Problems in uniform and weighted approximation

This project aims to advance the central theory and address open problems in the fields of uniform and weighted approximation, as well as in the adjacent areas of mathematical physics and numerical analysis.Our specific objectives are:i) to resolve a conjecture concerning minimax polynomials (also known as Chebyshev polynomials) of Jordan arcs and advance the associated theory in the complex plane.ii) to examine the distribution of zeros of minimax polynomials of Jordan curves as their degree increases, and to determine the limiting behavior of these zeros.iii) to explore the spectral theory of a novel periodic model of unitary operators and utilize these findings to address issues pertaining to orthogonal polynomials on the unit circle.My plan is to carry on with my ongoing research in collaboration with internationally renowned experts to achieve the stated objectives.

Additionally, I intend to organize a symposium towards the end of the project period that will function as a platform for disseminating new results and introducing fresh perspectives to the field.The research project will encompass both theoretical investigations and practical applications.

The main objective of the project is to explore novel mathematical physics models and advance the use of minimax polynomials in numerical analysis.