# 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!