Tensors of Minimal Border Rank and Their Role in Matrix Multiplication Complexity

Explore a mathematical seminar that delves into the classification and properties of concise (m,m,m)-tensors of minimal border rank and their crucial role in determining matrix multiplication complexity. Learn how this fundamental question from Bürgisser, Clausen, and Shokrollahi's "Algebraic Complexity Theory" connects to challenging problems in algebraic geometry and commutative algebra. Discover recent developments in the field, including the unexpected significance of degree seven zero dimensional local Gorenstein schemes in advancing our understanding of these tensors. Gain insights from Texas A&M University's Joseph Landsberg as he presents this advanced mathematical topic at the Institute for Advanced Study's Special Year Seminar series.