May 14, 2008:
A. Verbovetsky (Moscow)
Marvan's approach to the spectral parameter problem.
May 7, 2008:
R. Vitolo (Lecce, Italy)
On differential equations characterized by their Lie point symmetries. Abstract:
We study the geometry of differential equations determined uniquely
by their point symmetries. The action of the infinitesimal group
of point symmetries foliates the jet space where the equation live.
Equations which are uniquely determined by their point symmetries
are of two types: they either coincide with a leaf of the part of
the jet space where the action is regular or they coincide with
the singular subset of the action. Many examples are provided,
ranging from minimal submanifolds and geodesics to Monge-Ampere
equations and some of their generalizations.
April 16, 2008:
Yu. N. Bratkov (Moscow)
The hyperbolic Monge-Ampère equation: classical solutions on the whole
plane.
April 9, 2008:
M. F. Prokhorova (Ekaterinburg)
Graphene and the Atiyah–Singer index theorem.
April 2, 2008:
Paul Kersten (University of Twente, The Netherlands)
The Monge-Ampere equation: Hamiltonian and symplectic structures,
recursions. Abstract:
After a short introduction/description of equation structure and l- and
l*-covering, we describe as a quite complicated application: Monge-Ampere
equation. Results for Hamiltonian, symplectic and recursion structures are
obtained in a "standard" and "straight-forward" way, demonstrating the
intrinsic power of the geometrical picture.
March 26, 2008:
A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?VI.
March 12, 2008:
V. A. Yumaguzhin (Pereslavl)
On the obstruction to integrability of an almost complex structure.
March 5, 2008:
V. N. Chetverikov (Moscow)
An estimate for the order of inverse differential operator in one independent
variable.
February 27, 2008:
Ilja Miklaszewski (Moscow)
Formal solvability of overdetermined systems of differential equations. II.
February 20, 2008:
Ilja Miklaszewski (Moscow)
Formal solvability of overdetermined systems of differential equations. I.
February 13, 2008:
O. I. Morozov (Moscow)
Symmetry pseudo-groups and coverings of differential equations. Abstract:
My talk will be devoted to recent results about relations between
Maurer-Cartan forms of symmetry pseudo-groups and coverings of differential
equations. Examples will include the r-dmKP equation and Plebanski's second
heavenly equation.
February 6, 2008:
R. Vitolo (Lecce, Italy)
Gauge invariance, charge conservation, and variational principles. Abstract:
In this talk I will present new results on the correspondence between
symmetries, conservation laws, and variational principles for field
equations in general non-abelian gauge theories, obtained jointly
with Gianni Manno and Juha Pohjanpelto. Our main result states
that second order field equations possessing translational and
gauge symmetries and the corresponding conservation laws are always
derivable from a variational principle. Counterexamples show that
the above result fails in general for third order field equations.
December 19, 2007:
A. Kiselev (Moscow)
Operator-valued involutive distributions of evolutionary vector fields and
their affine geometry.
November 21, 2007:
R. A. Sarkisyan (Moscow)
Local classification problems in analysis according to Arnold. II.
November 14, 2007:
I. Men'shov (Moscow)
Some questions of hydrodynamic stability of vortical structures.
November 7, 2007:
R. A. Sarkisyan (Moscow)
Local classification problems in analysis according to Arnold. I. Abstract:
For any pseudogroup D acting on any manifold P there is a natural way
to define the jet spaces J^{k} and J^{∞} and to prolong the action
of D on J^{k} and J^{∞}. The Poincare series for every point of
J^{∞} may be defined too. For each "local classification problem
of analysis" naturally arise the corresponding pseudogroup D acting
on corresponding manifold P and we consider the prolong the action
on J^{k} and J^{∞}. V. I. Arnold proposed the following question:
Is it true that the Poincare series are a rational function
of t for almost any f (any f that does not belong to some set Z of
co-dimension infinity in the space J^{∞})?
Followig theorem guaranties only that codim Z is more or equal to 1.
Theorem. There is a dense set V (maximal stratum) in the
corresponding infinite jet space J^{∞} which is a disjoint
union of finite number of open sets V_{1},...,V_{S} (atoms) such that
any two points belonging to the same atom have the same Poincare
series and these series are rational.
This allows one to prove the Tresse theorem for each point of V.
