This will be a seminar on advanced topics in the homotopy theory of spaces. The precise list oftopics will be made to fit the background of the participants, but some of the following are likelyto be included: Postnikov towers and obstruction theory, cohomology operations and theirapplications, methods for the calculation of homotopy groups, localizations and completions ofspaces, homotopy (co)limits.
Es wird über die Themen der laufenden Bachelorarbeiten vorgetragen.
Die Vorlesung Lineare Algebra II wendet sich an Studierende des zweiten Semesters. Sie bildetzusammen mit der Vorlesung Analysis I/II die Grundlage für das weitere Studium der Mathematik(in den Studiengängen Bachelor Mathematik, Lehramt Mathematik vertieft). In der VorlesungLineare Algebra II werden die Grundbegriffe linearer Strukturen weiter ausgebaut. Insbesonderewerden die folgenden Themen behandelt: Normalformen für Endomorphismen und Modultheorie,euklidische und unitäre Vektorräume, multilineare Algebra.
The Seminar is concerned with the classification of certain singularities of differentiable functions of several variables. We will develop methods for the classification of these singularities and for the study of their genericity and stability properties. The topic of the Seminar forms a natural continuation of the lecture courses in Analysis. The Seminar talks will be held in German or English. The written reports can be submitted in German or English.
The seminar will focus on calculations of unstable and stable homotopy groups. For that purpose, we will introduce and study two important theoretical tools: first, the Serre spectral sequence and Serre class theory, and secondly, the Adams spectral sequence.
This seminar will introduce and study the homotopy theory of spectra and its relation to generalized(co)homology theories. Other topics to be discussed include: Spanier-Whitehead duality, calculationsusing spectral sequences, cohomology operations, and applications to the calculation of cobordismrings.