Seminar
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Location: | SLMath: Online/Virtual |
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
Real Differential Forms And Currents On Non-Archimedean Spaces, Reloaded
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appeared on arXiv in 2012, and I will try to emphasize aspects which emerged since we started to revise this still unpublished manuscript.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.
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 |