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Dear colleagues,

During my recent visit France I was asked to distribute through 
Reduce electronic forum the announcement given below.

Vladimir Gerdt

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ERCIM

Advanced 5-day course on
PARTIAL DIFFERENTIAL EQUATIONS AND GROUP THEORY
New perspectives in computer algebra and engineering sciences

April 6-10, 19
1992
Bonn, Germany

INRIA, Institut National de Recherche en Informatique et en Automatique
GMD,Gesellschaft fur Mathematik und Datenverarbeitung

PURPOSE OF THE COURSE

Ordinary differential control theory studies input/output relations
defined by systems of ordinary differential equations (ODE). The
various concepts that can be introduced (controllability,
observability, invertibility,...)must be tested on formal objects
(matrices, vector fields,...) by means of formal operations (product,
bracket, rak,...) but without appealing to the explicit intergration
of the given ODE. However, certain problems (invariance, equivalence,
linearization, ...) lead to systems of partial differential equations
(PDE). More generally, partial differential control theory studies
input/output relations defined by systems of PDE (mechanics, ther
modynamics, hydrodynamics,...) but new algorithms are needed in order
to extend the classical approch. Also mathematical physics is based
on deifferential identities arising in the theory of PDE and groups
of transformation but exterior or tensor calculus and Lie group
theory are not sufficient.

Meanwhile but independently, the formal theory of systems of PDE has
been created and developped during the years 1960-1975 under the
impulsion of D.C.  Spencer in USA. It intends to study the spaces of
solutions of systems of PDE without integrating them explicitly.
However, though his work supersedes the classical approach (M. Janet,
E. Cartan) it is still largely unknown by mathematicians and has
never been applied by physicists.

The aim of the first part of this course is to provide a self-
contained introduction to these methods in the case of linear and non
linear systems of PDE. In particular, we shall show on specific
examples coming from engineering sciences, how these new tools
(diagram chasing, Spencer cohomology,...) exactly furnish the proper
algorithms for applications. These algorithms will be presented in
such a way as to give the possibility to use computer algebra(
MACSYMA,REDUCED,MAPLE,...) for the intrinsic study of all types of
formal problems involving PDE or purely algebraic equations.

However, Spencer also introduced the formal theory of PDE in order to
study Lie pseudogroups, namely groups of transformations solutions of
systems of PDE. Hence, we may conceive that the already quoted
techniques must also open a new way for computer algebra, linking the
integration of PDE to the theory of Lie pseudogroups.

The purpose of the second part of this course will be to give a brief
introduction to differential algebra and the Galois theory for
systems of algebraic PDE simply called "Differential Galois Theory".
We shall insist on the constructive aspect through many explicit
examples.

Program
Day 1 Monday April 6th. 1992
Outline of the course
Homological algebra (sequences and diagrams)
Jet theory (fibered operations, jet bundles)
Nonlinear systes (1) (Symbol, Spencer cohomology)

Day 2 Tuesday April 7th. 1992
Nonlinear systems(II) formal integrability
Nonlinear systems (III) differential algebra
Applied sessio (I) explicit computations
Applied session(II) explicit computations
An algorithm for theorem proving in
differential geometry (G. CARRA FERRO, ITALY)

Day 3, Wednesday April 8th. 1992
Linear systems (linear Janet and Spencer sequences)
Applied session(III) linear elasticity revisited
Applied session(IV) explicit computations
Prolongation algebras of nonlinear PDE
P. GRAGERT(Germany)
The computer algebra package CRACK for investigating
PDE (T. WOLF, GERMANY)

DAY 4, Thursday April 9th. 1992
Group theory(I) Lie groups and pseudogroups
Group theory (II) differential invariants
Groupe theory (III) nonlinear Janet and Spencer sequences
Group theory (IV) cascade integration
Generalized symmetries (P. KERSTEN, THE NETHERLANDS)

Day 5, Friday April 10th. 1992
Applied session (V) analytical mechanics revisited
An algorithm for determining the size of symmetry
groups (F. SCHWARZ, GERMANY)
Perspectives (I) Differential Galois theory
Perspectives (II) continuum physics

COURSE MATERIAL
Lecture notes (300 pages)
Copies of overhead transparencies
Reprints on selected course topics

GENERAL INFORMATION

Course Director : J.F. Pommaret (Center of Applied Mathematics
at Ecole Centrale des Ponts et Chaussees)

Secretariat	:M. Dresen,
Tel : 49 2241 14 27 76
Fax : 49 2241 14 26 18
Email : dresen@gmdzi.gmd.de

Schedule :
	Monday-Friday 9:30 - 12:30
	             14:00 - 17:00
	Tuesday,Wednesday,Thursday
		      9:30 - 12:30
		     14:00 - 18:00

Location :
	GMD, Schloss Birlinghoven
	5205 SANKT AUGUSTIN (near Bonn), GERMANY

Course fee:
	Ecus 600 (value added tax will not be charged for this
course), including course material, refreshments, party on monday
April 6 and dinner on wednesday April 8th.

Registration :
	The number of participants is limited so early registration
is advised. Upon receipt of your registration form, confirmation
additional information and invoice will be sent.

Hotel accomodation :
It is difficult to find accomodation in the area at that
period. Rooms in two conveniently located hotels
have been reserved from Sunday April 5th. at a reasonable
price of 75DM per day breakfast included.

Cancellation :
No reimbursement of the registration fee willbe made for
cancellations received less than two weeks before the first
day of the course.
Cancellations received earlier will be reimbursed less 10%
administrative charges
The organizers reserve the right to cancel the course in case
of insufficient participation.

REGISTRATION FORM

PDE and GROUP THEORY

NAME :...................First Name : ...........
Affiliation:		Department : ..........
Address: ...............Postal code:.............
City: ..................Country: ...............
Tel: ...................Fax:...................
Email : ................
Send me a hotel reservation form at the above mentioned address:
I am arriving by car O	by train O	by plane O

Date and signature

RETURN TO

GMD
Mrs. M. DRESEN
Institut fur methodische Grundlagen (F1 P)
Postfach 1316
W- 5205 SANKT AUGUSTIN 1
GERMANY
email: dresen@gmdzi.gmd.de


For more information please contact with

Annick Theis-Viemont
email: theis@nuri.inria.fr

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