Zurich Colloquium in Applied and Computational Mathematics

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Date / Time Speaker Title Location
26 April 2017
16:15-17:15
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
16:15-17:15
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
16:15-17:15
Prof. Dr. Ivan Oseledets
INM RAS and SkolTech, Moscow
Deep learning and tensors for the approximation of multivariate functions: recent results and open problems.  Y27  H 25
Speaker invited by: Christoph Schwab
Abstract: In this talk I overview recent results in the algorithms and theory for the approximation of multivariate functions using low-rank tensor decompositions and deep neural networks (DNN), outline connections between two areas and also discuss open problems that need to be addressed. Tensor decompositions can be applied in DNN in several ways: first, they can be used to compress layers of DNN; second, DNN can be viewed as a generalized tensor network. A separate part will be denoted to the generalization ability of DNN, which is not fully described by the standard methods, and I will show our recent experimental study of the existence of "bad" local minima for neural networks.
17 May 2017
16:15-17:15
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
14:00-15:00
Prof. Dr. Mikhail Shashkov
Los Alamos National Laboratory
Title T.B.A.  KO2  F 152
Speaker invited by: Remi Abgrall
31 May 2017
16:15-17:15
Dr. Maxim Rakhuba
SkTech Institute, Moscow, Russia
Title T.B.A.  Y27  H 25
Speaker invited by: Christoph Schwab
4 October 2017
16:15-17:15
Prof. Dr. Bertrand Maury
Universite de Paris Sud
Title T.B.A.  HG E 1.2 
Speaker invited by: Habib Ammari
11 October 2017
16:15-17:15
Prof. Dr. Dirk Bloemker
University of Augsburg, FRG
Title T.B.A.  HG E 1.2 
Speaker invited by: Arnulf Jentzen
13 December 2017
16:15-17:15
Prof. Dr. Olaf Steinbach
TU Graz, Österreich
Title T.B.A.  HG E 1.2 
Speaker invited by: Christoph Schwab

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25.04.2017
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