Lehrende: Prof. Dr. Christoph Schweigert
Veranstaltungsart: Vorlesung
Anzeige im Stundenplan: M-VFT-V
Semesterwochenstunden: 4
Unterrichtssprache: Deutsch
Min. | Max. Teilnehmerzahl: 5 | -
Kommentare/ Inhalte: 1. Elliptic functions 2. Elliptic modular forms 3. Covering spaces and Riemann surfaces 4. Compact Riemann surfaces
Lernziel: The goal of this lecture course is to present some topics that extend and deepen the theory of complex functions as it is presented in ``Funktionentheorie I'' of classes for physicists. The two most important topics are: Modular forms: To make more explicit the theory of analytic functions, we introduce and discuss modular forms. These functions enter in fields as different as number theory, geometry, algebra and representation theory. They arise as string amplitudes as well. Riemann surfaces Problems like defining a complex square root require a careful rethinking of the domains of analytic functions. The answer is provided by Riemann surfaces, a theory of much use in itself. (E.g. the world sheet of a string essentially carries the structure of a Riemann surface.) For more information, we refer to http://www.math.uni-hamburg.de/home/schweigert/ss11/funktionentheorie2.html
Vorgehen: The class addresses students in all bachelor and master programs in mathematics and physics; a knowledge of complex functions correspondingly roughly to Chapter 1-4 of my Lecture Notes from Winter 2009/2010 is sufficient. It is accessible and actually aims at bachelor students with these prerequesites as well. Many of the methods have applications in mathematical physics. The class is suitable for students in the bachelor or master program in physics and in mathematical physics as well.
Literatur: R. Busam, E. Freitag: Funktionentheorie 1, Springer 2006 O. Forster, Lectures on Riemann surfaces, Springer Graduate Texts in Mathematics, 1991 M. Koecher, A. Krieg: Elliptische Funktionen und Modulformen, Springer 2007 J.P. Serre: A course in Arithmetic. Springer Graduate Text in Mathematics 7, 1973, see Chapter 7
Modulkürzel: Ma-M-VFT_n
Zusätzliche Hinweise zu Prüfungen: Written exam. First exam immediately in July 2011; precise date to be announced.
