401-4580-66L Characteristic Classes and Elliptic Genus
Semester | Herbstsemester 2016 |
Dozierende | Q. Chen, G. Felder |
Periodizität | einmalige Veranstaltung |
Lehrsprache | Englisch |
Kommentar | Maximale Teilnehmerzahl: 12 |
Kurzbeschreibung | Characteristic classes, spin structures and Dirac opertor, applications of the Atiyah-Signer index theorem, elliptic genus and modular forms. |
Lernziel | Characteristic classes, spin structures and Dirac opertor, applications of the Atiyah-Signer index theorem, elliptic genus and modular forms. |
Inhalt | Tentative Syllabus 1. Vector bundles and differential forms (1 lectures) 2. Basics for Chacteristic classes such as Stiefel-Whitney classes, Wu Classes, Chern Classes and Pontryagin classes (3 lectures) 3. Spin structures and Dirac operators (2 lectures) 4. Atiyah-Singer Index theorem and its application (1-2 lectures) 5. Multiplicative sequences and various genera (1 lecture) 6. Elliptic genus and modular forms (1 lecture) 7. Miraculous cancellation formulas for Hirzebruch L genus (1 lecture) 8. Miscellaneous topics (1 lecture) |
Literatur | 1. Characteristic Classes by Milnor 2. Differential Forms in Algebraic Topology by Bott & Tu 3. Manifolds and Modular Forms by Hirzebruch, Berger and Jung |
Voraussetzungen / Besonderes | Prerequisite: Algebraic Topology. |