Arithmetic Geometry, Homotopy, And String Theory

Fall 2017: Elliptic Cohomology

This semester we are studying elliptic curves and elliptic cohomology.

We meet Fridays from 1—2 PM in RLM 11.176.

Schedule

Date	Topic	Speaker
Sep 18	Elliptic curves	Jonathan Lai
Sep 29	Modular forms	Rok Gregoric
Oct 6	Level structures	Yuri Sulyma
Oct 13	Formal groups I	Adrian Clough
Oct 20	Formal groups II	Richard Wong
Oc 27	Schemes and stacks	Yuri Sulyma

References

Elliptic curves and modular forms

Milne, Elliptic Curves
Silverman, The Arithmetic of Elliptic Curves
WCATSS 2016 notes. Lectures 5, 10, 17.

Formal groups

Strickland, Functorial philosophy for formal phenomena
Strickland, Formal schemes and formal groups
Ando, Notes on formal groups. Secret notes, privately distributed.
Lurie's notes on chromatic homotopy theory. Mainly lectures 11–14 and 21
WCATSS 2016 notes. Lectures 2, 7, maybe 20, 21.
Hazewinkel, Formal groups and applications

Stacks

Complex oriented cohomology theories and the language of stacks
WCATSS 2016 notes. Lectures 15 and 17.

Topological modular forms

Massive list of resources
TMF book. Chapters 1–4 are great and (relatively) elementary. It gets harder after that.
Supplementary notes for Math 512. These are great, and more elementary/hands-on than the TMF book.