Biosketch
Martin Burger obtained his PhD in 200 at the Johannes Kepler University in Linz. After working as an assistant professor at UCLA and in Linz he moved to a position of full professor for applied mathematics at the WWU Münster in 2006. Since 2018 he is a professor at the FAU Erlangen-Nürnberg. His research comprises inverse problems, nonlinear mathematical imaging, partial differential equations and the development of mathematical models in the life and social science, which together drive interdisciplinary research developments e.g. in biomedical imaging. Martin Burger has received several awards and honors for his scientific contributions, such as the Calderon price for distinguished contributions in the field of inverse problems and an ERC consolidator grant in 2013. He serves in the editorial board of several journals and is one of the editors-in-chief of the European Journal of Applied Mathematics.
Research area
Inverse problems and their regularization have become a mainstream topic in applied mathematics due to a variety of important applications. The underlying ill-posedness of the problem needs to be compensated by introducing prior knowledge about possible or desired solutions. From a mathematical point of view the analysis of modern (variational) regularization methods poses challenging novel questions at the intersection of variational calculus, convex analysis, functional analysis, and infinite-dimensional statistics. In addition to the classical questions of asymptotic behaviour of regularized solutions as the noise in the data decreases, recently the characterization of the structure of solutions and their bias have played a significant role. The most recent development concerns the suitable connection of regularization techniques and machine learning using training data. More information can be found in the recent survey paper Modern regularization methods for inverse problems.