# Challenges in Combinatorics on Words (Day 5)

My knees were killing me, but that wouldn’t stop me from going to a talk that relates algebra and automata theory!

• Kiran Kedlaya gave two talks on Christol’s theorem. Christol’s theorem says that a formal Laurent series is algebraic over the field $\mathbb F_q(t)$, where $q$ is a prime power, if and only if it is automatic. The second of his two talks was about a theorem of his which generalized Christol’s theorem to apply for general power series.
• Eric Rowland gave a neat talk on characterizing $p$-automatic sequences using 1-dimensional cellular automata. There’s actually a lot more algebra to cellular automata than I would’ve expected was possible (and even some connections to Kedlaya’s talk on Christol’s theorem). Then again, I don’t really know much about cellular automata other than Conway’s Game of Life.

So even though I didn’t really contribute at the workshop and I was kind of wandering around as a lone graduate student, it was a really interesting experience. At the very least, I got to meet some interesting people working on interesting things and I have a pile of interesting things to look up over the summer before I head to Kingston and ramp up into hardcore math research mode.

And now, some miscellany.

• Lunch notes: tried Mother’s Dumplings again and opted for a double order of dumplings this time around. I went with boiled again, because I couldn’t justify paying a bit more to get a bit less, even if the steamed dumplings were supposed to be amazing. Maybe that’ll happen if I’m there with other people in the future.
• Commuting notes: I got a ride to and from Fields, since it probably wouldn’t be a good idea to be on the TTC for long periods of time with my knees in their current state. The morning trip involved going across Eglinton, which is an absurdly wide road and I don’t really know why people are mad about LRTs on that road when it’d essentially be replacing a lightly used HOV lane (or maybe even not). Once we hit the DVP, traffic got heavy and Bloor was pretty bad. We went down Sherbourne, where I saw the Minnan-Wong bike lanes and we continued on Carlton and College.
• The evening commute was also interesting. My dad usually takes Lake Shore through to The Beaches and up Kingston, but apparently, there’s some construction going on there, so we went along Gerrard through the east end of old Toronto instead. We ended up cutting across to Southwest Scarborough on Danforth and back up to STC to pick up a new phone. This was a much better route than the one proposed by my dad, who wanted to go up to the DVP.
• Replacement phone notes: Got a new phone and restoring service was pretty easy. The tough part was restoring from iCloud backups since, Apple, in their sometimes questionable wisdom, decided that you could only restore iCloud backups when you first set up your phone, which the Koodo lady zipped past while we were at the booth. So I had to reset the iPhone, which was baffling, since it required downloading the latest iOS update, which I’m pretty sure I’d already downloaded. But after all of that, my phone was in pretty much the same state as I had it in yesterday.