Zurich Colloquium in Applied and Computational Mathematics

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Archive 2013

Date / Time

Speaker

Title

Location

30 January 2013
16:15-17:15

Prof. Dr. Zhiming Chen
Chinese Academy of Science, Beijing

Event Details

Speaker invited by	R. Hiptmair

Perfectly Matched Layers

HG G 19.2

27 February 2013
16:15-17:15

Giuseppe Maria Coclite
Università di Bari, Italy

Event Details

Speaker invited by

S. Mishra

Abstract

We consider a system of scalar balance laws in one space dimension coupled with a system of ordinary differential equations. The coupling acts through the (moving) boundary condition of the balance laws and the vector fields of the ordinary differential equations. We prove the existence of solutions for such systems passing to the limit in a vanishing viscosity approximation. The results were obtained in collaboration with Professor Mauro Garavello.

Systems with moving boundaries

HG E 1.2

7 March 2013
14:00-16:00

Prof. Dr. Philip Gressman
University of Pennsylvania

Event Details

Minicourse on "The Boltzmann Equation and Harmonic Analysis"

HG G 19.1

8 March 2013
13:00-15:00

Prof. Dr. Philip Gressman
University of Pennsylvania

Event Details

Minicourse on "The Boltzmann Equation and Harmonic Analysis"

HG G 19.1

13 March 2013
15:00-17:00

Prof. Dr. Philip Gressman
University of Pennsylvania

Event Details

Minicourse on "The Boltzmann Equation and Harmonic Analysis"

HG G 19.1

14 March 2013
14:00-16:00

Prof. Dr. Philip Gressman
University of Pennsylvania

Event Details

Minicourse on "The Boltzmann Equation and Harmonic Analysis"

HG G 19.1

20 March 2013
16:15-17:15

Prof. Dr. Victor Nistor
Penn State University, USA

Event Details

Speaker invited by

Ch. Schwab

Abstract

We establish optimal higher orders of convergence for Galerkin approximations for parametric, second order elliptic partial differential equations on polyhedral domains. This method combines a good refinement strategy for meshes on the given polyhedral domain with an adaptive choice of Finite Element space for each component in a generalized chaos expansion using tensorized Lagendre polynomials. Similar results hold for parametric transmission problems in two dimensions. A common feature of these results is that they require a uniform "shift theorem" in the uncertainty parameter for equations with coefficients of minimal regularity. As in the non-parametric case, our results rely on weighted Sobolev (or Babuska-Kondratiev) spaces. These results are part of joint works with H. Li, Y. Qiao, and C. Schwab.

High order Galerkin approximations for parametric elliptic partial differential equations on polyhedral domains

HG E 1.2

27 March 2013
16:15-17:15

Prof. Dr. Gitta Kutyniok
TU Berlin, Germany

Event Details

Speaker invited by

Ph. Grohs

Abstract

Modern imaging data are often composed of several geometrically distinct constituents. For instance, neurobiological images could consist of a superposition of spines (pointlike objects) and dendrites (curvelike objects) of a neuron. A neurobiologist might then seek to extract both components to analyze their structure separately for the study of Alzheimer specific characteristics. However, this task seems impossible, since there are two unknowns for every datum. Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered from what was previously considered highly incomplete linear measurements, by using efficient algorithms. Utilizing the methodology of Compressed Sensing, the geometric separation problem can indeed be solved both numerically and theoretically. For the separation of point- and curvelike objects, we choose a deliberately overcomplete representation system made of wavelets (suited to pointlike structures) and shearlets (suited to curvelike structures). The decomposition principle is to minimize the $\ell_1$ norm of the representation coefficients. Our theoretical results, which are based on microlocal analysis considerations, show that at all sufficiently fine scales, nearly-perfect separation is indeed achieved. This project was done in collaboration with David Donoho (Stanford University) and Wang-Q Lim (TU Berlin).

Imaging Science meets Compressed Sensing

HG E 1.2

3 April 2013
00:00-00:00

Event Details

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