Tom Ilmanen: Catalogue data in Spring Semester 2023 |
| Name | Prof. Dr. Tom Ilmanen |
| Field | Mathematik |
| Address | Professur für Mathematik ETH Zürich, HG G 62.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 54 43 |
| Fax | +41 44 632 14 04 |
| tom.ilmanen@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~ilmanent |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-2534-00L | Geometry   | 6 credits | 3V + 2U | T. Ilmanen | |||||||||||||||||||||||
| Abstract | The course will treat Möbius transformations and hyperbolic geometry. | ||||||||||||||||||||||||||
| Learning objective | Theorems, proofs, techniques, calculations, pictures, software and examples in geometry. | ||||||||||||||||||||||||||
| Content | Isometry groups; hyperbolic plane; parallels and ultraparallels; getting lost; games and apps; stereographic projection, Möbius transformations, cross ratio; Poincare model, metric, isometries, geodesics, distances; upper half-plane model, ideal triangles, angle-excess formula; Klein model; Minkowski space model; comparisons to spherical and flat geometry; no embedding in R^3; stars appear farther, tidal forces, dangers; possibly compact hyperbolic surfaces, Gauss-Bonnet formula, tesselations, trees. | ||||||||||||||||||||||||||
| Prerequisites / Notice | Linear algebra, first-year analysis, group theory, complex analysis | ||||||||||||||||||||||||||
| Competencies |
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| 401-5350-00L | Analysis Seminar | 0 credits | 1K | F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, T. Rivière, J. Serra, University lecturers | |||||||||||||||||||||||
| Abstract | Research colloquium | ||||||||||||||||||||||||||
| Learning objective | |||||||||||||||||||||||||||
| Content | Research seminar in Analysis | ||||||||||||||||||||||||||