Time: 4:40 p.m.
Location: 106 McAllister Building
Name: Yulij Ilyashenko
Affiliation: Cornell, Moscow State and Independent Universities
Title: Total rigidity of polynomial foliations
Abstract: Polynomial foliations of the complex plane have a property of topological rigidity. Roughly speaking, this property means that topological equivalence of foliations implies their affine equivalence. This property holds for generic foliations of fixed degree. The first rigidity theorems of this kind were obtained by the speaker about 30 years ago. The genericity conditions at that time were very restrictive. Since then the subject was developed by Scherbakov, Gomez-Mont, Nakai, Lins Neto - Scardua - Sad, Loray - Rebelo and others. They improved the genericity conditions and increased the dimension of the foliation. The major conjecture is that for a generic foliation there is but a finite number of foliations topologically equivalent to it. A survey of these investigations will be presented, together with recent results by Moldavskis, Pyartli, Yakovenko and others, that will show, how far are we now from the major conjecture above.
