The PI's main research interests lie at the (less and less clearly defined) border between mathematics and theoretical physics. Physics provides an ever-evolving source of inspiration and intuition for the formulation of mathematical problems. The two subjects currently pursued are both inspired by surface physics, namely the description of the behavior of two-dimensional objects, such as membranes, or interfaces between different media, with possible applications to biology (membrane in a solvent, protein folding). Remarkably, new mathematical tools needed to develop our understanding of surface physics have emerged in the very different context of string theory, which aims at a unified description of the matter and space interactions in the universe. Surfaces emerge in this framework as the trajectories of loop-like particles (strings). The research is principally concerned with (1) The physical and mathematical aspects of discrete two- dimensional quantum gravity, a simple model of string theory, in which discretized surfaces resembling fishing nets are generated by a powerful tool: the random matrix models and (2) The various combinatorial and algebraic problems linked to the concept of folding in surface and polymer physics. In particular, the PI will investigate possible crumpling or folding transitions of surfaces when physical parameters such as temperature or bending rigidity are varied.
