Grandes matrices aléatoires – GranMA

Random matrix theory developed during the two last decades in numerous fields of physics and mathematics, in connection with combinatorics, with operator algebra theory (in particular free probability), with number theory (in particular in connection with Riemann hypothesis), with algebraic geometry (in particular with moduli spaces and Calabi-Yau 3-folds), with random surfaces, with random growth models and tilings, with integrable systems etc. The central goal of this project is to put together a large group of researchers working on random matrices from different perspectives so that they share their knowledge and cross-fertilize. In particular, this project wishes to improve collaborations between french physicists and mathematicians working in the area. Realistic goals are for instance -Further uses of the relation between random matrices and combinatorics (with applications for instance in free probability, planar algebras, algebraic geometry etc), -Significant results on matrix models, with applications in free probability, combinatorics and random surfaces, -A rigorous mathematical exploration of the relation between random lattice and regular lattice critical behaviors, -Exploration of the universality class of Tracy-Widom law, -Study of the norm of the inverse of random matrices, in particular in connection with the study of the spectral measure of non-symmetric operators. -Study of new matrix models, as encountered for instance in convex bodies analysis. The members of our team are actively participating to the research on large random matrices. They belong to several areas of mathematics or theoretical physics. However, they are already trained to understand (part of) the culture of the other participants, as can be seen by several existing collaborations, by the interests in common subjects (in particular shared by physicists and mathematicians) and numerous cross-citations. With such a team, the goal is to rapidly obtain new and significant results in a domain of high international competition.