Manfred Einsiedler: Katalogdaten im Herbstsemester 2018

Name	Herr Prof. Dr. Manfred Einsiedler
Lehrgebiet	Mathematik
Adresse	Professur für Mathematik ETH Zürich, HG G 64.2 Rämistrasse 101 8092 Zürich SWITZERLAND
Telefon	+41 44 632 31 84
E-Mail	manfred.einsiedler@math.ethz.ch
URL	http://www.math.ethz.ch/~einsiedl
Departement	Mathematik
Beziehung	Ordentlicher Professor

Nummer	Titel	ECTS	Umfang	Dozierende
401-3110-68L	Fractal Geometry Number of participants limited to 12. Registration to the seminar will only be effective once confirmed by the organisers. Please contact roland.prohaska@math.ethz.ch.	4 KP	2S	M. Einsiedler, weitere Referent/innen
Kurzbeschreibung	Introductory seminar about the mathematical foundations of fractal geometry and its applications in various areas of mathematics
Lernziel
Inhalt	Foundations: - classical examples - notions of dimension and their calculation - local structure - projections, products, intersections Possible Applications: - Dynamical Systems: iterated function systems, self-similar and self-affine sets - Pure Mathematics: the Kakeya problem, fractal groups and rings, graphs of functions - Complex Dynamics: Julia sets and the Mandelbrot set, Vitushkin's conjecture - Number Theory: distribution of digits, continued fractions, Diophantine approximation - Probability Theory: random fractals, Brownian motion
Literatur	Kenneth Falconer: Fractal Geometry, Mathematical Foundations and Applications.
Voraussetzungen / Besonderes	Prerequisites: Content of the first two years of the ETH Bachelor program in mathematics, especially measure theory and topology. Some applications require complex analysis and probability theory. In order to obtain the 4 credit points, each student is expected to give two 1h-talks and regularly attend the seminar.
401-3461-00L	Functional Analysis I Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar.	10 KP	4V + 1U	M. Einsiedler
Kurzbeschreibung	Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
Lernziel	Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Literatur	We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Voraussetzungen / Besonderes	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).
401-5370-00L	Ergodic Theory and Dynamical Systems	0 KP	1K	M. Einsiedler, Uni-Dozierende, weitere Dozierende
Kurzbeschreibung	Research colloquium
Lernziel
401-5530-00L	Geometry Seminar	0 KP	1K	M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, Uni-Dozierende
Kurzbeschreibung	Research colloquium
Lernziel
406-3461-AAL	Functional Analysis I Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.	10 KP	21R	M. Einsiedler
Kurzbeschreibung	Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
Lernziel	Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Literatur	We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.