• Andrei Agrachev (SISSA-ISAS, Italy)
  Dissipative systems and infinite horizon variational problems

  We are going to discuss the long-time behaviour of mechanical systems with an isotropic friction. Such a system admits a natural least action principle with the time-varying Lagrangian. We study the long-time behaviour in the Euler representation.
  The Euler representation means that an observer is sitting in the given point of the configuration space and is measuring velocity of the particle passing the point. The "long-time" means that time spent by the particle to arrive to the point at the moment of the measurement is much bigger than the initial velocity of the particle.
  We are interested in the limiting value of the velocity as the ratio <time>/<absolute value of the initial velocity> tends to infinity. The limit exists at every point and forms a smooth potential vector field that has a natural variational and geometric characterization if the friction is sufficiently strong.
  Critical value of the friction has a geometric meaning: bigger "the curvature of the system" stronger friction we need to guarantee the existence of the limiting velocity. Another important tool besides the curvature is partially hyperbolic dynamics. The topic is indeed an interplay of Geometry, Dynamics, and Optimal Control. I am going to explain all necessary background (mainly in the expositary style).
  

• Dmitry Alekseevsky (University of Hull, England)
  Conformal Geometry and Vision

  The first 2 lectures contain an elementary exposition of conformal geometry of the sphere, (including theory of conformal circles («conformal geodesics») and conformal curves); basic facts of contact and symplectic geometry.
  Two last lectures are devoted to application of conformal geometry to vision. One lecture gives a short description of basic facts of early vision: basic principles, transformation of information in retina, retinotopic conformal map from retina to LGN and visual V1 cortex.
  The last lecture gives an exposition of some geometric models: Petitot contact model of V1 cortex, Petitot-Citti-Sarti symplectic model, Bressloff-Cowan spherical model of hypercolumns and some unification of these models.
  

• Jean-Paul Gauthier (LSIS, France)
  Motion Planning in the Sub-Riemannian Context

  A sub-riemannian metric being given, I shall give a series of lectures about the problem of approximating or interpolating a non-horizontal curve by an horizontal one. These approximations or interpolations are constructed explicitly, with applications to robotics and more generally to the control of nonholonomic kinematic systems.
  

• Yanqi Qiu (LATP, France)
  Determinantal Point Processes

  In this lecture, I will first recall the materials on the theory of determinantal point processes and then I will mainly focus on the tolerance and rigidity phenomenon in the sense of Ghosh and Peres for several interesting determinantal point processes.
  

• Stanislav Smirnov (Université de Genève, Switzerland)

  TBA

Докладчики:

• Evgeny Abakumov (University Paris-Est, France).
  On growth of holomorphic embeddings in Cn
  
• Alexander Bufetov (Steklov Mathematical Institute of RAS, Russia)
  The Borodin-Olshanski Problem and Determinantal Point Processes
  
• Alexey Klimenko (Steklov Mathematical Institute of RAS, Russia)
  Josephson Equation: Nontrivial non-Generic Behaviour of Arnold Tongues
  
• Tatiana Smirnova-Nagnibeda (Université de Genève, Switzerland)
  Substitutional Dynamics and Spectra of Graphs Associated with Grigorchuk’s Group of Intermediate Growth