Teaching

Information regarding the course Model Theory of differential fields in characteristic zero.

Practical information

The lectures take place on the Fridays from 9.45am to 11.15am and from 11.30am to 1.00 pm with a fifteen minutes break in the middle. The rooms for each lecture are indicated below. Be careful the room change with the lectures.

• Lectures 1/2 on 12/01/2024. Quai 43, s.104 (1er étage)
• Lectures 3/4 on 19/01/2024. Darwin D71 (RDC)
• Lectures 5/6 on 26/01/2024. Braconnier Séminaire 1
• Lectures 7/8 on 02/02/2024. Darwin C salle Caullery (RDC)
• Lectures 9/10 on 09/02/2024. Darwin C salle Caullery (RDC)
• Lectures 11/12 on 23/02/2024. Darwin C salle Caullery (RDC)
• Lectures 13/14 on 08/03/2024. Braconnier Séminaire 1
• Lectures 15/16 on 15/03/2024. Braconnier Séminaire 1

More information about the location of each of the rooms can be found here .

Lecture notes

• Lecture 1. Motivation
• Lecture 2. Ritt-Raudenbush theory
• Lecture 3. Differentially closed fields
• Lecture 4. The Seidenberg embedding Theorem
• Lecture 5. Space of one-forms of a differential field extension
• Lecture 6. Rosenlicht lemma and Ax Theorem
• Homework. A theorem of Liouville about integration.
• Lecture 7. The canonical base property
• Lecture 8. Differential algebraic groups *Lecture 9. Strongly minimal sets and Zilber trichotomy

Références

• David Marker, Model Theory of differential fields (second chapter of the book Model Theory of fields) pdf.
• Rosenlicht, On Liouville theory of elementary functions, Pacific Journal of Mathematics, Vol. 65, No. 2, 1976. pdf.
• Bouscaren E., Model Theory and Algebraic Geometry, Lecture notes in Mathematics link .