Manfred Einsiedler: Catalogue data in Spring Semester 2022

Name	Prof. Dr. Manfred Einsiedler
Field	Mathematics
Address	Professur für Mathematik ETH Zürich, HG G 64.2 Rämistrasse 101 8092 Zürich SWITZERLAND
Telephone	+41 44 632 31 84
E-mail	manfred.einsiedler@math.ethz.ch
URL	http://www.math.ethz.ch/~einsiedl
Department	Mathematics
Relationship	Full Professor

Number	Title	ECTS	Hours	Lecturers
401-3226-01L	Unitary Representations of Lie Groups	8 credits	4G	M. Einsiedler
Abstract	This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R).
Learning objective	The goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations. In the second part we will consider concrete representations of SL(2,R) and decompose these into irreducible representations or at least understand whether spectral gap is present.
Content	The course will start with the general framework of unitary representations of locally compact groups, which is in some sense a general theory of Fourier analysis related to groups. For this some functional analysis (in particular spectral theory of bounded selfadjoint operators, Krein-Milman and Choquet) will be important. In the interest of time we will only summarise the case abelian groups and use the abelian theory to understand some metabelian groups. After this we will discuss some more general theory. Some of the general phenomena will be discussed for the concrete group of SL(2,R). Moreover, we will understand the unitary dual of SL(2,R), discuss the notion of spectral gap for SL(2,R), and decompose the unitary representation of SL(2,R) arising from the hyperbolic plane into irreducible representation.
Lecture notes	Unitary Representations and Unitary Duals, book project joint with Tom Ward, see https://tbward0.wixsite.com/books/unitary
Literature	Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Prerequisites / Notice	Prerequisites: Functional Analysis I and a bit of Lie Groups I. The simultaneous course Functional Analysis II in SS 22 by M. Burger will treat some of the prerequisites of this course and also some related but different aspects of unitary representations. This course will be cancelled if it should it be impossible to teach in presence, but according to info by Bundesrat and ETH it seems that we will be able to hold the course.
401-3227-DRL	Unitary Representations of Lie Groups Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“.	2 credits	4G	M. Einsiedler
Abstract	This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R).
Learning objective	The goal is to acquire familiarity with the basic formalism and results concerning Lie groups and their unitary representations. In the second part we will consider concrete representations of SL(2,R) and decompose these into irreducible representations or at least understand whether spectral gap is present.
Content	The course will start with the general framework of unitary representations of locally compact groups, which is in some sense a general theory of Fourier analysis related to groups. For this some functional analysis (in particular spectral theory of bounded selfadjoint operators, Krein-Milman and Choquet) will be important. In the interest of time we will only summarise the case abelian groups and use the abelian theory to understand some metabelian groups. After this we will discuss some more general theory. Some of the general phenomena will be discussed for the concrete group of SL(2,R). Moreover, we will understand the unitary dual of SL(2,R), discuss the notion of spectral gap for SL(2,R), and decompose the unitary representation of SL(2,R) arising from the hyperbolic plane into irreducible representation.
Lecture notes	Unitary Representations and Unitary Duals, book project joint with Tom Ward, see https://tbward0.wixsite.com/books/unitary
Literature	Bekka, de la Harpe and Valette: "Kazhdan's Property (T)", Cambridge University Press.
Prerequisites / Notice	Prerequisites: Functional Analysis I and a bit of Lie Groups I. The simultaneous course Functional Analysis II in SS 22 by M. Burger will treat some of the prerequisites of this course and also some related but different aspects of unitary representations. This course will be cancelled if it should it be impossible to teach in presence, but according to info by Bundesrat and ETH it seems that we will be able to hold the course.
401-5370-00L	Ergodic Theory and Dynamical Systems	0 credits	1K	M. Akka Ginosar, M. Einsiedler, University lecturers
Abstract	Research colloquium
Learning objective
401-5530-00L	Geometry Seminar	0 credits	1K	M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers
Abstract	Research colloquium
Learning objective