Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Institutskolloquium am 27.01.2015

  • Wann 27.01.2015 von 17:00 bis 19:00
  • Wo RUD 25, 1.013
  • iCal

Prof. Dr. Albert C o h e n
Universite Pierre et Marie Curie, Paris


"Estimating the n-width of solution manifolds of parametric PDE's".

Abstract: Numerous computational model reduction methods, such as
reduced basis and its generalization, proper orthogonal decomposition,
generalized empirical interpolation, rely on the implicit assumption
that the solution manifold, that gathers the solution to a PDE as
parameters vary, can be well approximated by low dimensional spaces.
This is made more precise by assuming that the Kolmogorov n-width of the
manifold has certain decay. In this talk, I shall discuss strategies
that allow to rigorously establish rates of decay for the Kolmogorov
n-width of solution manifolds associated with relevant parametric PDE’s,
where the parameters are infinite dimensional. One key result is that
the rate of decay of n-width of sets in Banach space is almost preserved
under the action of holomorphic maps.

About Albert Cohen: His early research focused on wavelet analysis,
where he has made many fundamental contributions, e.g. together with I.
Daubechies and J. C Feauveau the construction of biorthogonal wavelet
bases which are used in the state of the art image compression standard
JPEG 2000. Since then, his research is oriented in various application
directions, with as a common denominator its theoretical foundations in
nonlinear approximation theory and harmonic analysis. Some of the most
significant results are concerned with the analysis of adaptive
numerical methods for PDE's, the Banach space BV, greedy algorithms, and
statistical learning theory.

Albert Cohen was invited speaker at the ICM, Beijing, in 2002 and
plenary invited speaker at ICIAM, Zürich, in 2007. He received several
distinctions, among which the V.A. Popov prize in approximation theory
in 1995, the J. Herbrant prize of the French Académie des Sciences in
2002 and the Blaise Pascal prize in 2004. He is associate editor of
several first rank journals, including Applied and Computational
Harmonic Analysis, SIAM Journal on Numerical Analysis and Numerische
Mathematik. He is currently member of the Institut Universitaire de

The Colloquium will take place on 27.01.2015 at 17 c.t. at Rudower
Chaussee 25 in room I.013.