Position Associate Professor,
Deputy director for information technology
Address Mathematical Institute
Silesian University in Opava
Na Rybnicku 1
746 01 Opava, Czech Republic
Phone +420 553 684 662
Fax +420 553 684 680
E-mail

Curriculum

– Undergraduate study at J.E. Purkyne University, Brno, Department of Mathematics (1976–1981).
– Graduate study at Moscow State University, Chair of Higher Geometry and Topology (1983–1987).
– Ph.D. Thesis: "Horizontal cohomology with general coefficients" (Moscow, 1989).
– Habilitation at the Mathematical Institute of the Silesian University, Opava (2000).

Research

The keyword is diffiety, the object of the category of differential equations, introduced by A.M. Vinogradov at the end of seventies. The diffiety structure determines symmetries, conservation laws, zero-curvature representations, recursion operators, Bäcklund transformations, and many invariants of partial differential equations.

Memberships

– A member of the Diffiety Institute.

Projects

Jets — a set of Maple procedures for routine computations on jet spaces and diffieties. Emphasis is laid on solution of equations in total derivatives, linear and nonlinear, such as those determining infinitesimal symmetries, generating functions of conservation laws, zero-curvature representations, etc.

List of publications

  1. H. Baran and M. Marvan, Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation, Nonlinearity, 23 (2010) 2577–2597.
  2. H. Baran and M. Marvan, On integrability of Weingarten surfaces: a forgotten class J. Phys. A: Math. Theor. 42 (2009) 404007 full text
  3. M. Marvan, On the spectral parameter problem. Acta Appl. Math. 109 (2010) 239–255.
  4. M. Marvan, Sufficient set of integrability conditions of an orthonomic system. Foundations of Computational Mathematics 9 (2009) 651-674.
  5. M. Marvan and O. Stolín, On local equivalence problem of spacetimes with two orthogonally transitive commuting Killing fields, J. Math. Phys. 49 (2008), no. 2, 022503, 17 pp. Preprint LANL arXiv: 0709.4185
  6. M. Marvan, A.M. Vinogradov and V.A. Yumaguzhin, Differential invariants of generic hyperbolic Monge–Ampère equations, Cent. Eur. J. Math. 5 (2007) 105–133. Preprint LANL nlin.SI/0604038
  7. M. Marvan and M. Pobořil, Recursion operator for the IGSG equation, Fundam. Prikl. Mat. 12 (2006) (7) 117–128 (in Russian); English translation: J. Math. Sci. (N. Y.) 151 (2008) 3151–3158. Preprint LANL nlin.SI/0605015
  8. H. Baran and M. Marvan, A conjecture concerning nonlocal terms of recursion operators, Fundam. Prikl. Mat. 12 (2006) (7) 23–33 (in Russian); English translation: J. Math. Sci. (N. Y.) 151 (2008) 3083–3090.
  9. M. Marvan, Sufficient set of integrability conditions of an orthonomic system: Extended abstract, in: J. Calmet, W.M. Seiler and R.W. Tucker (eds.), Global Integrability of Field Theories, Proc. GIFT 2006, Cockcroft Inst., Daresbury, November 1–3, 2006 (Universitätsverlag, Karlsruhe, 2006), 243–247.
  10. M. Marvan, A.M. Vinogradov and V.A. Yumaguzhin, Differential invariants of generic hyperbolic Monge–Ampère equations, Russian Acad. Sci. Dokl. Math. 405 (2005) 299–301 (in Russian); English translation: Doklady Mathematics 72 (2005) 883–885.
  11. M. Marvan, Recursion operators for the Einstein equations with symmetries, in: Proc. Conf. Symmetry in Nonlinear Mathematical Physics, Kyiv, Ukraine, June 23–28, 2003. Proc. Inst. Math. NAS Ukraine 50 (2004), Part I, 179–183. Annotation.
  12. M. Marvan, Reducibility of zero curvature representations with application to recursion operators, Acta Appl. Math., 83 (2004) 39–68. Annotation, Preprints: DIPS 03/2003 and nlin.SI/ 0306006
  13. M. Marvan and A. Sergyeyev, Recursion operator for Nizhnik–Novikov–Veselov equation, J. Phys. A: Math. Gen. 36 (2003) L87–L92, Annotation, full text
  14. M. Marvan, Scalar second order evolution equations possessing an irreducible sl2-valued zero curvature representation, J. Phys. A: Math. Gen. 35 (2002) 9431–9439, Annotation, full text (subscribers), preprints: DIPS and solv-int
  15. M. Marvan, On the horizontal gauge cohomology and non-removability of the spectral parameter, Acta Appl. Math., 72 (2002) 51–65, Annotation, preprint: DIPS
  16. M. Marvan, Geometric aspects of S-integrability, in: Proc. Seminar Diff. Geom., Math. Publ. 2 (Silesian University, Opava, 2000) 131–144. Annotation
  17. I.S. Krasil'shchik and M. Marvan, Coverings and integrability of the Gauss-Mainardi-Codazzi equations, Acta Appl. Math. 56 (1999) 217–230 Annotation, full text in solv-int
  18. M. Marvan, A direct procedure to compute zero-curvature representations. The case sl2, in: Proc. Conf. Secondary Calculus and Cohomological Physics, Moscow, Aug. 24–31, 1997. Annotation, full text in ELibEMS
  19. M. Marvan, Some local properties of Bäcklund relations, Acta Appl. Math. 54 (1998) 1–25. Annotation
  20. M. Marvan, Another look on recursion operators, in: Differential Geometry and Applications, Proc. Conf. Brno, 1995 (Masaryk University, Brno, 1996) 393–402. Annotation, full text in ELibEMS
  21. M. Marvan, On zero curvature representations of partial differential equations, in: Differential Geometry and Its Applications, Proc. Conf. Opava, Czechoslovakia, Aug. 24–28, 1992, Math. Publ. 1 (Silesian University, Opava, 1993) 103–122. Annotation, full text in ELibEMS
  22. M. Marvan, On the C-spectral sequence with "general" coefficients, in: Differential Geometry and Its Applications, Proc. Conf. Brno, Czechoslovakia, Aug. 27–Sept. 2, 1989 (World Scientific, Singapore, 1990) 361–371. Annotation
  23. M. Marvan, On the horizontal cohomology with general coefficients, Rend. Circ. Mat. Palermo Ser. II, 22 (1989) Suppl., 161–170. Annotation
  24. M. Marvan, A note on the category of partial differential equations, in: Differential Geometry and its Applications (Communications), Proc. Conf. Brno, Czechoslovakia, Aug. 24–30, 1986 (J.E. Purkyne Univ., Brno, 1987) 235–244. Annotation
  25. M. Marvan, On global Lepagean equivalents, in: Geometrical Methods in Physics, Proc. Conf. on Differential Geometry and its Applications, Nove Mesto na Morave, Sept. 5–9, 1983 (J.E. Purkyne Univ., Brno, 1984) 185–190. Annotation
  26. M. Marvan, On covarieties of coalgebras, Arch. Math. (Brno) 21 (1985) 51–64. Annotation