I am writing a section on expanders for my book, and to avoid doing that I figured I should try to code up some expanders in tikz. Here’s the famous 3-regular expander based on Selberg’s theorem, connecting x to x+1,x-1,1/x mod p (and 0 to itself), on 127 nodes:
[Edit: Added new picture on 12/22]:
And here’s the same but on 23 and 101 nodes:
You’ll have to make choices… in Chinese. Use Google translate from images:
We’re all spoiled now, but I still can’t help but marvel that this is possible in my lifetime.
Keyboard is for pinyin. Install GBoard app.
Phone calls: You will be asked for a “password” even though you never set it up. Reset your *voicemail* password. Call #793# to reset your password. Now you can call.
SMS: Won’t send/receive. Settings -> system & updates -> reset network settings. Reboot. Now you can text.
Unfortunately, it defaults to a slow “EDGE” network, corresponding to a little “E” next to the bars. To get 4g network you have to root the phone which is a complicated process explained here and then use an app to force the phone to connect to 4g. I haven’t done this yet, hoping to view this as a feature rather than a bug. We’ll see, and if anyone knows of an alternative simple way to get 4g, let me know.
Check out our theory group page. If you’re into rankings, you may want to check this out. The PhD call is mainly for the Boston area, but Northeastern also has campuses in other locations offering various opportunities, including in Oakland less than 10 miles from the Simons institute, Seattle, Toronto, London, etc.
Deadline Dec 15. In particular, I am looking for students, so if you’re interested in complexity, cryptography, math, or related things, consider applying.
