Theme «Algebraic combinatorics and logic »

Researchers :

Pierre Damphousse et Cédric Lecouvey

Abstract :

Cédric Lecouvey works on interactions between graph and group theories. These interactions permits to solve certain optimization problems in groups (notably inspired by similar problems in additive number theory) by optimizations methods in graphs.
In a similar direction, on studies matching problems in groups or fields directly motivated by graph theory.

Another aspect of the works by CL is concerned with linear analogues (i.e. in fields) of some results in additive number theory or of optimization in groups. In contrast with the situation in groups, these problems cannot be immediately connected to graph theory. They lead to use linear versions of certain transformations introduced by Dyson and Kemperman. Numerous difficulties are specific to the linear structure. Moreover, there often exit fewer linearizations of the same result in additive number theory.

The topics logic is the center of interest of Pierre daphousse. Works are in progress on natural transformations between fonctorial versions (of Lawere type) of P (set of all subsets).
The study of natural transformations between the corresponding iterations makes appear new connections between language theory, calculability and classical results in set theory.