Today, I spent the day at IAS, listening to Alex Eskin talk about Teichmuller dynamics.
I don’t know why, but I somehow struggle on some deeper level when it comes to that topic. These talks always start relatively similarly with billiards and the (non-)existence(?) of periodic orbits thereof before providing a dictionary between billiards and Riemann surface theory, an introduction to basic notions in ergodic theory (Ergodic, Uniquely Ergodic…), and then – apparently at some point when my brain shuts down – there’s really deep stuff including conjectures by Fields medalists, etc. etc. Somehow, I understand all the pieces before brain shut-down, but even so, the shut down always seems to happen and leave me scratching my head and wondering wtf happened during.
Maybe it’s a tumor.
I’ve been focusing more on stuff about universal circles. In particular, I’ve found some other documents online that summarize the Calegari-Dunfield paper a bit, and I’ve been using Calegari’s wonderful book to help get new views on things. It’s slow, but it’s progressing way better than it ever has.
Last week, there were three Minerva lectures at Princeton University by Maryam Mirzakhani. The creative ways in which she applies and broadens the scope of hyperbolic geometry is staggering, and as much as I’d like to say I understood a lot of things, I understood very small fragments of a handful of things. It was an amazing experience that I’ll cherish for a long time, but man – I was so tangibly outclassed during that it was almost embarrassing. Wonderful, but (almost) embarrassing.
Besides that, I’ve been working: Mostly boring monotonous things for Wolfram with the exception of breaking Wolfram|Alpha today, and then finally some progress on fixing the very badly-done FSU Financial Math pages. It’s a lot happening, but it’s all mostly enjoyable and I like being kept busy, etc. Always good.
Unfortunately (or perhaps fortunately for my progress on things that matter), I haven’t typed up any more interesting proofs or anything. At some point, I hope I can blog regularly without feeling like I’m missing out on more important things but honestly? Now is not that time.
I hope this finds everyone well, and if I don’t see you again first: Happy holidays!