Seminář z diferenciálních rovnic se koná v pondělí 3. 12. 2018 od 12 hodin v učebně M5.

doc. RNDr. Michal Veselý, Ph.D. (Ústav matematiky a statistiky, PřF MU)

Critical oscillation case for linear and half-linear equations.

Další seminář z diferenciální geometrie proběhne 26.11. od 10:00 v učebně M5.

Yaroslav Bazaikin:

Losik classes for codimension one foliations

Abstrakt:

This is a joint work with A. Galaev. Following Losik's  approach to Gelfand formal geometry, certain characteristic classes  for codimension one foliations coming from Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality  in terms of the dynamical properties of generators of the holonomy groups are found. The non-triviality for the Reeb foliation is shown; this is in contrast with some classical theorems on the Godbillon-Vey class, e.g, the Mizutani-Morita-Tsuboi Theorem about triviality of the Godbillon-Vey class of foliations almost without holonomy is not true for the classes under consideration. It is shown that the considered classes are trivial for a large class of foliations without holonomy. The question of triviality is related to ergodic theory of dynamical systems on the circle and to the problem of smooth conjugacy of local diffeomorphisms. Certain classes are obstructions for the existence of  transverse affine and projective connections.