## Some information for students## If you need a recommendation letterFirst rule: you should find someone who is familiar with you (at least to some extent). If I feel like I do not know you well enough (but I am willing to write a letter for you), we may need to schedule a meeting to have a little chat. Second rule: give me as much information about you as possible. Here are some advices you should follow. Usually, you need to ask me at least one month before the deadline. The earlier, the better. Short time notice sometimes is acceptable, but it is in no one's best interest. ## If you want to do research in algebraic geometryThat is great! Something to keep in mind: ## UndergradsMy general advice is to learn as many things as possible, not just algebraic geometry. Having a broad view will help you, one way or another, eventually. If you are interested in doing undergraduate research with me, first schedule an appointment with me by email. ## PhD studentsIf you are interested in pursuing your PhD degree with me, here are things you should do: Read the research page first, especially the two survey articles (link at the top of the page), to get an idea of the sort of problems I am interested in, and see if that agrees with your personal taste.
Talk to me. We can set up a regular meeting schedule, and you should attend my seminars for a period of time so that we get to know each other. During this time, we will decide if we are a good match for the advisor/adivsee relationship.
Pass my exam on algebraic geometry. See below for details.
To do research in algebraic geometry, you should finish Hartshorne Chapter 2 and 3, and Griffiths-Harris, Chapter 0 and 1. Both are fundamental. By finishing these two chapters in Hartshorne, I mean that you have a reasonably good understanding of the text, including theorems and examples, you are able to do 80% of the exercises, and you are familiar with the rest.
You should also understand some basic geometry of curves and surfaces, especially how to use the general machinery to study them, as done in Hartshorne or Griffiths-Harris. I also recommend reading the book of Eisenbud-Harris ‘‘3264 and all that". After reading this book (or even just part of it), you will learn how to apply the general machinery to study concrete geometric questions. I will give you an exam, either oral or written, to test your knowledge on these two books. I expect that a student is able to pass the test by the end of his or her second year. Only Read some general adivices to students. |