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An asymptotic minors property for ranks of higher-dimensional tensors

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  • UserThomas Karam (Cambridge)
  • ClockThursday 10 March 2022, 14:30-15:30
  • HouseMR12.

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It is a standard fact that every matrix of rank k contains a k x k minor with rank k. In this talk I will discuss an asymptotic generalisation of this fact to various notions of rank for higher-dimensional tensors, in particular the tensor rank, slice rank and partition rank: for each of these notions of rank and each dimension d there exist functions f,g such that if the rank of every minor of size g(l) of an order d tensor T has rank at most l, then the rank of T is at most f(l). If time allows I will then discuss some other applications of the methods used in the proof.

This talk is part of the Combinatorics Seminar series.

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