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Ergodic theorems for polynomials in nilpotent groups
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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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Cited by 1 Pith paper
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Global well-posedness of the cubic nonlinear Schr\"odinger equation on $\mathbb{T}^{2}$
Global well-posedness of mass-critical cubic NLS on T² is proved for arbitrary defocusing data and sub-ground-state focusing data via a new inverse Strichartz inequality from additive combinatorics.
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