Choosing your faculty advisor is probably one of the most important decisions you'll make for your graduate and research career. There are a number of books and articles written for graduate students that give advice about this crucial choice. We have summarized Cornell's rules and regulations about the advisor and the special committee in sections 1.4 and 1.5. Now, some advice on how to make a good choice.
Cornell requires that you have an advisor within three weeks of first registering in the graduate school. In some cases, this may just be a temporary advisor. Some departments assign their Director of Graduate Studies to be every first-year student's advisor, for example. Then, when you eventually decide who you want to work with, you can easily change by filling out the appropriate forms. Your advisor serves as the chair of your special committee. (See Section 1.4.)
While choosing an advisor, you should consider several factors: research interests, type of research projects, seniority, relationship with past students, usual time it takes to graduate while working with him/her, how much independence his/her students enjoy, type of funding offered, etc. Then think about your own needs and expectations. It may be difficult to find a faculty who would fulfill all of your expectations so you may have to find a balance. Different people give different weights to different factors and so the decision will have to be your own!
To find more about a faculty member's research, you should attend any seminars they give, take/audit courses they teach, and read the papers written by them in past. If you need more clarification, go talk to them. Remember, this is the beginning of a research career for you and you should really feel interested in your work. Besides, by attending classes taught by them or their talks, you will get a chance to know them better.
Regarding seniority, here is an excerpt from ``How to be a Good Graduate Student" (a URL for this article is provided in the last section of this chapter) :
``How long have they been on the faculty? There are advantages and disadvantages to being one of the first members of a new research group. On the positive side, you often have more freedom to choose your research topic and to influence the direction of the group's research. On the negative side, you may be more isolated (since there won't be older graduate students in the group), and your advisor won't have as much experience. . . ."
One thing to keep in mind is whether your potential advisor has tenure or not. There are advantages and disadvantages to each choice.
First, junior faculty have vast incentives to produce a lot of high-quality research. Thus, it probably won't be hard to find a project. On the other hand, as junior faculty they are highly motivated to promote their own work. Tenured faculty may have a bit more flexibility and may be more inclined to let graduate students take the lead in research. Senior faculty, however, are not always as prolific as in their pre-tenure days, and therefore you may have to be more assertive about getting publications out and projects underway. Senior faculty generally have more ``clout", both in their research area and in their departments. It never hurts to have a senior faculty member's backing throughout your graduate career -- if not as your official advisor then as a mentor. Junior faculty are often very enthusiastic and are often actively looking for graduate students to work with.
To find out more about the relationship of faculty members with their past students, talk to the senior students and recent graduates. You should be asking questions about the nature of their interactions (how often and whether collaborative or not) and level of independence they enjoy(ed) while working with them. Ask about the average time their students take to graduate. How much interest do they take in finding a topic for their new students? Also ask about the quality of the research they do, how helpful they were in job searches, the kind of reputation they enjoy in academia and industry, etc. If you are interested in an academic position after graduation, the reputation of the advisor may be important; many in academia believe that a student will possess some of the qualities of the advisor that he/she worked with.
Type of funding you may get while working with a faculty member is also important. If a faculty member does not get a lot of research grants, then you may have to rely on teaching assistantships and you may not get as much time to focus on your research.
Even if you were careful while choosing your advisor, it's quite possible that after some time you may find it difficult to work with him/her. Your advisor may lack the technical knowledge to help you, may not be very accessible or interested in your work, may not have a positive attitude, and, in some extreme cases, may try to harass you. In such cases, it may be advisable to consider changing your advisor. Obviously, you should not make such a decision in haste: changing advisors could mean restarting your research from scratch. Sometimes, it helps to let the faculty member know politely when your expectations are not met; talking may eliminate your grievances. You may also want to use one of the resources mentioned in section 3.7; in many cases, you may be able to find a less-drastic solution than changing advisors.