# Seminar DGA: Geometric control, sub-Riemannian geometry, and their applications

#### Brno - 08-25-2013/08-30-2013

This Mini-workshop on applications of sub-Riemannian geometry (in Neuroscience etc.) in the next week after the DGA2013 will include following topics:

1. Introduction to geometric control theory

1.1. Control systems

1.2.Controllability

1.3.Optimal control problems

2. Differential geometry

3. Sub-Riemannian structures

4. Chow-Rashevskii theorem

5. Existence of minimizers (Filippov theorem)

6. Pontryagin maximum principle

7. Left-invariant problems on Lie groups

8. Sub-Riemannian problem on Heisenberg group

9. Euler elasticae

10. Sub-Riemannian problem on the group of motions of the plane

11. Applications

11.1.1 Neurogeometry and vision

11.1.2 Geometry, classical mechanics and robotics

11.1.3 Quantum mechanics