Polynomials, as a family of functions in analysis, are known for their simplicity and a wide range of interesting properties. Thus, approximating a function with polynomials is a significant simplification.  The concept of approximation for holomorphic functions traces back to two fundamental theorems published in 1885. One of these theorems, credited to K. Weierstrass, focuses on the polynomial approximation of continuous functions over compact intervals in real numbers R. The second theorem, introduced by Runge, states that every holomorphic function defined on a neighborhood of a compact set K in the complex plane can be uniformly approximated by rational functions that have no poles within K. In cases where the complement of K is a connected set, the rational functions can be replaced by holomorphic polynomials. The attempt to extend this result to several variables by K. Oka and A. Weil in the 1930s led to the development of the concept of polynomial convexity. 

My research focuses on the study of both polynomial convexity and polynomial approximation of compacts in C^n.