The following topics are planning to discuss:
Introduction to contact geometry with applications by VALENTIN LYCHAGIN (University of Tromsø, Norway)
- Contact and symplectic structures on manifolds, their interaction and main examples.
- Contact and symplectic transformations and Lie algebras of contact and Hamiltonian vector fields. Generating functions and Poisson, Lagrange, Jacobi brackets.
- Lagrangian and Legendrian manifolds, caustics.
- Exterior algebras and analyse on contact and symplectic manifolds.
- Contact geometry and PDEs: Partial differential equations of the 1st order.
- Contact geometry and PDEs: Partial differential equations of the 2nd order.
- Symmetries, conservation laws, singularities and shock waves for solutions of PDEs.
- Contact Geometry and variational calculus.
- Contact Geometry and Thermodynamics. Legendrian manifolds and thermodynamic states, phase transitions.
- 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 email@example.com or fill the registration form.
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