Among other results we emphasize the following ones:
In principle one can explicitly derive conditions defining each
atom from Lie pseudogroup equations (using finite number of
differentiations and algebraic operations).
In principle for each atom the corresponding Poincare series can
be computed explicitly.
In principle basic invariants and invariant differentiations for
each point of the maximal stratum can be computed explicitly (using
differentiations, algebraic operations and solution of systems of
algebraic equations via implicit function theorem).
We shall discuss also some relating questions concerning
pseudogroups.
October 10, 2007:
D. Tunitsky (Moscow)
Differential geometric structures associated with Monge-Ampère equations.
October 3, 2007:
I. Krasil'shchik, V. Golovko (Moscow)
Parallel computations for the Camassa–Holm equation.
September 26, 2007:
E. Beniaminov (Moscow)
Quantization as approximate description of a diffusion process.
September 19, 2007:
Sergey Igonin (Utrecht, The Netherlands)
Coverings and the fundamental group in the category of differential equationsV.
September 12, 2007:
A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?V.
June 13, 2007:
Sergey Igonin (Utrecht, The Netherlands)
Coverings and the fundamental group in the category of differential equationsIV.
March 7, 2007:
I. S. Krasil'shchik (Moscow)
On the structures related to a 3rd-order Monge-Ampere equation. Abstract: Symmetries, conservation laws, Hamiltonian and symplectic structures for a
3rd-order Monge-Ampere equation are described.
March 21, 2007:
V. Poberezhny (Moscow)
Isomonodromic deformations.
March 7, 2007:
I. S. Krasil'shchik (Moscow)
The the work Differential-geometric invariants of the Hamiltonian systems of
pde's by O. Bogoyavlenskij [Commun. Math. Phys. 265 (2006), 805-817].
February 21, 2007:
A. Verbovetsky (Moscow)
Kruglikov-Lychagin multi-brackets(after paper arXiv:math.DG/0610930).
February 14, 2007:
V. Tolstoy (Moscow)
Extremal projectors for algebras and superalgebras Lie.
February 7, 2007:
I. S. Krasil'shchik (Moscow)
On some nonlinear differential equations. Abstract: Computational problems related to particular nonlinear differential
equations will be exposed and discussed.
January 10, 2007:
Sergey Igonin (Bonn, Germany)
Coverings and the fundamental group in the category of differential equationsIII.
November 15, 2006:
A. Verbovetsky (Moscow)
The Marvan theorem on sufficient set of integrability conditions of an
orthonomic system.
November 8, 2006:
Discussion of I. S. Krasil'shchik's talk "How to commute nonlocal shadows?" of
September 27.
November 1, 2006:
V. Golovko (Moscow)
Poisson-Nijenhuis structures for nonlocal operators.
October 25, 2006:
Gerard Helminck (University of Twente, the Netherlands)
A flag variety relating matrix hierarchies and Toda-type hierarchies. Abstract: Commutative subalgebras of the complex k × k-matrices are
known to generate both matrix and Toda-type hierarchies. In this
talk a certain class of infinite chains of closed subspaces of a
separable Hilbert space H will be introduced. To each such a
flag one associates a sequence of solutions of the matrix hierarchy
related to this subalgebra. They compose to a solution of the
lower triangular Toda hierarchy corresponding to the transposed
algebra. Both solutions can be expressed in determinants of
suitable Fredholm operators, the so-called τ-functions.
These last functions also have a geometric interpretation in terms
of line bundles over the flagvariety. They measure the failure
of equivariance w.r.t. to the commuting flows of certain global
sections.
October 18, 2006:
R. A. Sarkisyan (Moscow)
On the regularity theorem and the Tresse theorem for Lie pseudogroups. II.
October 11, 2006:
R. A. Sarkisyan (Moscow)
On the regularity theorem and the Tresse theorem for Lie pseudogroups. I.
October 4, 2006:
M. Pavlov (Moscow)
WDVV equation and its solutions. Abstract: We consider WDVV equation derived by Marshakov, Mironov, Morozov.
We found new set of solutions using some symmetry approaches.
September 27, 2006:
I. Krasil'shchik (Moscow)
How to commute nonlocal shadows? Abstract: The problem of a well-defined commutator for shadows of nonlocal symmetries is discussed.
September 20, 2006:
O. I. Morozov (Moscow)
Coverings of differential equations and Cartan's structure theory of Lie
pseudo-groups.II.
