12 décembre 2017

Marin Mišur (Université de Zagreb)
Spaces of distributions of non-integer order and applications

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Lieu : Salle 113-115 (Bâtiment 425)

Résumé : In this talk, we review the notion of the order of a distribution and extend it to the case of positive real numbers.
The first part of the talk is about the functional-analytic properties of the Hölder test function spaces and its duals.
Of particular interest are the C^0,\alpha+_c(\Omega) and the \mathcal D’_\alpha+(\Omega) spaces which have notably better properties such as reflexivity, compared to classical Hölder spaces.
Next, we give a few examples of distributions of fractional order.
As an application of our results, using results and tools from classical Fourier analysis, we give (in a certain sense) sharp estimates on the order of distributions which are the Fourier transform of L^p functions for p > 2.
The results presented here can easily be extended to the case of differentiable manifolds and de Rham’s currents.
This is joint work with Ljudevit Palle (Christian-Albrechts-Universität zu Kiel).

Spaces of distributions of non-integer order and applications  Version PDF

Johannes Nicaise (Imperial College London / University of Leuven)
Specialization of (stable) rationality in families with mild singularities

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Lieu : Bât. 425, salle 117-119

Résumé : I will present joint work with Evgeny Shinder, where we use Denef and Loeser’s motivic nearby fiber and a theorem by Larsen and Lunts to prove that stable rationality specializes in families with mild singularities. The proof yields new obstructions to stable rationality that can be applied in concrete examples. I will also discuss an improvement of our results by Kontsevich and Tschinkel, who defined a birational version of the motivic nearby fiber to prove specialization of rationality.

Specialization of (stable) rationality in families with mild singularities  Version PDF