PhD dissertation advisor

If you are not yet a graduate student at Michigan State, please read these information for prospective students first.

Thinking about asking me to be your advisor?

Make sure to take a look at my research interests; though the list is neither exhaustive nor exclusive when it comes to possible PhD topics.

Then you should make an appointment to drop by for a chat. If you have a specific problem or general area that you wish to pursue (largely in the areas of partial differential equations, differential geometry, or general relativity), you can let me know. I am perfectly happy to tell you more about what it is like working in my fields of specialty, and discuss with you a possible study plan if you were to choose to work with me.

I would also encourage you to chat with some of my current or past graduate students. They maybe able to give you a different perspective and afford you a more complete picture.

Expectations of current students

What you can expect of me

Once I take you on as a student, you can expect that I will offer you advice and guidance through your completion of the PhD program (and beyond if you wish), that I will help you acquire mathematical knowledge, and that I will train you in the profession. More specifically, I will

  • Help you choose a general research direction (if you don't have a clear idea yourself)
  • Suggest to you specific research problems
  • Direct you in your studies of the literature
  • Guide you in choosing courses
  • Answer your questions about mathematics and academia
  • Assist in your training as a teacher
  • Help develop your career

I will also guarantee you, on average, at least one hour of my time each week to discuss your progress. (For example, this can be in the form of biweekly two-hour-long meetings; if you are more independently minded, you can also choose not to make use of the time.) If I have multiple students, this may in part be in the form of group meetings. I will inform you in a timely manner of any alterations to our meeting schedule, and keep you informed of my travel schedule.

I will support your application to workshops and summer schools relevant to your research and professional development. I will also inform you of any such opportunities when it comes to my knowledge. I will, when I have available funding, support these travels.

I will provide you with a detailed list of comprehensive exam topics from which the committee will draw questions for the written portion of the exam. The list will be reflective of your planned research direction. (To illustrate the level of detail, a topic can be "Prove the decay of solutions to the linear wave equation via the Klainerman-Sobolev inequality. (See C. Sogge, Nonlinear wave equations.)")

What I will expect of you

Basically, work hard and follow the guidelines in the Graduate Student Handbook (a copy is available on the graduate program website).

General and academic

  • You are expected to be familiar with the departmental requirements of graduate students as described in the graduate student handbook, especially the various deadlines.
  • You are expected to contact and arrange your committees (comprehensive exam and dissertation).
  • You are to keep me informed of your progress in exam preparation (pre-Quals and pre-Comps) as well as your dissertation research (post-Comps).
  • You should participate in all training programs that the department and the university requires of you.
  • You should advise me of your travel plans, especially those during term.
  • For your qualifying courses, please take PDE, Geometry/Topology, and Analysis. (In rare occasions I may ask you to take Numerical Analysis in place of one of those three.)
  • You should take notes during our discussions.
    • A good way to supplement your notes is to take an audio recording of the discussion on your smart-phone.
    • Suggested but not required: type up those notes. Electronic copies are easier to keep and read, and harder to lose.
  • You will go to seminars. (I generally expect you to be present at the Analysis and PDE seminars as well as all departmental colloquia; depending on your research focus, there may be other seminars you should regularly participate in.)

Professional training

  • You will strive to become a good teacher, this includes, but is not limited to, participation in the CIM program and activities.
  • When called upon, you will help mentor undergraduate research students.
  • You will learn and use git:
  • You will learn to prepare documents using LaTeX: