Forschungsseminar Geometrie und Topologie
Winter Term 2019/20
Prof. Dr. Holger Reich - Prof. Dr. Elmar Vogt - Dr. Gabriel Angelini-Knoll
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Time and place: Tuesday, 16 - 18h, Arnimallee 7, SR 140
Content: Talks by masters and Phd students about ongoing work and selected research topics as well as guest talks.
This winter term our selected research topic will cover the field of chromatic homotopy theory.
The field of chromatic homotopy theory produces a filtration of stable homotopy groups by invoking the deep connection between formal groups and complex cobordism. This perspective provides a better understanding of global phenomena in the stable homotopy category as well as concrete tools for computing stable homotopy groups. This seminar will cover topics such as the theory of complex oriented cohomology theories, formal groups and their deformation theory, moduli stacks, Bousfield localization, generalized Adams spectral sequences, and the chromatic spectral sequence.
Schedule
| Date | Ttitle | Speaker |
| 15.10. | 1) Formal Group laws and Lazard's theorem (Lect.1-3) | Gabriel Angelini-Knoll |
| 22.10. | 2) Complex oriented cohomology theories I (Lect.4-5) | Alexander Müller |
| 29.10. | 3) Complex oriented cohomology theories II (Lect.6-7) | Georg Lehner |
| 05.11. | 4) The E-Adams spectral sequence (Lect.8-9) |
Elmar Vogt |
| 12.11. | 5) Quillen's Theorem (Lect.10) | Gabriel Angelini-Knoll |
| 19.11. | 6) Formal groups and their classification I (Lect.11-12) | Vincent Boelens |
| 26.11. | 7) Formal groups and their classification II (Lect.13-14) | Vincent Boelens |
| 27.11. | guest talk at 11:30am in room 210, A7 | |
| The K-Theory of discrete quantum group algebras | Roland Vergnioux | |
| 03.12. | 8) Landweber exact functor theorem using stack language (Lect.15,16,18) (Skip Lect. 17 on phantom maps for now.) |
Alexander Müller |
| 10.12. | 9) Morava stabilizer groups (Lect.19) | Georg Lehner |
| 17.12. | 10) Lubin-Tate theory (Lect.21) | Gabriel Angelini-Knoll |
| 2020 | ||
| 07.01. | 11) Morava E-theory and Morava K-theory (Lect.22) | Gabriel Angelini-Knoll |
| 14.01. | 12) Bousfield Localization and the Bousfield Classes of E(n) and K(n) (Lect.20,23) | Georg Lehner |
| 16.01. | guest talk at 2am | |
| Splittings and computations of (higher) THH | Eva Höning | |
| 21.01. | 13) Uniqueness of Morava K-theory and Bousfield classes (Lect.23,24) | Gabriel Angelini-Knoll |
| 28.01. | 14) Nilpotence Theorem and Thick Subcategory Theorem (Lect.25-26) | Alexander Müller |
| 04.02. | 15) Periodicity theorem (Lect.27) | Georg Lehner |
| 11.02. | 16) Chromatic convergence (Lect.32, 33) | Vincent Boelens |