MATH4900E - Seminar - 2020/21
Prof. Yi-Jen LEE
- Office: 412 AB1
Time and Venue
- Lecture: Mondays 3:30-6:15pm via Zoom (Meeting ID and password announced via email and Blackboard)
We will explore the interesting world of Non-Euclidean geometry, with emphasis on the most interesting case—Hyperbolic Geometry.
- [A] Hyperbolic geometry, by James W. Anderson, Springer, 1999.
- [BP] Lectures on Hyperbolic geometry, by Benedetti, C. Petronio, Springer-Verlag, 1992.
- [K] Fuchsican Groups, by Svetlana Katok, Chicago Lectures in Mathematics, 1992.
- [CFKP] Lecture notes, by J. W. Cannon, W. J. Floyd, R. Kenyon, W. R. Parry; see link below.
- [S] Lecture notes by C. Series ; see link below.
- [W] Lecture notes by C. Walkden; see link below.
- [N] Visual Complex Analysis, by Needham.
- [B] Low-dimensional geometry, by F. Bonahon.
- [P] Notes by Pollicott; see link below
- [KL] Hyperbolic Geometry from a Local Viewpoint, by Keen & Kakic
- [M] The Foundations Of Geometry and the Non-Euclidean Plane, by G. Martin
- [PM] Non-Euclidean Geometries, Edited by Preokopa & Molnar.
- [I] Hyperbolic Geometry, by Iverson
- [KM] The Non-Euclidean, Hyperbolic Plane, by Kelly & Matthews
- [F] Elementary Geometry in Hyperbolic Space, by Fenchel
- [Be] The Geometry of Discrete Groups, by Beardon
- Recording: Sept 28 (Passcode: 3C+Qh6NA )
- Recording: Oct 5 (Passcode: XEds^588 )-- first 10-20 minutes missing
- Recording: Oct 12 (Passcode: =4F@Azba )- first 10-20 minutes missing
- Recording: Oct 19 (Passcode: V3SCZ$+K )
- Recording: Nov 2 (Passcode: b&j8P8$9 )
- Recording: Nov 9 (Passcode: 8k2N0Z+! )
- Recording: Nov 16 (Passcode: M0&nM=Sj )
- Slides: Sep 28 (Chan)
- Slides: Oct 5 (Cheng & Hui)
- Slides: Oct 12 (Kung & Wong)
- Slides: Oct 19 (Kan & Lau)
- Slides: Nov 2 (Ma & Kwok)
- Slides: Nov 9 (Cheng & Hui)
- Slides: Nov 16 (Kung & Wong)
- Sep 28 [Team 1: Kwok & Ma] Three types of geometries in dimension 2: Euclidean, Sperical, Hyperbolic; History of Non-Euclidean Geometry. Cf. e.g. [CFKP] Sections 1-5; [W] Section 1; [N] Chapters 1,6; [B] Chapters 1, 3; [P] Lecture 1; [KL] Chapter 1; [M]; [PM] Part I; [I] Chapter 2, Appendix; [KM] Chapters 1, 2, Appendix.
- Oct 5 [Team 2: Cheng & Hui] Models of 2-dimensional hyperbolic space and relations among them; Hyperbolic length, lines, and distances cf. e.g. [A] ch.1, 4, 6; [BP] A.1; [CFKP] Ch.7, [W] Sections 2, 6.
- Oct 12 [Team 3: Kung & Wong] Möbius transformations Cf. e.g. [A] Ch.2; [S], [W]
- Oct 19 [Team 4: Kan & Lau] Hyperbolic distances and geodesics in Plane and Poincare models; Mobius transformations as isometries on the 2-d hyperbolic space; Convexity. Cf. e.g [A] Ch.3; 5.1; [S] Sect. 2, 3; [W].
- Nov 2 [Team 1: Kwok & Ma] Hyperbolic trigonomy, polygons, Hyperbolic area; Gauss Bonnet, Hyperbolic tessellations Cf. e.g [A] Ch. 5, [W] Ch.7-8; [S] 2.2
- Nov 9 [Team 2: Cheng & Hui] Basics of group actions and Fuchsian groups; Fundamental domains; Dirichlet polygons Cf. e.g [W] Ch.12-15; [S] Ch. 4-5; [K] Ch. 2-3; [P] (tentative)
- Nov 16 [Team 3: Kung & Wong] Side-pairing transformations, Elliptic/parabolic cycles, Poincaré’s Theorem Cf. e.g [W] Ch.16-20; [S] Ch. 6; [K]; [P] (tentative)
- Nov 23 [Team 4: Kan & Lau] Gluing constructions; hyperbolic surfaces (possibly with cusps); Euler characteristics; signature of Fuchsian group; covering spaces; uniformization Cf. e.g. [W] Ch. 21-22 (including Exercise 21.2; 21.3 (i)); [S] Ch.7; [K] Ch. 4; [Be] Ch.6.
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:http://www.cuhk.edu.hk/policy/academichonesty/
and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: November 16, 2020 17:16:52