Manfred Einsiedler: Catalogue data in Autumn Semester 2018

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
401-3110-68L	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 credits	2S	M. Einsiedler, further speakers
Abstract	Introductory seminar about the mathematical foundations of fractal geometry and its applications in various areas of mathematics
Learning objective
Content	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
Literature	Kenneth Falconer: Fractal Geometry, Mathematical Foundations and Applications.
Prerequisites / Notice	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 At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics.	10 credits	4V + 1U	M. Einsiedler
Abstract	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.
Learning objective	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.
Literature	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.
Prerequisites / Notice	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 credits	1K	M. Einsiedler, University lecturers, further lecturers
Abstract	Research colloquium
Learning objective
401-5530-00L	Geometry Seminar	0 credits	1K	M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers
Abstract	Research colloquium
Learning objective
406-3461-AAL	Functional Analysis I 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.	10 credits	21R	M. Einsiedler
Abstract	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.
Learning objective	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.
Literature	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.