The quals process has changed since I got here, and I'm one of the last few people to be using the old process, which entails taking two written exams ("theory" and "systems") and then taking an oral exam in one's particular research area. Some of the guidelines given for the oral are:
- "The oral qualifier examines your deep knowledge of a research area (e.g., databases). Within that specialized area, coverage should be broad; the area should not be construed as the thesis topic."
- "The oral is not for presentation or examination of your research plans, which are examined in the proposal defense."
- "Unlike the written qualifiers, which test breadth, the oral area qualifier tests your knowledge and mastery of the more specialized research domain in which you expect to do your research."
So, to answer your question, my topic is "programming languages", but since that's hopelessly broad, my topic is actually more like "semantics of programming languages and type systems". There's a slant toward systems that admit flexibility in the amount of static verification of types, because that's what I'm finding I care about, but I can't just do that, since I think it would be considered too narrow a topic for the oral.
(The new quals process seems better in terms of actually assessing one's ability to do research, but I was already partway through the old process when they made the switch, so I decided to just keep going with it, for better or worse.)
...I forgot about Turbak and Gifford! I should look at that denotational semantics chapter. When the book came out last year, Dan told me that he might just stop writing textbooks. Of course, Dan can be a little dramatic sometimes.