A Bijection Between Rigid and Integer Labeled Quadrangulations - 11

Explore the combinatorial structure of rigid quadrangulations through this 49-minute conference talk that establishes a fundamental bijection between rigid quadrangulations and integer-labeled quadrangulations of the sphere. Learn about rigid quadrangulations as a specialized subclass of flat quadrangulations of the disk where all non-boundary vertices maintain degree 4, and discover how this bijection connects to the recent enumeration work by Bousquet-Mélou and Elvey Price. Examine how natural statistics on rigid quadrangulations correspond to different but equally natural statistics on integer-labeled spherical quadrangulations, revealing deep structural relationships between these combinatorial objects. Gain insights into the scaling limits of large rigid quadrangulations and related models of random flat metrics on the disk, including their connections to physics applications and motivations in the study of random geometry.