THE DIFFIETY SCHOOL

From October 23, 2007, all information
about Diffiety schools can be found
on http://school.diffiety.org


Last updated March 5, 2008
The annual International Diffiety School was founded in 1998. The School are designed to form a step-by-step introduction to the methods and ideology of Diffeotopy and Secondary Calculus, in particular, to a number of mathematical theories, such as the theory of infinite dimensional jet manifolds, contemporary differential geometry and topology, Lie groups and algebras, commutative and cohomological algebra.


The aim of the school is 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

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. There are strong indications that secondary calculus may become 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.

Initial ideas of the area can be got from the books:

  1. J. Nestruev: Smooth manifolds and Observables . - Springer-Verlag, Graduate Texts in Mathematics, Vol. 220, 2002.
  2. Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. - AMS, Mathematical Monographs, Vol. 182, 1999.
  3. A. M. Vinogradov: Cohomological Analysis of Partial Differential Equations and Secondary Calculus. - AMS, Mathematical Monographs, Vol. 204, 2001.
  4. I. S. Krasil'shchik and A. M. Verbovetsky: Homological methods in equations of mathematical physics. - Open Education, Opava, 1998, 150 pp. See also Diffiety Inst. Preprint Series, DIPS 7/98.
1998 – 2007 schools
The first Russian school (Pereslavl-Zalessky, January 26 - February 5, 1998).

The first Italian school (Forino in July 17 - 31, 1998).

The second Russian school (Pereslavl-Zalessky, January 26 - February 5, 1999).

The second Italian school (February 22 - March 3, 1999).

The third (join Russian-Italian) school (Pereslavl-Zalessky, August 17 - 31, 1999).

The fourth Russian school (Pereslavl-Zalessky, January 31 - February 6, 2000).

The fourth Italian school (Forino, July 17 - 29, 2000).

The fifth Russian school (Pereslavl-Zalessky, January 26 - February 5, 2001).

The fifth Italian school (Santo Stefano del Sole, July 19 - 31, 2002).

The sixth Italian school (Santo Stefano del Sole, July 13 - 28, 2003).

The seventh Italian school (Santo Stefano del Sole, July 19 - 31, 2004).

The eighth Italian school (Santo Stefano del Sole, July 16 - August 1, 2005).

The sixth Russian school (Kostroma, January 25 - February 5, 2006).

The ninth Italian school (Santo Stefano del Sole, July 14 - 31, 2006).

The seventh Russian school (Kostroma, February 1 - 12, 2007).

The tenth Italian school (Santo Stefano del Sole, July 18 - August 3, 2007). (For the last information see here.)

For later schools see http://school.diffiety.org.