The foliated topology-Joseph Ayoub

Talk 1: Foliated topology, an introduction.

Thursday, May 22 (Oberseminar) 16:45-17:45

Abstract: The idea of the foliated topology will be explained using analogy with 
the etale topology (the precise definition will be given in Talk 3). 
We define the foliated homotopy type of a variety (or a foliation)
and state a theorem given a complete description of the foliated 
homotopy type of the generic point of a variety. We explain how this
can be used to compute the foliated cohomology with values in discrete 
sheaves.

Talk 2: A quick introduction to differential algebra. 

Friday, May 23, 14-16 Uhr, N-U-3.04

Abstract: We cover some basic notions and tools from differential algebra
such as Malgrange involutivity theorem which will play an important
role later. We recall the classical differential Galois theory 
of Picard-Vessiot and Kolchin. 


Talk 3: Foliated topology, definitions.

Monday, May 26, 16-18 Uhr, N-U-4.04

Abstract: We recall the notion of a (schematic) foliation and explain 
some basic constructions. We also make the link with differential algebras.
Then, we give the precise definition of a foliated cover leading to 
the foliated topology. We end with some basic properties. 

Talk 4: Foliated homotopy type and computation.

Tuesday, May 27, 14-16 Uhr, N-U-4.04

Abstract: The goal of this lecture is to explain the computation of the 
foliated homotopy type of the generic point of an algebraic 
varieties. We give some computational applications.

Talk 5: Miscellaneous. 

Wednesday, May 28, 14-16 Uhr, N-U-3.01

Topics to be determined, suggestions from the audience welcome!