Translation Surfaces

Jayadev Athreya (University of Washington) , Ozgur Yilmaz (University of British Columbia)

Jan 5, 2025 — Mar 13, 2025

About the course

Translation surfaces and their moduli spaces have been the objects of extensive recent study and interest, with connections to widely varied fields including (but not limited to) geometry and topology; Teichmüller theory; low-dimensional dynamical systems; homogeneous dynamics and Diophantine approximation; and algebraic and complex geometry. This course will serve as an introduction to some of the big ideas in the field, centered on the ergodic properties of translation flows and counting problems for saddle connections, and associated renormalization techniques, without attempting to reach the full state of the art (an aim that is in any case impossible given the speed at which the field is evolving).


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Translation Surfaces
Jan 5, 2025 — Mar 13, 2025
Course Number
- University of Washington: MATH 583C - WDA Students: UBC Course number TBA
Section Number
Section Code


For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details

Remote Access

The instructor will use a tablet and Zoom. The tablet will be displayed locally in the classroom and via zoom. Lecture notes will be distributed in PDF format.