14th International Summer School on Geometry, Mechanics and Control
Organizing Committee
 Angel Ballesteros (Universidad de Burgos, Spain)
 Alfonso Blasco (Universidad de Burgos)
 Leonardo Colombo (ICMAT, Madrid, Spain)
 Iván GutiérrezSagredo (Universidad de Burgos, Spain)
 Edith Padrón (Universidad de La Laguna, Spain)
Scientific Committee
 Anthony Bloch (University of Michigan, USA)
 Jair Koiller (Fundação Getulio Vargas, Brazil)
 Manuel de León (Instituto de Ciencias Matemáticas (CSICUAMUC3MUCM), Spain)
 Juan Carlos Marrero (Universidad de La Laguna, Spain)
 Eduardo Martínez (Universidad de Zaragoza, Spain)
 Miguel Muñoz Lecanda (Universidad Politécnica de Cataluña, Spain)

Accommodation no later than April 30, 2020.

Application for scholarship no later than April 30, 2020.

Abstract submission for short talks/posters no later than May 15, 2020.

Registration no later than June 1, 2020.
A limited number of scholarships for PhD students, advanced undergraduate students, and postdocs, will be provided by the Organisation in order to partially cover the travel and/or lodging expenses.
If you want to apply for a scholarship, please send your CV including names for recommendation letters (and a transcript in case you are an undegraduate student) to mathematicalphysicsubu.es, no later than April 30, 2020.
The fee for PhD students, postdocs and retired scientists is 80 Euros.
Prize of the single room: 141,9 eur (5 nights, breakfast and VAT included).
Applications for reservations have to be sent to mathematicalphysicsubu.es by April 30, and will be considered in a first come basis.
No alternative dates have been decided yet. Any relevant information will appear here as soon as possible.
Lec 2: The free final time optimal control problem and the statement of the Pontryagin Maximum Principle (PMP). Start the proof: Temporal and Spatial perturbations
Lec 3: The propagation of the perturbed trajectory, convexity arguments, the adjoint system and the separating hyperplane
Lec 4: Completion of the proof and two examples: the minimum time problem for a translating mass, and the linearquadratic regulator problem.
Lec 5: From the continuous time to discrete time: The Boltyanski Maximum Principle for discrete time systems; incorporation of constraints.
“Topics on spectral geometry”, by Alberto Enciso and Álvaro Romaniega (ICMATCSIC)
The main idea behind the noncommutative geometry is to "algebralize" geometric notions and then generalize them to noncommutative algebras. This way noncommutative geometry offers a generalised notion of the geometry. Quantum groups or Hopf algebras play the role of 'group objects' in noncommutative geometry and they provide a 'quantum groups' approach to the development of the theory much as Lie groups do in differential geometry. The term "quantum group" first appeared in the theory of quantum integrable systems and later was formalized by V. Drinfeld and M. Jimbo as a particular class of Hopf algebras with connection to deformation theory (as deformation of universal enveloping Lie algebra). Such deformations are classified in terms of classical rmatrix satisfying the classical YangBaxter equation.
We will start with the quantization of PoissonLie groups (i.e. Lie groups equipped with a Poisson structure) which provide a natural example of quantum groups. Other examples of Hopf algebras arising from Lie algebras through their universal enveloping algebras will also be discussed. The deformation procedure via Drinfel'd twist (2cocycle) and some examples of deformed Hopf algebras will be presented together with the twisted deformation of the differential calculus.