Programme
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lundi 8 juin 2026 |
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10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
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›10:30 (40min)
Valeria Banica
Title: On the binormal flow for infinite curves. Abstract: The binormal flow is a geometric flow of curves in R^3 that models vortex filament dynamics in fluids. We construct solutions for infinite curves data including the known examples of solutions that generate singularities in finite time. In this general low regularity context we use geometric measure theory tools. More precisely, we introduce a notion of renormalized length for infinite curves and work in the framework of locally integral currents. This is a joint work with Bob Jerrard and Didier Smets.
›11:20 (40min)
Kenji Nakanishi
Title: Scattering for the 4D Zakharov system below the ground states. Abstract: This is joint work with Timothy Candy. For the Zakharov system in four space dimensions, we prove that all solutions inside the potential well of the ground states are scattering in the energy space. It is an extension from the radial case and the proof in the non-radial case was already reduced by Candy to exclusion of a minimal non-scattering solution. The main difficulty, compared with the radial case and with the nonlinear Schrodinger or wave equation, comes from absence of a center moving by the momentum and the Galilei/Lorentz invariance. It is resolved by combination of two distinct arguments depending on the motion of center, subsonic or supersonic. The former is a virial-variational argument for the Zakharov system, and the latter is a space-time estimate for the linear wave equation.
›15:00 (40min)
Nikolay Tzvetkov
Title: On the statistical description of the flow of non linear dispersive PDE. Abstract: We study the three dimensional cubic defocusing wave equation with Gaussian initial data. We show that the law of the solution is quasi-Gaussian in low regularity regimes exploiting renormalised energies, normal form reductions, remarkable cancellations, non commutative Khinchin inequalities and cut-offs designed according to the probabilistic well-posedness theory developed by Nicolas Burq and the speaker around 2010. This is a joint work with Chenmin Sun and Leonardo Tolomeo.
›15:50 (40min)
Isabelle Gallagher
Title: Fourier analysis on the Heisenberg and Engel groups, and applications. Abstract: The Heisenberg and Engel groups are prototypes of Carnot groups of steps 2 and 3 respectively. We shall present properties of the sublaplacian on these groups, which are related via the Fourier transform to the quadratic and quartic oscillators. The spectral analysis of these operators leads to estimates on the convolution kernel of operators of the type $F(-\Delta)$, which in turn allow to recover classical functional embeddings, and estimates on the Schrödinger propagator for instance, via Fourier techniques. This corresponds to joint works with Hajer Bahouri, Davide Barilari and Matthieu Léautaud.
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Discours/Intervention |
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Logistique |
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