New Edition of the Diffiety School
The IV Italian School
Forino (Avellino), ITALY, 17 July -- 29 July 2000
In cooperation with
- Istituto Italiano per gli Studi Filosofici, Naples;
- Diffiety Institute of the
Russian Academy of Natural Sciences;
- Municipality of Forino
and under the scientific direction of
Prof. A. M. Vinogradov
(Universita' di Salerno), we are announcing the
fourth edition of the Diffiety School.
Contents
- On the School (home page)
- On this edition of the School
- Staff of the School
- Beginners' courses
- Veterans' courses
- Our address
On this edition of the School
In this edition the School will offer two series of courses, one for
beginners and one for veterans. Teachers and programs are
listed below. Beginners' course material is the same as first edition
school, and is available here.
We invite interested people to look in our web site or to mail us for information about past editions and
current activities. Here is also a
poster of our
School in .pdf format; it would be of great help for us if you could print
it out and show up in your In
stitution.
Staff of the School
Here follows the list of teachers and tutors in the School:
A. M. Vinogradov, Director (Universita' di Salerno)
V. Chetverikov (Technical University of Moscow)
A. De Paris (Universita' "Federico II" di Napoli)
S. Igonin (Independent University of Moscow)
N. Khorkova (Moscow State Tecnical University "Bauman")
M. Marvan (Silesian University at Opava, Czech Rep.)
A. Verbovetsky (Independent University of Moscow)
M. Vinogradov (Diffiety Institute)
R. Vitolo (Universita' di Lecce)
V. Yumaguzhin (State University of Pereslavl'-Zalessky, Russia)
And here's the organising committee:
C. Bove, F. Canfora,
D. Catalano,
S. Cioffi,
A. De Paris
G. Manno,
B. Prinari,
F. Pugliese,
L. Vitagliano,
R. Vitolo.
Beginners' courses
- General Introduction
- Observation mechanism in classical physics
- Commutative algebrae
- States of a classical system
- Spectra of a commutative algebra
- Spectral theorem (manifolds as spectra of commutative algebrae)
- First order differential calculus on man
ifolds
- Tangent vectors and absolute and relative vector fields. D functor
- Behaviour of tangent vectors and vector fields with respect to
smooth
mappings of manifolds
- The flow of a vector field. Lie derivative of vector fields.
Commutators and Lie algebrae
- Tangent covectors and differential forms. Tensors. Main operations
on
tensors. Algebra of differential forms
- Behaviour of differential forms and covariant tensors with respect
to
differentiable mappings of manifolds. Lie derivatives of covariant
tensors.
- Exterior differential and de Rham cohomology
- Cartan's formula and homotopy property of de Rham cohomology
- Integration theory as de Rham cohomology
- Introduction to differential calculus on commutative
algebrae
- Rings and commutative algebrae. Modules and bi-modules
- Linear differential operators between modules
- Comparison with the analytical definition of differential operator
- Examples of algebraic differential operators
- Bi-module structure in the set of linear differential operators
- Composition of differential operators
- Symbol of a linear differential operator. Algebra of symbols
- Categories and functors, representative objects
- Functors of the algebraic calculus and their representability
- Derivations and multi-derivations
- Differential forms and the de Rham complex
- Interior product and Lie derivative. Comparison with the geometric
approach
Veterans' courses
-
Contact and symplectic multi-valued solutions
of 1st order scalar differential equations
- Elements of symplectic geometry
- Lagrangian Manifolds
- Multi-valued solutions of Hamilton-Jacobi equation
- Elements of contact geometry
- Geometrical interpretation of 1st order scalar differential
operators
- Multi-valued generalized solutions of 1
st order equations
- Relations between symplectic and contact geometry
- R-manifolds and multi-valued solutions of
PDE's
- Jet manifolds and partial differential equations (PDE)
- Geometric interpretation of solutions. R-manifolds
- High order contact transformations
- Extrinsic and intrinsic geometries of PDE
- Singularities of solutions of PDE and associated singularity
equations
- Singularity equations for second order equations in two variables
- Symbols and propagation of singularities
- R-manifolds and generalized functions (distribution). "Quantization
condition"
- Singularity rays, singular R-panes and R-Grassmannians
- Basic functors of differential calculus over
commutative algebras
- Generalities on functors of differential calculus
- Functors Di and Pi and Diff-Spencer complexes
- Algebraic jet-spaces and de Rham complexes
- Spencer-type complexes associated with a differential operator and
differential equations
- (-Spencer type cohomologies and their geometric interpretation
- Higher Spencer and de Rham cohomology
- Green formula
- Algebraic Lagrangian formalism
The deadline has been shifted to 30 June 2000.
As for accommodation, we invite interested people to
read this.
Detailed information on how to reach
Forino is here.
Address
For more details about past edi
tions of the School and current activities,
look in our web site, drop us an e-mail request, fax or phone to us at
- Internet:
http://diffiety.ac.ru
- E-mail: diffiety @ tiros.dmi.unisa.it
- Fax: +39 089 965226
- Telephone: +39 089 965395
Questions and suggestions should go to
diffiety @ tiros.dmi.unisa.it