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UID:6112@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220324T140000
DTEND;TZID=Europe/Paris:20220324T150000
DTSTAMP:20250118T132822Z
URL:https://www.i2m.univ-amu.fr/evenements/semi-analytic-points-of-a-suban
 alytic-variety-revisiting-two-theorems-of-pawlucki/
SUMMARY:Octave CURMI (Institut de Mathématiques Alfréd Rényi de Budapest
 ): Semi-analytic points of a subanalytic variety: revisiting two theorems 
 of Pawlucki
DESCRIPTION:Octave CURMI: It is now a classical result that when projecting
  a (real or complex) algebraic set\, one will obtain a semialgebraic set\,
  that is\, a set that can locally be described with algebraic equalities o
 r inequalities. On the other hand\, a projection of an analytic set will n
 ot in general be semianalytic\, that is\, described locally by analytic eq
 ualities or inequalities. The class of sets obtained by such projections i
 s wider and its elements are called subanalytic sets.\nIn 1990\, W. Pawluc
 ki stated that the set of points at which a subanalytic set is not semiana
 lytic is itself a subanalytic set\, of codimension at least 2. In 1992\, a
 s a consequence of this first result\, Pawlucki obtained that the set of p
 oints at which an analytic morphism is not regular is a proper analytic se
 t. Unfortunately\, the proof of the first result was very long and technic
 al\, and remains widely misunderstood by the community.\nWe provide a new 
 approach to this problem\, through a direct proof of the second theorem. W
 e introduce a new class of subrings of the rings of formal power series in
  several variables over an algebraically closed field\, which we call temp
 erate power series. This allows us to reformulate the problem in a more ge
 neral algebraic framework\, in which we can apply the main ideas of our pr
 evious work on Gabrielov’s ranks theorem\, presenting the second theorem
  as a Gabrielov theorem with parameters. Finally we deduce the first theor
 em from the second one.\nI will start by explaining the basic definitions 
 involved and the statements\, and will give a flavor of our proof of these
  two difficult results.\nThis is a joint work with André Belotto da Silva
  and Guillaume Rond.\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Octave_Curmi.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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