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Zurich Colloquium in Applied and Computational Mathematics
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Date / Time  Speaker  Title  Location  

26 April 2017 16:1517:15 
Prof. Dr. XueMei 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 semigrouops: the lower bound of the Ricci curvature by gradient bounds on the heat semigroup; 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 selfadjoint operator, which is the sum of the LaplaceBeltrami 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 FeynmanKac formulas, and the role of the Brownian bridges and the semiclassical Brownian bridges. 

3 May 2017 16:1517:15 
Prof. Dr. Dmitri Kuzmin Technische Universität Dortmund 
FluxCorrected Transport Schemes for HighOrder Bernstein Finite Elements  Y27 H 25  
Speaker invited by:
Remi Abgrall
Abstract: This talk presents the first extensions of the fluxcorrected transport (FCT) methodology to discontinuous and continuous highorder 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 accuracypreserving FCT schemes for highorder BernsteinBezier 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 16:1517:15 
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 lowrank 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 16:1517:15 
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 14:0015:00 
Prof. Dr. Mikhail Shashkov Los Alamos National Laboratory 
Title T.B.A.  KO2 F 152  
Speaker invited by:
Remi Abgrall


31 May 2017 16:1517:15 
Dr. Maxim Rakhuba SkTech Institute, Moscow, Russia 
Title T.B.A.  Y27 H 25  
Speaker invited by:
Christoph Schwab


4 October 2017 16:1517:15 
Prof. Dr. Bertrand Maury Universite de Paris Sud 
Title T.B.A.  HG E 1.2  
Speaker invited by:
Habib Ammari


11 October 2017 16:1517:15 
Prof. Dr. Dirk Bloemker University of Augsburg, FRG 
Title T.B.A.  HG E 1.2  
Speaker invited by:
Arnulf Jentzen


13 December 2017 16:1517:15 
Prof. Dr. Olaf Steinbach TU Graz, Österreich 
Title T.B.A.  HG E 1.2  
Speaker invited by:
Christoph Schwab
