Terry Tao's generals My examiners were Stein, Kleinermann and Rudnick. (Kleinermann came in about five minutes late). The first questions asked were about Harmonic analysis. They asked me what I knew, and I said basically singular integrals and functional analysis - no real harmonic theory at all. So they examined me on singular integrals instead, essentially. Give examples of singular integrals (Calderon-Zygmund). What theorems do you know about them, how to prove boundnedness. (I stated a T(b) theorem, which nobody seemed very acquainted with, and said with some brief explanation that knowing boundedness on L^2 - L^2 was sufficient to prove L^p-L^p for 1

=5). What other simple groups do you know. (The monster? But I backed down quickly, saying I knew not how to define it.) Then the discussion meandered a bit as the professors talked among themselves whether the group of order 168 (which I mentioned) was sporadic. After this, they decided to pass me, though they said that my harmonic analysis was far from satisfactory. :( They didn't ask any real or complex analysis, but I guess from my handling of the special topics they decided that wasn't necessary. Besides, we were almost getting snowed in. The exam lasted 2 hours.