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, Reducibility of zero curvature representations with
Acta Appl. Math.,83 (2004) 39–68.
M. Marvan and A. Sergyeyev, Recursion operator for the
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 sl2-valued zero curvature representation,
J. Phys. A: Math. Gen.35 (2002) 9431–9439;
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,
I.S. Krasil'shchik and M. Marvan, Coverings and integrability of the
Gauss–Mainardi–Codazzi equations, Acta Appl. Math. 56
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 sl2, in: Proc. Conf. Secondary Calculus and
Cohomological Physics, Moscow.
M. Marvan, Another look on recursion operators, in: Differential
Geometry and Applications, Proc. Conf. Brno, 1995 (Masaryk University,
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,
M. Marvan, On the C-spectral sequence with "general"
in: Differential Geometry and Its Applications, Proc. Conf. Brno,
Czechoslovakia, Aug. 27–Sept. 2, 1989 (World Scientific, Singapore, 1990)
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.