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Manfred Einsiedler: Catalogue data in Spring Semester 2016

Name Prof. Dr. Manfred Einsiedler
Professur für Mathematik
ETH Zürich, HG G 64.2
Rämistrasse 101
8092 Zürich
Award: The Golden Owl
Telephone+41 44 632 31 84
RelationshipFull Professor

401-3226-01LUnitary Representations of Lie Groups and Discrete Subgroups of Lie Groups8 credits4GM. Einsiedler
AbstractThis course will contain three parts:
* Classification of simple Lie algebras
* Introduction to unitary representations of Lie groups
* Introduction to the study of discrete subgroups of Lie groups, the quotient space, and some applications.
ObjectiveThe goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations, and to apply these to the study of discrete subgroups, especially lattices, in Lie groups.
Content* Classification using Dynkin diagrams
* Unitary representations of compact Lie groups: Peter-Weyl theory, weights, Weyl character formula
* Introduction to unitary representations of non-compact Lie groups: the examples of SL(2,R), SL(2,C)
* Example: Property (T) for SL(n,R)
* Discrete subgroups of Lie groups: examples and some applications
LiteratureBekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Prerequisites / NoticeFunctional analysis I and
Lie Groups I or Differential geometry I.
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, V. Schroeder, A. Sisto
AbstractResearch colloquium