(Hyper)Complex Function Theory, Dolbeault Cohomology, Fractals, and Physics

(Hyper)Complex Function Theory, Dolbeault Cohomology, Fractals, and Physics

23 - 30 July, 2011, Będlewo

The seminar was organized by Banach Center and University of Łódź.

The main topics of the seminar were:
  1. influence of the Lvov School on generalizations of Complex Analysis (CA) and on General Physical Ideas (GPI),
  2. influence of the Łódź – Paris VI direct cooperation agreement (since 1986) on our results in CA and GPI,
  3. regression, complex and para-quaternionic approximation for crystals, semiconductors, and nanoparticles in nanowires,
  4. para-quaternionic, Clifford-geometrical, Randers-Ingarden, and fractal structures vs. surface and optical properties of crystals,
  5. Clifford, Jordan, and Ingarden geometry in teleparallel equivalents of general relativity and in quantum information theory.

Organizing Committee

  • Pierre Dolbeault (Paris),
  • Ralitza Kovacheva (Sofia),
  • László Kozma (Debrecen),
  • Julian Ławrynowicz (Łódź),
  • Dariusz Partyka (Lublin),
  • Hariton Polatoglou (Thessaloniki),
  • Waldyr A. Rodrigues, Jr. (Campinas, SP)

List of lectures

  1. Address dedicated to Professor Pierre Dolbeault (prof. Zofia Wysokińska, Łódź)
  2. Submanifolds of para-quaternionic manifold (prof. Massimo Vaccaro, Rome)
  3. Twistor theory for CR quaternionic manifolds and related structures (prof. Stefano Marchiafava, Rome)
  4. Introduction of the $\overline\partial$-cohomology (prof. Pierre Dolbeault, Paris)
  5. Taylor expansion and Sobolev spaces (prof. Bogdan Bojarski, Warsaw)
  6. Report on mathematics and physics in Kazan (prof. Evgeny Yashagin, Kazan)
  7. Obituary: Roman Stanislaw Ingarten († July 12, 2011) (prof. László Kozma, Debrecen; Julian Ławrynowicz, Łódź and Lajos Tamássy, Debrecen)
  8. Problems in hypercomplex analysis over some matrix hypercomplex systems (prof. Lilia N. Apostolova, Stancho Dimiev and Peter Stoev, Sofia)
  9. A procedure allowing to decrease the number of terms in a quaternionic polynomial and to check whether two given quaternionic polynomials are identically equal (dr Dmytro Merzheyevskyy, Zhytomyr)
  10. About motion and hypercomplex algebras (dr Alena Khmelnitskaya, Kazan)
  11. Atomic Force Microscopy (AFM) and nanotechnology (prof. Hariton Polatoglou, Thessaloniki)
  12. Study and use of noise for the AFM cantilever response in time and frequency domain (prof. Hariton Polatoglou and mgr Demetra Georgakaki, Thessaloniki)
  13. Synchronous and asynchronous regression structures I (prof. Dariusz Partyka, Lublin and Chelm)
  14. Synchronous and asynchronous regression structures II (prof. Dariusz Partyka, Lublin and Chelm)
  15. Surface relaxation in binary alloys in Valenta-Sukiennicki model vs. the experimental data (mgr Malgorzata Nowak-Kępczyk, Radom)
  16. Linearly convex complex analysis (prof. Yuri Zelinskiĭ, Kyiv)
  17. Is torsion needed in a theory of gravity?- A critical review (prof. Janusz Garecki, Szczecin)
  18. Some extremal problems in nonoverlapping domains with free poles (mgr Iryna Denega, Kyiv)
  19. Model of coupled harmonic oscillators in Zwanzig-type chains (mgr Agnieszka Niemczynowicz, Olsztyn)
  20. Internal and space-time symmetries vs. quaternions and octonions (prof. Kazimierz Jezuita, Warsaw)
  21. Structure fractals and para-quaternionic geometry (prof. Julian Ławrynowicz, Łódź)
  22. On quaternionic analysis applied to force-free magnetic firlds with a non-constant proportionality factor (dr Rodrigo Gómez Mendoza, México)
  23. Biomechanics given from first principles (mgr Krzysztof Pomorski, Cracow and dr Przemyslaw Prokopow, Warsaw)
  24. Transport properties of the firld induced Josephson functions (mgr Krzysztof Pomorski, Cracow and dr Przemyslaw Prokopow, Warsaw)
  25. The problem of regression for the Hilbert space-valued functions (mgr Marek Stojecki, Chelm)


  1. Lilia N. Apostolova (Sofia)
  2. Bogdan Bojarski (Warszawa)
  3. Iryna Denega (Kyiv)
  4. Stancho Dimiev (Sofia)
  5. Pierre Dolbeault (Paris)
  6. Janusz Garecki (Szczecin)
  7. Demetra Georgakaki (Thessaloniki)
  8. Rodrigo Gómez Mendoza (México, D.F.)
  9. Kazimierz Jezuita (Warszawa)
  10. Alena Khmelnitskaya (Kazan)
  11. László Kozma (Debrecen)
  12. Julian Ławrynowicz (Łódź)
  13. Stefano Marchiafava (Roma)
  14. Dmytro Merzheyevskyy (Zhytomyr)
  15. Agnieszka Niemczynowicz (Olsztyn)
  16. Małgorzata Nowak-Kępczyk (Radom)
  17. Dariusz Partyka (Lublin/Chełm)
  18. Hariton Polatoglou (Thessaloniki)
  19. Krzysztof Pomorski (Kraków)
  20. Przemyslaw Prokopow (Warsaw)
  21. Peter Stoev (Sofia)
  22. Marek Stojecki (Chełm)
  23. Lajos Tamássy (Debrecen)
  24. Massimo Vaccaro (Roma)
  25. Zofia Wysokińska (Łódź)
  26. Evgeny Yashagin (Kazan)
  27. Yuri Zelinskii (Kyiv)