Program

The conference will consist in three courses given by renowned researchers, short talks aimed at young researchers, and a poster session.

You can download the schedule of the workshop here and the booklet here.

Mini-courses

• Maria Teresa Chiri (Queen's University)

Title: Optimal control of propagation fronts and moving sets

Reaction-diffusion equations are widely used to describe phenomena such as population dynamics and the spreading of invasive species. In this course will consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population, and derive a simpler model describing the controlled evolution of a contaminated set. First, we analyze the optimal control of 1-dimensional traveling wave profiles. Using Stokes’ formula, explicit solutions are obtained, which in some cases require measure-valued optimal controls. Then we will introduce a family of optimization problems for a moving set and show how these can be derived from the original parabolic problems, by taking a sharp interface limit. Assuming that the initial contaminated set is convex, we prove that an eradication strategy is optimal if and only if at each given time the control is active along the portion of the boundary where the curvature is maximal.

References:

A.Bressan, M.T. Chiri, and N.Salehi, On the optimal control of propagation fronts, Math. Models Methods Appl. Sci.  32 (2022), 1109--1140.

A.Bressan, M.T. Chiri, and N.Salehi, Optimal control of moving sets. J. Differential Equations,  361, (2023), 97--137.

S.Bianchini, A.Bressan, M.T. Chiri, Optimal Solutions for a Class of Set-Valued Evolution Problems, Submitted (2023)

• Jordi Gaset (CUNEF University)
  Title: Elements of Geometric Field Theory

Geometric field theory was born in the latter half of the XX century, with the objective of extending the success of symplectic geometry from classical mechanics to classical field theories. This mini-course will present the core con- cepts underlying current lines of investigation in Geometric Field Theory. We will start with the geometric notion of a field, and continue with the formal- ization of variational principles and field equations. Then, we will delve into the problem of defining the appropriate bundle of momentum. After introduc- ing the notions of symmetry and conserved quantity, we will conclude with an incursion into the ongoing search for an adequate bracket structure.

• Agustin Moreno (Heidelberg University)
  Title: A modern symplectic approach to the restricted three-body problem

In this mini-course, I will survey recent advances and new perspectives in the classical (circular, restricted) three-body problem, from the point of view of modern symplectic geometry. I will touch upon theoretical aspects, as well as its applications in connection to astrodynamics and trajectory design for space missions. The material will be taken from the author's recent book draft.

Contributed talks

• Carlos Barrera-Anzaldo (University of Padova)
  Title: Uniform bifurcation: Finding an infinitely many periodic solutions in perturbed Lagrangian systems

• Ronen Brilleslijper (Vrije Universiteit Amsterdam)
  Title: Generalizing fundamental results from symplectic geometry to field theory

• Oscar Carballal (Universidad Complutense de Madrid)
  Title: Curvature-dependent reductions of contact Lie systems on curved spaces 

• Irene De Blasi (University of Torino)
  Title: Billiards with Keplerian potentials: reflective and refractive case

• Rubén Izquierdo (UNIR)
  Title: Graded structures of classical field theory

• Arnau Mas (ICMAT)
  Title: Differential geometry beyond manifolds

• Antonio Michele Miti (Università La Sapienza, Roma)
  Title: Constraint Algebras of Multisymplectic Observables

• Damiano Rigo (University of Verona)
  Title: Geometric methods for aircraft planning and control

• Luca Schiavone (University of Napoli)
  Title: A multisymplectic coisotropic embedding theorem for Geometric Field Theories

• Kenzo Yasaka (University of Antwerp)
  Title: Exterior differential systems on Lie algebroids