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Dr. Wolfgang Dahmen

Williams-Hedberg-Hedberg Endowed Chair of Mathematics Data Analysis, Simulation, Imaging, and Visualization

CENTER OF ECONOMIC EXCELLENCE

  • Internationally recognized research in Approximation Theory, Numerical and Applied Analysis; Co-Editor-in-Chief of the Journal Constructive Approximation; nonlinear approximation concepts in machine learning, computational harmonic analysis, and compressive sensing.
  • Development of novel adaptive solution concepts for partial differential or singular integral equations and multiscale modeling using wavelet type multiscale concepts as well as problem tailored stable variational formulations; development of certifiable methods for high-dimensional problems in the context of Uncertainty Quantification (UQ), for instance, based on stable tensor formats.
  • Development of certifiable reduced basis methods and their applications in UQ, data assimilation, and parameter estimation; integration of model based and data driven methodologies.
  • Interdisciplinary collaborations in fluid mechanics, chemical engineering, structural imaging, e.g. in electron microscopy.
  • Gottfried-Wilhelm-Leibniz Award, Keck Future initiative Award, Robert-Piloty Award, Member of German National Academy of Sciences, Leopoldina, member of the scientific steering committee of the Isaac Newton Institute, Cambridge University, UK, member of the IMU Circle, member of the Board of Directors of Foundations of Computational Mathematics and former Chair.

Wolfgang Dahmen was born in Linnich, Germany and studied mathematics (and physics as a secondary subject) at RWTH Aachen where he received his diploma (master’s) in 1974. After defending his PhD (Dr. rer. nat.) in July 1976 he joined the University of Bonn, Germany, as a “scientific assistant” (assistant professor). In 1979 he was awarded an IBM Postdoctoral Research Fellowship at the T.J. Watson Research Center, Yorktown Heights where he stayed until fall 1980. After receiving his Habilitation in Fall 1981 at the University of Bonn he accepted a tenured position as an Associate Professor at the Department of Mathematics of the University of Bielefeld. In 1987 he accepted an offer from the Free University of Berlin where he stayed as a Full Professor until spring 1992. He returned to RWTH Aachen in 1992 as a Full Professor and later held a Distinguished RWTH Professorship. Since 2005 he was International Director of Research of the Interdisciplinary Mathematics Institute (IMI) at the Mathematics Department of the University of South Carolina in the capacity of an Adjoint Professorship. Since fall 2017 he has been holding a SmartState Chair and the WillIams-Hedberg-Hedberg Chair in Mathematics.

Wolfgang Dahmen’s PhD related research concerned Approximation Theory and Fourier Analysis where he was able settling several long standing conjectures. With his move to Bonn his research interests shifted to the emerging area of multivariate splines. First groundbreaking contributions earned him the IBM Fellowship. Aside from applications in Computer Aided Geometric Design (CAGD) part of this work found later surprising applications in Combinatorial Number Theory and Algebra. His joint results with A. Cavaretta and C.A. Micchelli on Subdivison Algorithms, collected in a highly cited article in Memoirs of the American Mathematical Society, was a natural link between Spline Theory and the emerging field of Wavelet- and Multi-Scale analysis. His guiding objective in this field was to build a “Fourier-free’’ theory that paved the way to using these concepts for the numerical solution and analysis of partial differential and singular integral equations. After establishing first optimal wavelet-based matrix compression results with R. Schneider he started a still lasting collaboration with P. Binev, A. Cohen and R. DeVore. A central contribution of this direction of research was a first rigorous development of adaptive solution concepts with optimal complexity for a wide range of operator equations. Moreover, the deep roots of this work in Nonlinear Approximation Theory allowed them subsequently to develop together with other members of the IMI optimal (in the sense of rate-distortion theory) image compression schemes optimally performing universal estimators in Machine Learning and instance optimal decoders in Compressed Sensing. First convergence proofs for Reduced Basis methods then led to research on forward and inverse problems in Uncertainty Quantification with a focus on the role of model order reduction in this context. In this area high-dimensionality is an intrinsic obstruction. His results with M. Bachmayr on Low-Rank and Hierarchical Tensor Methods mark a rigorous approach that defeats the Curse of Dimensionality for a range of problems. His theoretical research has always benefitted greatly from intense interdisciplinary collaborations on multiscale methods in Fluid Mechanics and Process Monitoring at RWTH Aachen as well as on Structural Imaging in Electron Microscopy (together with P. Binev, D. Blom, and T. Vogt) at UofSC.

In 2002 he was awarded the Gottfried-Wilhem-Leibniz Prize, the highest science recognition in Germany. Together with P. Binev and T. Vogt he received a Keck Future initiative Award in 2010. In 2019 he received the Robert-Piloty Prize and was elected as a SIAM-Fellow.

Among his nearly hundred invited lectures the ICM 94, Zürich, and ICIAM 2019, Valencia, stand out. He has held 16 Lecture series 16 (e.g. Guangzhou, New Delhi, Texas A&M, ETH Zürich, Cambridge). He had numerous research visits (e.g. Princeton, IBM, N.Y., Texas A&M, Tel Aviv, Amsterdam, Warsaw, Cambridge, Beijing, Columbia, Alberta, Paris, Copenhagen, Minneapolis, Prague) and lecture series (e.g. Barcelona, Dobiacco, Guangzhou, New Delhi, Texas A&M, Bern, ETH Zürich, Cambridge).

Since 2003 he has been co-Editor-in-Chief of the Journal Constructive Approximation and has been serving on the editorial boards of the Journal of Approximation Theory and Applications, Advances in Computational Mathematics (- 2004), Applied Computational and Harmonic Analysis, SIAM Journal Mathematical Analysis (-2012), SIAM Journal Numerical Analysis (-2012), Journal of Foundations of Comp. Math., Journal of Approximation Theory, Numerische Mathematik; (-2014), M2AN, Acta Numerica, Advanced Structural and Chemical Imaging (ASCI); SIAM Journal of Uncertainty Quantification (JUQ), Research in the Mathematical Sciences (RMS).

Since 2009, he has been a member of the German National Academy of Sciences, Leopoldina. He served on a number of high ranking committees such as the Chair of the selection committee for the Gauss-Award 2010 of the International Union of Mathematicians, the IMU Circle, the advisory board of the Cluster of Excellence “Future Ocean”, University of Kiel, 2007-2010, the advisory board of the Department of Mathematics, University of Aveiro, Portugal, 2008-2010, the Senate of the DFG, 2005-2011, the ERC (European Research Council) Panel PE1: Mathematics, Physical Sciences, 2006–2010, Executive Committee of FoCM (Foundations of Computational Mathematics), 1995-present, the Scientific Board of the ZIF (Center for Interdisciplinary Research), Bielefeld, 1994-2009, the selection board for the Cantor Medal awarded by DMV, the panel 16 for ICM06, 2006, the Scientific Committee of the CRM (Centre de Recerca Matemàtica), Barcelona, 2011-2015, Scientific Advisory Committee of the Isaac-Newton Institute, University of Cambridge, UK, Chair of the Board of Directors of FoCM, 2014-2017.

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