Zurich colloquium in applied and computational mathematics

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Spring Semester 2013

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Speaker

Title

Location

30 January 2013
16:15-17:15

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

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Perfectly Matched Layers
Speaker, Affiliation	Prof. Dr. Zhiming Chen, Chinese Academy of Science, Beijing
Date, Time	30 January 2013, 16:15-17:15
Location	HG G 19.2

Perfectly Matched Layers

HG G 19.2

27 February 2013
16:15-17:15

Giuseppe Maria Coclite
Università di Bari, Italy

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Systems with moving boundaries
Speaker, Affiliation	Giuseppe Maria Coclite, Università di Bari, Italy
Date, Time	27 February 2013, 16:15-17:15
Location	HG E 1.2
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 boundariesread_more

HG E 1.2

7 March 2013
14:00-16:00

Prof. Dr. Philip Gressman
University of Pennsylvania

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Minicourse on "The Boltzmann Equation and Harmonic Analysis"
Speaker, Affiliation	Prof. Dr. Philip Gressman, University of Pennsylvania
Date, Time	7 March 2013, 14:00-16:00
Location	HG G 19.1

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

Zurich Colloquium in Applied and Computational Mathematics

Title	Minicourse on "The Boltzmann Equation and Harmonic Analysis"
Speaker, Affiliation	Prof. Dr. Philip Gressman, University of Pennsylvania
Date, Time	8 March 2013, 13:00-15:00
Location	HG G 19.1

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

Zurich Colloquium in Applied and Computational Mathematics

Title	Minicourse on "The Boltzmann Equation and Harmonic Analysis"
Speaker, Affiliation	Prof. Dr. Philip Gressman, University of Pennsylvania
Date, Time	13 March 2013, 15:00-17:00
Location	HG G 19.1

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

Zurich Colloquium in Applied and Computational Mathematics

Title	Minicourse on "The Boltzmann Equation and Harmonic Analysis"
Speaker, Affiliation	Prof. Dr. Philip Gressman, University of Pennsylvania
Date, Time	14 March 2013, 14:00-16:00
Location	HG G 19.1

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

Zurich Colloquium in Applied and Computational Mathematics

Title	High order Galerkin approximations for parametric elliptic partial differential equations on polyhedral domains
Speaker, Affiliation	Prof. Dr. Victor Nistor, Penn State University, USA
Date, Time	20 March 2013, 16:15-17:15
Location	HG E 1.2
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 domainsread_more

HG E 1.2

27 March 2013
16:15-17:15

Prof. Dr. Gitta Kutyniok
TU Berlin, Germany

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Imaging Science meets Compressed Sensing
Speaker, Affiliation	Prof. Dr. Gitta Kutyniok, TU Berlin, Germany
Date, Time	27 March 2013, 16:15-17:15
Location	HG E 1.2
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 Sensingread_more

HG E 1.2

3 April 2013
00:00-00:00

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Easter break - no colloquium
Speaker, Affiliation
Date, Time	3 April 2013, 00:00-00:00
Location

Easter break - no colloquium

10 April 2013
16:15-17:15

Dr. Dmitry Savostyanov
University of Southampton, UK

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Alternating minimal energy methods for linear systems in higher dimensions
Speaker, Affiliation	Dr. Dmitry Savostyanov, University of Southampton, UK
Date, Time	10 April 2013, 16:15-17:15
Location	HG E 1.2
Abstract	We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and follow the alternating directions framework, but in contrast to ALS methods, in each iteration a tensor subspace is expanded by a set of vectors chosen similarly to the steepest descent algorithm. The convergence is analysed in the presence of approximation errors and the geometrical convergence rate is estimated and related to the one of the steepest descent. The complexity of the presented algorithms is linear in the mode size and dimension and the convergence demonstrated in the numerical experiments is comparable to the one of the DMRG--type algorithm. Numerical comparison with conventional tensor methods is provided. Application to high--dimensional problem of quantum chemistry (NMR simulation) is demonstrated.

Alternating minimal energy methods for linear systems in higher dimensionsread_more

HG E 1.2

17 April 2013
16:15-17:15

Prof. Dr. Gheorghe Craciun
University of Madison, Wisconsin, USA

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Multiple equilibria, global injectivity and persistence for mathematical models of biological networks
Speaker, Affiliation	Prof. Dr. Gheorghe Craciun, University of Madison, Wisconsin, USA
Date, Time	17 April 2013, 16:15-17:15
Location	HG E 1.2
Abstract	Mathematical models of biological interaction networks give rise to nonlinear dynamical systems with many unknown terms or parameters. We describe criteria for existence of multiple equilibria in these models (i.e., for the network to be able to implement a "biological switch"), and for persistence of solutions (i.e., for the variables not to "go extinct"). We also describe how these criteria can be generalized to analyze global injectivity of general nonlinear functions which are not necessarily derived from interaction networks, and to analyze persistence of general polynomial and power-law dynamical systems. We will also point out connections to Hilbert's 16th problem and the Jacobian Conjecture.

Multiple equilibria, global injectivity and persistence for mathematical models of biological networksread_more

HG E 1.2

24 April 2013
16:15-17:15

Prof. Dr. Helmut Harbrecht
Universität Basel

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Modelling and simulation of elliptic PDEs on random domains
Speaker, Affiliation	Prof. Dr. Helmut Harbrecht, Universität Basel
Date, Time	24 April 2013, 16:15-17:15
Location	HG E 1.2
Abstract	We consider the numerical solution of elliptic boundary value problems on random domains. The proposed method computes the mean and the variance of the random solution with leading order in the amplitude of the random boundary perturbation relative to an unperturbed, nominal domain. The variance is computed from the solution's two point correlation which satisfies a deterministic boundary value problem on the tensor product of the nominal domain. We solve this moderately high-dimensional problem by either a low-rank approximation by means of the pivoted Cholesky decomposition or the combination technique. Both approaches are presented and compared by numerical experiments with respect to their efficiency.

Modelling and simulation of elliptic PDEs on random domainsread_more

HG E 1.2

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08:00-10:00

Prof. Dr. Ivan Oseledets
Russian Academy of Sciences, Moscow, Russia

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	SNF ProDoc Minicourses on 'Numerik' 2013: Numerical computations in higher dimensions: theory, algorithms, software
Speaker, Affiliation	Prof. Dr. Ivan Oseledets, Russian Academy of Sciences, Moscow, Russia
Date, Time	NaN undefined NaN, 08:00-10:00
Location	HG D 16.2

SNF ProDoc Minicourses on 'Numerik' 2013: Numerical computations in higher dimensions: theory, algorithms, software

HG D 16.2

22 May 2013
16:15-17:15

Prof. Dr. Angela Kunoth
Universität Paderborn

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Sparse Adaptive Tensor Galerkin Approximations of Parametric PDE-Constrained Control Problems
Speaker, Affiliation	Prof. Dr. Angela Kunoth, Universität Paderborn
Date, Time	22 May 2013, 16:15-17:15
Location	HG E 1.2
Abstract	Optimization problems constrained by linear parabolic evolution PDEs are challenging from a computational point of view, as they require to solve a system of PDEs coupled globally in time and space. For their solution, conventional time-stepping methods quickly reach their limitations due to the enormous demand for storage. For such a coupled PDE system, adaptive methods which aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities in the data or domain, with respect to both space and time, appear to be most promising. Employing wavelet schemes for full weak space-time formulations of the parabolic PDEs, we can prove convergence and optimal complexity. Yet another level of challenge are control problems constrained by evolution PDEs involving stochastic or countably many infinite parametric coefficients: for each instance of the parameters, this requires the solution of the complete control problem. Our method of attack is based on the following new theoretical paradigm. It is first shown for control problems constrained by evolution PDEs, formulated in full weak space-time form, that state, costate and control are analytic as functions depending on these parameters. Moreover, we establish that these functions allow expansions in terms of sparse tensorized generalized polynomial chaos (gpc) bases. Their sparsity is quantified in terms of p-summability of the coefficient sequences for some 0 < p <= 1. Resulting a-priori estimates establish the existence of an index set, allowing for concurrent approximations of state, co-state and control for which the gpc approximations attain rates of best N-term approximation. These findings serve as the analytical foundation for the development of corresponding sparse realizations in terms of deterministic adaptive Galerkin approximations of state, co-state and control on the entire, possibly infinite-dimensional parameter space. The results were obtained jointly with Christoph Schwab.

Sparse Adaptive Tensor Galerkin Approximations of Parametric PDE-Constrained Control Problemsread_more

HG E 1.2

29 May 2013
16:15-17:15

Martin Bauer
Universität Wien

Event Details

Zurich Colloquium in Applied and Computational Mathematics

Title	Riemannian Geometry of Shape Spaces
Speaker, Affiliation	Martin Bauer, Universität Wien
Date, Time	29 May 2013, 16:15-17:15
Location	HG E 1.2
Abstract	I will provide an overview of various notions of shape spaces, including the space of parametrized and unparametrized surfaces. I will discuss the Riemannian metrics that can be defined thereon, and what is known about the properties of these metrics. I will put particular emphasis on the induced geodesic distance, the geodesic equation and its well-posedness, geodesic and metric completeness and properties of the curvature. In addition I will present selected numerical examples illustrating the behavior of these metrics.

Riemannian Geometry of Shape Spacesread_more

HG E 1.2

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Organizers: Philipp Grohs, Ralf Hiptmair, Arnulf Jentzen, Siddhartha Mishra, Christoph Schwab

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09