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UID:890@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151013T110000
DTEND;TZID=Europe/Paris:20151013T120000
DTSTAMP:20150928T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/can-we-compute-everything/
SUMMARY: (...): Can we compute everything?
DESCRIPTION:: It is often desirable to solve mathematical problems as a lim
 it of simpler problems. However\, are such techniques always guaranteed to
  work? For instance\, the problem of finding roots of polynomials of degre
 e higher than three was only solved in the 1980s (Newton's method isn't gu
 aranteed to converge)! Doyle and McMullen showed that this is only possibl
 e if one allows for multiple independent limits to be taken\, not just one
 . They called such structures "Towers of Algorithms". In this talk I will 
 apply this idea to other problems (such as computational quantum mechanics
 \, inverse problems\, spectral analysis)\, show that Towers of Algorithms 
 are a necessary tool\, and introduce the Solvability Complexity Index -- a
  measurement of the complexity of a given problem. An important consequenc
 e is that solutions to some problems can never be obtained as a limit of f
 inite dimensional approximations (and hence can never be solved numericall
 y). If time permits\, I will mention connections with analogous notions in
  logic and theoretical computer science.Joint work with Anders Hansen (Cam
 bridge)\, Olavi Nevalinna (Aalto) and Markus Seidel (Zwickau).http://www.i
 mperial.ac.uk/people/j.ben-artzi
CATEGORIES:Séminaire,Analyse Appliquée
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DTSTART:20150329T030000
TZOFFSETFROM:+0100
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