The Geometry of Tensors - Carolina Araujo

Explore the fundamental concepts and applications of tensors in this 46-minute lecture by Carolina Araujo from IMPA. Delve into the world of multilinear algebra and discover how tensors play crucial roles in matrix multiplication complexity, signal processing, phylogenetics, and algebraic statistics. Learn about the importance of minimal tensor decomposition and the concept of tensor rank. Examine the geometric interpretation of determining tensor rank, a problem that has garnered significant attention in recent years. Gain insights into new findings on tensor ranks, presented in collaboration with Alex Massarenti and Rick Rischter, as the lecture bridges the gap between tensor theory and algebraic geometry.