Rational Convexity in Complex Euclidean Space

The proposed project is focused on a research area of great interest that my supervisor, Dr. Rasul Shafikov, and Dr. Alexander Sukhov of the University of Lille, have devised in a number of coauthored papers published during the past few years. The research investigates the polynomial and rational convexity of compact sets in Euclidean complex space, notions that are of crucial importance in the general theory of approximation of continuous functions, uncovering deep connections to topology, Banach algebras, symplectic geometry, and other areas of mathematics. The objective of the project is to build on the existing work done by Shafikov, Sukhov and other researchers in the field, by giving a concrete answer to a still open problem that follows from their work. As a first step toward that goal, we seek to provide a criterion for the rational convexity of compact subsets of Euclidean complex space, with finitely many singular points of a certain type: hyperbolic complex points.

Faculty Supervisor:

Rasul Shafikov

Student:

Partner:

Université Lille1 - Sciences et Technologies

Discipline:

Mathematics

Sector:

Life Sciences (not health); Other

University:

Western University

Program: