The seminar of the team Géométrie is under the responsibility of Michel Raibaut.
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Year 2020

Thursday 14th May 2020 at 14h Yimu Yin (Santa Monica, California),
À venir

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Thursday 16th April 2020 at 14h Alicia Dickenstein (Universidad de Buenos Aires),
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Thursday 2nd April 2020 at 14h Fernand Pelletier (LAMA),
Quelques problèmes sur le passage de la dimension finie à la dimension infinie en géométrie différentielle

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Thursday 20th February 2020 at 15h30 Frédéric Mangolte (LAREMA (Angers)),
Modèles algébriques de la droite dans le plan affine réel

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On étudie la version réelle suivante d'un théorème célèbre d'Abhyankar-Moh : quelles applications rationnelles de la droite affine dans le plan affine, dont le lieu réel est un plongement fermé non singulier de R dans R^2, sont équivalentes, à difféomorphisme birationnel du plan près, au plongement trivial ? Dans ce cadre, on montre qu’il existe des plongements non équivalents. Certains d’entre eux sont détectés pas la non-négativité de la dimension de Kodaira réelle du complémentaire de leur image. Ce nouvel invariant est dérivé des propriétés topologiques de « faux plans réels » particuliers associés à ces plongements. (Travail en commun avec Adrien Dubouloz.)

Thursday 13th February 2020 at 14h Krzysztof Kurdyka (LAMA),
Separately Nash and arc-Nash functions over real closed fields

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Let $R$ be a real closed field. We prove that if $R$ is uncountable, then any separately Nash (resp. arc-Nash) function defined over $R$ is semialgebraic (resp. continuous semialgebraic). To complete the picture, we provide an example showing that the assumption on $R$ to be uncountable cannot be dropped. Moreover, even if $R$ is uncountable but non-Archimedean then the shape of the domain of a separately Nash function matters for the conclusion. For $R = R$ we prove that arc-Nash functions coincide with arc-analytic semialgebraic functions. Joint work with W. Kucharz and A. El-Siblani.

Thursday 6th February 2020 at 14h Adam Parusinski (Laboratoire JA Dieudonné (Nice)),
Zariski's dimensionality type. Case of dimensionality type two.

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In 1979 O. Zariski proposed a general theory of equisingularity for algebraic or algebroid hypersurfaces over an algebraically closed field of characteristic zero. It is based on the notion of dimensionality type that is defined recursively by considering the discriminants loci of subsequent ``generic'' projections. The singularities of dimensionality type 1 are isomorphic to the equisingular families of plane curve singularities. In this talk we consider the case of dimensionality type 2, the Zariski equisingular families of surface singularities in 3-space. Using an approach going back to Briançon and Henry, we show that in this case generic linear projections are generic in the sense of Zariski (this is still open for dimensionality type greater than 2). Over the field of complex numbers, we show that such families are bi-Lipschitz trivial, by construction of an explicit Lipschitz stratification. (Based on joint work with L. Paunescu.)

The seminar of the team Géométrie is under the responsibility of Michel Raibaut.
Settings: See with increasing date . Hide abstracts
Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, all years together.