis, its Applications and Computation Life-member
  • Membership in Editorial Board:
  • - Ukrainian Mathematical Journal Editorial Board Member
  • - Eurasian Mathematical Journal Editorial Board Member
  • - Analele Stiintifice ale Universitatii Ovidius Constanta (Seria Matematica) Editorial Board Member
  • - Journal of Algerian Mathematical Society Editorial Board Member
  • 1994 – 1995 - ISF Grant UB 4000
  • 1995 – 1996 - ISF Grant UB 4200
  • 1995 – 1998 - INTAS Grant 94-1474
  • 1997 – 1998 - Ukrainian - Polish Grant 2M/1401-97
  • 1999 - ISAAC Award for outstanding research achievements in mathematics
  • 2000 – 2003 - INTAS Grant 99-00089
  • 2008 - Grant of London Mathematical Society
  • 2015 – 2017 - Grant of National Academy of Sciences of Ukraine and Polish Academy of Sciences 39/2014
  • 2018 – 2020 - Grant of National Academy of Sciences of Ukraine and Polish Academy of Sciences №32
  • 2022 – 2023 - Grant of University of Padova in the framework of the “Visiting Scholars” Call 2022-2023
  • 2023 – 2024 - Grant of INDAM in the framework of the Visiting Professors Program
  • 2023 – 2024 - Grant of University of Padova in the framework of the “Visiting Scholars” Call 2023-2024