info@viam.science.tsu.ge (+995 32) 2 30 30 40 (+995 32) 2 18 66 45

Riemann-Hilbert problems on Riemann surfaces and invariants of holomorphic bundles (FR17-96)


Funded by

SRNSFGShota Rustaveli National Science Foundation of Georgia

Start Date: 2017-01-31       End Date: 2020-01-30

Project members:

Talks

  • ON THE SPLITTING TYPE OF THE TWO RANK VECTOR BUNDLES ON RIEMANN SPHERE , by Gega Gulagashvili (Speaker) at XXXI International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU) Dedicated to the 110th Birthday Anniversa, 2017, Tbilisi, Georgia.
  • Analytic differential equations on plane and equilibria of point charges., by Gia Giorgadze (Speaker) at 20st international workshop on computer algebra. JINR, Dubna, Russia, 2018, Dubna, Russia.
  • ON THE COMPLEX STRUCTURES OF VECTOR BUNDLES INDUCED FROM FUCHSIAN SYSTEM, by Gega Gulagashvili (Speaker) at XXXII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, 2018, Tbilisi, Georgia.
  • Some properties of generalized singular Coushy-Riemann systems, by Gia Giorgadze (Speaker) at 12st ISAAC Congress, Aveiro University, Portugal, 2019, Aveiro, Portugal.
  • On the partial indices of piecewise matrix functions, by Gia Giorgadze (Speaker) at Factorisation of matrix functions: New techniques and applications, 2019, Cambridge, UK.
  • On the problem of computation the partial indices of matrix. , by Gia Giorgadze (Speaker), Gega Gulagashvili at 21st International workshop on Computer algebra. JINR, Dubna, Russia, 2019, Dubna, Russia.
  • On the type of splitting of vector fibrationon the Riemann sphereinduced by hypergeometric equation., by Gega Gulagashvili (Speaker) at XXXIII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (ESSVIAM2019), 2019, Tbilisi, Georgia.
  • On the algorithm for computing the splitting type of holomorphic vector bundles on Riemann sphere, by Gega Gulagashvili (Speaker) at X ANNUAL INTERNATIONAL CONFERENCE OF THE GEORGIAN MATHEMATICAL UNION, 2019, Batumi, Georgia.
  • On the splitting type of vector bundles on the Riemann sphere induced from second order fuchsian system , by Gega Gulagashvili (Speaker) at XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, 2020, Tbilisi, Georgia.
  • On the algorithm for computation of partial indices of a piecewise constant matrix function. , by Gia Giorgadze (Speaker) at 22nd Workshop on Computer Algebra (Online) JINR, Dubna, Russia , 2021, Dubna, Russia.

Publications

  • Gia Giorgadze, On the structure of the space of generalized analytic functions, Bull. Georg. Natl. Acad. Sci 12 (4), Georgian National Academy of Sciences, 2018.
  • Giorgi Akhalaia, George Giorgobiani, Gega Gulagashvili, The analysis of vortex equations using methods of generalized analytic function, Bulletin of TICMI, 22 (2), 135-141, Tbilisi University Press, 2018.
  • Gega Gulagashvili, ON THE SPLITTING TYPE OF VECTOR BUNDLE ON THE RIEMANN SPHERE, Proceedings of I. Vekua Institute of Applied Mathematics, Vol. 68, 36-45, Tbilisi University Press, 2018.
  • Giorgi Akhalaia, Gia Giorgadze, Giorgi Makatsaria, Nino Manjavidze, Deformation of Complex Structures and Boundary Value Problem with Shift, Analysis as a Life, Dedicated to Heinrich Begehr on the Occasion of his 80th Birthday, Part of the Trends in Mathematics book series (TM), Birkhäuser, 1-17, Springer, 2019.
  • Gega Gulagashvili, HOLOMORPHIC TYPE OF VECTOR BUNDLES ON THE RIEMANN SPHERE INDUCED FROM SECOND ORDER FUCHSIAN SYSTEMS, Proceedings of I. Vekua Institute of Applied Mathematics, Vol. 69, 35-46, Tbilisi University Press, 2019.
  • Gia Giorgadze, Gega Gulagashvili, Riemann-Hilbert Boundary Value Problem with Piecewise Constant Transition Function, Journal of Dynamical and Control Systems, 1-11, Springer, 2020.
  • Gia Giorgadze, Giorgi Khimshiashvili, On three point charges on a flexible arc, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., vol.177, p. 63-68, Steklov Mathematical Institute RAS, 2020.
  • Gia Giorgadze, Gega Gulagashvili, On the splitting type of holomorphic vector bundles induced from regular systems of differential equation, Georgian Mathematical Journal, 29(1): 25–35, Walter de Gruyter GmbH, 2022.