**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:**

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

- A. VINOGRADOV
- J. GRABOWSKI
- J. KIJOWSKI
- GAETANO VILASI

**Friday, July 6**

**Satellite Thematic Sessions – all at AGH University of Science and Technology:**

9:00-13:00 (Room 12, A3)

Reports:

- M. Eugenia ROSADO MARĺA
- E. VISHNYAKOVA
- D. CATALANO-FERRAIOLI
- V.S. KALNITSKY*

*** to be confirmed**** **

**Abstracts**

- 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”.
- J. GRABOWSKI, “Tulczyjew triples in mechanics and field theories”
- J. KIJOWSKI, “Jets of solutions of variational PDS’s: fundamental symplectic structure and basic properties”
- M. Eugenia ROSADO MARĺA, “Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism”
- E. VISHNYAKOVA, “On the splitting problem for a complex homogeneous supermanifold”
- N. PONCIN, “Lie infinity algebroids, higher morphisms and symmetries”
- G.MARMO, TBA
- D. CATALANO-FERRAIOLI, “Contact Geometry of Parabolic Monge-Ampere Equations”
- 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