Category Archives: research

conf

Summer school on geometrical methods in control theory and mathematical physics.

Wisła, Poland
August 28- September  6, 2017
Organizing Committee
A. Barszcz, P.Kowalski, J.Smit, R.
Szymczyk, M.Ułan
poster_gm2017_web

 The following topics are planning to discuss:

Introduction to contact geometry with applications by VALENTIN LYCHAGIN (University of Tromsø, Norway)

  1. Contact and symplectic structures on manifolds, their interaction and main examples.
  2. Contact and symplectic transformations and Lie algebras of contact and Hamiltonian vector fields. Generating functions and Poisson, Lagrange, Jacobi brackets.
  3. Lagrangian and Legendrian manifolds, caustics.
  4. Exterior algebras and analyse on contact and symplectic manifolds.
  5. Contact geometry and PDEs: Partial differential equations of the 1st order.
  6. Contact geometry and PDEs: Partial differential equations of the 2nd order.
  7. Symmetries, conservation laws, singularities and shock waves for solutions of PDEs.
  8. Contact Geometry and variational calculus.
  9. Contact Geometry and Thermodynamics. Legendrian manifolds and thermodynamic states, phase transitions.
  10. Contact structures in visual cortex and neurogeometry. Differential invariants and the problem of image recognition.

Variations, Geometry and Physics by OLGA ROSSI(University of Ostrava, Czech Republic):
We shall present foundations of the calculus of variations on manifolds.
The main focus will be on a modern setting for Euler-Lagrange and
Hamilton theory, including constraints, symmetries and conservation
laws. We shall give examples and applications in geometric mechanics and
control theory, as well as in variational field theories, and discuss
geometries arising from variational equations.

School fee* is 350 EUR
*The fee includes meals, accommodation (2 beds rooms with private bathroom) and lectures. 
To apply please send an e-mail to office@baltinmat.eu or fill the registration form.
Your request will be considered by the Organizing Committee. 

Financial Support
We expect that some support will be available to fund students and other young researchers. If you are requesting financial support, please complete the registration form and send a pdf of your CV as soon as possible.

The Organizing Committee can be contacted for any question and suggestion via the e-mail address: office@baltinmat.eu

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Satellite Thematic Session: 6th European Congress of Mathematics

Description:

Besides pure mathematics, most challenging and difficult problems in the modern mathematical and theoretical physics belong to the realm of nonlinear PDEs and related algebraic and geometrical structures. New methods of geometrical theory of PDEs, explicitly or implicitly based on Secondary Calculus and the language of differential calculus over commutative algebras, have already manifested their high efficiency in approaching above problematics.

The scope of this Thematic Session is, from one side, to discuss recent developments in the modern geometry of nonlinear partial differential equations with a special emphasis on new techniques based on Secondary Calculus, as well as the recent progress in the theory of solution singularities of nonlinear PDEs and in formal integrability theory, and, from another side, the related Poisson-like structures emerging in this context such as algebroids, multiple Lie algebra structures, etc. A special attention will be given to actual and perspective of applications to geometry, physics and mechanics.

This STS will take place on one afternoon during the 6th European Congress of Mathematics. The exact day and time as well as the venue will be set later by the Congress organizers. Participants are supposed to register to the Congress.

Speakers:

  1. A. VINOGRADOV, Levi-Civita institute, President, Italy
  2. J. GRABOWSKI, Institute of Mathematics, PAN, Poland
  3. J. KIJOWSKI, Center for Theoretical Physics, PAN, Poland
  4. M. Eugenia ROSADO MARĺA, Universidad Politécnica de Madrid, Spain
  5. E. VISHNYAKOVA, Ruhr-Universitat Bochum, Germany
  6. N. PONCIN, Université du Luxembourg, Louxembourg
  7. G. MARMO, Università degli Studi di Napoli Federico II, Italy
  8. D. CATALANO-FERRAIOLI, Universidade Federal da Bahia (UFBA) – Brazil
  9. GAETANO VILASI, Universitа degli Studi di Salerno, Italy

Schedule: http://www.6ecm.pl/en/programme/schedule

 Monday, July 2

Satellite Thematic Sessions – all at AGH University of Science and Technology:
16:15-20:15 (Room 12, A3)

Reports:

  1. A. VINOGRADOV
  2. J. GRABOWSKI
  3. J. KIJOWSKI
  4. GAETANO VILASI

Friday, July 6

Satellite Thematic Sessions – all at AGH University of Science and Technology:
9:00-13:00 (Room 12, A3)

Reports:

  1. M. Eugenia ROSADO MARĺA
  2. E. VISHNYAKOVA
  3. D. CATALANO-FERRAIOLI
  4. V.S. KALNITSKY*

* to be confirmed 

Abstracts

  1. A. VINOGRADOV, “Assembling Lie algebras from lieons” Abstract: Any finite-dimensional Lie algebra can be assembeled from two “elementary particles”, called lieons. This fact will be explained and illustrated together with some other results of Lie algebra “chemistry”.
  2. J. GRABOWSKI, “Tulczyjew triples in mechanics and field theories”
  3. J. KIJOWSKI, “Jets of solutions of variational PDS’s: fundamental symplectic structure and basic properties”
  4. M. Eugenia ROSADO MARĺA, “Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism”
  5. E. VISHNYAKOVA, “On the splitting problem for a complex homogeneous supermanifold”
  6. N. PONCIN, “Lie infinity algebroids, higher morphisms and symmetries”
  7. G.MARMO, TBA
  8. D. CATALANO-FERRAIOLI, “Contact Geometry of Parabolic Monge-Ampere Equations”
  9. GAETANO VILASI, “Einstein metrics with 2-dimensional Killing leaves: Geometric and Physical Aspects”

This Thematic Session is related to a satellite conference:

XV Summer Diffiety
Gdynia, Poland
16-28 July, 2012
www.levi-civita.org