Manfred Einsiedler: Katalogdaten im Frühjahrssemester 2019

Auszeichnung: Die Goldene Eule
NameHerr Prof. Dr. Manfred Einsiedler
LehrgebietMathematik
Adresse
Professur für Mathematik
ETH Zürich, HG G 64.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 31 84
E-Mailmanfred.einsiedler@math.ethz.ch
URLhttp://www.math.ethz.ch/~einsiedl
DepartementMathematik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
401-3378-19LEntropy in Dynamics Information 6 KP3GM. Akka Ginosar, M. Einsiedler
KurzbeschreibungDefinition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Connection to coding theory. Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points.
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. Finally we will use these methods to classify certain natural homogeneous measures and use this to prove equidistribution of periodic points on compact quotients of hyperbolic surfaces.
SkriptEntropy book under construction, available online under
https://tbward0.wixsite.com/books/entropy
Voraussetzungen / BesonderesMeasure Theory will be very important. No prior knowledge of dynamical systems will be assumed. Doctoral students are welcome to attend the course but cannot take it for credit.
401-3462-00LFunctional Analysis II Information 10 KP4V + 1UM. Einsiedler
KurzbeschreibungSobolev spaces, weak solutions of elliptic boundary value problems, elliptic regularity, spectral theory, and unitary representations.
LernzielAcquiring the language and methods for boundary value problems, Sobolev spaces, Banach algebras, Spectral theory of bounded and unbounded selfadjoint operators, and Unitary representations.
SkriptFunctional Analysis, Spectral Theory and Applications.
Manfred Einsiedler and Thomas Ward, GTM Springer 2017
LiteraturFunctional Analysis, Spectral Theory and Applications.
Manfred Einsiedler and Thomas Ward, GTM Springer 2017
Voraussetzungen / BesonderesFunctional Analysis I plus a solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
401-5370-00LErgodic Theory and Dynamical Systems Information 0 KP1KM. Akka Ginosar, M. Einsiedler, Uni-Dozierende
KurzbeschreibungResearch colloquium
Lernziel
401-5530-00LGeometry Seminar Information 0 KP1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, Uni-Dozierende
KurzbeschreibungForschungskolloquium
Lernziel
406-3461-AALFunctional Analysis I Information
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.
10 KP21RM. Einsiedler
KurzbeschreibungBaire category; Banach spaces and linear operators; Fundamental theorems: Open Mapping Theorem, Closed Range Theorem, Uniform Boundedness Principle, Hahn-Banach Theorem; Convexity; reflexive spaces; Spectral theory.
Lernziel
Voraussetzungen / BesonderesThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.