Assistant Professor at the Silesian University in Opava

- 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" (A. M. Vinogradov, Moscow, 1989)

The keyword is *diffiety*, an 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, Backlund transformations, and many
invariants of partial differential equations.

- 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. - M. Marvan, Reducibility of zero curvature representations with
application to
recursion operators,
*Acta Appl. Math.,***83**(2004) 39–68. Preprints: DIPS 03/2003 and nlin.SI/0306006. - M. Marvan and A. Sergyeyev, Recursion operator for the
Nizhnik–Veselov–Novikov equation,
*J. Phys. A: Math. Gen.***36**(2003) L87–L92. Full text freely available from stacks.iop.org/0305-4470/36/L87. - M. Marvan, Scalar second order evolution equations possessing an
irreducible sl
_{2}-valued zero curvature representation,*J. Phys. A: Math. Gen.***35**(2002) 9431–9439; preprint DIPS–4/2002; LANL nlin.SI/0203043. - Michal Marvan, On the horizontal gauge
cohomology and non-removability of the spectral parameter,
*Acta Appl. Math.***72**(2002) 51–65. - M. Marvan, Geometric Aspects of S-Integrability,
*Proc. Seminar on Differential Geometry, Math. Publications*2 (Silesian Univ. Opava, Opava, 2000) 131–144. - I.S. Krasil'shchik and M. Marvan, Coverings and integrability of the
Gauss–Mainardi–Codazzi equations,
*Acta Appl. Math.*56 (1999) 217–230, LANL solv-int/9812010 - M. Marvan, Some local properties of Baecklund relations,
*Acta Appl. Math.*54 (1998) 1–25. - M. Marvan, A direct procedure to compute zero-curvature representations.
The case sl
_{2}, in:*Proc. Conf. Secondary Calculus and Cohomological Physics*, Moscow. ELibEMS - M. Marvan, Another look on recursion operators, in:
*Differential Geometry and Applications*, Proc. Conf. Brno, 1995 (Masaryk University, Brno, 1996). ELibEMS - M. Marvan, On zero curvature representations of partial differential
equations, in:
*Differential Geometry and Its Applications*, Proc. Conf. Opava, Czechoslovakia, Aug. 24–28, 1992 (Silesian University, Opava, 1993) 103–122. ELibEMS - 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. - M. Marvan, On the horizontal cohomology with general coefficients,
*Rend. Circ. Mat. Palermo Ser. II*,**22**(1989) Suppl., 161–170. - 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.

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

Last updated:October 22, 2004.