Seminar on the Geometry of Differential Equations and Related Topics
In Winter-Spring 2008
the seminar take place
on Wednesdays
in
the building of Independent University of Moscow
(B. Vlasjevskij per., 11), room 308 at 19.10.
The seminar is devoted to algebra and
to geometry of nonlinear differential equations, secondary (quantized) calculus,
etc.
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.