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{\Large המחלקה למתמטיקה, בן-גוריון}

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

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\textbf{ב}\emph{יום שלישי,  4 בינואר, 2022}
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\textbf{בשעה} \emph{14:30 -- 15:30}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Finite determinacy of maps. Group orbits vs their tangent spaces\par}
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תינתן על-ידי
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{\large\scshape Dmitry Kerner 
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  (BGU)
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\textbf{תקציר:}
  A function at a non-critical point can be converted to a linear form by a local coordinate change. At an isolated critical point one has the weaker statement: higher order perturbations do not change the group orbit. Namely, the function is determined (up to the local coordinate changes) by its (finite) Taylor polynomial.

This finite-determinacy property was one of the starting points of Singularity Theory. Traditionally such statements are proved by vector field integration.  In particular, the group of local coordinate changes becomes a ``Lie-type`` group.

I will show such determinacy results for maps of germs of (Noetherian) schemes. The essential tool is the ''vector field integration`` in any characteristic.   This equips numerous groups acting on filtered modules with the ``Lie-type`` structure.
(joint work with G. Belitskii, A.F. Boix, G.M. Greuel.)
  


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