Institute of Physics Belgrade
University of Belgrade
About the Institute
Short history
Virtual tour
How to reach us
Graduate School

:: home :: news


14.11.2008. :: IX Winter Diffiety School


School in Geometry of Partial Differential Equations and Secondary Calculus

Kostroma, Russia.
February 1-12, 2009.

The aim of the permanent Diffiety School is to introduce undergraduate and Ph. D. students in Mathematics and Physics as well as post-doctoral researchers in a recently emerged area of Mathematics and Teoretical Physics:


A diffiety is a new geometrical object that properly formalizes the concept of the solution space of a given system of (nonlinear) PDEs, much as an algebraic variety does with respect to solutions of a given system of algebraic equations. Secondary Calculus is a natural diffiety analogue of the standard Calculus on smooth manifolds, and as such leads to a very rich general theory of nonlinear PDEs. It appears that it is this the only natural language of quantum physics, just as the standard Calculus is for classical physics.

The School is organized by:

Levi-Civita Institute (; Foundation "Science against ages"; Istituto Italiano per gli Studi Filosofici (; Diffiety Institute (

With the participation of the Mathematics and Mechanics Faculty of the
Saint Petersburg State University, and under the scientific direction
of Prof. A. M.Vinogradov (Università di Salerno, Italy, and Diffiety Institute, Russia).

In this edition of the School, four courses will be proposed.
The general classification of Diffiety School`s courses is as follows:

B-COURSE(S): courses for beginners;
A-COURSE(S): advanced courses;
C-COURSE(S): courses for veteran participants.

Course B0.
Title: Introduction to differential calculus over commutative algebras and geometry of smooth manifolds.

Course B1.
Title: Differential calculus over commutative algebras.

Course B2.
Title: Geometric structures in the theory of PDEs.

Course A1.
Title: Basic differential complexes and cohomology.

Course A2.
Title: Introduction to Secondary Calculus: symmetries, conservation laws and Lagrangian formalism.

Further activities.
In addition, some special lectures and seminars will be organised for veterans.


Kostroma (Russian: Кострома́) is a historic city in central Russia, administrative centre of the Kostroma Oblast. A part of the Golden ring of the Russian towns, it is located at the confluence of the rivers Volga and Kostroma, 65 km east of Yaroslavl. Detailed information about the actual location of the school in Kostroma and how to reach it will be duly given later on.

Application, Selection and Admission

To apply, please choose among the registration forms the one which better fits your personal profile, and fill it in all its compulsory fields. Applicants will be selected by the Director of the School, prof. A. M. Vinogradov. During the selection phase, applicants may be requested to provide their curriculum and/or scientific background. Selection criteria are mainly based on the following: participants are required to be familiar with fundamentals of Commutative Algebra, Topology and Differential Geometry (see the next section: Prerequisites). Admitted participants will be duly informed by e-mail. The school, including a full board accomodation in double room in a hotel (see, is free for admitted participants. Travel expenses are on charge of participants.

DEADLINE: Application must be sent not later than Sunday, 18th of January, 2009.


Suitable fundamentals for a fruitfull participation in the school may be
found in the following references:

* M. F. Atiyah, I. G. MacDonald, - Introduction to Commutative Algebra, -Westview Press, 1969, Chapters 1,2. A beginner participant should be able to solve exercise from these two chapters.

* John M. Lee, - Introduction to Smooth Manifolds, - Springer-Verlag, Graduate Texts in Mathematics, Vol. 218, 2003. Appendix + Chapters 1-4, 6(Chapter 1 is also available on the author`s web page).

* Jet Nestruev, - Smooth manifolds and Observables . - Springer-Verlag,
Graduate Texts in Mathematics, Vol. 220, 2002. First chapters of this book will introduce you to the spirit of the school.

People who have read this book and solved 70% of the exercises will be able to follow the veteran courses.

Accommodation, Meals and Classes

Participants will lodge in double room and have meals in the

Sanatorij "Kostromskoj"
micro-rajon Malyshkovo,
156011 Kostroma, RUSSIA.
Exact geographical coordinates are: 57° 43`45" N, 40° 55`27" E, 117m a.s.l., planet Earth.
You may also be interested at the Russian web site

Classes and seminars will take place in the Sanatorij itself. A detailed schedule of the school activities will be published later.

Organizing committee:

M. Bachtold, V. Kalnitsky, G. Moreno, M. M. Vinogradov, L. Vitagliano.

Questions and suggestions should be sent to the e-address:
Institute of Physics Belgrade - Pregrevica 118 - 11080 Belgrade - Serbia, Switchboard: +381 11 3713000, Fax: +381 11 3162190