A gentle introduction to tensors

Tensors are objects naturally defined in multilinear algebra, and they yield to meaningful structures and properties in complex algebraic geometry. Due to their versatility in parameterising data, they also appear in many life sciences, for which the real (or non-negative) setting is more natural. However, in the latter case there is a lack of results. In this talk we will provide the main notions concerning tensors in both complex and real algebraic geometry, state some results and sketch basic examples of applications.