Random planar maps and their scaling limits

This project concerns the study of random surfaces and related objects such as random curves and random trees. These objects are relevant for several different branches of both mathematics (e.g. combinatorics and complex analysis) and physics (e.g. statistical physics, conformal field theory and string theory). The PI will mentor and support students and early-career researchers. More specifically, the PI will study the random discrete surfaces known as random planar maps and their scaling limits. She will establish scaling limit results for random planar maps, study the limiting random surfaces (Liouville quantum gravity, or LQG, surfaces), and explore various related topics, including the random fractal curves called Schramm-Loewner evolutions (SLE), discrete conformal geometry, and random walk and other processes in random environment. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.