Algebra/Topology pre-talk

A student's guide to A^1-algebraic topology

As a student of algebraic topology, I was once intimidated by this thing that plenty of fancy people call "motives." In this pre-talk, I hope to explain how I got over this fear by thinking of the subject (as Morel did) as "A^1-algebraic topology." To do this, I offer the audience a rather esoteric selection of ideas/concepts/calculations which I can explain:

1. Long exact sequences in homotopy groups and detection principles. 

2. How to calculate A^1-homotopy groups of homogeneous spaces and classifying spaces.

3. What A^1-connected components mean and calculations.

4. Postnikov Towers.

5. The place of algebraic K-theory in the theory.

...and more!