# Department of **Mathematics**

## Directory

## Wolfgang Dahmen

Title: |
SmartState Endowed Chair in Data Analysis, Simulation, Imaging and Visualization,
Williams-Hedberg-Hedberg Chair in Mathematics |

Department: |
Mathematics College of Arts and Sciences |

Email: |
dahmen@math.sc.edu |

Phone: |
803-576-5630 |

Office: |
LeConte 317H |

Resources: |
Department of Mathematics DASIV |

### 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 |

### 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

**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)