September 13, 2006:
O. I. Morozov (Moscow)
Coverings of differential equations and Cartan's structure theory of Lie
pseudo-groups.I. Abstract:
We establish relations between Maurer-Cartan forms of symmetry
pseudo-groups and coverings of differential equations. Examples
include Liouville's equation, the Khokhlov-Zabolotskaya equation,
and the Boyer-Finley equation.
June 21, 2006:
Sergey Igonin (Bonn, Germany)
Coverings and the fundamental group in the category of differential equationsII. Abstract:
In the category of PDEs there is a notion of coverings, which generalize Bæcklund transformations and Lax pairs from
soliton theory. As is well known, in topology the fundamental group is responsible for coverings. In this talk we continue
to describe an analog of fundamental group for coverings in the category of PDEs. This analog is not a group, but a system
of (often infinite-dimensional) Lie algebras.
May 15, 2006:
M. Pavlov (Moscow)
WDVV and hydrodynamic reductions of 2+1 quasilinear equations. Abstract:
We consider hydrodynamic reductions of the dispersionless limit of dKP
equation (as example) for construction of new solutions for WDVV equation.
May 10, 2006 (Wednesday):
M. Pavlov (Moscow)
Integrability and classification of hydrodynamic chains and
corresponding 2+1 quasilinear systems. Abstract:
Several approaches allowing classification of hydrodynamic chains are
presented. Infinitely many particular solutions are found.
April 24, 2006:
V. Golovko (Moscow)
Jacobi bracket on shadows of symmetries and nonlocal Hamiltonian operators.
April 17, 2006:
A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?III.
March 27, 2006:
I. R. Miklaszewski (Moscow)
Basics of topos theoryIII.
March 20, 2006:
P. M. Akhmet'ev (Moscow)
On high-order analogs of magnetic helicity integralII.
March 13, 2006:
Marina Prokhorova (Institute of Mathematics and Mechanics, Ural Branch of RAS)
Structure of the category of parabolic equations. Abstract: The symmetry group is one of the most important notions
in the group analysis
of differential equations. We generalize this notion, introducing a certain
category, whose objects are systems of PDE and their automorphism groups are
the corresponding symmetry groups: our contribution is a proposed notion of a
morphism between the systems. We are mostly interested in a subcategory that
arises from second order parabolic equations on arbitrary manifolds; an
example that deals with nonlinear reaction-diffusion equation is discussed in
detail.
March 6, 2006:
Sergey Igonin (Bonn, Germany)
Coverings and the fundamental group in the category of differential equations. Abstract: In the category of PDEs there is a notion of coverings, which
generalize Bæcklund transformations and Lax pairs from soliton theory.
As is well known, in topology the fundamental group is responsible for coverings.
In this talk we describe an analog of fundamental group for coverings
in the category of PDEs. This analog is not a group,
but a system of (often infinite-dimensional) Lie algebras.
February 27, 2006:
P. M. Akhmet'ev (Moscow)
On high-order analogs of magnetic helicity integralI.
February 20, 2006:
I. R. Miklaszewski (Moscow)
Basics of topos theoryII.
February 13, 2006:
I. R. Miklaszewski (Moscow)
Basics of topos theoryI.
February 6, 2006:
V. N. Chetverikov (Moscow)
Flat partial differential equations with control on the boundary.
December 19, 2005:
A. M. Lukatsky (Moscow)
Structural geometrical properties of infinite-dimensional Lie groups as
applied to equations of mathematical physics.
December 12, 2005:
A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?II.
December 5, 2005:
A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?I.
November 28, 2005:
I. M. Paramonova (Moscow)
Deformations of Poisson and Buttin Lie superalgebras.
November 21, 2005:
I. R. Miklaszewski (Moscow)
Translation of geometry of differential equations into the language of
algebraIII.
November 14, 2005:
I. R. Miklaszewski (Moscow)
Translation of geometry of differential equations into the language of
algebraII.
November 7, 2005:
I. R. Miklaszewski (Moscow)
Translation of geometry of differential equations into the language of
algebraI.
October 31, 2005:
R. A. Sarkisyan (Moscow)
On the Tresse theorem for geometric structuresV.
October 24, 2005:
R. A. Sarkisyan (Moscow)
On the Tresse theorem for geometric structuresIV.
October 17, 2005:
R. A. Sarkisyan (Moscow)
On the Tresse theorem for geometric structuresIII.
