Surface group seminar

List of topics that I aim to cover, in chronological order ( to be updated periodically!) :

Shear parameters of hyperbolic surfaces

References: Martelli's book (listed above), Bonahon's book on "Low dimensional geometry", Bestvina-Bromberg-Fujiwara-Souto.

Notes: Lecture 1 (7/8/2019) Lecture 2 (14/8)

Complex shears and surface-group representations into PSL(2,C)

References: Fundamentals of Hyperbolic Manifolds (edited by Canary-Epstein-Green), also Bonahon's paper on shearing hyperbolic surfaces.

Notes: Lecture 3 (21/8)

Fock-Goncharov coordinates and surface-group representations into PSL(n,C)

References: Notes on the work of Fock-Goncharov by F. Palesi, available here.

Notes: Lectures 4 and 5 (28/8 and 30/8)

Geodesic laminations on a hyperbolic surface

References: Fundamentals of Hyperbolic Manifolds, Casson-Bleiler's book , Bonahon's notes.

Notes: Lectures 6 and 7 (4/10 and 11/10)

Guest Lecture by Gianluca Faraco on 9/10

References: Goldman's paper (for the portion on the character variety of the punctured torus)

Measured laminations and earthquakes

References: Thurston's article in Fundamentals of Hyperbolic Manifolds, Jun Hu's article in Handbook of Teichmüller Theory Volume III, Chapter 18 of Gardiner-Lakic's book, Chapter 11 of Kapovich's book on Hyperbolic Manifolds, Appendix to Otal's book on Hyperbolization for Fibered Manifolds, Alex Wright's notes on Mirzakhani's work on the Earthquake flow.

Notes: Lecture 8, Lecture 9 and Lecture 10 (25/10, 30/10 and 8/11)

Quasifuchsian groups and the Bending Lamination Conjecture

References: Chapter 8 of Thurston's notes, final two chapters of Bonahon's book on "Low dimensional geometry", Chapter 5.1 of Martelli's book, Part II in Fundamentals of Hyperbolic Manifolds (by Epstein and Marden), Outer Circles by Marden.

Notes: Lecture 11 and Lecture 12 (13/11 and 15/11)