### Les mardis à 17h avec un thé dès 16h30

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## Exposés à venir :

26 février 2019
English
Tamped functions: A rearrangement in dimension 1
We propose here to define and construct a new rearrangement, that we called the rearrangement by tamping, for non-negative measurable functions defined on ${\mathbb R}_+$. This rearrangement has many properties in common with the well-known Schwarz non-increasing rearrangement, such as the preservation of the homogeneous semi linearities but also the Pólya–Szegő inequality which tells whether a rearrangement decreases the $L^p$ norm of the gradient of the functions. The rearrangement by tamping has also one more property: it preserves the dirichlet boundary condition of a function. This construction is also the opportunity to introduce some tools for the manipulation of the superlevel sets of a function in a rearrangement context.

BIBLIOGRAPHY : introductions to rearrangement problems :
- LIEB,E. and LOSS, M., Analysis 2nd version (chap 3.), Am. Math.Soc. (14), 2010.
- BURCHARD, A., A Short Course on Rearrangement Inequalities (available online at www.math.utoronto.ca/almut/rearrange.pdf)
5 mars 2019
Lillian Glaudin (LJLL)
A valider

Optimisation (titre provisoire)
TBA
12 mars 2019
English
Penrose condition and two stream instability in plasma physics
The Penrose condition, due to Penrose in 1960, is a criterion for a stationary solution to some equations in plasma physics (typically, the Vlasov-Poisson equation) to be linearly stable. In this talk, I will present this condition, and I will describe some of its consequences and mathematical difficulties that we have to handle at the nonlinear level in the unstable case. Along the way, I will present the so-called kinetic Euler equation, which is the limiting equation that we formally get when we look at the Vlasov-Poisson equation in the realistic regime of small Debye length, and discuss its ill-posedness.
19 mars 2019
Jean Rax (LJLL)
A valider

Boundary layer (temporary)
TBA
26 mars 2019
Daniel Eceizabarrena (BCAM)
A valider

Talbot effect (temporary)
TBA
2 avril 2019
Federica Bubba (LJLL)
A valider

TBA
Du maniement du de la bouteille de parfum

## Exposés passés :

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### Le séminaire a lieu sur le site de Jussieu:

4 Place Jussieu 75005 Paris
Salle des séminaires au 3ème étage, couloir 15-16
Accès : et , station Jussieu.

Pour tout renseignement sur le GTT, contacter: Jules Pertinand (pertinand@ljll.math.upmc.fr), Gabriela López Ruiz (lopez-ruiz@ljll.math.upmc.fr)