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Mathematics Department Técnico Técnico

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Jorge Drumond Silva 14/06/2018, 16:00 — 17:00 — Abreu Faro Amphitheatre
, CAMGSD, Instituto Superior Técnico - Universidade de Lisboa

The Interplay Between Dispersive Partial Differential Equations and Fourier Analysis

Partial differential equations have always been a subject of fruitful interaction with Fourier analysis, starting precisely with the study of the heat equation. In the last few decades, nonlinear partial differential equations of hyperbolic and dispersive type, in particular, have been at the center of a significant new interplay and mutual progress between these two fields, through the works of prominent mathematicians like Tosio Kato, Charles Fefferman, Jean Bourgain, Carlos Kenig and Terence Tao.

In this talk, we will review some of the basic concepts and ideas that play a central role in this connection between techniques from Fourier analysis and properties of solutions of dispersive PDEs, covering topics like Strichartz estimates, smoothing effects, local and global well posedness of initial value problems at low regularity, among others.

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The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.

Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.