Over the last few decades, a very strong interaction between mathematics and computer science has developed. Thus, classical topics such as geometry, topology, algebra, category theory or probability allow the description and understanding of discrete structures arising from computer science problems.
Reciprocally, tools from computer science allow to better understand certain mathematical properties. The main objectives can be summarized as follows: to give discrete representations of continuous objects, to develop mathematical tools to study discrete structures, to explore certain mathematical properties by means of computation, to optimize and specify the limits of the complexity of the algorithms used, to develop a theory of computer-assisted proof.
The Institut de Mathématiques de Toulouse has developed themes at the interface between discrete mathematics and theoretical computer science. Here is a non-exhaustive list of some of the axes developed:
symbolic dynamics, automata and formal languages, cellular automata, tilings defined by local rules;