Session A2 - Computational Algebraic Geometry
July 10, 18:30 ~ 18:55
Symmetrizing the matrix multiplication tensor
University of Notre Dame, USA - firstname.lastname@example.org
Determining the exponent of matrix multiplication is a central question in algebraic complexity theory. We propose a novel approach to bounding this exponent via the rank of cubic polynomials that are closely related to matrix multiplication. This allows us to exploit the vast literature of the algebraic geometry of cubic hypersurfaces and perform many numerical computations to study the exponent of matrix multiplication.
Joint work with Luca Chiantini (Universita di Siena, Italy), Christian Ikenmeyer (Max Planck Institute for Informatics, Germany), Giorgio Ottaviani (Universita di Firenze, Italy) and J.M. Landsberg (Texas A&M University, USA).