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