Abstract: Le equazioni di Schrödinger nonlineari appaiono in numerosissimi contesti in fisica: ad esempio sono spesso utilizzate come modelli per la propagazione di onde in mezzi dispersivi debolmente nonlineari, oppure per descrivere la dinamica di condensati di Bose-Einstein (equazione di Gross-Pitaevskii). In questo seminario presenteremo gli strumenti principali per l'analisi delle soluzioni ad energia finita di una classe di equazioni di Schrödinger nonlineari, localmente e globalmente in tempo. Inoltre discuteremo l'estensione di alcuni modelli, tramite l'aggiunta di ulteriori termini nell'equazione, studiandone le proprietà delle soluzioni.
]]>Prof. Guido Sciavicco, Università di Murcia - Spagna
In this talk I will survey the most important aspects in automated reasoning over temporal logics, and in particular interval-based ones - ITLs. In ITLs properties are defined over extended intervals of time, instead of points, giving rise to a huge variety of syntactical as well as semantical possibilities. While reasoning in ITLs is generally very difficult, as their satisfiability problems are often undecidable, I will focus on those interesting exceptions that have been found in the last 15 years of research, and try to point out the different ideas and stratiegies that have been proven useful in searching for computationally well-behaved ITLs. I will also try to give a sufficiently clear idea on how ITLs can be applied, and how the research in this sense is still very much active.
]]>Title: On the root uncertainty principle.
Abstract:
This talk will focus on a recent result of Bourgain, Clozel and Kahane. One of its versions states that a real-valued function which equals its Fourier transform and vanishes at the origin necessarily has a root which is larger than c>0, where the best constant c satisfies 0.41<c<0.64. A similar result holds in higher dimensions. I will show how to improve the one-dimensional result to 0.45<c<0.60, and the lower bound in higher dimensions. I will also argue that extremizers for this problem exist, and necessarily possess infinitely many double roots. Time permitting, I will make the connection to several related problems. This is joint work with Felipe Gonçalves and Stefan Steinerberger.
preprint: https://arxiv.org/abs/1602.03366
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