For Prospective Graduate Students
I have been receiving increasingly frequent requests for advice from prospective graduate students interested in applying to the University of Oregon to work with me as their PhD advisor. While I am delighted to hear of students' enthusiasm, I do not have time to provide personalized responses to most of these requests. Here is general information that addresses most of the inquiries I receive:
Graduate admissions is through the department, not through individual faculty members. Writing to me is unlikely to influence your admission case. I do not currently serve on the graduate admission committee.
Students typically choose a PhD advisor after passing their qualifying exams. Many students spend their first year of graduate school preparing for these exams, as well as learning about different areas of research. If you have the opportunity to take graduate-level courses now, take them.
One of the best ways to prepare is to build a strong foundation through coursework and/or self-study in algebra, analysis, geometry, and topology. If possible, also learn about modular forms or other topics of central importance in number theory. An enthusiasm for learning and relearning material is essential.
Although I have many interests, I only supervise PhD dissertations related to research expertise. If you are set on working exclusively in algebra or on avoiding a particular branch of math, my research area will probably be a poor fit. Modern algebraic number theory relies on more than algebra.
Where can you get more tips? Professors who have taught you are often uniquely positioned to give you personalized advice. Beyond talking to individual mathematicians, you might find resources on the internet helpful for learning about graduate school, exploring research in number theory, and planning what to do next.
I hope you find some of this information helpful as you embark on the next steps of your education.