# Saint-Nazaire workshop

This workshop will take place

from August 27th to August 30th 2019 on
Campus Gavy of Nantes Université

At the second floor (Rooms 239-240) of the building, located at "Centre Universitaire Gavy-Océanis" on the map of the campus via google maps: https://www.google.com/maps/d/u/0/viewer?msa=0&ll=47.25774292414318%2C-2.2657590000000027&spn=0.045671%2C0.111494&mid=1N1hZu-MO0XOE8XflMR8bD7GTORk&z=13

There will be a minicourse given by Mateus Sousa : Reconstruction of functions and the Fourier transform

One of the oldest question in Fourier analysis is the problem of recovering a function $f:\mathbb{R}\rightarrow\mathbb{C}$ using only its values over a small subset of $\mathbb{R}$ and some information about its Fourier transform $\widehat{f}$. One of the most classical results in this direction is the Shannon--Whittaker interpolation theorem, which says that a $L^2(\mathbb{R})$ function whose Fourier transform is supported in $[-2\pi\delta,2\pi\delta]$ is completely determined by its values over the set $\tfrac{1}{\delta}\mathbb{Z}$. Another such result is the Radchenko--Viazovska interpolation theorem, which says that a even Schwartz function $f$ is completely determined by the values of $f$ and $\widehat{f}$ over the set $\{\sqrt{n}:n\in\mathbb{Z}_+\}$. A first version of the Shannon--Whittaker interpolation dates back to 1898, while the striking result of Radchenko and Viazovska was announced in 2017, which separates these theorems by more than a century. The goal of this mini-course will be to present some of the mathematics that interpolates between these two beautiful theorems and what is the current state of the research connected to these results.

***** (Tentative) Schedule *****

Tuesday, August 27th (Rooms 239 and 240)
12:30 - 14:00: Welcome lunch
14:00 - 16:00: Discussions
16:00 - 16:30:  Coffee break
16:30 - 18:30: Discussions

Wednesday, August 28th (Rooms 239 and 240)
09:30 - 10:30: Mateus Sousa I
10:30 - 11:00: Coffee break
11:00 - 12:00: Chelin Gu I
12:00 - 14:00:  Lunch
14:00 - 15:00: Cynthia Bortolotto

15:00 - 16:00: Tainara Borges

16:00 - 16:30:  Coffee break
16:30 - 17:30: Sarai Quintero

Thursday, August 29th (Rooms 239 and 240)
09:30 - 10:30: Mateus Sousa II
10:30 - 11:00: Coffee break
11:00 - 12:00: Chelin Gu II
12:00 - 14:00:  Lunch
14:00 - 15:00: Younes Zine

15:00 - 16:00: Eric Timpel
16:00 - 16:30:  Coffee break
16:30 - 17:30: Emeric Roulley

Friday, August 30th (Rooms 239 and 240)
09:30 - 10:30: Mateus Sousa III
10:30 - 11:00: Coffee break
11:00 - 12:00 Thomas Cometz

12:00 - 13:30:  Lunch