Marc Burger: Catalogue data in Spring Semester 2022 |
| Name | Prof. Dr. Marc Burger |
| Field | Mathematics |
| Address | Dep. Mathematik ETH Zürich, HG G 37.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 49 73 |
| Fax | +41 44 632 10 85 |
| marc.burger@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~burger |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-2000-00L | Scientific Works in Mathematics Target audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | 0 credits | M. Burger | ||
| Abstract | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | ||||
| Learning objective | Learn the basic standards of scientific works in mathematics. | ||||
| Content | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | ||||
| Lecture notes | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | ||||
| Prerequisites / Notice | Directive https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-en/declaration-of-originality.pdf | ||||
| 401-3462-DRL | Functional Analysis II   Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“. | 3 credits | 4V + 1U | M. Burger | |
| Abstract | Sobolev spaces, weak solutions of elliptic boundary value problems, basic results in elliptic regularity theory (including Schauder estimates), maximum principles. | ||||
| Learning objective | Acquire fluency with Sobolev spaces and weak derivatives on the one hand, and basic elliptic regularity on the other. Apply these methods for studying elliptic boundary value problems. | ||||
| Literature | Michael Struwe. Funktionalanalysis I und II. Lecture notes, ETH Zürich, 2013/14. Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi. Lectures on elliptic partial differential equations. Springer - Edizioni della Normale, Pisa, 2018. David Gilbarg, Neil Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer, Berlin, 2001. Qing Han, Fanghua Lin. Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011. Michael Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011. Lars Hörmander. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Classics in Mathematics. Springer, Berlin, 2003. | ||||
| Prerequisites / Notice | Functional Analysis I plus a solid background in measure theory, Lebesgue integration and L^p spaces. | ||||
| 401-3462-00L | Functional Analysis II | 10 credits | 4V + 1U | M. Burger | |
| Abstract | The course will focus essentially on the theory of abelian Banach algebras and its applications to harmonic analysis on locally compact abelian groups, and spectral theorems. Time permitting we will talk about a fundamental property of highly non abelian groups, namely property (T); one of the spectacular applications thereof is the explicit construction of expander graphs. | ||||
| Learning objective | Acquire fluency with abelian Banach algebras in order to apply their theory to harmonic analysis on locally compact groups and to spectral theorems. | ||||
| Content | Banach algebras and the spectral radius formula, Guelfand's theory of abelian Banach algebras, Locally compact groups, Haar measure, properties of the convolution product, Locally compact abelian groups, the dual group, basic properties of the Fourier transform, Positive definite functions and Bochner's theorem, The Fourier inversion formula, Plancherel's theorem, Pontryagin duality and consequences, Regular abelian Banach algebras, minimal ideals and Wiener's theorem for general locally compact abelian groups. Applications to Wiener-Ikehara and the prime number theorem, Guelfand's theory of abelian C*-algebras and applications to the spectral theorem for normal operators, Property (T). | ||||
| Literature | M.Einsiedler, T. Ward: Functional Analysis, Spectral Theory, and Applications, GTM Springer, 2017 I. Gelfand, D. Raikov, G. Shilov: Commutative Normed Rings, Chelsea 1964 E. Kaniuth: A Course in Commutative Banach Algebras, GTM Springer, 2009 W. Rudin: Fourier Analysis on Groups, Dover, 1967 M. Takesaki: Theory of Operator Algebras, Springer, 1979 | ||||
| Prerequisites / Notice | Point set topology, Basic measure theory, Basics of functional analysis specifically: Banach-Steinhaus, Banach-Alaoglu, and Hahn-Banach. | ||||
| 401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, University lecturers | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||