General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
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Explicit construction of improved-size variety-evasive subspace families for degree-d varieties via better Chow-form hitting sets.
Exact border subranks and tight bounds are determined for k-fold matrix multiplication and several other algebra structure tensors at all orders, together with a proof that degeneration propagates from higher to lower order.
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Asymptotic Rank Speedup Theorems, Revisited
General asymptotic rank speedup theorems are established via Strassen calculus, proving the asymptotic rank of cw_2 is below 3.931 and yielding an upper bound below d^{2ω/3} for any d×d×d tensor.
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An Improved Construction of Variety-Evasive Subspace Families
Explicit construction of improved-size variety-evasive subspace families for degree-d varieties via better Chow-form hitting sets.
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Border subrank of higher order tensors and algebras
Exact border subranks and tight bounds are determined for k-fold matrix multiplication and several other algebra structure tensors at all orders, together with a proof that degeneration propagates from higher to lower order.