**Time and place:** Tuesday, 10:30-12:00 (with the exception of the first two sessions!), room: HG03.085 (Hilbert room)

In the first part of the seminar we want to study some classical aspects of stable homotopy theory. In the last part, we will scratch the surface of chromatic homotopy theory. A detailed program will appear soon.

**Prerequisites:** Some maturity in Algebraic Topology.

**References:** There are many references for such a seminar including the following ones (more will follow soon!).

Adams; Stable Homotopy and Generalized Homology

Atiyah; K-Theory

Husemoller; Fibre Bundles

Margolis; Spectra and the Steenrod Algebra

Mosher-Tangora; Cohomology Operations and Applications in Homotopy Theory

Ravenel; Complex Cobordism and Stable Homotopy Groups of Spheres

Rudyak; On Thom Spectra, Orientability, and Cobordism

Steenrod-Epstein; Cohomology Operations

**Tentative schedule for the first sessions:**

Talk 01, 02.10.13: An introduction to the Stable Homotopy Category (Javier Gutiérrez)

Talk 02, 07.10.13: Stable oo-categories and the oo-category of spectra (Yonatan Harpaz)

Talk 03, 15.10.13: Model categorical approaches to spectra (Ieke Moerdijk)

Talk 04, 22.10.13: The Steenrod algebra and its dual (Moritz Groth)

Talk 05, 29.10.13: The Steenrod algebra and its dual II (Moritz Groth)

Talk 06, 05.11.13: Topological K-theory and Bott periodicity (Giovanni Caviglia)

Talk 07, 12.11.13: Adams operations (Matan Prezma)

Talk 08, 19.11.13: The J-homomorphism (Urs Schreiber)

Talk 09, 26.11.13: Cobordism and the Pontrjagin-Thom construction (Joost Nuiten)

Talk 10, 03.12.13: The spectral sequence associated to a filtration of spectra I (Urs Scheiber)

Talk 11, 04.02.14: The spectral sequence associated to a filtration of spectra II (Urs Scheiber)

Talk 12, 11.02.14: The classical Adams spectral sequence (Dimitri Ara)

Talk 13, 18.02.14: Calculation of the complex cobordism ring

Adams; Stable Homotopy and Generalized Homology

Atiyah; K-Theory

Husemoller; Fibre Bundles

Margolis; Spectra and the Steenrod Algebra

Mosher-Tangora; Cohomology Operations and Applications in Homotopy Theory

Ravenel; Complex Cobordism and Stable Homotopy Groups of Spheres

Rudyak; On Thom Spectra, Orientability, and Cobordism

Steenrod-Epstein; Cohomology Operations