October 10, 2005:
R. A. Sarkisyan (Moscow)
On the Tresse theorem for geometric structuresII.
October 3, 2005:
R. A. Sarkisyan (Moscow)
On the Tresse theorem for geometric structuresI.
September 26, 2005:
V. Poberezhnii (Moscow)
Fuchsian systems: Riemann-Hilbert problem, isomonodromic deformations,
Painlevé equations.
September 19, 2005:
A. Verbovetsky (Moscow)
Involutive systems of differential equations of different orders (after a
paper by B. Kruglikov and V. Lychagin) - arXiv:math.DG/0503124.
September 12, 2005:
J. Krasil'shchik (Moscow)
On the dispersionless Boussinesq equation. Abstract:
The dispersionless Boussinesq equation, which is equivalent to the
Benney-Lax equation, being a system of equations of hydrodynamical
type, is discussed. The results include: a description of local
and nonlocal Hamiltonian and symplectic structures, hierarchies of
symmetries, hierarchies of conservation laws, recursion operators
for symmetries and generating functions of conservation laws
(cosymmetries). Highly interesting are the appearances of operators
that map conservation laws and symmetries to each other but are
neither Hamiltonian nor symplectic. These operators give rise to a
noncommutative infinite-dimensional algebra of recursion operators.
May 16, 2005:
V. A. Yumaguzhin (Pereslavl)
Differential invariants of generic classical hyperbolic
Monge-Ampère equations.
May 12, 2005:
A. Kushner (Astrakhan)
Contact geometry of hyperbolic Monge-Ampère equations.
May 5, 2005:
V. N. Chetverikov (Moscow)
Flat control systems with time delay. Abstract:
The concept of flat system is extended to delay systems. We show how
the flatness of a delay system may be used to track given reference
trajectories with stability. Besides, for every autonomous control
system with time delay we construct a control system without delay.
The flatness of the first system implies the flatness of the second
one. This fact gives a necessary condition for the flatness of delay
systems.
April 25, 2005:
V. N. Chetverikov (Moscow)
A linearization method for problems of flatness and searching compatibility
operatorII.
April 18, 2005:
V. N. Chetverikov (Moscow)
A linearization method for problems of flatness and searching compatibility
operator. I. Abstract: We solve the total parametrization problem for systems
of partial differential equations and the dual problem
of the search of compatibility operators. Our approach
consists of the following two steps. First the
corresponding linear problem is solved. Then the
linearization of a nonlinear solution is selected among
linear solutions. Necessary and sufficient conditions
for the selection are implied by the exactness of a
nonlinear Spencer complex for the pseudogroup of
invertible C-differential operators. The result
about the exactness is formulated. Other applications
of the obtained results are discussed.
April 11, 2005:
V. Golovko (Moscow)
Darboux coverings and their applications to KP hierarchy.
April 4, 2005:
A. Kushner (Astrakhan)
E-structures of Monge-Ampère equations of variable type.
March 28, 2005:
A. Kushner (Astrakhan)
Contact and symplectic invariants of Monge-Ampère equations and
Jacobi systems.
March 21, 2005:
V. L. Chernyshev (Moscow)
Differential equations on geometric graphs. Asymptotic and spectral properties.
March 14, 2005:
A. V. Penskoi (Moscow)
Discrete Lagrangian systems.
March 9, 2005:
Enrique G. Reyes (Santiago, Chile)
Integrability, differential geometry and nonlocal symmetries.
February 28, 2005:
V. Golovko (Moscow)
Deformation of Poisson manifolds of hydrodynamics type.
February 21, 2005:
A. Verbovetsky (Moscow)
Integrable Systems, bihamiltonian approach (part 6).
February 14, 2005:
J. Krasil'shchik (Moscow)
Symmetries, recursion operators, and Hamiltonian structures of
integrable systems. Abstract:
An extensive review of Artur Sergyeyev's recent works will be given.
