**Karine Beauchard: ***Null controllability of hypoelliptic equations*

**Daniel Beltita**: *Dynamical systems and finite-dimensional approximations in Hilbert spaces *

**Lucian Beznea**:* Multiple-fragmentation stochastic processes driven by a spatial flow*

**Yann Brenier**: *Solving the initial value problem for Euler and Burgers equations by convex minimization*

Abstract : We show that it possible to solve the initial value problem by convex optimization:

i) for short times, in the case of the Euler equations of both compressible and incompressible fluids (and more generally for systems of conservation law admitting a convex entropy),

ii) for arbitrarily large time intervals, in the case of Kruzhkov's entropy solutions to the (non-viscous) Burgers equation.

The convex minimization problem is related to the concept of sub-solution in the sense of convex integration theory and can also be interpreted as a kind of generalized variational mean-field game.

**Francis Filbet: ***Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system*

*Résumé : We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlocal reaction-diffusion FitzHugh-Nagumo system. Our approach is based on a relative entropy method, where the macroscopic quantities of the kinetic model are compared with the solution to the nonlocal reaction-diffusion system. This approach allows to make the rigorous link between kinetic and reaction-diffusion models.*

**Paola Goatin**: *Traffic management by macroscopic models*

**Colin Guillarmou: ***On the marked length spectrum of Anosov manifolds*

**Alexandru Kristaly**: *Geometric inequalities: Riemannian vs. sub-Riemannian*

**Mihai Maris**: *On some minimization problems in R^N*

Abstract : We present some recent improvements of the concentration-compactness principle and show that they give a new insight in some minimization problems arising in the study of solitary waves for nonlinear dispersive equations.

We consider both local and nonlocal equations having a Hamiltonian structure.

**Clair Poignard**: *The potential impact of mathematics in clinical oncology: the example of electroporation ablation*

Abstract : Electroporation-based therapies (EPT) consist in applying high voltage short pulses to cells (typically several hundred volts per centimeter during about one hundred microseconds) in order to create defects in the plasma membrane. They provide interesting alternatives to standard ablative techniques, in particular for deep seated tumors (located near vital organs or important vessels). In this talk we present the rationale of electroporation and its modeling at different scales. We will also show that combining well suited clinical workflow with mathematical models can help physicians.

**Tudor Ratiu**: The Ericksen-Leslie equations

Abstract : I will begin by presenting the geometric structure of the Ericksen-Leslie equations without dissipation. This will lead to a reformulation as a system of four first order equations. In these new variables, the dissipation terms are added and shown that this new system is equivalent to the original Ericksen-Leslie equations. Using this reformulation, short time existence and uniqueness of strong solutions for the initial value problem for the periodic case and in bounded domains with both Dirichlet- and Neumann-type boundary conditions will be shown.

**Eugen Varvaruca: ***Large-amplitude steady gravity water waves with constant vorticity*

*Abstract: We consider the problem of two-dimensional traveling water waves*

propagating under the influence of gravity in a flow of constant vorticity

over a flat bed. By using a conformal mapping from a strip onto the fluid

domain, the governing equations are recasted as a one-dimensional

pseudodifferential equation that generalizes Babenko’s equation for

irrotational waves of infinite depth. We explain how an application of the

theory of global bifurcation in the real-analytic setting leads to the

existence of families of waves of large amplitude that may have critical

layers and/or overhanging profiles. Some new a priori bounds and geometric

properties of the solutions on the global bifurcating branches will also

be presented. This is joint work with A. Constantin and W. Strauss.

**Vlad Vicol**: *On distributional solutions of the Navier-Stokes equation*

Abstract : In this talk, we address the question of uniqueness of distributional solutions, or equivalently of mild solutions, of the Navier-Stokes equations with finite kinetic energy. This talk is based on joint work with T. Buckmaster.

**Enrique Zuazua**: *C**ontrol of a population dynamics model with age structuring and diffusion*

Abstract : This lecture is devoted to present recent joint work in collaboration with D. Maity and M. Tucsnak (Univ. Bordeaux) on a linear system in population dynamics involving age structuring and spatial diffusion (of Lotka-McKendrick type). The control is localized in space and age. We prove that the whole population can be steered to zero in a uniform time, without, as in the existing literature, excluding some interval of low ages. And we do it in a sharp time. We also show that the system can be steered between two positive steady states by controls preserving the positivity of the state trajectory, something that plays a key role in applications.