Home /  DDC - Valuation Theory: Real differential forms and currents on non-archimedean spaces, reloaded

Seminar

DDC - Valuation Theory: Real differential forms and currents on non-archimedean spaces, reloaded December 02, 2020 (12:00 PM PST - 01:00 PM PST)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Antoine Chambert-Loir (Institut de Mathematiques de Jussieu)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Real Differential Forms And Currents On Non-Archimedean Spaces, Reloaded

Abstract/Media

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

I will describe some aspects of joint work with Antoine Ducros (https://arxiv.org/abs/1204.6277) where we define, for the non-archimedean analytic spaces of Berkovich, an analogue of the classical calculus of differential forms and currents on complex analytic manifolds. A first version of the theory appeared on arXiv in 2012, and I will try to emphasize aspects which emerged since we started to revise this still unpublished manuscript. Besides the complex analytic picture which is used as a guide throughout our work, the theory is built on ideas from tropical geometry, a construction of A. Lagerberg on R^n, and on the presence, within non-archimedean spaces, of polyhedral real subspaces (skeleta) on which real calculus can be performed.

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Real Differential Forms And Currents On Non-Archimedean Spaces, Reloaded

H.264 Video 25145_28643_8664_Real_Differential_Forms_and_Currents_on_Non-Archimedean_Spaces__Reloaded.mp4