This is a topics course on topological modular forms and related areas of math. We will use the historical development of topological modular forms to guide us through various important concepts in modern algebra, geometry, and topology.

The course syllabus can be found here.

My daily lecture notes are available in the table below. These are full of my accidental mistakes, intentional omissions, and other compromises made to strike a narrative balance for the diverse backgrounds of the 50 registered students. If you happen to catch any mistakes, whether small typos or glaring errors, I'm always grateful for corrections.

Dates Topic Resources
September 5th Introduction and Kepler's laws Notes
September 7th Kepler's laws and elliptic functions Notes
September 12th Elliptic functions and cobordism Notes
September 14th Signature, Thom spaces, and Thom spectra Notes
September 19th Pontryagin--Thom construction Notes
September 21st Pontryagin--Thom (continued) Notes
September 26th Hirzebruch signature theorem and the Weierstrass p-function Notes
September 28th The Weierstrass p-function and friends Notes
October 3rd Modular forms Notes
October 5th Basic algebraic geometry Notes
October 10th Elliptic curves and period integrals Notes
October 12th Period integrals and the moduli space of complex elliptic curves Notes
October 17th Moduli stack of elliptic curves Notes
October 19th Categories fibered in groupoids Notes
October 24th Descent and ring spectra Notes
October 26th Ring spectra, even periodic cohomology, and complex orientations Notes
October 31st Formal group laws and elliptic genera Notes
November 2nd Elliptic cohomology Notes
November 7th The Witten genus Notes
November 9th E-infty ring spectra Notes
November 14th Constructing TMF Notes
November 16th Constructing Tmf Notes
November 21st Homotopy of TMF, Tmf, and tmf Notes
November 23rd Thanksgiving break
November 28th String orientation (part 1) Notes
November 30th String orientation (part 2) Notes
December 5th String orientation (part 3) Notes