
February 27th, 2009
03:06 pm  the five steps to advising a student Told to me by a Rice postdoc: 1) Think of a problem for your student. 2) Explain the problem to your student. 3) Solve the problem. 4) Explain the solution to your student. 5) Convince your student that she solved it herself.
My advisor is currently trying to convince me I just proved a theorem. But I'm not sure I even understand the statement of the theorem. To rephrase, if I knew the statement of the theorem, I would probably agree that I proved it.
This may be the theorem I just proved: Let M and N be a branched hyperbolic surfaces with k branch points of order 2. Let f be a harmonic map between M and N such that f is a bijection between branch points. Then f has finite energy, and the associated Hopf differential has at worst simple poles.
Or it could be: Let M and N be a branched hyperbolic surfaces with k branch points of order 2. Let f be a harmonic map between M and N such that f is a bijection between branch points and such that f restricted to an epsilon neighborhood of each branch point is homotopic to the identity. Then f has finite energy, and the associated Hopf differential has at worst simple poles.
Or maybe I'm missing something and it's something else entirely. I am going to try to write it up before I leave for Spring Break because I won't remember what I was doing if I wait until I come back. Current Mood: worried about homotopy classes


