Had the interview, just finished. It's amazing how being nervous can completely screw you.
People online have said that Goldman has no imagination and likes to ask repeat questions. I suppose that's kind of the case. I feel I should've known everything. Well, here were the questions.
Introductions and fit questions, wanted to know about my research.
Programming: Asked me about encapsulation and polymorphism. I was able to discuss polymorphism a bit (he wanted nothing about C++ though, interestingly enough). I'm not sure he liked my response though.
Probability: He next asked me probability. I was so flustered after the programming question that I was a little nervous. He asked me the following: If I toss a fair coin 400 times, what is the probability I get at least 220 heads? I drew a complete blank and attempted this via counting, which was dumb. Afterwards I thought of the central limit theorem, but couldn't remember the standard deviation for tossing coins. Ugh, terrible.
Finance: Finally, he asked me to consider a situation in which we have 3 European calls with the same expiry and with strikes 10, 20, and 30. He told me the market prices have c(10) = 12, c(20) = 7, and c(30) = 1, and asked me to find an arbitrage opportunity. I told him to sell 2 units of the 20-strike call, and to buy the 10-strike and 30-strike call, and explained why you will get a profit in each case no matter what.
He finished by asking if I had any other questions, which I didn't (because let's not kid ourselves, I'm not getting hired there).
Overall I think I probably applied too early. I applied because Goldman sent out an email saying they were hiring, and after the reports of a hiring freeze in August, I thought I should at least try. I guess this can be taken as a good learning experience, although I'm embarrassed about that probability question.
Anyways, for the benefit of all who apply to Goldman, you have yourself a practice interview now.