Hi, I’m Nathan, a first-year PhD student in the Theory of Computation group at MIT, advised by the inimitable Ryan Williams. I did my undergrad at MIT as well. I’m broadly interested in discrete math and complexity theory — currently working on “whatever I find that seems cool and possibly tractable”; at some point maybe I will have a more slick focus to describe here. A list of papers I’ve coauthored can be found here. A couple topics I’m generally interested in, progressing from “areas I’ve worked in” to “areas I don’t have experience with but which seem like they’d be really good to figure out”:

• Graph theory. I’ve done a bit of pure graph theory (see these papers), but am especially happy about cases where tools from graph theory let you say things about computation — see e.g. this paper.
• Space-bounded complexity. Here’s one paper I’ve written in this area, trying to understand the weirdness of catalytic computing in a more information-theoretic setting.
• Average-case complexity and crypto foundations. Understanding average-case complexity is tricky, but also very fundamental, and it seems like the meta complexity people are doing a lot of really great work. I’m currently working on something maybe a little related, but would like to do more.
• AI safety. If AI continues to improve, are there ideas from CS theory (e.g. cryptography or complexity theory) that can help mitigate potential dangers? I have yet to have good ideas personally, but this feels worth thinking more about.

Some things I like outside of math:

• Quizbowl. I ran our clubs back in high school and undergrad; currently I’m not as involved but still enjoy academic trivia in moderate doses.
• Fiction and poetry. I enjoy reading all sorts of literature, maybe especially if it’s from the 20th century and slightly weird. I also try to do a little creative writing sometimes — I have a couple of posts at various interpolation points between math exposition and narrative fiction on my blog.
• Puzzles. I puzzlehunt with the 17th Shard team! I especially like puzzles involving cryptics or wordplay.
• Zumba. My ratio of “enthusiasm about dancing” to “dance ability” is extremely high. It makes me very happy to listen to loud music and jump around — I call this activity “zumba”, although maybe in standard usage “zumba” just refers to a special case of this? Unclear.
• Walking. I’m a big fan of long walks, including proper hiking, but also including things like “walk by the side of the road for 40 miles”. If you’re interested in joining such an activity, let me know and I’d be super down. I’ve also been beginning to get into running lately, because somebody told me this was like walking but even faster — we’ll see how that progresses.