This school was organized also in cooperation with
- Istituto Italiano per gli Studi Filosofici
- Municipality of Santo Stefano del Sole (AV), Italy
and under the scientific direction of Prof. A. M. Vinogradov
(Universita' di Salerno, Italy, and Diffiety Institute, Russia).
The aim of the school was to introduce undergraduate and graduate
students in Mathematics and Physics, as well as post-doctoral
researchers and other mathematicians into a recently emerged area
of mathematics and theoretical physics:
Secondary calculus is the result of a
natural evolution of the classical geometrical theory of partial
differential equations (PDE) originated by Sophus Lie. In
particular, it allows the construction of a general theory of PDE,
in the same manner as algebraic geometry does with respect to
algebraic equations. It became also clear that secondary calculus
is a natural language for quantum field theory, just in the same
way as standard calculus is for classical physics. From the
mathematical point of view secondary calculus is a complex
mathematical construction putting into a natural interrelation
many parts of modern mathematics such as commutative and
homological algebra, algebraic and differential topology,
differential geometry, etc. The strategic goal of the school
is to involve interested participants into a series of large scale
research programs the Diffiety Institute is launching.
idea of the area can be got from the books:
Symmetries and Conservation Laws for Differential Equations
of Mathematical Physics. - AMS, Mathematical Monographs, volume
A. M. Vinogradov: Cohomological Analysis of
Partial Differential Equations and Secondary Calculus. - AMS,
Mathematical Monographs, volume 204, 2001.
Smooth manifolds and Observables -. MCCME, Moscow, 2000 (in
Russian); Springer-Verlag, New York, 2002 (in English),
Graduate Texts of Mathematics series.
In this edition of the school the following two courses was
Diplomas of participation in the School were handed to all participants.
Moreover, there were examinations for all courses, which were organized as
follows. For each course students received a list of examination problems.
To pass an examination one had to solve reasonably large number of problems.
Students having passed an examination received (or will receive) a diploma
certifying this fact. Students having not passed all examinations yet, can do
this by email. Click here
for school pictures.
During the School there was discussed the following
starting programs, intended to involve interested participants
into our research projects:
Singular Lagrangians and
Differential Invariants: theory
Towards Differential Algebraic
Also there was organized a scientific session on the
base of research interests of the participants.