Geometriska Inversions Problem i PDE.
Tidsperiod: 2013-01-01 till 2016-12-31
Projektledare: Leo Tzou
Budget: 3 200 000 SEK
This project studies the mathematical models arising from a variety of imaging techniques. These problems are formulated mathematically as "inverse problems" where one deduces information about the differential equation from data about the solutions. In particular, the goal of this project is to extend our current understandings of these problems from the Euclidean setting to more general geometric structures. These additional geometric features introduces a new set of phenomena and many of the techniques used in Euclidean spaces are no longer suitable in this general setting. Therefore, as in many of the applicant´s previous works, methods from various fields of geometry will be employed to understand the interplay between analysis and geometry in these problems. More specifically, this project will introduce notions of complex geometry to the study of inverse problems.For the purpose of applications, this project will enable imaging techniques to be used on a wider range of objects having intricate geometrical or topological structures. As a result, this will enhance the applicability of these types of imaging techniques.From a scientific perspective, this project will introduce concepts from a variety of geometric disciplines to the study of inverse problems in PDE. Such advances serve not only to improve our understanding of the field but also to enrich the subject by broadening its horizon.