**
CIP - EFAG**

**Functional spaces, Automats and Graphs**

The seminar **EFAG** is an open seminar with a stable group of participants. Its main topic is detailed below.

Opposite to the CIP-CAPC (Algebraic Combinatorics and Combinatorial Physics) seminar, whose program is fixed before the meeting and available on different web sites, the program of this semanar may be fixed or modified at any time as well as fixed long before. This is important in the dynamics of the seminar.

Indeed, it does not necessarily have a direct pedagogical aim. If the seminar lets place to teaching, it does not teach new knowledge (the participants are supposed to be autonomous) for themselves, but rather research by research. The seminar lets a great place to the flow of ideas.

The roles of this seminar are various:

- Accompagnements d'autres événements (pré et post discussion)
- Link of the
**main stream**of the CIP with complex systems (especially the experimental part of informatics: simulations and demonstrations), and exploration of experimental mathematics). - Examples, counterexamples and detailedproofs.
- Sharing of a reading (in an active way: it is much better if all the participants read the text and if the speaker goes beyond the scope of the text).
- Shotgun seminar

The aim of this seminar is the study of functions on graphs. Here is a (non complete) list of the topics that may be dealt with:

- Complex systems and its links with representation theory of automats and operators;
- Functions in a mathematical way (function spaces) and in a categorical way (combinatorial functors: symmetric and quasi-symmetric functions, polynomials functors, Frobenius charateristic);
- Variation of scalars (rings, semi-rings and fields);
- Transition graphs (automats and other machines);
- Transition operator sets and their structures.

Here is the program of the seminar.