241216 Seminar Geometrie und Topologie (S) (SoSe 2022)

Contents, comment

Es soll der Index-Satz von Atiyah-Singer besprochen werden. Konkret umfasst dies folgende Themen:
- Analytischer und topologischer Index
- Überblick einiger Resultate der topologischen K-Theorie
- Differentialoperatoren auf Vektorbündeln
- Analytische Indizes einiger konkreter Operatoren
- Überblick einiger Resultate der Funktionalanalysis
- Sobolev-Theorie, Pseudo-Differentialoperatoren
- Kobordismeninvarianz des analytischen Indexes
- Anwendungen

Requirements for participation, required level

Das Seminar wendet sich an Masterstudierende, die ihre Kenntnisse in der globalen Analysis vertiefen wollen. Dies Seminar und ein parallel von Herrn Behrens geleitetes Seminar über topologische K-Theorie ergänzen sich gegenseitig.

Bibliography

R. Palais et al.: Seminar on the Atiyah-Singer Index Theorem
B. Lawson, M.-L. Michelsohn: Spin Geometry

Teaching staff

Dates ( Calendar view )

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Subject assignments

Module Course Requirements  
24-M-MM Master Module Mastermodul Masterseminar Study requirement
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24-M-P1a Profile Module 1, Part A Profilierung 1 Teil A Profilierungsseminar Study requirement
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24-M-P1b Profile Module 1, Part B Profilierung 1 Teil B Profilierungsseminar Study requirement
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24-M-S2-AL Spezialisation Courses in Algebra Spezialisierung 2 - Algebra Masterkurs 1 Algebra - Variante 3 Teil 2 Study requirement
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Masterkurs 2 Algebra - Variante 3 Teil 2 Study requirement
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24-M-S2-AN Spezialisation Courses in Analysis Spezialisierung 2 - Analysis Masterkurs 1 Analysis - Variante 3 Teil 2 Study requirement
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Masterkurs 2 Analysis - Variante 3 Teil 2 Study requirement
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24-M-V2-AL Advanced Algebra Vertiefung 2 - Algebra Masterkurs 1 Algebra - Variante 3 Teil 2 Study requirement
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24-M-V2-AN Advanced Analysis Vertiefung 2 - Analysis Masterkurs 1 Analysis - Variante 3 Teil 2 Study requirement
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The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.

Das Seminar ist konzipiert als interaktiver Lesekurs mit Kurzvorträgen. Von Teilnehmenden wird erwartet, sich in konkrete Themenbereiche einzulesen, gelegentlich Kurzvorträge zu halten und sich aktiv an Diskussionen zu beteiligen.

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Last update basic details/teaching staff:
Wednesday, January 12, 2022 
Last update times:
Monday, April 11, 2022 
Last update rooms:
Monday, April 11, 2022 
Type(s) / SWS (hours per week per semester)
seminar (S) / 2
Department
Faculty of Mathematics
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