The Geometry and Algebra of Curves on Surfaces

Dylan Thurston, Fall 2012

(These notes are very rough!)

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: Teichm├╝ller space and Markov triples
Lecture 9: Cluster algebras
Lecture 10: More about cluster algebras
Lecture 11: Cross-ratio coordinates
Lecture 12: Laminations and compactifying Teichm├╝ller 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