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Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 1) by Subhojoy Gupta
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ORGANIZERS : C. S. Aravinda and Rukmini Dey
DATE & TIME: 16 June 2018 to 25 June 2018
VENUE : Madhava Lecture Hall, ICTS, Bangalore
This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This will enable lecturers from institutions all over India to get acquainted with various areas of geometry and topology which are active fields of research.
Topics will include: Geometry and Topology of surfaces; Hyperbolic geometry and moduli spaces of Riemann surfaces; Minimal surfaces, maximal surfaces and solitons; Fundamental Groupoid.
The workshop will have 4 pedagogical lecture series. There will also be discussion sessions aimed at promoting research and collaborations amongst the participants. The lecturer-participants themselves will also have a chance to present papers (which could be their own too in the area). In addition, there will be small projects which may later on develop into research projects.
PROGRAM LINK
0:00:00 Geometry and Topology for Lecturers
0:00:10 Hyperbolic Geometry, Fuchsian groups and moduli spaces (Lecture 1)
0:00:27 Introduction to Hyperbolic Geometry
0:02:47 1. Upper half-plane model
0:04:06 Fact 1 Automorphism (H2) = PSL(2,R)
0:06:34 Fact 2
0:08:22 Why invariant ?
0:10:19 Can check
0:14:02 Properties of the hyperbolic metric
0:14:10 1. Geodesics
0:17:42 Consequence
0:20:16 2. The metric is complete
0:24:41 3. Sum of interior angles of any geodesic triangle is less than Pi !
0:26:38 Example of conformal model of the hyperbolic geometry
0:29:22 In fact
0:36:23 4. The hyperbolic metric has constant curvature
0:41:27 2. Disk model
0:49:05 Note
0:54:41 Hyperbolic Trigonometry - Warmup
0:55:54 Lemma
0:56:15 Proof
1:01:35 Note: In Euclidean geometry
1:07:38 3. Hyperboloid model
1:11:24 Claim
1:12:35 Example
1:18:05 Relation with unit disk model
1:20:53 Q&A
DATE & TIME: 16 June 2018 to 25 June 2018
VENUE : Madhava Lecture Hall, ICTS, Bangalore
This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This will enable lecturers from institutions all over India to get acquainted with various areas of geometry and topology which are active fields of research.
Topics will include: Geometry and Topology of surfaces; Hyperbolic geometry and moduli spaces of Riemann surfaces; Minimal surfaces, maximal surfaces and solitons; Fundamental Groupoid.
The workshop will have 4 pedagogical lecture series. There will also be discussion sessions aimed at promoting research and collaborations amongst the participants. The lecturer-participants themselves will also have a chance to present papers (which could be their own too in the area). In addition, there will be small projects which may later on develop into research projects.
PROGRAM LINK
0:00:00 Geometry and Topology for Lecturers
0:00:10 Hyperbolic Geometry, Fuchsian groups and moduli spaces (Lecture 1)
0:00:27 Introduction to Hyperbolic Geometry
0:02:47 1. Upper half-plane model
0:04:06 Fact 1 Automorphism (H2) = PSL(2,R)
0:06:34 Fact 2
0:08:22 Why invariant ?
0:10:19 Can check
0:14:02 Properties of the hyperbolic metric
0:14:10 1. Geodesics
0:17:42 Consequence
0:20:16 2. The metric is complete
0:24:41 3. Sum of interior angles of any geodesic triangle is less than Pi !
0:26:38 Example of conformal model of the hyperbolic geometry
0:29:22 In fact
0:36:23 4. The hyperbolic metric has constant curvature
0:41:27 2. Disk model
0:49:05 Note
0:54:41 Hyperbolic Trigonometry - Warmup
0:55:54 Lemma
0:56:15 Proof
1:01:35 Note: In Euclidean geometry
1:07:38 3. Hyperboloid model
1:11:24 Claim
1:12:35 Example
1:18:05 Relation with unit disk model
1:20:53 Q&A
1:22:10
Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 1) by Subhojoy Gupta
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Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 2) by Subhojoy Gupta
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Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 3) by Subhojoy Gupta
1:45:22
Fuchsian Groups and Hyperbolic Surfaces
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Hyperbolic Geometry 5.4. Fuchsian groups: Locally finite fundamental domains
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Hyperbolic Geometry 5.1. Fuchsian groups: Motivation: a Riemann surface structure for the torus
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Hyperbolic Geometry 5.6. Fuchsian groups: the Dirichlet polygon
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Hyperbolic Geometry Review 5.3. Fuchsian groups: Basic algebraic, topological and geom properties
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Hyperbolic almost-Fuchsian manifolds
1:01:57
Hyperbolic Geometry 5.3. Fuchsian groups: Basic algebraic, topological and geometric properties
1:25:34
Hyperbolic Geometry 5.5. Fuchsian groups: Locally finite fund doms (concl), the Dirichlet polygon
1:33:17
Alan Reid 'The geometry and topology of arithmetic hyperbolic manifolds' | The Vinberg Lec...
0:05:03
Poincaré's theorem for hyperbolic polygons
1:25:33
Hyperbolic Geometry 5.2. Fuchsian groups: Topol prelims; Properly discont actions vs discrete subgps
0:00:17
Schottky / Fuchsian Groups
0:21:00
Orbit closures of unipotent flows for hyperbolic manifold with Fuchsian ends - Minju Lee
0:00:51
Quasi-Fuchsian Groups
1:11:10
Boundaries of quasi-Fuchsian spaces and continuous/discontinuous (Lecture -1) by Ken'ichi Ohshi...
0:52:13
Cheeger constants of arithmetic hyperbolic surfaces (GGD/GEAR Seminar)
1:05:34
Spencer Dowdall - Hyperbolic geometry in group extensions
0:55:31
HG.05.01. Fuchsian groups: Topological preliminaries
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Hyperbolic Geometry
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