Kun Meng: Statistical Analysis of Shapes and Images via the Euler Characteristic

In the 21st century, we have seen a growing availability of shape-valued and imaging data, prompting the development of new statistical methods to analyze them. Importantly, bridging the new methods and existing frameworks is advisable. In this talk, I will introduce several statistical inference methods for shapes and images based on the Euler characteristic. These methods have applications in many fields, such as geometric morphometrics and radiomics. From a statistical perspective, these methods are naturally connected to functional data analysis and tensor regression. From a mathematical viewpoint, they are grounded in solid foundations, bridging various branches of mathematics: algebraic and tame topology, Euler calculus, functional analysis, and probability theory. I will also briefly discuss some of my ongoing and future research directions.