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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, December  2, 2025}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Dmitry Kerner 
  %
  (BGU)
}
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will talk about
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{\Large\bfseries Mommy, I can't solve this equation\par}
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\textsc{Abstract:}
A significant part of Mathematics boils down to ``resolving systems of equations'', e.g. equations of implicit function type, F(x,y)=0. In many cases one has to resolve these just ``order-by-order''. The obtained power series, y(x), do not need to be analytic.

Artin approximation (A.P.) ensures: every formal solution is approximated by analytic solutions. This goes in contrast to various other (functional or differential) equations, for which the formal and analytic words are very different.

I will give a brief introduction to this topic, and then explain the recent results: A.P. for (quivers) of morphisms of scheme-germs. In simple words: A.P. holds for an additional class of functional equations (not of implicit function type).








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