<p>My ignorance for terminology – is “classical algebraic geometry” just to say we’re working over the complex numbers (say, in contrast with “arithmetic” geometry)?</p>
<p>I think the standard thing is that if you’re at Berkeley and want to study algebraic geometry, you’ll find an adviser, but probably much tougher if you want to do something else! </p>
<p>The one thing one famous professor at Berkeley (where I’m an undergraduate) told me is that one of the places I’d be able to find an adviser in some form of K-theory (maybe it’s sort of a phase, but I want to learn more about it) with relative certainty is Chicago. I’m sure their AG faculty is terrific as well, unless it’s changed in several years (after all, Prof. Eisenbud went to graduate school there). </p>
<p>Wow, a term on category theory. Our first-year algebra sequence (one of the more intense classes we offer) spends the first month or so on it, and it’s usually a tough unit, but definitely not longer than that! That sounds fun in a way, though in some senses after an intro, seeing category theory pop up naturally in several different areas and picking it up as one goes sounds the easiest way. </p>
<p>
</p>
<p>This is particularly important to me. I’d really like to spend my first year or two doing lots and lots of this. </p>
<p>Hmm, Chicago sounds quite terrific – the only one point is that I love to have the freedom to read whatever math I want. Out of curiosity, I looked up the site, and it says:</p>
<p>
</p>
<p>What exactly is the process to satisfying them, some sort of examination? (Or could you just demonstrate you took a similar course?) For instance, you probably had at the very least the standard analysis and algebra before coming into UChicago.</p>
<p>And great to know you’re happy at your school – more to the point, great to know there’s A grad student out there who’s happy!</p>
<p>EDIT: Your name is even happyentropy!</p>