References:
[1] On recursion operators and nonlocal symmetries of evolution
equations, Proc. Sem. Diff. Geom. (Opava, 2000), D. Krupka ed.,
p.159-173, http://arxiv.org/nlin.SI/0012011
[2] A remark on nonlocal symmetries for the
Calogero-Degasperis-Ibragimov-Shabat equation, J. Nonlinear
Math. Phys., 10 (2003) 78-85, http://arxiv.org/nlin.SI/0309023
(with J.A.Sanders)
[3] On sufficient conditions of locality for hierarchies of symmetries
of evolution systems, Rep. Math. Phys. 50 (2002) 307-314,
http://www-sfb288.math.tu-berlin.de/abstractNew/531
[4] Why nonlocal recursion operators produce local symmetries: new
results and applications, http://arxiv.org/nlin.SI/0410049
[5] A simple way of making a Hamiltonian system into a bi-Hamiltonian
one, Acta Appl. Math., 83 (2004) 183-197,
http://arxiv.org/nlin.SI/0310012
December 27, 2004:
H. M. Khudaverdian (UMIST, Manchester, UK)
Berezinians, Exterior Powers, and Recurrent Sequences.
December 20, 2004:
A. Verbovetsky (Moscow)
Integrable systems, bihamiltonian approach (part 5).
December 13, 2004:
O. I. Morozov (Moscow)
Lie pseudo-groups, Cartan's equivalence method, and symmetries of
differential equations (part 3).
December 6, 2004:
O. I. Morozov (Moscow)
Lie pseudo-groups, Cartan's equivalence method, and symmetries of
differential equations (part 2).
November 29, 2004:
O. I. Morozov (Moscow)
Lie pseudo-groups, Cartan's equivalence method, and symmetries of
differential equations (part 1). Abstract:
A method of computing Maurer-Cartan forms for symmetry pseudo-groups
of differential equations will be described. Examples of applications
will include the contact equivalence of the generalized Hunter-Saxton
equation and the Euler-Poisson equation, and finding basic
differential invariants for the classes of linear hyperbolic equations
and the Abel equations.
November 1, 2004:
A. Verbovetsky (Moscow)
Integrable Systems, bihamiltonian approach (part 4).
October 25, 2004:
A. Verbovetsky (Moscow)
Integrable Systems, bihamiltonian approach (part 3).
October 18, 2004:
A. Verbovetsky (Moscow)
Integrable Systems, bihamiltonian approach (part 2).
October 11, 2004:
A. Verbovetsky (Moscow)
Integrable Systems, bihamiltonian approach (part 1).
May 12, 2004:
V. Golovko (Moscow)
On computation of Poisson cohomology for Hamiltonian operators on jets.
April 28, 2004:
R. A. Sarkisyan (Moscow)
On differential invariants of geometric structures. Abstract:
All objects (functions, manifolds, etc.) and mappings are assumed to be
real and smooth. "Bundle" means locally
trivial fiber bundle.
The following theorem is proved in the first part of the talk:
Theorem 1. Let fiber dimension of the bundle
P --> X of geometric
structures be greater that dimension of base X. As the differential
invariant's order q (i.e., the greatest common degree of derivatives in
differential invariant expression) grows, the number t(q) of general
(i.e., defined for geometric structures in general position)
functionally independent scalar differential invariants of order q grows
to infinity at any general position point of P. An asymptotic lower
bound for t(q) is also given.
Note that for some geometric structures, including Riemann metrics, the
explicit values of t(q) for geometric structures in general position was
found in [1].
A generalization of Theorem 1 exists, in particular for the case of
tensor invariants.
The second part of the talk will deal with special bundles of geometric
structures, i.e., such bundles whose fiber dimension is no greater that
dimension of base.
It will be shown that in the neighborhood of general position point any
special bundle is locally isomorphic to one of 19 standard special
bundles P_{1},..., P_{19}.
The Darboux theorem states that differential 1-form in general position
on X can be locally transformed to canonical form with suitable change
of coordinates. Analogously, nonzero vector field on X can be
straightened. Similar statement is proved for typical special geometric
structures, i.e., for sections in general position of any standard
special geometric structure bundle. Each typical special geometric
structure can be transformed to its own canonical form with suitable
change of coordinates. These canonical forms are found and they are used
to formulate the following theorem:
Theorem 2. Let z be the general position point of some special geometric
structure bundle. Only a finite number of general independent
differential invariants exit at the point z and full collection of such
functionally independent invariants is written down for each of 19
types. Any general differential invariant of special bundle at point z
is a function of invariants from such collection.
Therefore, Theorems 1 and 2 establish a fundamental difference of
differential invariants for special and non-special bundles.
These results apply towards Tresse theorem.
1. T.Y. Thomas The differential invariants of generalized spaces,
Cambridge Univ. Press, 1934;
2nd (textually unaltered) ed. Chelsea, New York, 1991.
