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SUMMARY:Notions of difference closures of difference fields.
DTSTART;VALUE=DATE-TIME:20190904T120000Z
DTEND;VALUE=DATE-TIME:20190904T130000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3931@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zoé Chatzidakis ()\nIt is well known that a differe
ntial field K of characteristic 0 is contained in a differential field whi
ch is differentially closed and has the property that it K-embeds in every
differentially closed field containing K. Such a field is called a differ
ential closure of K\, and it is unique up to K-isomorphism. The difference
closure is what model-theorists call a "prime model". \n\nOne can ask th
e same question about difference fields: do they have a difference closure
\, and is it unique? The immediate answer to both these questions is no\,
for trivial reasons: in most cases\, there are continuum many ways of exte
nding an automorphism of a field to its algebraic closure. Therefore a n
atural requirement is to impose that the field K be algebraically closed.
Similarly\, if the subfield of K fixed by the automorphism is not pseudo-f
inite\, then there are continuum many ways of extending it to a pseudo-fin
ite field\, so one needs to add the hypothesis that the fixed subfield of
K is pseudo-finite. \n\nIn this talk I will show by an example that even t
hese two conditions do not suffice. \n\nThere are two (and more) natural
strengthenings of the notion of difference closure\, and we show that in c
haracteristic 0\, these notions do admit unique "closures" over any alge
braically closed difference field K\, provided the subfield of K fixed by
the automorphism is large enough. \n\nIn characteristic p\, no such resul
t can hold.\n\nAll definitions will be introduced.\n\nhttps://indico.math.
cnrs.fr/event/4569/contributions/3931/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3931/
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BEGIN:VEVENT
SUMMARY:Inverse problem for germs of parabolic diffeomorphisms of the comp
lex line
DTSTART;VALUE=DATE-TIME:20190905T143000Z
DTEND;VALUE=DATE-TIME:20190905T153000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3939@indico.math.cnrs.fr
DESCRIPTION:Speakers: Loïc Teyssier ()\nhttps://indico.math.cnrs.fr/event
/4569/contributions/3939/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3939/
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BEGIN:VEVENT
SUMMARY:Becker’s conjecture on Mahler functions
DTSTART;VALUE=DATE-TIME:20190905T130000Z
DTEND;VALUE=DATE-TIME:20190905T140000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3938@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frédéric Chyzak ()\nIn 1994\, Becker conjectured t
hat if $F(z)$ is a $k$-regular power series\, then there exists a $k$-regu
lar rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type
functional equation with polynomial coefficients where the initial coeffi
cient satisfies $a_0(z) = 1$. In this work\, we prove Becker’s conjectur
e in the best possible form\; we show that the rational function $R(z)$ ca
n be taken to be a polynomial $z^γ Q(z)$ for some explicit non-negative i
nteger $γ$ and such that $1/Q(z)$ is $k$-regular. (This is joint work wit
h Jason P. Bell\, Michael Coons\, and Philippe Dumas.)\n\nhttps://indico.m
ath.cnrs.fr/event/4569/contributions/3938/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3938/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Riemann-Hilbert mapping in genus two
DTSTART;VALUE=DATE-TIME:20190905T120000Z
DTEND;VALUE=DATE-TIME:20190905T130000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3937@indico.math.cnrs.fr
DESCRIPTION:Speakers: Viktoria Heu ()\nhttps://indico.math.cnrs.fr/event/4
569/contributions/3937/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3937/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Miyake's algorithm for formal reduction of linear differential
systems
DTSTART;VALUE=DATE-TIME:20190905T090000Z
DTEND;VALUE=DATE-TIME:20190905T100000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3936@indico.math.cnrs.fr
DESCRIPTION:Speakers: Joelle Saade ()\nhttps://indico.math.cnrs.fr/event/4
569/contributions/3936/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3936/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quotients and equations
DTSTART;VALUE=DATE-TIME:20190905T073000Z
DTEND;VALUE=DATE-TIME:20190905T083000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3935@indico.math.cnrs.fr
DESCRIPTION:Speakers: Martin Martin-Pizarro ()\nQuotients are ubiquitous i
n Mathematics\, and a general question is whether a certain category of se
ts allows quotients. For the category of definable sets in a given structu
re\, the model theoretic approach is called elimination of imaginaries. Fo
r algebraically closed fields\, Chevalley’s theorem and the existence of
a field of definition of a variety imply that a quotient of a Zariski con
structible set by a Zariski constructible equivalence relation is again co
nstructible. Similar results hold for other classes of fields\, such as di
fferentially closed fields.\nIn this talk\, we will focus on separably clo
sed fields and differentially closed fields of positive characteristic. In
joint work with Martin Ziegler\, we will provide a natural expansion of t
he language to achieve elimination of imaginaries\, by showing that these
theories are equational. Equationality\, introduced by Srour\, and later c
onsidered by Srour and Pillay\, is a generalisation of local noetherianity
. We will present the main ideas of the proof\, without assuming a deep kn
owledge of model theory.\n\nhttps://indico.math.cnrs.fr/event/4569/contrib
utions/3935/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3935/
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BEGIN:VEVENT
SUMMARY:The asymptotic proprieties of solutions of a q-difference equation
as q tends to a root of unity
DTSTART;VALUE=DATE-TIME:20190906T090000Z
DTEND;VALUE=DATE-TIME:20190906T100000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3934@indico.math.cnrs.fr
DESCRIPTION:Speakers: Changgui Zhang ()\nhttps://indico.math.cnrs.fr/event
/4569/contributions/3934/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3934/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ax-Lindemann-Weierstrass theorem for the genus 0 Fuchsian groups
DTSTART;VALUE=DATE-TIME:20190906T073000Z
DTEND;VALUE=DATE-TIME:20190906T083000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3933@indico.math.cnrs.fr
DESCRIPTION:Speakers: Guy Casale ()\nhttps://indico.math.cnrs.fr/event/456
9/contributions/3933/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3933/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integration on Darbouxian foliations
DTSTART;VALUE=DATE-TIME:20190904T133000Z
DTEND;VALUE=DATE-TIME:20190904T143000Z
DTSTAMP;VALUE=DATE-TIME:20190821T030541Z
UID:indico-contribution-4569-3932@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thierry Combot ()\nConsider a Darbouxian function $f
=F_0+\\sum \\lambda_i \\ln F_i$ with $F_i$ rational functions in two varia
bles\, and the foliation of curves $\\mathcal{C}_h=\\{f(x\,y)=h\\}$. We co
nsider the problem of symbolic integration of a rational function $G$ alon
g $\\mathcal{C}_h$. If the monodromy of the integral satisfies a different
ial equation in $h$\, then it is linear with constant coefficients\, and t
he integral can be expressed in terms of Liouvillian functions restricted
to $\\mathcal{C}_h$. Such situation is exceptional\, but is however more g
eneral than elementary integration. We present an algorithm to test the ex
istence of such differential equation and return the Liouvillian expressio
n of the integral if it exists.\n\nhttps://indico.math.cnrs.fr/event/4569/
contributions/3932/
LOCATION:Strasbourg Salle séminaire
URL:https://indico.math.cnrs.fr/event/4569/contributions/3932/
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