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Department of Mathematics


Wolfgang Dahmen

Title: Williams Hedberg Chair Emeritus
Department: Mathematics
College of Arts and Sciences
Phone: 803-576-5630

LeConte 331
Sumwalt 206F, phone: 803-576-6349

Office Hours: 11:30 - 12:30 Tuesday, Thursday
Resources: Department of Mathematics
Wolfgang Dahmen


Habilitation Mathematics University of Bonn, Germany 1981
Ph.D. Mathematics RWTH Aachen, Germany 1976
Diploma Mathematics/Secondary Physics RWTH Aachen, Germany 1974


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

Course Taught

  • 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.)


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 free-form optical surfaces for laser optics by methods of optimal transport (with K. Brix, E. Friebel)
  • Development and analysis of adaptive low-rank schemes for high-dimensional 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 non-coercive 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 well-conditioned variational formulations and their computational realization.
  • Analyzing tensor-sparsity of solutions to high dimensional PDEs like Fokker-Planck 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. Campos-Pinto, C. Canuto).

Honors and Awards

  • 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, 2011-present
  • 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 (2005-2011)
  • Member of the Steering Committee of the Isaac-Newton-Institute, Cambridge, UK (2014 -)
  • Chair of the society Foundations of Computational Mathematics (2015–)

(For complete list see CV)

Selected Publications

  • W. Dahmen, Wavelet and Multiscale Methods for Operator Equations, (invited contribution) % to Acta Numerica, Cambridge University Press, 6(1997), 55-228.
  • A. Cohen, W. Dahmen, R. DeVore, Adaptive wavelet methods for elliptic operator equations -- Convergence rates, Math. Comp., 70 (2001), 27-75.
  • P. Binev, W. Dahmen, R. DeVore, Adaptive Finite Element Methods with Convergence Rates, Numer. Math., 97(2004), 219-268.
  • A. Barron, A. Cohen, W. Dahmen, R. DeVore, Approximation and learning by greedy algorithms, Annals of Statistics, 3(1)(2008), 64-94.
  • 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), 1457-1472.

(For complete list see CV)

Challenge the conventional. Create the exceptional. No Limits.