The CombPhysMat2Tens (Combinatorial Physics, from Matrix to Random Tensor Models) is an ANR-funded project gathering 7 young scientists, both combinatorists and physicists (at the PhD and post-doc levels, as well as permanent researchers). The project lies at the intersection between combinatorics (algebraic, enumerative etc.), graph theory and theoretical physics.

More precisely, the project gravitates around the notion of ribbon graphs (also known as combinatorial maps or graphs embedded on surfaces) and their generalization to tensor graphs. Our scientific objectives include the study of ribbon graphs in relation to the problem of colorability in graph theory and the study of the connection between the Jacobian conjecture and (purely) combinatorial quantum field theories. We also work on the generalization of ribbon graphs to tensor graphs and study various combinatorial properties of the associated random tensor models.