Sullivan introduced the idea of localizing and completing spaces at primes, which led to important advances in topology and homotopy theory. For example, it allowed natural actions of the Galois groups on objects associated to manifolds to be studied in relation with periodicity theorems. One concrete result of this theory is the proof of the Adams conjecture using etale homotopy. We will follow Sullivan's notes [S2] in this seminar. Aside from some algebraic topology which we will spend some time reviewing, these notes build this theory essentially from scratch.

- Organizer: Caleb Ji
- When: Monday 5:00 pm - 6:00 pm
- Where: Math 622
- References:

**[S1]**Dennis Sullivan, Genetics of Homotopy Theory and the Adams Conjecture

**[S2]**Dennis Sullivan, Geometric Topology: Localization, Periodicity, and Galois Symmetry

- Additional notes from the seminar will be compiled here.

- Jan 30
- Caleb Ji
**Organizational meeting, Algebraic constructions**

We will explain the plan for this seminar and begin Chapter 1 of [S1]. We will spend some extra time reviewing sme topological background, including equivariant cohomology and K-theory.