Prof. Prof. Kari Astala
In residence at
Dr Athanasios Batakis
Harmonic analysis, conformal structures and random geometry
Conformal and quasi-conformal maps are basic tools in harmonic analysis and in particular in the study of elliptic operators. Besides their own fundamental properties, they provide a key ingredient in a large number of modern and classical topics in mathematics. Conformal invariance is for instance, a fundamental property of Brownian motion, optimal transport and percolation and of many random growth processes. More recently, these tools have been applied in image processing through the inverse Calderon problem. The aforementioned areas are well represented in the Department of Mathematics of the University of Orleans. Furthermore, MAPMO researchers are active in related domains such as stochastic processes on continuous trees, percolation, random growth processes, Calderòn-Zygmund operators, inverse problems, elliptical partial differential equations, image analysis, conformal dynamics and quantum gravity. These are central areas including my research interest and recent activity. The study of physical problems provides the basic ingredients to deal with concrete models and applications.