Paul D. Nelson: Katalogdaten im Herbstsemester 2016 |
| Name | Herr Dr. Paul D. Nelson |
| URL | http://www.math.ethz.ch/~nelsonpa |
| Departement | Mathematik |
| Beziehung | Assistenzprofessor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-3225-00L | Introduction to Lie Groups | 8 KP | 4G | P. D. Nelson | |
| Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | ||||
| Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | ||||
| Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A.Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F.Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S.Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A.Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | ||||
| Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. Course webpage: http://www.math.ethz.ch/education/bachelor/lectures/hs2014/math/introlg | ||||
| 401-5110-00L | Number Theory Seminar  | 0 KP | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |
| Kurzbeschreibung | Research colloquium | ||||
| Lernziel | |||||