Notes for potential students

Stages of PhD advising

  • Step 0: Arrive at Rice University
  • Step 1: Come talk to me (for example during office hours, or before/after seminar).
  • Step 2: Pass Quals (I do not advise reading courses until after you pass all your quals).
  • Step 3: Reading course for 1-2 semesters
  • Step 4: Advanced Exam
  • Step 5: Preparation for thesis problem
  • Step 6: Thesis fun

What math you should know. My main research area is symplectic and contact topology with a focus on defining and computing modern homological invariants like contact and symplectic homology. For an informal introduction to the field and my work see my survey article, From Dynamics to Contact and Symplectic Topology and Back. Stating and making meaningful progress on these problems requires a lot of background work, which will extend at least a semester after passing your advanced exam. Precisely what background is needed depends on what you will work on, with some problems requiring more analytic abilities and others more topological or algebraic in nature. Before working with me you should be comfortable with differential forms, vector fields and flow on manifolds, and the basics of Riemannian manifolds (see Lee's textbooks). It is helpful to have some exposure to Morse theory (and the desire to learn more about this on your own). Mastery of all the below texts is not expected, though you should expect to be able to read from these independently by the end of your third or fourth year. Prior to that, reading courses will focus on working through these texts (including doing exercises).

Reference Texts

Current PhD Students

Videos of Lectures from Summer Schools and Workshops

Syllabi from past Advanced exams

We will work together on developing your Advanced exam syllabus, depending on your interests, strengths, weaknesses, and thesis problem. The below are meant to be helpful reference templates.


I take collegiality very seriously, as it is crucial for mathematical learning, development, and research. I expect all my potential and present mentees to abide by the Rice Mathematics Statement on Collegiality, Respect, and Sensitivity.