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Zurich colloquium in applied and computational mathematics

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Autumn Semester 2023

Date / Time Speaker Title Location
27 September 2023
16:30-17:30 		Prof. Dr. H. Gimperlein
Leopold-Franzens-Universität Innsbruck
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Zurich Colloquium in Applied and Computational Mathematics

Title Boundary integral equations in space and time: Higher order Galerkin methods and applications
Speaker, Affiliation Prof. Dr. H. Gimperlein, Leopold-Franzens-Universität Innsbruck
Date, Time 27 September 2023, 16:30-17:30
Location HG E 1.2
Abstract Boundary integral formulations are well-known to lead to efficient numerical methods for time-independent scattering and emission problems. In this talk we consider corresponding formulations for the time-dependent acoustic and elastic wave equations. We survey recent work on space-time Galerkin methods for the numerical solution, including higher order approximations by h- and hp-versions, a posteriori error estimates and adaptive mesh refinements, and illustrate them for applications in traffic noise.
Boundary integral equations in space and time: Higher order Galerkin methods and applicationsread_more
HG E 1.2
4 October 2023
16:30-17:30 		Prof. Dr. Wenjia Jing
Tsinghua University
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Zurich Colloquium in Applied and Computational Mathematics

Title Quantitative homogenization of elliptic problems in periodic high contrast environments
Speaker, Affiliation Prof. Dr. Wenjia Jing, Tsinghua University
Date, Time 4 October 2023, 16:30-17:30
Location HG E 1.2
Abstract We consider elliptic equations with periodic high contrast coefficients and study the asymptotic analysis when the periodicity is sent to zero and/or the contrast parameters are sent to extreme values. Those coefficients model small inclusions that have very different physical properties compared to the surrounding environment. Homogenization captures the macroscopic effects of those inclusions. We report some quantitative results such as the convergence rates of the homogenization (with proper correctors), uniform regularity for the solutions of the heterogeneous equations, and so on. The talk is based on joint works with Mr. Xin Fu.
Quantitative homogenization of elliptic problems in periodic high contrast environmentsread_more
HG E 1.2
11 October 2023
16:30-17:30 		Dr. Théophile Chaumont-Frelet
Inria
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Zurich Colloquium in Applied and Computational Mathematics

Title Asymptotically optimal a priori and a posteriori error estimates for edge finite element discretizations of time-harmonic Maxwell's equations
Speaker, Affiliation Dr. Théophile Chaumont-Frelet, Inria
Date, Time 11 October 2023, 16:30-17:30
Location HG E 1.2
Abstract Time-harmonic Maxwell's equations model the propagation of electromagnetic waves, and their numerical discretization by finite elements is instrumental in a large array of applications. In the simpler setting of acoustic waves, it is known that (i) the Galerkin Lagrange finite element approximation to a Helmholtz problem becomes asymptotically optimal as the mesh is refined. Similarly, (ii) asymptotically constant-free a posteriori error estimates are available for Helmholtz problems. In this talk, considering Nédélec finite element discretizations of time-harmonic Maxwell's equations, I will show that (i) still holds true and propose an a posteriori error estimator providing (ii). Both results appear to be novel contributions to the existing literature.
Asymptotically optimal a priori and a posteriori error estimates for edge finite element discretizations of time-harmonic Maxwell's equationsread_more
HG E 1.2
25 October 2023
16:30-17:30 		Prof. Dr. Gianluca Crippa
Departement Mathmatik und Informatik, Universität Basel
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Zurich Colloquium in Applied and Computational Mathematics

Title Anomalous dissipation in fluid dynamics
Speaker, Affiliation Prof. Dr. Gianluca Crippa, Departement Mathmatik und Informatik, Universität Basel
Date, Time 25 October 2023, 16:30-17:30
Location HG E 1.2
Abstract Kolmogorov's K41 theory of fully developed turbulence advances quantitative predictions on anomalous dissipation in incompressible fluids: although smooth solutions of the Euler equations conserve the energy, in a turbulent regime information is transferred to small scales and dissipation can happen even without the effect of viscosity, and it is rather due to the limited regularity of the solutions. In rigorous mathematical terms, however, very little is known. In a recent work in collaboration with M.~Colombo and M.~Sorella we consider the case of passive-scalar advection, where anomalous dissipation is predicted by the Obukhov-Corrsin theory of scalar turbulence. In my talk, I will present the general context and illustrate the main ideas behind our construction of a velocity field and a passive scalar exhibiting anomalous dissipation in the supercritical Obukhov-Corrsin regularity regime. I will also describe how the same techniques provide an example of lack of selection for passive-scalar advection under vanishing diffusivity, and an example of anomalous dissipation for the forced Euler equations in the supercritical Onsager regularity regime (this last result has been obtained in collaboration with E.~Bru\`e, M.~Colombo, C.~De Lellis, and M.~Sorella).
Anomalous dissipation in fluid dynamicsread_more
HG E 1.2
1 November 2023
16:30-17:30 		Prof. Dr. Daniele Boffi
KAUST
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Zurich Colloquium in Applied and Computational Mathematics

Title On the numerical approximation of parameter dependent PDE eigenvalue problems
Speaker, Affiliation Prof. Dr. Daniele Boffi, KAUST
Date, Time 1 November 2023, 16:30-17:30
Location HG E 1.2
Abstract In this talk I will discuss the numerical approximation of PDE eigenvalue problems depending on a finite number of deterministic parameters. The parameters can be part of the problem or can be introduced by the discretization. It turns out that eigenvalue problems are influenced by the presence of parameters in a way that doesn't compare to the corresponding source problem. We present several examples and counterexamples, showing the difficulties arising when eigenvalues and eigenfunctions need to be approximated accurately. A crucial aspect of parametric eigenvalue problems is the lack of regularity with respect to the parameter, unless a special sorting is considered, taking into account appropriately possible crossings and clustering. On the other hand, parameters arising from the discretizing scheme can be source of spurious solutions.
On the numerical approximation of parameter dependent PDE eigenvalue problemsread_more
HG E 1.2
15 November 2023
16:30-17:30 		Prof. Dr. Svitlana Mayboroda
ETH Zurich, Switzerland
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Zurich Colloquium in Applied and Computational Mathematics

Title Wave Localization
Speaker, Affiliation Prof. Dr. Svitlana Mayboroda, ETH Zurich, Switzerland
Date, Time 15 November 2023, 16:30-17:30
Location HG E 1.2
Abstract Waves of all kinds permeate our world. We are surrounded by light (electromagnetic waves), sound (acoustic waves), and mechanical vibrations. Quantum mechanics revealed that, at the atomic level, all matter has a wavelike character. And classical gravitational waves have been very recently detected. At the cutting edge of today’s science, it has become possible to manipulate individual atoms. This provides us with precise measurements of a world that exhibits myriad irregularities — dimensional, structural, orientational, and geometric— simultaneously. For waves, such disorder changes everything. In complex, irregular, or random media, waves frequently exhibit astonishing and mysterious behavior known as ‘localization’. Instead of propagating over extended regions, they remain confined in small portions of the original domain. The Nobel Prize–winning discovery of the Anderson localization in 1958 is only one famous case of this phenomenon. Yet, 60 years later, despite considerable advances in the subject, we still notoriously lack tools to fully understand localization of waves and its consequences. We will discuss modern understanding of the subject, recent results, and the biggest open questions.
Wave Localizationread_more
HG E 1.2
29 November 2023
16:30-17:30 		Prof. Dr. Daniel Freeman
Saint Louis University, USA
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Zurich Colloquium in Applied and Computational Mathematics

Title Vector recovery from saturated frame coefficients
Speaker, Affiliation Prof. Dr. Daniel Freeman, Saint Louis University, USA
Date, Time 29 November 2023, 16:30-17:30
Location HG E 1.2
Abstract A frame (x_j) for a Hilbert space H allows for a linear and stable reconstruction of any vector x in H from the linear measurements (). However, there are many situations where some information of the frame coefficients is lost. In applications such as signal processing, electrical engineering, and digital photography one often uses sensors with an effective range and any measurement above that range is registered as the maximum. Depending on the context, recovering a vector from such measurements is called either declipping or saturation recovery. We will discuss a frame theoretic approach to this problem in a similar way to what Balan, Casazza, and Edidin did for phase retrieval. This perspective motivates many interesting open problems. The talk is based on joint work with W. Alharbi, D. Ghoreishi, B. Johnson, and N. Randrianarivony.
Vector recovery from saturated frame coefficientsread_more
HG E 1.2
13 December 2023
16:30-17:30 		Dr. Dmitry Batenkov
Tel Aviv University
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Zurich Colloquium in Applied and Computational Mathematics

Title Super-resolution of sparse measures: recent advances
Speaker, Affiliation Dr. Dmitry Batenkov, Tel Aviv University
Date, Time 13 December 2023, 16:30-17:30
Location HG E 1.2
Abstract The inverse problem of computational super-resolution is to recover fine features of a signal from bandlimited and noisy data. Despite long history of the question and its fundamental importance in science and engineering, relatively little is known regarding optimal accuracy of reconstructing the high resolution signal components, and how to attain it with tractable algorithms. In this talk I will describe recent progress on deriving optimal methods for super-resolving sparse sums of Dirac masses, a popular model in numerous applications such as spectral estimation, direction of arrival, imaging of point sources, and sampling signals below the Nyquist rate. Time permitting, I will also discuss generalizations of the theory and algorithms in several directions.
Super-resolution of sparse measures: recent advancesread_more
HG E 1.2

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