Department of Complex Analysis and Potential Theory

Roman Pukhtaievych

Ph.D. in Mathematics

Research Fellow, Institute of Mathematics
of the National Academy of Sciences of Ukraine

ORCID: 0000-0002-7279-8213
  • 2019 - now - Research Fellow, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.
  • 2015 - 2018 - Ph.D. student in Mathematics, Department of Mathematics "Tullio Levi-Civita", University of Padua, Padua, Italy.
  • 2016 - 2018 - Senior Research Fellow, Department of Mathematical Analysis, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine.
  • 2014 - 2015 - Junior Research Fellow, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.
  • 2012 - 2014 - Junior Research Fellow, Department of Mathematical Analysis, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine.
  • 2011 - 2014 - Postgraduate student, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.
  • Boundary value problems for elliptic equations
  • Singular and regular perturbation problems
  • Integral equations and operators
  • Potential and Homogenization theories
  • Effective properties of composit materials
  • Quaternionic analysis
  • Monogenic functions in commutative Banach algebras
  • 2015 - 2018 - Ph.D. in Mathematics, Department of Mathematics "Tullio Levi-Civita", University of Padua, Padua, Italy.
  • 2011 - 2014 - Degree of Candidate of Physical and Mathematical Sciences, Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, Ukraine.
  • 2010 - 2011 - Master's degree in Mathematics, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine.
  • 2006 - 2010 - Bachelor's degree in Mathematics, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine.
  • 2017 - Department of Mathematics of Aberystwyth University, Aberystwyth, UK, (October 10, 2017 - December 9, 2017).
  • 2019 - Luzzini P., Musolino P., and Pukhtaievych R., Shape analysis of the longitudinal flow through a periodic array of cylinders, J. Math. Anal. Appl., 477(2): 1369-1395, 2019.
    DOI: 10.1016/j.jmaa.2019.05.017
  • 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, 2019.
    DOI: 10.1007/s00605-019-01288-4
  • 2019 - Dalla Riva, M., Musolino, P., and Pukhtaievych R., Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface, Asymptotic Analysis, 111(3-4): 217-250, 2019.
    DOI: 10.3233/ASY-181495
  • 2018 - Pukhtaievych R., Effective conductivity of a periodic dilute composite with perfect contact and its series expansion, Z. Angew. Math. Phys., 69-83, 2018.
    DOI: 10.1007/s00033-018-0976-z
  • 2018 - Pukhtaievych R., Asymptotic behavior of the solution of singularly perturbed transmission problems in a periodic domain, Math. Methods Appl. Sci., 41(9): 3392-3413, 2018.
    DOI: 10.1002/mma.4832
  • 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, 2017. DOI: 10.1515/auom-2017-0043
  • 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, 2014.
    DOI: 10.2478/auom-2014-0018
  • 2014 - Plaksa S. A. and Pukhtaievych R. P., Constructive description of monogenic functions in finite-dimensional semisimple commutative algebra, Dopov. Nac. akad. nauk Ukr., 1: 14-21, 2014. (Ukrainian. English summary).
    DOI: 10.15407/dopovidi2014.01.014
  • 2013 - Plaksa S. A. and Pukhtaievych R. P., Constructive description of monogenic functions in a threedimensional harmonic algebra with one-dimensional radical, Ukr. Math. J., 65(5): 740-751, 2013. DOI: 10.1007/s11253-013-0810-x
  • 2015 - Pukhtaievych R. P. and Plaksa S. A., The Cauchy type integral on the straight line in three-dimensional harmonic algebra with one-dimensional radical, Zb. Pr. Inst. Mat. NAN Ukr. 12(3), 2015, P. 212-219. (Ukrainian. English summary), Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, 2015.
  • 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, editors, Complex Analysis and Potential Theory with Applications, Proceedings of the 9th ISAAC Congress, Krakow, Poland, 5-9 August, 2013, P. 148-155, Cambridge Scientific Publishers, Cottenham, UK, 2014.
  • 2013 - Pukhtaievych R., Monogenic functions in a three-dimensional harmonic semi-simple algebra, Zb. Pr. Inst. Mat. NAN Ukr. 10(4-5), 2013, P. 352-361, Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, 2013.
  • 2012 - Pukhtaievych R., Power series and Laurent series in three-dimensional harmonic algebra with a onedimensional radical, Zb. Pr. Inst. Mat. NAN Ukr. 9(2), 2012, P. 311-326. (Russian. English summary), Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine, 2012.
  • 2018 - A functional analytic approach to solve the Dirichlet problem for the Laplace operator in a periodically perforated domains, Ser Cymru COFUND Training Day on the Functional Analytic Approach, July 23, 2018, Department of Mathematics of Aberystwyth University, Aberystwyth, UK, Invited Speaker.
  • 2018 - Series expansion for the effective conductivity of ideal and non-ideal two-phase dilute composites, 15th International Conference on Integral Methods in Science and Engineering (IMSE 2018), July 16-20, 2018, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, UK.
  • 2018 - Dependence of the effective thermal conductivity of periodic composites on the diameter of inclusions, Mini-courses in Mathematical Analysis 2018, July 2-6, 2018, University of Padua, Padua, Italy.
  • 2017 - Effective conductivity and its series expansion for a non-ideal dilute composite, Ser Cymru COFUND Workshop on Pure and Applied Mathematics, November 20, 2017, Department of Mathematics of Aberystwyth University, Aberystwyth, UK, Invited Speaker.
