13th International ICMAT Summer School on Geometry, Mechanics and Control

INVITED TALK:

Roberta Ghezzi (Institut de Mathématiques de Bourgogne, France): Jacobi fields in sub-Riemannian geometry.

In Riemannian geometry, Jacobi fields along geodesics are defined as solutions of Jacobi equation, which involves the curvature tensor. Using a Lagrangian point of view, a classical result states that Jacobi fields are projections of solutions of the complete lift (to the double tangent) of the optimal control problem associated with the length-minimization problem on the base manifold. In a sub-Riemannian manifold M the metric tensor is only defined on a (nonholonomic) sub-bundle of TM and there is no analogous to the Levi-Civita connection. As a consequence, there is not a direct correspondent of Jacobi equation. Nevertheless, by a Hamiltonian approach which amounts to study the Legendre transformed optimal control problem on T^*M, Agrachev-Barilari-Rizzi provide in [Memoires AMS 2018] a notion of "Jacobi curve" on sub-Riemannian geodesics. Starting by the aforementioned interpretation of Jacobi fields in Riemannian geometry, we provide a new interpretation of Jacobi curves in sub-Riemannian geometry leading to the analysis of a Hamilton equation on T^*TM, from which a notion of sub-Riemannian curvature can be extracted. 

This is a joint work with D. Iglesias Ponte, J.C. Marrero, E. Padron 

SHORT TALKS:

Jacob Goodman (ICMAT, Spain): On the existence and uniqueness of Poincaré maps for systems with impulsive effects.

Ernesto Aranda Escolástico (University of Almería, Spain): Targeted formation control of Lagrangian systems with time delay.

Alexandre Simoes (ICMAT, Spain): Exact discrete Lagrangian for nonholonomic mechanics: an open problem.

Miguel Ángel Berbel (Instituto de Ciencias Matemáticas, Spain): Reduction (by stages) of Lagrange-Poincaré bundles.

Víctor M. Jiménez (ICMAT, Spain): Groupoids and distributions with applications to material bodies.

José Luis Carmona (Universidad Complutense de Madrid, Spain): Locally homogeneous Riemannian spaces.

Joaquim Brugués Mora (Universitat Politècnica de Catalunya, Spain): The construction of Floer homology.

Anastasia Matveeva (Universitat Politècnica de Catalunya, Spain): Quasi-Hamiltonian spaces and complex-valued moment maps.

Julia Lange (University of Warsaw, Poland): Foliated PDE Lie systems.

Iván Gutiérrez Sagredo (Universidad de Burgos, Spain): Quantum observers from Poisson-Lie geometry.

Daniel Wysocki (University of Warsaw, Poland): Gradations, Grassmann algebras and solutions to the classical Yang-Baxter equation.

POSTERS:

Verónica Arroyo Rodríguez (Universidad Politécnica de Madrid-ICMAT, Spain): Control-oriented learning for formation control of mechanical systems.

Jordi Gaset (Universitat Politècnica de Catalunya, Spain): k-contact formalism: a framework for field theories with dissipation.

Enric Florit Simón (ICMAT-Univesitat Politècnica de Catalunya, Spain): A decentralised strategy for collision avoidance of multi-agent systems on a Riemannian manifold.

Sándor Hajdú (University of Antwerp, Belgium): Stability aspects of Lagrangian systems with symmetry.

David Iglesias Ponte (University of La Laguna, Spain): Dirac geometry and integration of Poisson quotients.

Manuel Lainz (ICMAT, Spain): Singular Lagrangians and precontact Hamiltonian systems.

Konstantina Panagiotidou (Hellenic Army Academy, Greece): New tensor fields of real hypersurfaces in non-flat complex space forms.

Rafael Ramírez (Universitat Rovira i Virgili, Spain): On the integrability of vector fields in R^N.

Rodrigo Sato (ICMAT, Spain): A variational derivation of the forced Euler-Lagrange equations and applications to error analysis.

Omayra Yago Nieto (Universidad Politécnica de Madrid-ICMAT, Spain): Inexact interpolation of the centroid for the formation of a team of quadrotors.