Discreteness of Asymptotic Tensor Ranks

Explore a 40-minute conference talk on the discreteness of asymptotic tensor ranks presented by Jeroen Zuiddam from the University of Amsterdam at IPAM's Tensor Networks Workshop. Delve into the central role of tensor parameters in algebraic complexity theory, quantum information, and additive combinatorics. Discover a general discreteness theorem for asymptotic tensor parameters of order-three tensors and its applications in proving the absence of accumulation points for asymptotic subrank and slice rank over various coefficient sets. Examine new lower bounds on the asymptotic subrank of tensors and their implications for tensor diagonalization. Investigate the relationship between tensor dimensions and asymptotic subrank, including the cube-root lower bound for concise three-tensors and the maximal asymptotic subrank for "narrow" tensors. Learn about novel lower bounds on maximum rank in matrix subspaces derived from three-tensor slicing, and their significance in proving large max-rank in distinct directions for concise tensors. Gain insights into this collaborative research effort and its potential impact on tensor network theory and applications.