Laurent Fargues ((IMJ/CNRS & Chicago) )
p-adic twistors

Abstract: It has become more and more clear that vector bundles on the curve we constructed with Fontaine are the p-adic analog of Simpson's twistor structures. I will develop this point of view, the links with Kottwitz set B(G) and will state a few conjectures/speculations about the curve, ramified local systems on it and an eventual p-adic Fourier transform