Seminars take place in the seminar room, first floor of the building Le Chablais, (see How to come ?).

## Next seminar:

**Thursday 20th February 2020 at 15h30
**
Frédéric Mangolte
(LAREMA (Angers)),
*à venir*

Abstract:(Hide abstracts)

à venir

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

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Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
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# Year 2020

**Thursday 16th April 2020 at 14h
**
Alicia Dickenstein
(Universidad de Buenos Aires),
*À venir*

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À venir

**Thursday 20th February 2020 at 15h30
**
Frédéric Mangolte
(LAREMA (Angers)),
*à venir*

Abstract:(Hide abstracts)

à venir

**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:**
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increasing date
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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.