Colloquium: Tuesday, January 19, 2 pm. Speaker: Dmitry Kerner (Ben Gurion) . Title: “Finite determinacy”.

On many occasions a local object (e.g. the germ of a map at a point) is essentially
determined (up to a group action) by its finite jet, i.e. its restriction onto some N’th-infinitesimal
neighborhood of the point. This “minimalistic stability” is called the Finite Determinacy. It is
extremely useful e.g. in deformation theory and in the study of local moduli.
For function germs/power series the finite determinacy has been classically known. For the
(formal/smooth/analytic) germs of maps it has been intensively studied since 1960’s.
After the general introduction I will speak about our recent results. We extend the classical
criteria to the broad class of rings (over a field of zero characteristic) and group actions on
filtered modules. As an application we compute (or give tight bounds to) the orders of determinacy
for numerous scenarios, e.g.: germs of maps, stalks of sheaves/modules over local rings,
quadratic/skew-symmetric forms.

Joint work with G. Belitskii.