Thematic Programme cancelled due to COVID-19.

Nevertheless, a workshop will take place from May 17 - 18, 2021 online. 

We will focus on important recent developments and progress in applied functional and harmonic analysis. Leading experts and promising young researchers will be brought together to tackle some challenging open problems, and to discuss future research directions in applied harmonic analysis and in high-dimensional approximation. The  thematic programme will cover several topics in applied harmonic analysis, constructive approximation theory, numerical and functional analysis, sparse approximation, and discretization which represent research interests of the majority of the participants. The programme  would emphasize several new exciting and promising directions in applied functional analysis, aiming to present the most recent results, and to advance the mathematical understanding of the deep interplay between functional analysis, approximation theory, and probability.

Online-Workshop on "CHEBYSHEV-200", May 17 - 18, 2021

Monday at 16:00 (Vienna time)
Ron DeVore (Texas A&M University)
Title: Learning from Data:  From Chebyshev to Deep Learning

Abstract:
Deep Learning (DL)  is the current method of choice for recovering a function from data observations.
The theoretical optimal recovery  performance was  already given by Chebyshev. Deep learning seeks a numerical algorithm to achieve optimality based on neural network approximation and optimization of loss functions.  We discuss to what extent this approach is close to optimal.

Monday at 17:00 (Vienna time)
Aleksander Aptekarev (Keldysh Institute for Applied Mathematics, Moscow State University)
Title: On the Sharp Constants in the Rate of Convergence of the Tchebyshev Rational Approximation for Analytic Functions

Abstract: 
We discuss theorems  describing sharp constants for the rate of approximation for a general class of analytic functions by rational functions. The glorious story  on the sharp constants for the approximation of e^{-z}  on [0,∞] was one of the most remarkable application of such type of theorems. For the proof of the theorems a construction of rational interpolants possessing Tchebyshov alternance property  is  proposed. The equioscillation of the error term leads to certain eqiulibrium problems for the logarithmic potentials for measures and for signed charges. Asymptotically sharp formulas for the interpolations points, for the points of alternance, and general theorems on the strong asymptotics for the error term of the best rational approximants  are  presented.  The proofs are based on the strong asymptotics for polynomials orthogonal on the extremal compacts of the complex plane with respect to complex varying weights. Techniques of BVP on Riemann Surfaces and Matrix Riemann-Hilbert problems are employed for the proofs. Several recent applications of the above theorems also will be presented. 

Tuesday at 16:00 (Vienna time)
Andrey Bogatyrev (Institute of Numerical Mathematics)
Title: Chebyshev heritage in new Millennium

Abstract:  P.L. Chebyshev was a bright representative of mathematicians who are motivated by real life problems and  practical applications of this science. Many of his ideas still allow us to analyze and solve sophisticated rational approximation problems. In this talk we consider several problems stemming from optimization of numerical algorithms and electrical engineering, which were solved on the basement of works of the prominent scholar.

Tuesday at 17:00 (Vienna time) - Informal session for Russian speaking audience:
Vladimir M. Tikhomirov (Moscow State University) will talk about Chebyshev's life and ideas