Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New lower bounds for the rank of matrix multiplication   The rank of the matrix multiplication operator for nxn matrices is one of the
most studied quantities in algebraic complexity theory. I prove that the rank
is at least n^2-o(n^2). More precisely, for any integer p\leq n -1, the rank is
at least (3- 1/(p+1))n^2-(1+2p\binom{2p}{p-1})n. The previous lower bound, due
to Blaser, was 5n^2/2-3n (the case p=1).
  The new bounds improve Blaser's bound for all n>84. I also prove lower bounds
for rectangular matrices significantly better than the the previous bound.

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The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph