Mon, 24 Apr 2023
14:15
L4

Non-Archimedean Green's functions

Sébastien Boucksom
(CNRS / Institut de Mathématiques de Jussieu-Paris Rive Gauche)
Abstract

Pluripotential theory studies plurisubharmonic functions and complex Monge-Ampère equations on complex manifolds, and has played a key role in recent progress on Kähler-Einstein and constant scalar curvature Kähler metrics. This theory admits a non-Archimedean analogue over Berkovich spaces, that can be used to study K-stability. The purpose of this talk is to provide an introduction to this circle of ideas, and to discuss more specifically recent joint work with Mattias Jonsson studying Green's functions in this context.

Thu, 16 May 2019
11:30
C4

An Imaginary Ax-Kochen-Ershov principle

Silvain Rideau
(CNRS / Institut de Mathématiques de Jussieu-Paris Rive Gauche)
Further Information

 (work in progress with Martin Hils)

Abstract

In the spirit of the Ax-Kochen-Ershov principle, one could conjecture that the imaginaries in equicharacteristic zero Henselian fields can be entirely classified in terms of the Haskell-Hrushovski-Macpherson geometric imaginaries, residue field imaginaries and value group imaginaries. However, the situation is more complicated than that. My goal in this talk will be to present what we believe to be an optimal conjecture and give elements of a proof.

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