Fourier transforms and nonlinear dynamics

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• Connor Stevens (University of Manchester)
• Thursday 10 February 2022, 15:00-16:00
• Zoom.

If you have a question about this talk, please contact David Craven.

Currently there is a great deal of research being produced in the area of Fourier transforms for measures. There is particular interest in when such objects exhibit (polynomial) decay. Much of this research in the context of nonlinear-map invariant measures stems from the ground-breaking paper of Bourgain–Dyatlov (2017) on Patterson–Sullivan measures for Hyperbolic Surfaces. In this talk we will discuss some of the methods used in this paper, and how large deviation theory can be used to apply their main tool of Discretized Sum-Product theory to the setting of expanding nonlinear maps rather than Fuchsian groups. We will conclude by looking at the assumptions necessary to use the Sum-Product theory, and heuristically how to prove these assumptions.

This talk is part of the Topology and Dynamics seminar series.

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• School of Mathematics events
• Topology and Dynamics seminar
• Zoom

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