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Effective equidistribution for twisted averages of the horocycle flow

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Interactions between Dynamics of Group Actions and Number Theory

We describe an approach, based on scaling, to bounds on twisted ergodic averages of the classical horocycle flow. As far as we know the best estimates available so far are due to A. Venkatesh and are based on effective equidistribution and rate of mixing for the horocycle flow itself. Our bounds are significantly better, in particular they are independent of the spectral gap of the representation. The main motivations come from the general question of establishing effective rate of equidistribution for unipotent flows and from the particular case of effective equidistribution for horocycle maps (or for the horocycle flow along polynomial sequences). We present joint work with L. Flaminio (Lille) and J. Tanis (Rice).

This talk is part of the Isaac Newton Institute Seminar Series series.

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