# Prof Gabriele Steidl

## Speaker

## Technische Universität Berlin

Gabriele Steidl received her PhD and Habilitation in Mathematics from the University of Rostock (Germany), in 1988 and 1991, respectively. From 1992 to 1993 she worked as a consultant at the Verband Deutscher Rentenversicherungsträger in Frankfurt am Main. Between 1993 and 2020 she held professorships at the Departments of Mathematics at the TU Darmstadt, University of Mannheim, and TU Kaiserslautern, and was Consultant of the Fraunhofer Institute for Industrial Mathematics. Since 2020, she is Professor at the Department of Mathematics at the TU Berlin.

She worked as a Postdoc at the University of Debrecen (Hungary), the Banach Center Warsaw and the University of Zürich and was a Visiting Professor at the ENS Paris/Cachan and the Université Paris East Marne-la-Vallée and the Sorbonne.

Since 2020 she is a member of the DFG Fachkollegium Mathematik and the Program Director of SIAG-IS (SIAM).

She is a member of the Editorial board of Journal of Mathematical Imaging and Vision, SIAM Journal on Imaging Sciences, The Journal of Fourier Analysis, Inverse Problems and Imaging, Journal of Optimization Theory and Applications, Transactions in Mathematics and its Applications, Acta Applicandae Mathematicae (ACAP), and Sampling Theory, Signal Processing and Data Analysis.

## Talk

###### Curve Based Approximation of Measures on Manifolds

The approximation of probability measures on compact metric spaces and in particular on Riemannian manifolds by atomic or empirical ones is a classical task in approximation and complexity theory with a wide range of applications.

Instead of point measures we are concerned with the

approximation by measures supported on Lipschitz curves.

Special attention is paid to push-forward measures of Lebesgue measures on the interval by such curves. Using the discrepancy as distance between measures, we prove optimal approximation rates in terms of Lipschitz constants of curves.

Having established the theoretical convergence rates, we are interested in the numerical minimization of the discrepancy between a given probability measure and the set of push-forward measures of Lebesgue measures on the interval by Lipschitz curves. We present various numerical examples.