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.
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
H. Baran and M. Marvan, Classification of integrable Weingarten
surfaces possessing an sl(2)-valued zero curvature representation,
Nonlinearity, 23 (2010) 2577–2597.
H. Baran and M. Marvan,
On integrability of Weingarten surfaces: a forgotten class
J. Phys. A: Math. Theor.42 (2009) 404007
full text
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
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
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.
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
M. Marvan and A. Sergyeyev, Recursion operator for
Nizhnik–Novikov–Veselov equation,
J. Phys. A: Math. Gen.36 (2003) L87–L92,
Annotation,
full text
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,
Annotation,
full text
(subscribers), preprints:
DIPS
and
solv-int
M. Marvan, On the horizontal gauge cohomology and
non-removability of the spectral parameter,
Acta Appl. Math.,72 (2002) 51–65,
Annotation,
preprint:
DIPS
M. Marvan, Geometric aspects of S-integrability, in:
Proc. Seminar Diff. Geom., Math. Publ. 2
(Silesian University, Opava, 2000) 131–144.
Annotation
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
M. Marvan, A direct procedure to compute zero-curvature
representations. The case sl_{2},
in: Proc. Conf. Secondary Calculus and Cohomological Physics,
Moscow, Aug. 24–31, 1997.
Annotation,
full text in
ELibEMS
M. Marvan, Some local properties of Bäcklund relations,
Acta Appl. Math.54 (1998) 1–25.
Annotation
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
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
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
M. Marvan, On the horizontal cohomology with general coefficients,
Rend. Circ. Mat. Palermo Ser. II,22 (1989) Suppl.,
161–170.
Annotation
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
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