June 4, 2003:
V. N. Chetverikov (Moscow)
Nonlinear Spencer complex for invertible differential
operators and compatibility operators.
May 21, 2003:
A. Verbovetsky (Moscow)
On the Zharinov sequence.
April 23, 2003:
A. Verbovetsky (Moscow)
Some bits about involutiveness.
April 16, 2003:
H. Khudaverdian (Manchester, UK)
On geometry of differential operators and odd Laplacians. Abstract:
In this talk we discuss geometrical structures naturally associated
with differential operators acting on functions on a manifold M.
Every such operator defines a bracket on functions and an "upper
connection" in the bundle of volume forms on M. It turns out that
the natural framework here is the algebra of densities of all weights
on the manifold M.
The results are applied to analysis and generalization of
Batalin-Vilkovisky geometry. The talk is based on a joint work with
T. Voronov (arXiv:math.DG/0301236
and arXiv:math.DG/0212311).
April 9, 2003:
V. A. Yumaguzhin (Pereslavl)
On the obstruction to linearizability of 2-order ODEs by point
transformations. Abstract:
In this talk, we discuss the action of pseudogroup of all point
transformations on the bundle F of equations
We calculate the 1-st nontrivial differential invariant of this
action. It is a horizontal differential 2-form on the jet bundle
J^{2}F with values in some algebra. We prove that this form is a
unique obstruction to linearizability of the considered equations by
point transformations. Note that the construction of this invariant
recall the well known construction of structure functions of
prolongations of G--structures.
April 2, 2003:
A. Verbovetsky (Moscow)
Kupershmidt's dark equations.
March 19, 2003:
Paul Kersten (University of Twente, Holland)
All in one: conservation laws for classical KdV-equation.
March 12, 2003:
I. S. Krasil'shchik (Moscow)
A simple method to establish locality of
integrable hierarchies. Abstract:
It is well known that integrable hierarchies are usually
generated by recursion operators containing nonlocal terms
of the D^{-1} type. Thus, dealing with such hierarchies
the problem to establish their locality arises. To see
nontriviality of this problem it is sufficient to have
a look at the beautiful but rather complicated proof for the
KdV hierarchy given in the book by I. Dorfman (Dirac Structures
and Integrability of Nonlinear Evolution Equations, John Wiley
& Sons, 1993, p. 87).
We propose a simple scheme of proving locality for scaling
invariant scalar equation based on graded structure of polynomial
functions on such equations and Green's formula. For more
details see
here.
March 5, 2003:
M. M. Vinogradov (Moscow)
De Rham complex in the diole category (part II).
February 26, 2003:
M. M. Vinogradov (Moscow)
De Rham complex in the diole category (part I).
February 19, 2003:
V. N. Chetverikov (Moscow)
Nonlinear Spencer complex for the group of invertible differential
operators and its applications (part II).
February 12, 2003:
V. N. Chetverikov (Moscow)
Nonlinear Spencer complex for the group of invertible differential
operators and its applications (part I).
October 30, 2002:
A. V. Kiselev (Moscow)
On Toda equations associated to Lie algebras.
October 9, 2002:
A. V. Kiselev (Moscow)
On the Hamiltonian and Lagrangian structures of time-dependent
reductions of evolutionary PDEs
(arXiv:math.DG/0112255
by Monica Ugaglia).
September 18, 2002: A. Verbovetsky (Moscow)
What is the cotangent bundle to a differential equation?
The talk covers a joint work with P. Kersten and I.S.Krasil'shchik
Hamiltonian operators and-coverings.
September 11, 2002: J. Krasil'shchik (Moscow)
On symmetries and cohomological invariants of equations possessing
flat representations.
September 4, 2002: S. Igonin (Yaroslavl, Twente)
Coverings and the fundamental group in the category of differential
equations.
May 6, 2002: Joseph Krasil'shchik (Moscow)
From recursion operators to Hamiltonian structures. The factorization
method. Abstract:
A simple algorithmic method of constructing Hamiltonian structures for
nonlinear PDE will be described. It is based on the geometrical
theory of nonlinear differential equations and is in a sense inverse
to the well-known Magri scheme. As an illustrative example, the KdV
equation and the Boussinesq equation will be discussed. Further
applications include the construction of previously unknown
Hamiltonian structures.
