# Activity

### Introduction:

**IMPORTANT:**

**The School has bee****n postponed due to the CoVid-19 emergency.**

No alternative dates have been decided yet. Any relevant information will appear here as soon as possible.No alternative dates have been decided yet. Any relevant information will appear here as soon as possible.

**Geometry, Mechanics and Control (GMC) Network**.

**Burgos, Spain, in July 6-10, 2020**(arrival, sunday 5 in the afternoon; departure, friday 10 in the afternoon).

**Undegraduate students and master students are also welcome!!!**

**Venue**: Aula C15, Facultad de Ciencias Económicas y Empresariales, Campus de San Amaro, Universidad de Burgos.

### Important dates:

### Courses:

**"Optimal control and the Maximum Principle"**, by Ravi Banavar (Indian Institute of Technology en Bombay, India)

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 linear-quadratic 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 (ICMAT-CSIC)

**“Introduction to Lie Systems with Compatible Geometric Structures”**, by Javier de Lucas (University of Warsaw)

**“Hopf algebras, quantum groups and non-commutative geometry”**, by Anna Pachol (Queen Mary University of London)

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 r-matrix satisfying the classical Yang-Baxter equation.

We will start with the quantization of Poisson-Lie 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 (2-cocycle) and some examples of deformed Hopf algebras will be presented together with the twisted deformation of the differential calculus.

### Registration:

**The standard registration fee for participants is 160 Euros.**

**The fee for PhD students, postdocs and retired scientists is 80 Euros.**

**registration form**.

### Financial Support:

A **limited number of scholarships** for PhD students, advanced undergraduate students, and post-docs, 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.

### Lodging reservation:

**A limited number of single rooms**will be available at the Colegio Mayor San Jerónimo (https://colegiomayorsanjeronimo.com/), located in the historical center of Burgos.

**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.

### Committees:

Organizing Committee

- Angel Ballesteros (Universidad de Burgos, Spain)
- Alfonso Blasco (Universidad de Burgos)
- Leonardo Colombo (ICMAT, Madrid, Spain)
- Iván Gutiérrez-Sagredo (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 (CSIC-UAM-UC3M-UCM), Spain)
- Juan Carlos Marrero (Universidad de La Laguna, Spain)
- Eduardo Martínez (Universidad de Zaragoza, Spain)
- Miguel Muñoz Lecanda (Universidad Politécnica de Cataluña, Spain)