Welcome to XV International ICMAT Summer School on Summer School on Geometry, Dynamics and Field theory, organised by the Geometry, Dynamics and Field theory Network.

The fifteenth edition of the International Summer School on Summer School on Geometry, Dynamics and Field theory will be held at La Cristalera, in Miraflores de la Sierra, in Madrid, Spain, in July 10-11, 2023.

The school is oriented to young researchers, Ph.D. and postdoctoral students in Mathematics, Physics and Engineering, in particular those interested in focusing their research on geometric control and its applications to mechanical and electrical systems, and optimal control. It is intended to present an up-to-date view of some fundamental issues in these topics and bring to the participants attention some open problems, in particular problems related to applications.

Undegraduate students and master students are also welcome!!!

This year the courses will be delivered by:

  • Arjan van der Schaft (Groningen University, The Netherlands) Course title: The geometry of port-Hamiltonian systems
  • Alejandro Cabrera (Universidade Federal do Rio de Janeiro-UFRJ, Brasil Brazil) Course title: About the structure of local symplectic groupoids
    - Sumary:
    The aim of this minicourse is to present some results about the explicit description of the structure of a local symplectic groupoid integrating a given Poisson manifold M, with an eye on using these to obtain discretizations of flows on M. We will first define local groupoids, describe the symplectic case and its relation to Poisson structures on the space of units and present examples. Then, we will show how, starting with M and an auxiliary choice of Poisson spray, to construct a local symplectic groupoid structure on T*M and obtain a generating function for it. We will also review results involving explicit asymptotic formulas for these structures in the case M=R^n.