Unlike the matrix case, there are many different types of ranks for tensors. Unlike the matrix case, these types of ranks are rarely multiplicative, requiring us to look at amortized/regularized/asymptotic versions. Asymptotic ranks have important applications ranging from computational complexity to combinatorics to quantum information (my favorite corner of the world). I will present a bunch of results (and a conjecture!) on (1) weighted slice rank and (2) symmetric subrank that might amuse fans of Strassen, Comon or Tao.
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