The seminar takes place on Fridays in Santo Stefano del Sole (Avellino),
Piazza del Sole, 3, at 11.00.
The seminar is devoted to algebra and geometry of nonlinear differential
equations,
secondary (quantized) calculus, etc. and addresses to under- and
post-graded students.
July 9, 2005: The potential formula for trivial Lagrangians.
July 2, 2005: Bicomplex structure in CE0 and expicit computation of the
d1 differential.
May 25, 2005: Computing cohomologies Lp(κ) of the subcomplex
CDiff(p)alt(κ;)
of CDiff(p)(κ;) via the action of the symmetric group
Sp.
May 19, 2005: Computing cohomologies of the complex
Diff(P1,...,P1;Λ*).
May 12, 2005: Techniques for computing the E1 term of the C-spectral sequence
and its differential. Skew-adjoint multi-C-differential operators acting
on κ. Generalized Euler operators. Solution of the inverse problem of
the Calculus of Variations, and historical facts.
April 21, 2005: Action of differential operators on the Berezin module. property
of adjoint operators and the linear Green formula. Application of the C-Green
formula to variational problems.
April 14, 2005: Introducing the E1 term of the C-spectral sequence and its
differential. Euler operator and Euler-Lagrange equations. Theory of adjoint
operators, arising as cochain maps of suitable differential operators complexes.
First and second class constraints, restricted symplectic form, Dirac bracket,
modified Poisson bracket. Relationship between Legendre transformation and
Green formula. Secondary Poisson structures.
April 07, 2005: Introducing "common" conservation laws, and conserved currents.
Generalized conservation laws. Control problem in PDEs. Basic operations
on the E0 term of the C-spectral sequence. The distribution of cones associated
with a constrained Lagrangian system. A counterexample to Dirac's conjecture.
February 17, 2005: Computation of symmetries for PDE.
Universal linearization operator, understood as a secondary universal derivation.
Higher symmetries of PDE, with examples.
February 4, 2005: Contact fields. Lie fields on J∞.
Coordinate description. Generating functions and generating sections. Evolutionary
derivations and corresponding Poisson bracket. Introducing the Lie algebra κ
of higher symmetries of J∞, and C-differential operators.
January 20, 2004: Some topics in Differential Topology.
January 14, 2005: Introducing the Cartan distribution
on J∞ and the corresponding C-spectral sequence.
)
of CDiff(p)(κ;