## The Geometry and Algebra of Curves on Surfaces

### Dylan Thurston, Fall 2012

Notes are unedited. Any errors introduced are mine.Lecture 1: Introduction

Lecture 2: Mapping class groups

Lecture 3: More about mapping class groups

Lecture 4: Hyperbolic geometry

Lecture 5: Ideal polygons

Lecture 6: Dehn-Thurston coordinates (Alex), more about ideal polygons

Lecture 7: Horocycles and lengths

Lecture 8: Teichmüller space and Markov triples

Lecture 9: Cluster algebras

Lecture 10: More about cluster algebras

Lecture 11: Cross-ratio coordinates

Lecture 12: Laminations and compactifying Teichmüller space

Lecture 13: More about laminations (text only)

Lecture 14: Compactifications, skein theory (updated)

Lecture 15: Orbifolds (Felikson)

Lecture 16: Quantum skeins (Muller)

Lecture 17: The Laurent phenomenon (Kalman), miscellaneous

Lecture 18: Skein theory and the Laurent phenomenon

Lecture 19: Strong positivity

Lecture 20: More about strong positivity

Lecture 21: More about the geometry of skein relations

Lecture 22: Additive categorification of surface cluster algebras (Christof)

Lecture 23: More about additive categorification of surface cluster algebras (Christof)

Lecture 24: Monoidal categorifications of skein algebras

Lecture 25: Types of multicurves

Lecture 26: Even more about the geometry of skein relations