Hyperbolic Analysis and Geometry
| Title | ΥΠΕΡΒΟΛΙΚΗ ΑΝΑΛΥΣΗ ΚΑΙ ΓΕΩΜΕΤΡΙΑ / Hyperbolic Analysis and Geometry |
| Code | 0648 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Anestis Fotiadis |
| Common | No |
| Status | Active |
| Course ID | 40000036 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A2 | 1 | 1 | 10 |
| Academic Year | 2017 – 2018 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600112019
|
Course Type 2021
Specialization / Direction
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600112019
General Competences
- Advance free, creative and causative thinking
Course Content (Syllabus)
Mobious transformations, hyperbolic geometry models, groups of isometries, hyperbolic metrics, fundamental domains, limit set, hyperbolic surfaces, heat kernel estimates
Keywords
hyperbolic space, heat kernel, Kleinian groups
Educational Material Types
- Notes
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 300 | 10 | ✓ | ||
| Total | 300 | 10 |
Student Assessment
Student Assessment methods
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1. Davies E.B. and N. Mandouvalos (1988). Heat Kernel Bounds on Hyperbolic
Space and Kleinian Groups. Proc. London Math. Soc. 57 (No 3): 182-208.
2. Davies E.B. and N. Mandouvalos (1987). Heat Kernel Bounds on Manifolds
with Cusps. J. Funct. Anal. 75 (No 2): 311-322.
3. Mandouvalos N. (1988). Spectral Theory and Eisenstein Series for Kleinian
4. http://homepages.warwick.ac.uk/~masbb/Papers/MA448.pdf
Groups. Proc. London Math. Soc. 57 (No 3): 209-238.
4. Mandouvalos N. (1989). Scattering Operator, Eisenstein Series, Inner Product
Formula and “Maass-Selberg” relations for Kleinian Groups. Memoirs Amer.
Math. Soc. 400.
Last Update
24-05-2023
