Differential Equations

Crystallization of point configurations to the Square Lattice in 2D.

Event Date: Aug 04, 2020 in Differential Equations, Seminars

Abstract: We consider minimum-energy configurations x_1, …, x_N in euclidean space, minimizing the energy given by the sum of V( |x_i-x_j| ) for all pairs of distinct indices i,j, with V an interaction potential. Recent breakthroughs (Viazovska Ann. Math. 2017, Cohn-Kumar-Miller-Radchenko-Viazovska Ann. Math. 2017) led to a proof in arXiv:1902.05438 that special lattices in dimensions 8 and 24 form “universally optimal configurations”, i.e. optimize our energy at fixed density for a large class of V’s. This was recently extended (P.-Serfaty, Proc. AMS 2020) to include...

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Models of collective behavior with singular couplings and their hydrodynamic and mean-field limits.

Event Date: Jul 21, 2020 in Differential Equations, Seminars

Abstract: TBA

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Relativistic kinetic theory with applications in astrophysics. & Fundamental solutions of time-fractional evolution equations.

Event Date: Jul 07, 2020 in Differential Equations, Seminars

16:00 hrs. Título: Relativistic kinetic theory with applications in astrophysics. Abstract: I will review the relativistic kinetic theory and apply it to two phenomena. The first phenomenon is the accretion of matter around the Schwarzschild black hole, where we calculated its accretion rate. The second phenomenon concerns the dynamics of the kinetic gas for a thin disk in the equatorial plane of the Kerr black hole. In this case, the so-called mixing phenomenon appears, which causes that the gas configuration relaxes to a stationary axisymmetric state. 17:00 hrs. Título: Fundamental...

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On the inhomogeneous nonlinear Schrödinger equation. & Una Versión No autónoma del Problema de Estabilidad Global.

Event Date: Jun 23, 2020 in Differential Equations, Seminars

 Título: On the inhomogeneous nonlinear Schrödinger equation. Abstract: In this talk we discuss some results for the inhomogeneous nonlinear Schrödinger equation, such as global well-posedness, scattering, concentration and blow-up of the critical norm. These results were obtained in collaboration with Luccas Campos (UFMG-Brazil), Mykael Cardoso (UFPI-Brazil) and Carlos Guzmán (UFF-Brazil). Título: Una Versión No autónoma del Problema de Estabilidad Global. Abstract: En esta charla introduciremos la versión no autónoma del problema de esta- bilidad global desde un punto de vista del espectro...

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Long-time asymptotics for the cubic NLS in 1d.

Event Date: Jun 09, 2020 in Differential Equations, Seminars

Abstract: I will discuss the long-time asymptotics of small solutions to the 1d cubic NLS with a potential. Using distorted Fourier transforms, localized dispersive estimates, we obtain the long-time asymptotics for the 1d cubic NLS under very mill assumptions on potentials. This is joint work with Fabio Pusateri.

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Coupling and mixing local and nonlocal equations

Event Date: May 26, 2020 in Differential Equations, Seminars

Abstract: In this talk we present a simple way of coupling a local and a nonlocal evolution equation in such a way that the usual properties (like existence and uniqueness of solutions, conservation of the total mass, etc) are satisfied. Moreover, we study the limit as we homogenize this setting mixing the regions in which local and nonlocal operators act.

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