Xi Dong, Alex Maloney, Henry Maxfield and I recently posted a paper to the arXiv with the title: Phase Transitions in 3D Gravity and Fractal Dimension. In other words, we’ll get about ten readers per year for the next few decades. Despite the heady title, there’s deep geometrical beauty underlying this work. In this post I want to outline the origin story and motivation behind this paper.
There are two different branches to the origin story. The first was my personal motivation and the second is related to how I came into contact with my collaborators (who began working on the same project but with different motivation, namely to explain a phase transition described in this paper by Belin, Keller and Zadeh.)
During the first year of my PhD at Caltech I was working in the mathematics department and I had a few brief but highly influential interactions with Nikolai Makarov while I was trying to find a PhD advisor. His previous student, Stanislav Smirnov, had recently won a Fields Medal for his work studying Schramm-Loewner evolution (SLE) and I was captivated by the beauty of these objects.
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