Advanced 5-day course

VARIATIONAL SEQUENCES AND BICOMPLEXES

August 20-24, 2001 
Opava, Czech Republic

organized by the Mathematical Institute of the Silesian University in Opava.

The course takes place immediately before
8-th International Conference on Differential Geometry and Its Applications (27-31 August 2001).
 
 

 SECOND ANNOUNCEMENT



LECTURES

Group Invariant Solutions to Differential Equations and Reduction of Variational Bicomplexes

Introduction to Variational Sequences

Geometric Aspects of Conservation Laws of Nonlinear Differential Equations

 

LECTURERS

Prof. Ian M. Anderson
Department of Mathematics and Statistics
Utah State University
Logan, Utah 84 322
USA
e-mail: anderson@math.usu.edu
 
Prof. Demeter Krupka
Mathematical Institute
Silesian University at Opava
Bezrucovo nam. 13, 746 01 Opava
Czech Republic
e-mail: Demeter.Krupka@math.slu.cz
 
Prof. Alexander Verbovetsky
Diffiety Institute
Independent University of Moscow
Bolshoi Vlasevsky Pereulok, Dom 11, Moscow
Russia
e-mail: verbovet@mccme.ru
 

PROGRAM OF THE COURSE

Group Invariant Solutions to Differential Equations and Reduction of Variational Bicomplexes (I. M. Anderson)
1. Simple G-manifolds and their generalizations
2. Introduction to Vessiot - a Maple package for differential geometry on jet spaces
3. The kinematic reduction diagram
4. Reduction of variational bicomplexes
5. The principle of symmetric criticality
6. The method of moving frames
7. Examples and applications
8. The variational bicomplex for PDE in the plane
Introduction to Variational Sequences (D. Krupka)
1. Introduction to finite order variational sequences
2. Discussion of recent results


Geometric Aspects of Conservation Laws of Nonlinear Differential Equations (A. Verbovetsky)

1. Introduction
2. Infinite jet spaces and nonlinear differential equations
3. Calculus of fields and forms over infinite prolongations
4. Conservation laws and horizontal cohomology
5. Vinogradov's C-spectral sequence on jets and differential equations
6. Geometric methods in Lagrangian formalism
7. Conservation laws and symmetries: Noether theorems, Hamiltonian structures of evolution differential equations

SCHEDULE

19 August (Sunday): Arrival day

20 August (Monday) 8:30 am: Registration and detailed schedule information, lecture hall B5 on the main floor of the Silesian University building Bezrucovo nam. 13. The lectures will start at about 9:00 am on Monday.

20-24 August

25 August (Saturday): Departure day

CONTACT:

If you have any questions, concerns or difficulties, do not hesitate to contact the facilitator Tomas Kopf directly or at:

e-mail: Tomas.Kopf@math.slu.cz

office phone: 684354 (please, do not leave messages on the message system as they are inaccessible due to technical problems)

home phone: 616823

(The area code of Opava is 0-653, if calling from outside the town).