Good day and welcome.
I am a final year PhD student supervised by Mark Pollicott—I started October 2017.
Research right now: bounding the dimension of the Rauzy gasket
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 1.2 and 1.825. Our self-appointed task is to improve upon this upper bound, and in a way that is maximally understandable.