April 24, 2002: A. Kiselev (Moscow)
Bicomplexes and Bæcklund transformations,
an overview of a paper by A. Dimakis and F. Muller-Hoissen
(J. Phys. A 34 (2001), 9163-9194;
arXiv:nlin.SI/0104071).
April 17, 2002: B. Kruglikov Mayer
brackets and solvability of scalar PDEs.
April 3, 2002: V. N. Chetverikov (Moscow)
Covering control systems by flat ones.
March 27, 2002: A. S. Dzhumadildaev (Alma-Ata, Kazakhstan)
N-commutators of vector fields. Abstract: The question whether the N-commutator is a well defined operation on Vect(n) is studied. It is if
N=n^{2}+2n-2. A theory of N-commutators with emphasis on
5- and 6-commutators on two-dimensional manifolds is developed.
March 20, 2002: M. Vinogradov (Moscow) Der-operators and frodules.
March 13, 2002: B. Kruglikov Are there pseudoholomorphic submanifolds of complex dimensions
greater than one?
March 6, 2002: A. Verbovetsky (Moscow) Asymptotic
conservation laws: survey of results (part II).
February 27, 2002: A. Verbovetsky (Moscow) Asymptotic
conservation laws: survey of results (part I).
February 20, 2002: I. V. Tyutin (Lebedev Phys. Inst., Moscow)
The general form of the *-deformations on the Grassman algebra.
December 5, 2001: V. Chetverikov (Moscow)
Secondary calculus framework for some control problems.
November 28, 2001: A. Kiselyov (Moscow)
The variational bicomplex for hyperbolic second-order
scalar partial differential equations in the plane,
an overview of a paper by I. Anderson and
N. Kamran, Duke J. Math. 87(1997), 265--319
(see full text
here).
November 14, 2001: V. Chetverikov (Moscow)
A survey of methods illustrated by the Benny equations,
an overview of a paper by N. H. Ibragimov, V. V. Kovalev,
and V. V. Pustovalov
(math-ph/0109012).
October 31, 2001: R.F.Polischuk (Moscow)
Nonlocal conservation laws in general relativity.
October 24, 2001: Alexander Verbovetsky (Moscow)
Geometry of Voronov-Tyutin-Shakhverdiev operators.
October 10, 2001: Joseph Krasil'shchik (Moscow)
On natural differential equations. Abstract: Dealing with particular differential equation, one can invent them
or take them from Nature. One of the sources of natural equations
is geometry. For example, we can consider equations describing
Poisson structures, flat connections in a certain bundle, integrable
distributions, etc. Equations of this type possess a gauge group and
thus are not "2-line ones".
For example, computing symmetries of the equation that describes
flat connections, Paul Kersten (Univ. of Twente) discovered
a family of symmetries depending on arbitrary functions on infinite
prolongation of this equation. Later, Sergei Igonin constructed a
complex whose 1-st differential delivers symmetries found by
Kersten.
We plan to explain these result in a general context and discuss
some problems arising in relation with natural equations.
October 3, 2001: S. Yu. Dobrokhotov (Moscow)
On the effects of the integrability of Hugoniot-Maslov chains for
vortex singular equations.
December 27, 2000:
V. Trushkov (Moscow)
Symmetries and conservation laws for some hydrodynamic systems
.
December 20, 2000:
V. Chetverikov (Moscow)
New flatness conditions for control systems
.
November 29, 2000:
D. Khangoulyan (Moscow)
Jumping Oscillator (Discontinuous trajectories of Lagrangian
systems with singular hypersurface),
an overview of a paper by F. Pugliese and A. M. Vinogradov
(DIPS 11/98).
November 22, 2000:
A. Verbovetsky (Moscow)
On the geometry of singular Lagrangians,
an overview of a paper by F. Pugliese and A. M. Vinogradov
(DIPS 2/99).
November 15, 2000:
I. S. Krasil'shchik (Moscow)
On integrability of homogeneous scalar evolution equatuins
, an overview of results
Jan Sanders and Jing Ping Wang.
May 31, 2000: V. Yumaguzhin (Pereslavl-Zalesski)
On Monge-Ampere Equations.
May 24, 2000: V. Chetverikov (Moscow)
Bihamiltonian Geometry and Bæcklund-Darboux transformations,
an overview of results by F. Magri, M. Pedroni, G. Falqui,
C. Morosi, G. Tondo, and others. II.
May 17, 2000: V. Yumaguzhin (Pereslavl-Zalesski)
On Classification of Linear ODE up to an Equivalence.
