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Forschungsseminar Geometrie und Topologie

Winter Term 2019/20

Prof. Dr. Holger Reich - Prof. Dr. Elmar Vogt - Dr. Gabriel Angelini-Knoll

  • 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.  


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
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
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