Differential Equations

Approximate and partial symmetries in Deep Learning.

Event Date: Nov 21, 2023 in Differential Equations, Seminars

Abstract: The image of a rotated cat still represents a cat: while this simple rule seems obvious to a human, it is not obvious to neural networks, which separately “learn” each new rotation of the same image. This applies to different groups of symmetries for images, graphs, texts, and other types of data. Implementing “equivariant” neural networks that respect symmetries, reduces the number of learned parameters, and helps improve their generalization properties outside the training set. On the other hand, in networks that “identify too much”, that is,...

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Desde las EDP a la educación

Event Date: Nov 06, 2023 in Differential Equations, Seminars

Abstract: El título de este seminario tiene varias lecturas: La primera es literal en el contexto de este seminario “Desde las Ecuaciones Diferenciales Parciales a la educación” lo que no parece tener mucho sentido, la segunda “Desde las Estrategias de Desarrollo Profesional a la educación escolar” sí tiene sentido y se relaciona con lo que actualmente hago en el ámbito de la investigación y principalmente en el ámbito del desarrollo. La tercera es la lectura que deja EDPa en forma ambigua y se refiere a lo que intentaré hacer en mi presentación: contar mi experiencia en la transición desde...

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The soliton problem for water waves models with a varying medium.

Event Date: Oct 30, 2023 in Differential Equations, Seminars

Abstract: We focus on the study of solitary waves for two deep water wave models: the Whitham equation and the Zakharov water waves system. In particular, we analyse the behaviour of a solitary wave when it encounters a change in the environment, for example when the bottom of the domain containing the fluid is altered. Zakharov water waves system arises as a free surface model for an irrotational and incompressible fluid under the influence of gravity. Such a fluid is considered in a domain with a rigid bottom and a free surface. In this talk, we are interested in analysing the behaviour of...

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Sphere Packings with Forbidden Distances.

Event Date: Oct 23, 2023 in Differential Equations, Seminars

  Abstract: We will introduce the sphere packing problem, survey past and recent developments, the breakthrough work of Viazovska, and report on recent work of mine.

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A gluing construction of singular solutions for a fully non-linear equation in conformal geometry.

Event Date: Oct 12, 2023 in Differential Equations, Seminars

Abstract:  We study construction of a complete non-compact Riemannian metrics with positive constant σ2-curvature, on the sphere Sn with a prescribed singular set Λ given by a disjoint union of closed submanifolds whose dimension is positive and strictly less than n−√n−22 . This is a fully non-linear problem, nevertheless, we show that the classical gluing method of Mazzeo-Pacard for the scalar curvature still works in this setting since the linearized operator has good mapping properties in weighted spaces. A necessary condition is that 2 ≤ 2k < n.

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Fourier transform restriction phenomena and applications to control of dispersive equations.

Event Date: Oct 10, 2023 in Differential Equations, Seminars

Abstract: In 93′ Jean Bourgain discovered a subtle smoothing property of solutions of the KdV equation posed on a periodic domain. Since this celebrated article, the smoothing properties for dispersive systems are now well known. In this talk, we will see that in the last 15 years, the Bourgain spaces are fundamental to addressing the global control problems in periodic frameworks. Precisely, we will show that the propagation of compactness and regularity have been observed thanks to these spaces in various control problems for dispersive systems.

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