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Benedict Sewell

Good day and welcome.

I am now a Young Researcher at the Alfréd Rényi Institute in Budapest.

Research right now: bounding the dimension of the Rauzy gasket

This autumn (2021) I defended my PhD thesis under Mark Pollicott.

The fourth chapter, recently condensed into a preprint (arXiv), is on the following project:

Bounding the dimension of the Rauzy gasket

The Rauzy gasket is a self-projective fractal in 3 dimensions that arises as an exceptional set in various settings (included but not limited to a special case of Novikov's conjecture, Arnoux–Rauzy interval exchange transformations, episturmian words on three symbols, tiling billiards and pseudogroups of circle rotations).

Fittingly then, it has been shown to be a bona fide fractal, having Hausdorff dimension between 1.19 and 1.825. Our self-appointed task is to improve upon this upper bound, and in a way that is maximally understandable.

Oui, c'est bon! We have an upper bound of 1.7407, much closer to the conjectured value of 1.72.