Nonlinearity, Complexity and Foundations in Mathematics

An overview of ultrafunctions

speaker: Lorenzo Luperi Baglini (Università di Pisa)

abstract: In 2013, Vieri Benci introduced a new space of generalized functions, called ultrafunctions, based on nonstandard analysis. Since then, several refined versions of spaces of ultrafunctions have been built and used to develop applications in many fields: functional analysis, mathematical physics, quantum mechanics, distributions theory, calculus of variations, PDE theory and so on. Our main aim in this seminar is to give an overview of the basic properties of these spaces and the kind of applications they allow to develop.

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