<p>I’m a math major and algebra is one of my favorite topics. I would like to know which are the best graduate schools in algebra. Please include programs from all over the world.</p>
<p>Thanks!</p>
<p>First, you should really discuss your graduate school options with your professors, not a random stranger on the internet.</p>
<p>Second, algebra is HUGE. Most decent graduate programs in math will have some strong algebraists on the faculty. Case in point, the US News list of the top 20 American math graduate programs in algebra is almost identical to the top 20 overall strongest math programs, with the single exception of Maryland being replaced by Utah. If you are very picky about the specialty within algebra that you want to pursue, that might narrow things down a bit. Otherwise you might be better off to use other criteria in your graduate school search and then do whatever branch of algebra (or not algebra) your favorite adviser at your favorite school happens to be doing.</p>
<p>I think I’m leaning towards the less topological/geometric.</p>
<p>It would make sense to ask “What are the best departments for noncommutative algebraic geometry / p-adic Hodge theory / algebraic K-theory?” Your question is too vague because many departments have faculty who are excellent in some area of algebra and it doesn’t make much sense to compare research groups across specialties.</p>
<p>Maybe a better question to ask your advisers is, “Which departments have enough strong algebraists that a beginning graduate student with a general inclination towards algebra has a good chance of finding a compatible adviser?” </p>
<p>Please don’t narrow down your options artificially if you don’t have specific interests yet. There are other factors (e.g. funding or the atmosphere in the department or location) that might be much more important to you.</p>