Seminar on Characteristic Classes
Prof. Dr. Anna Wienhard, Dr. Laura Schaposnik and Dr. Gye-Seon Lee
Time and Location
Thursdays 2 - 4 p.m. and INF 288, HS 1
Characteristic classes are invariants of fibre bundles or principal bundles on manifolds. They are important for the classification of manifolds. They also play an important role in differential geometry, gauge theory and related topics in physics. In this seminar we will introduce Stiefel-Whitney classes, the Euler class, Chern classes and Pontrjagin classes and study some of their properties. We will then discuss Chern-Weil theory, which describes how characteristic classes can be calculated using the curvature of the principal bundle. In the end we discuss an example of characteristic classes of flat bundles, due to Milnor, which shows us the limitations of Chern-Weil theory.
Students should ideally have some background in algebraic topology and differential geometry. Interested students from physics are also welcome to attend. The seminar will be taught in english.
Students who would like to sign up for the seminar should send an email to Laura Schaposnik (firstname.lastname@example.org) and let her know what talk they would like to give. If you are interested in one of the first talks, please be sure to contact her before the start of the semester. Once you have agreed on the date of your talk with Laura, you should contact the person who appears as advisor for your talk, Laura or Gye-Seon (email@example.com), to discuss the content of your talk in more detail. You should start preparing for your talk several weeks before you are scheduled to give speak. Please let Laura and Gye-Seon help you during the preparation.
|May 2||Sven||Vector bundles||Laura|
|May 9||Chr. Himmelf.|
|May 22||Laura||Homology and Cohomology||-|
|May 29||Axel||Axioms of Stiefel-Whitney and Chern classes||Laura|
|June 6||Gye-Seon||Constructions of Stiefel-Whitney and Chern classes||-|
|June 13||Tim||Pontrajagin classes and Pontrjagin numbers||Gye-Seon|
|June 20||Stephan||Chern-Weil theory I||Gye-Seon|
|July 11||Felipe||Chern-Weil theory II||Gye-Seon|
|July 18||Malte||Characteristic classes of flat bundles||Laura|