MAT477: Seminar in mathematics

Course information

Code: MAT477F
Instructor: Marco Gualtieri, office hours by appointment.
Class schedule: Monday 6-8PM and Wednesday 6-7PM, both in BA2139

This is a seminar course focusing on the relatively recent theory of discrete Riemann surfaces. This is a rapidly developing area with close connections to pure and applied mathematics as well as to physics. It underlies the recent work by Fields medallists Smirnov and his student Duminil-Copin, and it seems to provide, in some cases, a means of approaching a rigorous definition of conformal field theory in physics.

At the start of the semester, I will begin by teaching a crash course on classical Riemann surfaces, and then we will transition to a seminar format, with students selecting from a list of assigned topics and giving short presentations, which will be evaluated for both mathematical content and expository effectiveness. Consistent audience participation in the form of questions will also be incentivized.

Evaluation

Each week, we will have three student presentations; the evaluation will be in four parts:

  • (20%) Two days before the presentation, the presenter must hand in approximately 4 pages of clearly handwritten lecture notes via email.
  • (20%) The presentation itself will be evaluated based on clarity/pedagogy as well as knowledge/understanding.
  • (20%) Each presenter will be responsible for texing up their material for the final output of the class: a review article on Discrete Riemann Surfaces. This will proceed through a series of drafts.
  • (20%) Participation (this means attendance and engagement, mainly by asking questions)
  • (20%) One pedagogical exercise will be assigned by each presenter. These must be submitted at the start of the next class.

References

Lecture schedule

We may need to adjust depending on the material. Remember that your mission is to summarize the material and highlight the interesting parts, giving detail where it is most crucial. This means that it is supposed to feel like you are squeezing a lot of information into a short presentation.