MAT 1350, Combinatorial Teichmüller Theory, Fall 2023

Instructor

Kasra Rafi
Office: BA 6236 (Bahen Centre)
Email: rafi@math.toronto.edu

Meetings

Tuesdays and Thursdays 4 - 5:30 pm
Location: BA 6183

Office Hours

Tuesdays 3 pm -- 4 pm
Thursdays 3 pm -- 4 pm or by appointment.

Course Description

Teichmüller theorey is the study of deforomation space of geometric structures on a surface. This is an old and central subject with connection to may fields of mathematics such as Topology, Dynamics, Algebraic Geometry and Number Theory. The traditional approach to Teichmüller theorey is via the complex analysis where points on the space are considered as marked Riemann surfaces. However, combinatorial tools developed recently have found many application in Teichmüller theorey.

The goal of the class is to see how the coarse geometry of Teichmüller space can be understood by studying the intersection patterns of curves on the surface. Our main tools are spaces such as the curve complex and the space of measured lamination together with the action of the mapping class group on these spaces.

Here are some references for the topic that will be covered in class.

1. Curves and laminations
• Combinatorics of Train Tracks.   by R. C. Penner and J. L. Harer.
• Thurston's Work on Surfaces,   by Albert Fathi, François Laudenbach, and Valentin Poéna.
• Notes on the complex of curves,   by Saul Schleimer. You can find the notes here.
2. Hyperbolic Geometry
• Foundations of Hyperbolic Manifolds,   by John Ratcliffe.
• Hyperbolic geometry,   by Croline Series. You can find the notes here.
3. Teichmüller theorey
• Teichmüller Theor and Applications to Geometry, Topology, and Dynamics,   by John H. Hubbard.
• An Introduction to Teichmüller Spae   by Yoichi Imayoshi , Masahiko Taniguchi.

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 disability.services@utoronto.ca or visit here.