  • 2017 - Series expansion for the effective conductivity of a non-ideal dilute composite, ISAAC 2017, 11th International Society for Analysis, its Applications and Computation Congress, August 14-18, 2017, Vaxjo, Sweden.
  • 2016 - Some properties of monogenic functions in a finite-dimensional semi-simple commutative algebra, BFA 2016, Boundary value problems, Functional equations and Apllication, 3rd meeting, April 20-23, 2016, Rzeszow, Poland.
  • 2015 - Monogenic functions in a finite-dimensional semi-simple commutative algebra, ISAAC 2015, 10th International Society for Analysis, its Applications and Computation Congress, August 3-8, 2015, Macau, China SAR.
  • 2015 - Monogenic functions in certain harmonic algebras, Hypercomplex Seminar 2015, (Hyper)Complex and Dynamical Processes, Modelling and Simulations (30 years of the direct cooperation agreement Lodz - Roma), July 2-9, 2015, Bedlewo, Poland.
  • 2015 - The Cauchy type integral on the straight line in three-dimensional harmonic algebra with onedimensional radical, International Conference of Young mathematicians, June 3-6, 2015, Kyiv, Ukraine.
  • 2014 - The analog of the Cauchy integral formula for monogenic functions if finite-dimensional semisimple commutative algebra, International Conference "Differential equations, computational mathematics, theory of functions and mathematical methods of mechanics", April 23-24, 2014, Kyiv, Ukraine.
  • 2013 - Monogenic functions in a finite-dimensional semi-simple algebra, International Conference "Complex Analysis, Potential Theory and Applications", August 19-23, 2013, Kyiv, Ukraine.
  • 2013 - Monogenic functio>ns in a three-dimensional harmonic semi-simple algebra, ISAAC 2013, 9th International Society for Analysis, its Applications and Computation Congress, August 5-9, 2013, Krakow, Poland.
  • 2012 - Monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical, International Conference dedicated to 120-th anniversary of Stefan Banach, September 17-21, 2012, Lviv, Ukraine.
  • 2012 - Monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical, AMADE 2012, 7th International Workshop "Analytical Methods of Analysis and Differential Equations", September 10-15, 2012, Minsk, Belarus.
  • 2019 - Mini-courses in Mathematical Analysis 2019, (June 24-28, 2019, University of Padua, Padua, Italy), courses by: Prof. T. HytÃunen, Prof. A. Rodríguez-Bernal, Prof. J. Stubbe.
  • 2018 - Ser Cymru COFUND Training Day on the Functional Analytic Approach, (July 23, 2018, Department of Mathematics of Aberystwyth University, Aberystwyth, UK).
  • 2018 - IMSE 2018, 15th International Conference on Integral Methods in Science and Engineering, (July 16-20, 2018, School of Computing, Engineering and Mathematics, University of Brighton, Brighton, UK).
  • 2018 - Mini-courses in Mathematical Analysis 2018, (July 2-6, 2018, University of Padua, Padua, Italy), courses by: Prof. M. Dauge, Prof. A. Seeger, Prof. I. Stratis, Prof. V. Vespri.
  • 2017 - Working Seminar in Complex Analysis and Potential Theory, (November 22, 2017, Department of Mathematics of Aberystwyth University, UK).
  • 2017 - Ser Cymru COFUND Workshop on Pure and Applied Mathematics, November 20, 2017, Department of Mathematics of Aberystwyth University, Aberystwyth, UK.
  • 2017 - ISAAC 2017, 11th International Society for Analysis, its Applications and Computation Congress, August 14-18, 2017, Vaxjo, Sweden.
  • 2017 - Mini-courses in Mathematical Analysis 2017, (June 12-16, 2017, University of Padua, Padua, Italy), courses by: Prof. G. Auchmuty, Prof. J. Bennett, Prof. A. Kirsch, Prof. D. Natroshvili.
  • 2016 - IMSE 2016, 14th International Conference on Integral Methods in Science and Engineering, (July 25-29, 2016, University of Padua, Padua, Italy).
  • 2016 - Mini-courses in Mathematical Analysis 2016, (June 27 - July 01, 2016, University of Padua, Padua, Italy), courses by: Prof. B. Colbois, Prof. J. Duoandikoetxea, Prof. P. Sjogren.
  • 2016 - BFA 2016, Boundary value problems, Functional equations and Apllication, 3rd meeting, April 20-23, 2016, Rzeszow, Poland.
  • 2015 - ISAAC 2015, 10th International Society for Analysis, its Applications and Computation Congress, August 3-8, 2015, Macau, China SAR.
  • 2015 - Hypercomplex Seminar 2015, (Hyper)Complex and Dynamical Processes, Modelling and Simulations (30 years of the direct cooperation agreement Lodz - Roma), July 2-9, 2015, Bedlewo, Poland.
  • 2015 - International Conference of Young mathematicians, June 3-6, 2015, Kyiv, Ukraine.
  • 2014 - International Conference "Differential equations, computational mathematics, theory of functions and mathematical methods of mechanics", April 23-24, 2014, Kyiv, Ukraine.
  • 2013 - International Conference "Complex Analysis, Potential Theory and Applications", August 19-23, 2013, Kyiv, Ukraine.
  • 2013 - ISAAC 2013, 9th International Society for Analysis, its Applications and Computation Congress, August 5-9, 2013, Krakow, Poland.
  • 2012 - International Conference dedicated to 120-th anniversary of Stefan Banach, September 17-21, 2012, Lviv, Ukraine.
  • 2012 - AMADE 2012, 7th International Workshop "Analytical Methods of Analysis and Differential Equations", September 10-15, 2012, Minsk, Belarus.
  • 2016 - Assistant to the organization of IMSE 2016, 14th International Conference on Integral Methods in Science and Engineering, July 25-29, 2016, University of Padua, Padua, Italy.
  • Ukrainian - native language
  • Russian - near native language
  • English - fluent
  • Italian - basic