Habilitation à diriger des recherches

I will defend my habilitation à diriger des recherches soon. The memoir is titled Geometric Models of Concurrent Computations. The defense will take place on the 16th of September, at 14:00.

The room is the salle des thèses of Université Paris Diderot's halle aux farines building, located 10 rue Françoise Dolto 75013 Paris. It is located in 5th floor of hall F, which can be accessed from halle E, allée paire, elevator F (by foot you have to go on the second floor to go from hall E to hall F), more details here.

The jury will be constituted of Pierre-Louis Curien, Patrick Dehornoy, Jean Goubault, Kathryn Hess Bellwald, Timothy Porter and Glynn Winskel.

The defense is open to the public and anyone interested can come. You can also have a look at the memoir or at the slides.

Abstract

Since 90s, geometric models have been introduced for concurrent programs. In those, a point corresponds to a state, a path to an execution and a deformation of a path to an equivalence between executions. They are useful to analyze programs because they provide a convenient representation of their state space, on which one can use some of the well-developed tools and invariants from geometry (curvature, homology, etc.). Conversely, the study of the spaces arising as models brings new problems of purely geometric nature: most importantly, they are naturally equipped with a direction (of time), which requires adapting most usual notions. In this habilitation thesis, we present such models that we have developed and studied, as well as general techniques to do so and the results they have allowed us to obtain. Those have been applied to various notion of "concurrent programs": programs in an imperative language extended with a parallel construction and resources, but also distributed protocols, version control systems, or rewriting systems. The "geometric models" we have studied for those are also of various nature: precubical sets, directed topological spaces, generalized metric spaces, or polygraphs.