Colloquium: Tuesday, May 5 2:10pm. Speaker: Pawel Walczak (Lodz). Title: Integral formulae for foliated manifolds: old and new.

Integral formulae on foliated Riemannian manifolds provide obstructions for the existence of foliations satisfying given geometric properties.

Here, we shall  present a bit of history of this subject: from Reeb (1950) till Rovenski-Walczak (2012), and  brand new results obtained by Magdalena Lużyńczyk (and ourselves) in a bit more general situation:

our Riemannian manifold is equipped with a, either integrable or not, plane field of arbitrary dimension.

Some applications will be provided.