I forgot to mention some things in the last update:
- This summer I will be at MIT for SPUR, which should be a lot of fun. I debated for awhile between SPUR and applying to be a PROMYS counselor, but after thinking about it I’m too excited about the opportunity for research to turn it down.
- Next year I will be studying abroad at Cambridge. I’m really looking forward to this. Maybe I’ll even meet Timothy Gowers!
Incidentally, when I went to talk to David Jerison about SPUR, the conversation shifted to RSI (which he is also involved with). I told him I’d always been a little embarrassed about my RSI paper because the bulk of the argument in the first part of the paper is a rediscovery of a standard lemma in linear algebra (that two quadratic forms can be simultaneously diagonalized). Jerison replied that this wasn’t something to be embarrassed about; to the contrary, discovering a result “in the wild” meant that I would better understand its value (or something to that effect). Wise words.
I’ve been reading about a lot of interesting stuff; hopefully I’ll get some time to post about it during spring break.
Annoying Precision 
Welcome to Cambridge then! Which year will you be in? In any case, you might enjoy many of the Part III courses. There are also various other informal things organized, or rather organised 😉 by graduate students, like “Geometry Tea”. If you send me an email when you arrive I will let you know what’s happening, it’s usually not very well advertised. Also, in case it’s useful for you, I could put you in touch with an ex-Cambridge undergraduate who is now a graduate student at MIT.
Thank you! I’m not sure whether this corresponds to a year, but I’ll be taking mostly Part II courses, I think. I hadn’t actually looked at the Part III courses right now, but some of them look very interesting (although most I definitely don’t have the background for). The teas sound great – I’ll definitely keep that in mind!
Which college at Cambridge will you be staying at out of curiosity?
The way the program works is that I will just switch places with a student who’s coming to MIT from Cambridge. So I don’t know yet; I don’t think everything gets fully finalized until later this month.
I was fairly embarrassed about my RSI paper because the main result was incorrect (a mistake that I made on account of not actually knowing anything about algebraic geometry).
Incidentally, the link to SPUR doesn’t work.
That’s strange. Fixed.
Akhil, based on what I read of your paper, it was an accomplishment just to have understood the problem statement!