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

Education

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

Honors and Awards

• Keck Future Initiative Award (National Academies, USA) University of South Carolina (2011)
• Member Scientific Committee of the CRM (Centre de Recerca Matemàtica), Barcelona (2011 – present)
• ISI Highly Cited (2001 – present)
• Gottfried Wilhelm Leibniz Award (2002)
• Invited Lecture, International Congress of Mathematicians, Zürich, (1994)
• Election to the German National Academy of Sciences, Leopoldina, (2009)
• Member, Senate of the German Research Foundation (2005 – 2011)
• Member, Steering Committee of the Isaac-Newton-Institute, Cambridge, UK (2014 – present)
• Chair, Society Foundations of Computational Mathematics (2015 – present)

Experience

• Professor, University of South Carolina (2017 – Present)
• Adjunct Professor, University of South Carolina (2005 – 2015)
• Professor (C4), Institute of Geometry & Practical Mathematics, RWTH Aachen (1992 – 2017)
• Professor (C4), Free University of Berlin (1987 – 1992)
• Professor (C3), University of Bielefeld (1981 – 1987)
• IBM Postdoctoral Fellow, IBM T.J. Watson Research Center, NY (1979 – 1980)
• Wissenschaftlicher Assistant, Institute of Applied Mathematics, University of Bonn (1976 – 1981)
• Research Assistant, Lehrstuhl A fur Mathematik, RWTH Aachen (1974 – 1976)

Courses Taught

At USC

• Numerical methods for PDEs with emphasis on variational formulations
• Wavelet methods for PDEs
• Hyperbolic conservation laws

At RWTH Aachen

• Interpolation of Function Spaces and Approximation
• Adaptive solution concepts
• Mathematical foundations in image processing
• Numerical Analysis I - IV
• Numerical Analysis for Mechanical Engineers
• Numerical Analysis for Electrical Engineers
• Approximation in high dimensions
• Numerical methods for hyperbolic problems

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.