notes
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Lecture notes for Math 549, Spring 2018, in reverse chronological order

April 19, 2018. Enriched category theory and spectra as enriched functors.

April 17, 2018. An introduction to model categories II. I referred to slides from my 2017 Chicago talk.

April 12, 2018. An introduction to model categories. A recommended reference is the paper of Dwyer and Spalinski.

April 3 and 5, 2018. Lectures by Dionel Jaime on Yoneda’s 1954 paper on Ext groups and by Keping Huang and Kenneth Plante on material in McCleary related to the EilenbergMoore spectral sequence.

March 29, 2018. An introduction to spectra.

March 27, 2018. Semin Yoo lectured on Milnor’s 1958 paper, The Steenrod algebra and its dual. Here are her slides.

March 8, 2018. Two lectures today on the EilenbergMoore spectral sequence.

March 6, 2018. Hspaces, Hopf algebras and the double loops of the 3sphere.

March 1, 2018. Extension problems in spectral sequences, and loop spaces of spheres.

February 27, 2018. Exact couples and spectral sequences. The mother of all diagrams.

February 22, 2018. We met twice today. Toward the Adams spectral sequence III, and the spectral sequence associated with a filtered chain complex.

February 20, 2018. Toward the Adams spectral sequence II.

February 8, 2018. Toward the Adams spectral sequence.

February 6, 2018. More about mod 2 EilenbergMac Lane spaces and some long exact sequence associated with the Serre spectral sequence.

February 1, 2018. Still more about Steenrod operations. Today Anirudh lectured on the proof fo the Borel Theorem. It can be found on pages 9192 of Mosher and Tangora.

January 30, 2018. Serre’s program for computing homotopy groups and more about Steenrod operations.

January 25, 2018. The Borel theorem and Steenrod operations.

January 23, 2018. Cup products in the Serre spectral sequence.

January 18, 2018. Introduction to the Serre spectral sequence.