MAT 1341, Currents and counting of curves, Winter 2018


Kasra Rafi
Office: BA 6180 (Bahen Centre)


Tuesdays 11 - 12 pm BA 6180
Thursdays 10 - 12 pm BA 6183

Office hours

Thursdays 2 - 4 pm or by appointment.

Course description

We study the geometry and dynamical properties of Riemann surfarces and examine the set of closed curves on a surface. We start with background material, reviewing measured laminations, currents and the Weil-Peterson metric on Teichmüller space. We then cover some results of Mirzakhani, their applications and generalizations.

Below are some references for the topics covered in class:

  1. Curves and laminations.
  2. McShane identities and volumes of Moduli spaces.
  3. Counting Curves on a Hyperbolic Surface.
  4. Shape of a generic Riemann surface.
  5. Analogies with symmetric spaces.

Accessibility needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: email or visit here.