Wolfgang Dahmen
SmartState Chair 


Education
Habilitation  Mathematics  University of Bonn, Germany  1981 
Ph.D.  Mathematics  RWTH Aachen, Germany  1976 
Diploma  Mathematics/Secondary Physics  RWTH Aachen, Germany  1974 
Experience
2017 – Present  Professor  Department of Mathematics, University of South Carolina 
2005 – 2015  Adjunct Professor  Mathematics, University of South Carolina 
1992 – 2017  Professor (C4)  Institute of Geometry & Practical Mathematics, RWTH Aachen 
1987 – 1992  Professor (C4)  Mathematics, Free University of Berlin 
1981 – 1987  Professor (C3)  Mathematics, University of Bielefeld 
1979 – 1980  IBM Postdoctoral Fellow  IBM T.J. Watson Research Center, Yorktown Heights, NY 
1976 – 1981  Wissenschaftlicher Assistant  Institute of Applied Mathematics, University of Bonn 
1974 – 1976  Research Assistant  Lehrstuhl A fur Mathematik, RWTH Aachen 
Research
Research Interests
 approximation theory, especially nonlinear approximation
 computational harmonic analysis
 learning theory, compressed sensing
 image processing
 numerical analysis, especially adaptive multiscale methods for operator equations
 model order reduction methods
 interdisciplinary applications in fluid dynamics and process engineering
Current Projects
 Development of freeform optical surfaces for laser optics by methods of optimal transport (with K. Brix, E. Friebel)
 Development and analysis of adaptive lowrank schemes for highdimensional operator equations (with M. Bachmayr)
 Development of novel imaging techniques in electron microscopy (with P. Binev, R. Sharpley, T. Vogt, D. Blom) as well as mathematical learning theory in connection with regression and classification (with P. Binev, A. Cohen, R. DeVore).
 Multiscale modeling in aerodynamical applications.
 Reduced basis methods and related model order reduction concepts for noncoercive problems. This is related to the development and analysis of adaptive solvers for transport dominated PDEs (with G. Welper, C. Schwab). An important ingredient here is to establish new wellconditioned variational formulations and their computational realization.
 Analyzing tensorsparsity of solutions to high dimensional PDEs like FokkerPlanck equations modeling polymeric fluids (with R. DeVore, L. Grasedyck, E. Süli).
 Development of robust preconditioners for Discontinuous Galerkin methods on locally refined meshes with arbitrary polynomial order (with K. Brix, M. CamposPinto, C. Canuto).
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Teaching Activities
Previous Courses
 Interpolation of Function Spaces and Approximation (RWTH Aachen)
 Numerical methods for PDEs with emphasis on variational formulations (USC)
 Wavelet methods for PDEs (USC)
 Hyperbolic conservation laws (USC)
 Adaptive solution concepts (RWTH Aachen)
 Mathematical foundations in image processing (RWTH Aachen)
 Numerical Analysis I  IV (RWTH Aachen)
 Numerical Analysis for Mechanical Engineers (RWTH Aachen)
 Numerical Analysis for Electrical Engineers (RWTH Aachen)
 Approximation in high dimensions (RWTH Aachen)
 Numerical methods for hyperbolic problems (RWTH Aachen)
(This is a limited selection of all courses taught.)
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Honors and Other Special Scientific Recognition
 Keck Future Initiative Award (National Academies, USA), 2011 (together with Thomas Vogt, Peter Binev, University of South Carolina, Columbia)
 Member of the Scientific Committee of the CRM (Centre de Recerca Matemàtica), Barcelona, 2011present
 ISI Highly Cited (since 2001)
 Gottfried Wilhelm Leibniz Award (2002)
 Invitated lecture at the International Congress of Mathematicians, Zürich, 1994.
 Election to the German National Academy of Sciences, Leopoldina, (2009)
 Member of the Senate of the German Research Foundation (20052011)
 Member of the Steering Committee of the IsaacNewtonInstitute, Cambridge, UK (2014 )
 Chair of the society Foundations of Computational Mathematics (2015–)
(For complete list see CV)
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5 Selected Publications
 W. Dahmen, Wavelet and Multiscale Methods for Operator Equations, (invited contribution) % to Acta Numerica, Cambridge University Press, 6(1997), 55228.
 A. Cohen, W. Dahmen, R. DeVore, Adaptive wavelet methods for elliptic operator equations  Convergence rates, Math. Comp., 70 (2001), 2775.
 P. Binev, W. Dahmen, R. DeVore, Adaptive Finite Element Methods with Convergence Rates, Numer. Math., 97(2004), 219268.
 A. Barron, A. Cohen, W. Dahmen, R. DeVore, Approximation and learning by greedy algorithms, Annals of Statistics, 3(1)(2008), 6494.
 P.Binev, A.Cohen, W. Dahmen, R.DeVore, G. Petrova, P. Wojtaszczyk, Convergence Rates for Greedy Algorithms in Reduced Basis Methods, SIAM J. Math. Anal., 43 (2011), 14571472.
(For complete list see CV)
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IMI Preprints and Seminars
Go to the list of 15 preprints and 9 seminars by Wolfgang Dahmen.BACK TO TOP