Manfred Einsiedler: Catalogue data in Autumn Semester 2018

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

NumberTitleECTSHoursLecturers
401-3110-68LFractal Geometry Information Restricted registration - show details
Number of participants limited to 12.
Registration to the seminar will only be effective once confirmed by the organisers. Please contact Link.
4 credits2SM. Einsiedler, further speakers
AbstractIntroductory seminar about the mathematical foundations of fractal geometry and its applications in various areas of mathematics
Objective
ContentFoundations:
- 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
LiteratureKenneth Falconer: Fractal Geometry, Mathematical Foundations and Applications.
Prerequisites / NoticePrerequisites: 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.
401-3461-00LFunctional Analysis I Information
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 credits4V + 1UM. Einsiedler
AbstractBaire 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.
ObjectiveAcquire 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.
LiteratureWe 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 / NoticeSolid 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 credits1KM. Einsiedler, University lecturers, further lecturers
AbstractResearch colloquium
Objective
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers
AbstractResearch colloquium
Objective
406-3461-AALFunctional 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 credits21RM. Einsiedler
AbstractBaire 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.
ObjectiveAcquire 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.
LiteratureWe 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.