Manfred Einsiedler: Catalogue data in Spring Semester 2021

Name Prof. Dr. Manfred Einsiedler
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG G 64.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Award: The Golden Owl
Telephone+41 44 632 31 84
E-mailmanfred.einsiedler@math.ethz.ch
URLhttp://www.math.ethz.ch/~einsiedl
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-3378-19LEntropy in Dynamics Information 8 credits4GM. Einsiedler
AbstractDefinition 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.
ObjectiveThe 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.
Lecture notesEntropy book under construction, available online under
https://tbward0.wixsite.com/books/entropy
Prerequisites / NoticeNo 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 credits1KM. Akka Ginosar, M. Einsiedler, University lecturers
AbstractResearch colloquium
Objective
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers
AbstractResearch colloquium
Objective
406-2005-AALAlgebra I and II
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
12 credits26RM. Burger, M. Einsiedler
AbstractIntroduction 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.
Objective
ContentBasic 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
domains

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
LiteratureJoseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society