This workshop will take place

**from August 27th to August 30th 2019 on**

**Campus Gavy of Nantes Université**

**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*