May 10, 2000: V. Soloviev (Protvino)
Boundary Terms in the Field Theory Hamiltonian Formalism.
April 12, 2000: S. Igonin (Yaroslavl)
An overview of paper K. Yamaguchi, Differential systems
associated with simple graded Lie algebras.
Adv. Studies in Pure Math. 22, (1993), 413-494. I.
April 5, 2000: V. Chetverikov (Moscow)
Bihamiltonian Geometry and Bæcklund-Darboux transformations,
an overview of results by F. Magri, M. Pedroni, G. Falqui,
C. Morosi, G. Tondo, and others. I.
March 29, 2000: R. Matyushkin (Moscow) G-invariant
variational bicomplex,
an overview of results by I. Anderson and M. Fells. IV.
March 22, 2000: R. Matyushkin (Moscow) G-invariant
variational bicomplex,
an overview of results by I. Anderson and M. Fells. III.
March 15, 2000: R. Matyushkin (Moscow) G-invariant
variational bicomplex,
an overview of results by I. Anderson and M. Fells. II.
March 1, 2000: R. Matyushkin (Moscow) G-invariant
variational bicomplex, an overview of results by
I. Anderson and M. Fells. I.
February 23, 2000: A. Semenov (Moscow) Quantum SL(2), an overview
of results. III.
February 16, 2000: A. Semenov (Moscow) Quantum SL(2), an overview
of results. II.
February 9, 2000: A. Semenov (Moscow) Quantum SL(2), an overview
of results. I.
January 12, 2000: I. Miklashevsky (Moscow) Some aspects of
formal integrability.
January 5, 2000: V. Trushkov (Moscow),
The WDVV equations, an overview of results. III.
December 29, 1999: V. Trushkov (Moscow),
The WDVV equations, an overview of results. II.
December 8, 1999: V. Trushkov (Moscow),
The WDVV equations, an overview of results. I.
November 24, 1999: J. Krasil'shchik (Moscow), Overview of the paper
On the equivalence problem for partial nonlinear equations
by B. Kruglikov, V. Lychagin. III.
November 17, 1999: J. Krasil'shchik (Moscow), Overview of the paper
On the equivalence problem for partial nonlinear equations
by B. Kruglikov, V. Lychagin. II.
November 10, 1999: 1. S. Igonin (Yaroslavl),
Overview of the paper Fedosov manifolds by I. Gelfand. V. Retakh, M. Shubin.
2. J. Krasil'shchik (Moscow), Overview of the paper
On the equivalence problem for partial nonlinear equations
by B. Kruglikov, V. Lychagin. I.
November 3, 1999: M. Vinogradov (Moscow),
On multiple generalizations of graded Lie algebras and Poisson manifolds.
October 27, 1999: A. A. Verbovetsky (Moscow),
Overview of the paper Decomposition of higher order tangent fields
and calculus of variations by P. J. Alonso.
May 21, 1997: N. Khor'kova (Moscow) A criterion for local action of recursion operators.
May 14, 1997: Ye. Al'berdin (Moscow) Integro-differential equations in quantum statistics.
April 23, 1997: I. Krasil'shchik (Moscow) On SH-algebras and C-spectral sequence.
April 16, 1997: V. Shemarulin (Sarov) Conservation laws and initial-value problems.
April 9, 1997: V. Yumaguzhin (Pereslavl-Zalesski) On reducibility of ODE to $y'''=0$.
April 2, 1997: A. Samokhin (Moscow) On action of vector fields on differential operators.
March 19, 1997: B. Kruglikov (Moscow), On Nijenhujs structures.
March 12, 1997: N. Khor'kova (Moscow), On the Euler equation: bi-hamiltonian structure.
March 5, 1997: B. Kruglikov (Moscow), On connections and quantization.
February 26, 1997: V. Chetverikov (Moscow), On
symmetry approach to integro differential equationsII.
February 19, 1997: I. Krasil'shchik (Moscow),
Generalized Poisson structures and Nambu mechanics III. V. Chetverikov (Moscow), On symmetry approach to integro-differential equations I.
February 12, 1997: I. Krasil'shchik (Moscow),
Generalized Poisson structures and Nambu mechanics (a review of recent
symmetry approach to integro differential equations II.