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nhaliday : algebraic-complexity   19

Notes on the “slice rank” of tensors | What's new
In the previous blog post, one of us (Terry) implicitly introduced a notion of rank for tensors which is a little different from the usual notion of tensor rank, and which (following BCCGNSU) we will call “slice rank”. This notion of rank could then be used to encode the Croot-Lev-Pach-Ellenberg-Gijswijt argument that uses the polynomial method to control capsets.
tensors  concept  math  gowers  exposition  mathtariat  polynomials  algebraic-complexity  atoms  nibble  org:bleg 
september 2016 by nhaliday
Reflections on the recent solution of the cap-set problem I | Gowers's Weblog
As regular readers of this blog will know, I have a strong interest in the question of where mathematical ideas come from, and a strong conviction that they always result from a fairly systematic process — and that the opposite impression, that some ideas are incredible bolts from the blue that require “genius” or “sudden inspiration” to find, is an illusion that results from the way mathematicians present their proofs after they have discovered them.
math  research  academia  gowers  hmm  mathtariat  org:bleg  nibble  big-surf  algebraic-complexity  math.CO  questions  heavyweights  exposition  technical-writing  roots  problem-solving  polynomials  linear-algebra  motivation  guessing 
may 2016 by nhaliday

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