notes

Link to 2015 notes

Link to 2016 notes

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 Eilenberg-Moore 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 Eilenberg-Moore spectral sequence.

• March 6, 2018. H-spaces, Hopf algebras and the double loops of the 3-sphere.

• 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 Eilenberg-Mac 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 91-92 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.