MATH4900E  Seminar  2020/21
General Information
Lecturer

Prof. YiJen LEE
 Office: 412 AB1
 Email:
Time and Venue
 Lecture: Mondays 3:306:15pm via Zoom (Meeting ID and password announced via email and Blackboard)
Course Description
We will explore the interesting world of NonEuclidean geometry, with emphasis on the most interesting case—Hyperbolic Geometry.
References
 [A] Hyperbolic geometry, by James W. Anderson, Springer, 1999.
 [BP] Lectures on Hyperbolic geometry, by Benedetti, C. Petronio, SpringerVerlag, 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] Lowdimensional 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 NonEuclidean Plane, by G. Martin
 [PM] NonEuclidean Geometries, Edited by Preokopa & Molnar.
 [I] Hyperbolic Geometry, by Iverson
 [KM] The NonEuclidean, Hyperbolic Plane, by Kelly & Matthews
 [F] Elementary Geometry in Hyperbolic Space, by Fenchel
 [Be] The Geometry of Discrete Groups, by Beardon
Lecture Notes
 Recording: Sept 28 (Passcode: 3C+Qh6NA )
 Recording: Oct 5 (Passcode: XEds^588 ) first 1020 minutes missing
 Recording: Oct 12 (Passcode: =4F@Azba ) first 1020 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 )
Class Notes
 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)
Assignments
 Sep 28 [Team 1: Kwok & Ma] Three types of geometries in dimension 2: Euclidean, Sperical, Hyperbolic; History of NonEuclidean Geometry. Cf. e.g. [CFKP] Sections 15; [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 2dimensional 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 2d 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.78; [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.1215; [S] Ch. 45; [K] Ch. 23; [P] (tentative)
 Nov 16 [Team 3: Kung & Wong] Sidepairing transformations, Elliptic/parabolic cycles, Poincaré’s Theorem Cf. e.g [W] Ch.1620; [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. 2122 (including Exercise 21.2; 21.3 (i)); [S] Ch.7; [K] Ch. 4; [Be] Ch.6.
Assessment Scheme
Oral presentations  100% 
Useful Links
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Assessment Policy Last updated: November 16, 2020 17:16:52