# Agenda

Our agenda for the next few weeks looks something like this:

1. The discrete Cheeger inequality
2. The connection between ${\lambda_2}$ and the mixing time of random walks
3. Planar separators, eigenvalues, and circle packings
4. Expander graphs and rapid mixing
5. The small-set expansion problem and the Unique Games Conjecture
6. Higher-order Cheeger inequalities
7. Cheeger inequalities for very large eigenvalues (Arora-Barak-Steurer)
8. Mixing times and the spectral profile