Advanced 5day course
VARIATIONAL SEQUENCES AND BICOMPLEXES
August 2024, 2001
Opava, Czech Republic
organized by the Mathematical Institute of the Silesian University
in Opava.
The course takes place immediately before
8th International Conference on
Differential Geometry and Its Applications (2731 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

email: anderson@math.usu.edu


Prof. Demeter Krupka

Mathematical Institute

Silesian University at Opava

Bezrucovo nam. 13, 746 01 Opava

Czech Republic

email: Demeter.Krupka@math.slu.cz


Prof. Alexander Verbovetsky

Diffiety Institute

Independent University of Moscow

Bolshoi Vlasevsky Pereulok, Dom 11, Moscow

Russia

email: verbovet@mccme.ru

PROGRAM OF THE COURSE
Group Invariant Solutions to Differential Equations and Reduction of
Variational Bicomplexes (I. M. Anderson)

1. Simple Gmanifolds 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 Cspectral 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.
2024 August

Monday morning: Registration and detailed schedule information

Morning: lectures

Afternoon: discussions, excursions.
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:
email: 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 0653, if calling from outside the town).