Manfred Einsiedler: Katalogdaten im Frühjahrssemester 2021

NameHerr Prof. Dr. Manfred Einsiedler
Professur für Mathematik
ETH Zürich, HG G 64.2
Rämistrasse 101
8092 Zürich
Auszeichnung: Die Goldene Eule
Telefon+41 44 632 31 84
BeziehungOrdentlicher Professor

401-3378-19LEntropy in Dynamics Information 8 KP4GM. Einsiedler
KurzbeschreibungDefinition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group.
LernzielThe course will lead to a firm understanding of measure theoretic dynamical entropy and its applications within dynamics. We will start with the basic properties of (conditional) entropy, relate it to the question of effective coding techniques, discuss and prove the Shannon-McMillan-Breiman theorem that is also known as the ergodic theorem for entropy. Moreover, we will discuss a topological counter part and relate this topological entropy to the measure theoretic entropy by the variational principle. We will use these methods to classify certain natural homogeneous measures, prove equidistribution of periodic points on compact quotients of hyperbolic surfaces, and establish a measure rigidity theorem for commuting maps on the circle group.
SkriptEntropy book under construction, available online under
Voraussetzungen / BesonderesNo prior knowledge of dynamical systems will be assumed but measure theory will be assumed and very important. Doctoral students are welcome to attend the course for 2KP.
401-5370-00LErgodic Theory and Dynamical Systems Information 0 KP1KM. Akka Ginosar, M. Einsiedler, Uni-Dozierende
KurzbeschreibungResearch colloquium
401-5530-00LGeometry Seminar Information 0 KP1KM. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, Uni-Dozierende
406-2005-AALAlgebra I and II
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
12 KP26RM. Burger, M. Einsiedler
KurzbeschreibungIntroduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.

The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
InhaltBasic notions and examples of groups;
Subgroups, Quotient groups and Homomorphisms,
Group actions and applications

Basic notions and examples of rings;
Ring Homomorphisms,
ideals, and quotient rings, rings of fractions
Euclidean domains, Principal ideal domains, Unique factorization

Basic notions and examples of fields;
Field extensions, Algebraic extensions, Classical straight edge and compass constructions

Fundamentals of Galois theory
Representation theory of finite groups and algebras
LiteraturJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society