Gitta Kutyniok currently has a Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at the Ludwig-Maximilians Universität München and an Adjunct Professorship in Machine Learning at the University of Tromso. She received her Diploma in Mathematics and Computer Science as well as her Ph.D. degree from the Universität Paderborn in Germany, and her Habilitation in Mathematics in 2006 at the Justus-Liebig Universität Gießen. From 2001 to 2008 she held visiting positions at several US institutions, including Princeton University, Stanford University, Yale University, Georgia Institute of Technology, and Washington University in St. Louis, and was a Nachdiplomslecturer at ETH Zurich in 2014. In 2008, she became a full professor of mathematics at the Universität Osnabrück, and moved to Berlin three years later, where she held an Einstein Chair in the Institute of Mathematics at the Technische Universität Berlin and a courtesy appointment in the Department of Computer Science and Engineering until 2020.
She received various awards for her research such as an award from the Universität Paderborn in 2003, the Research Prize of Gießen and a Heisenberg-Fellowship in 2006, the von Kaven Prize by the DFG in 2007, and an Einstein Chair in 2008. She gave the Noether Lecture at the ÖMG-DMV Congress in 2013 and the Hans Schneider ILAS Lecture at IWOTA in 2016. She also became a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017, a SIAM Fellow and an IEEE Senior Member in 2019, received a Francqui Chair of the Belgian Francqui Foundation in 2020, and holds the first Bavarian AI Chair at LMU from 2020 on. She was Chair of the SIAM Activity Group on Imaging Sciences from 2018-2019 and is Co-Chair of the first SIAM conference on Mathematics of Data Science taking place this year. She was Scientific Director of the graduate school BIMoS at TU Berlin from 2014 to 2020 and is currently Chair of the GAMM Activity Groups on Mathematical Signal- and Image Processing and Computational and Mathematical Methods in Data Science. She is also the main coordinator of the Priority Programm of the German Research Foundation on theoretical foundations of deep learning.
Gitta Kutyniok's research work covers, in particular, the areas of applied and computational harmonic analysis, approximation theory, compressed sensing, deep learning, frame theory, imaging sciences, inverse problems, machine learning, numerical analysis of partial differential equations, and applications to life sciences and telecommunication. She is primarily interested to develop mathematical methodologies and associated theories to solve application motivated problems.
The most significant of Gitta Kutyniok's contributions is perhaps the introduction of the directional multiscale system of shearlets (see also www.ShearLab.org), which is by now exploited by various research groups worldwide. Since many important problem classes are governed by anisotropic structures such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images, and the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. By now, shearlets are the first anisotropic system which not only provides optimal sparse approximation rates for appropriate model classes, but also allows for faithful and highly efficient implementations.
In the area of inverse problems, Gitta Kutyniok pursued foremost the direction of sparse regularization, in which the regularizer is designed using an orthonormal basis or, more generally, a frame, which provides sparse approximations of the respective model class. Using results from harmonic analysis and microlocal analysis, Gitta Kutyniok provided a comprehensive analysis of this approach for several problems in imaging sciences by using shearlets, revealing the underlying reasons for its success.
Lately, she entered the area of machine learning. One of her main goals is to develop a theoretical foundation for deep learning, also for its application within mathematics. In this direction, some of her most well-known contributions are the analysis and construction of memory-optimal deep neural networks by using classical approximation theory as well as a theoretical analysis of deep neural networks and parametric partial differential equations. Another focus of hers is on optimal combinations of model- and data-based approaches, where she, for instance, developed a state-of-the-art algorithm for the limited-angle computed tomography problem using a combination of deep neural networks and sparse regularization by shearlets.