Séminaire Laurent Schwartz — EDP et applications

Séminaire Laurent Schwartz — EDP et applications

We will review modified gravity theories and in particular scalar tensor theories, where we have an additional scalar field coupling to the metric tensor. By means of a theorem given by Horndeski back in 1974 we will briefly discuss the most general of these theories. We will examine a particular sub-class of Horndeski theory which has interesting properties with respect to the cosmological constant problem. We will then find black hole solutions of this subclass which in some cases will be identical to GR solutions. The novel ingredient will be the presence of a time and space dependent scalar field. As we will see time dependence and higher order Galileon terms will bifurcate no hair theorems and provide scalar tensor black holes with a non trivial scalar field.

Many cellular and developmental processes are tightly controlled by regulatory logic that is similar across different species. Is this similarity the result of common ancestry or is it due to convergent evolution?
We address this question using in silico modeling of genetic networks controlling organ development in flowers. First, we determine the number of networks implementing a given logic and point to an open mathematical problem. Second, we take a computational approach based on Markov Chain Monte Carlo and sample uniformity that highly constrained space of networks. The production of a large number of samples in that ensemble reveals how structural features of genetic networks are shaped by the imposed regulatory logic. Thus, network structural features are expected to be shared across different species through convergent evolution.

The substrate for heredity, DNA, is chemically rather inert. However, it bears one of the elements of information that specify the form of the organism. How can a form be specified, starting from DNA ? Recent observations indicate that the dynamics of transcription — the process that decodes the hereditary information — can imprint forms of a certain topological class onto DNA. This topology allows both to optimize transcription and to facilitate the concerted change of the transcriptional status in response to environmental modifications. To the best of our knowledge, this morphogenetic event is first on the path from DNA to organism. It inspires new rules to optimize networks of transcriptional interactions 'à la manière de' synthetic biology. The latter new interdisciplinary domain will be briefly presented.

(ATTENTION jour inhabituel)
Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its generic fiber.

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(horaire d’hiver)

In this talk, we will introduce the theory of (φ,Γ)-modules for general adic spaces. This is a joint work with Kedlaya.

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Séminaire Laurent Schwartz — EDP et applications