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UID:8082@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150511T000000
DTEND;TZID=Europe/Paris:20150515T000000
DTSTAMP:20241120T210021Z
URL:https://www.i2m.univ-amu.fr/evenements/nested-subring-conditions-morle
 t-chair-herwig-hauser/
SUMMARY:Small group (CIRM\, Luminy\, Marseille): Nested Subring Conditions 
 (Morlet Chair - Herwig Hauser)
DESCRIPTION:Small group: \n\n\n\n CIRM - Jean-Morlet Chair \n Herwig Hauser
  &amp\; Guillaume Rond\n\nSingularities and Artin Approximation​\n\nSing
 ularités et approximation de Artin \n\n\n 2015-Semester 1 \n\n\n\n\n\n\n\
 n\n\n\n\n\n\n\n\n\n\n\nSMALL GROUP\nNested Subring Conditions (1311)\nCond
 itions d'emboîtements des sous-anneaux\nDates: 11-15 May 2015 at CIRM (Ma
 rseille\, France)\nPlace : CIRM (Marseille Luminy\, France)  \n\n\n  \n\n
 \n\n\n\n\n\n\n\n\n\n\n\n PARTICIPANTS \n\n\n\n\n\n\n\n\n\n\nDESCRIPTION\nI
 n many applications of Artin approximation\, certain components of the pow
 er series solutions are required to depend only on certain subsets of the 
 set of all variables. If these subsets are arbitrarily distributed\, there
  is no hope to find convergent solutions\, as examples of Gabrielov and Be
 cker demonstrate.\n\nHowever\, if the subsets are nested\, i.e.\, form an 
 ascending chain of subsets\, Artin approximation holds for algebraic syste
 ms of equations\, as was shown by Popescu and Spivakovsky. The proofs are 
 very long and require difficult machinery as e.g. Néron desingularization
 .\n\nThe proposed research program intends to clarify and simplify these p
 roofs. Already the case of linear equations is very interesting. In the cl
 assical situation of Artin approximation\, i.e.\, without constraints\, it
  corresponds to the flatness of the formal power series ring over the conv
 ergent power series ring\, and is proven for example by the extension by G
 rauert-Hironaka-Galligo of the Weierstrass division theorem to the case of
  ideals.\n\nIn the presence of constraints by nested subring conditions\, 
 the respective generalization of the division theorem fails already for co
 nvergent power series. However\, for algebraic series\, there is a good ch
 ance that the theorem can be proven\, using techniques developed by Alonso
 -Garcia\, Castro-Jiménez and Hauser. Once this is established\, it remain
 s to reduce the general nested subring approximation problem to the linear
  case. This is a linearization problem for textile maps between power seri
 es spaces as proposed by Bruschek-Hauser. For arc spaces\, i.e.\,one varia
 ble\, this has already been successfully applied.\n\n\n \n\nSCIENTIFIC &a
 mp\; ORGANIZING COMMITTEE\n\n\n 	Herwig Hauser (Vienna)\n 	Guillaume Rond 
 (Aix-Marseille)\n\n\n\nSPEAKERS\n\n\n 	Francisco Castro Jimenez (Sevilla)\
 n 	Christopher Chiu (Vienna)\n 	Doan Trung Cuong (Hanoi)\n 	Alberto Gioia 
 (Vienna)\n 	Herwig Hauser (Vienna)\n 	Hiraku Kawanoue (Kyoto)\n 	Gerhard P
 fister (Kaiserslautern)\n 	Guillaume Rond (Aix-Marseille)\n 	Josef Schicho
  (RICAM Austria)\n 	Mark Spivakovsky (CNRS\, Toulouse)\n 	Sebastian Woblis
 tin (Vienna)\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nSPONSORS\n\n  \n\n\n\n\n\n
 \n
CATEGORIES:Manifestation scientifique,Morlet Chair Semester,Morlet Small
 Group
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