Coauthors: Professor R. Pereira, Department of Mathematics and Statistics, University of Guelph

For many years, the classical numerical range of an operator has been studied extensively by mathematicians interested in the areas of functional analysis and matrix analysis. In this talk, we will discuss the recent discovery of the higher-rank numerical range introduced by Choi, Kribs and Zyczkowski and we shall explore its properties from an algebraic and geometric point of view. We will also present ways in which it has been used to develop techniques for quantum data error correcting codes. Emphasis will be given to the geometry of the higher-rank numerical range.