Zurich Colloquium in Applied and Computational Mathematics

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Date / Time Speaker Title Location
29 March 2017
Prof. Dr. Mathias Fink
Wave Control and Holography with Time Transformations  Y27  H 25
Speaker invited by: Habib Ammari
Abstract: Because time and space play a similar role in wave propagation, wave control can be achieved or by manipulating spatial boundaries or by manipulating time boundaries. Here we emphasize the role of time boundaries manipulation. We show that sudden changes of the medium properties generate instant wave sources that emerge instantaneously from the entire wavefield and can be used to control wavefield and to revisit the holographic principles and the way to create time-reversed waves. Experimental demonstrations of this approach with water waves will be presented and the extension of this concept to acoustic and electromagnetic waves will be discussed. More sophisticated time manipulations can also be studied in order to extend the concept of photonic crystals and wave localization in the time domain.
5 April 2017
Prof. Dr. Eitan Tadmor
University of Maryland
Hydrodynamic flocking: pressure-less equations and alignment-based commutator structure  Y27  H 25
Speaker invited by: Remi Abgrall
Abstract: We discuss the question of global regularity for a general class of Eulerian dynamics driven by a forcing with a commutator structure. The study of such systems is motivated by the hydrodynamic description of agent-based models for flocking driven by alignment. For commutators involving bounded kernels, existence of strong solutions follows for initial data which are sub-critical, namely - the initial divergence is “not too negative” and the initial spectral gap is “not too large”. Singular kernels, corresponding to fractional Laplacian behave better: global regularity persists and flocking follows. Singularity helps! A similar role of the spectral gap appears in the study of two-dimensional pressure-less equations. Here, we develop a new BV framework to prove the existence of weak dual solutions for the 2D pressure-less Euler equations as vanishing viscosity limits.
12 April 2017
Dr. Máté Gerencsér
Institute of Science and Technology, Austria
Characteristics of SPDEs  Y27  H 25
Speaker invited by: Arnulf Jentzen
Abstract: We discuss Feynman-Kac formulae for linear stochastic PDEs. Due to the adapted randomness of the equations to be represented, the associated backward flow does not make (Itô) sense, and hence the temporal inversion has to be replaced by a spatial inversion. Some applications of such formulae to numerics and the theory of SPDEs will be outlined. Based on joint work with I. Gyöngy.
26 April 2017
Prof. Dr. Xue-Mei Li
University of Warwick
Weighted heat kernels and 'Brownian bridges'  Y27  H 25
Speaker invited by: Arnulf Jentzen
Abstract: Gaussian upper and lower bounds for heat kernels are the basic tools for large deviation estimates. There are two well known characterisations on the derivatives of heat semi-grouops: the lower bound of the Ricci curvature by gradient bounds on the heat semi-group; and the validity of the Logarithmic Sobolev inequality for the distributions of the Brownian motion by bounds on the Ricci curvature. What can we say about their second order derivatives? What can we say about the kernels of the self-adjoint operator, which is the sum of the Laplace-Beltrami operator plus a gradient vector field and a potential function? This talk will not be technical. We will discuss why the stochastic damped parallel translation and the doubly damped stochastic parallel translation equation are the natural companions for the heat equations, we will also discuss the associated estimates, the second order Feynman-Kac formulas, and the role of the Brownian bridges and the semi-classical Brownian bridges.
3 May 2017
Prof. Dr. Dmitri Kuzmin
Technische Universität Dortmund
Flux-Corrected Transport Schemes for High-Order Bernstein Finite Elements  Y27  H 25
Speaker invited by: Remi Abgrall
Abstract: This talk presents the first extensions of the flux-corrected transport (FCT) methodology to discontinuous and continuous high-order finite element discretizations of scalar conservation laws. Using Bernstein polynomials as local basis functions, we constrain the variation of the numerical solution by imposing local discrete maximum principles on the coefficients of the Bezier net. The design of accuracy-preserving FCT schemes for high-order Bernstein-Bezier finite elements requires a major upgrade of algorithms tailored for linear and multilinear Lagrange elements. The proposed ingredients include (i) a new discrete upwinding strategy leading to low order approximations with compact stencils, (ii) a variational stabilization operator based on the difference between two gradient approximations, and (iii) new localized limiters for antidiffusive element contributions. The optional use of a smoothness indicator based on a second derivative test makes it possible to avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D. This is a joint work with R. Anderson, V. Dobrev, Tz. Kolev, C. Lohmann, M. Quezada de Luna, S. Mabuza, R. Rieben, J.N. Shadid, and V. Tomov.
10 May 2017
Prof. Dr. Ivan Oseledets
INM RAS and SkolTech, Moscow
Title T.B.A.   Y27  H 25
Speaker invited by: Christoph Schwab
17 May 2017
Prof. Dr. Thanasis Fokas
University of Cambridge
Revisiting the greats: Fourier, Laplace and Riemann  Y27  H 25
Speaker invited by: Habib Ammari
Abstract: The unified transform (also referred to as the Fokas method) will be reviewed. In particular, it will be shown that this transform yields unexpected results for such classical problems as the heat equation on the half line which was first investigated by Fourier,as well as for the Laplace equation in the interior of a polygon. Interesting connections of this approach with the Riemann hypothesis has led to the proof of the Lindelof hypothesis for a close variant of the Riemann zeta function.
24 May 2017
Prof. Dr. Mikhail Shashkov
Los Alamos National Laboratory
Title T.B.A.  KO2  F 152
Speaker invited by: Remi Abgrall
31 May 2017
Dr. Maxim Rakhuba
SkTech Institute, Moscow, Russia
Title T.B.A.  Y27  H 25
Speaker invited by: Christoph Schwab
11 October 2017
Prof. Dr. Dirk Bloemker
University of Augsburg, FRG
Title T.B.A.  HG E 1.2 
Speaker invited by: Arnulf Jentzen

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