Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic theorems for polynomials in nilpotent groups   The principal results proved in this expository thesis are the IP polynomial
Szemer\'edi theorem for nilpotent groups and the multiple term return times
theorem with nilsequence weights. It also contains extensions of the
convergence theorem for nilpotent polynomial multiple ergodic averages and the
return times theorem to locally compact second countable amenable groups.

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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio