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SUMMARY:An asymptotic minors property for ranks of higher-dimensional tens
 ors  - Thomas Karam (Cambridge) 
DTSTART:20220310T143000Z
DTEND:20220310T153000Z
UID:TALK171566@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION: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 generali
 sation of this fact to various notions of rank for higher-dimensional tens
 ors\, in particular the tensor rank\, slice rank and partition rank: for e
 ach 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 pro
 of. 
LOCATION:MR12
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