## Recordings of Lectures

HZ=Harmony Zhan, discrete walks; GC=Gabriel Coutinho, continuous walks; CG=Chris Godsil

1. Jan 12 (GC)
2. Jan 14 (HZ)
3. Jan 19 (GC)
4. Jan 21 (HZ)
5. Jan 26 (GC)
6. Jan 28 (HZ)
7. Feb 2 (GC)
8. Feb 4 (HZ)
10. Feb 11 (HZ)
11. Feb 16 (GC)
12. Feb 18 (HZ)
13. Feb 23 Alastair Kay, slides only
14. Feb 25:video and notes (Tom Wong)
15. March 2 (GC)
16. March 4 (Renato Portugal)
17. March 9 (HZ)
18. March 11 (Sougato Bose)
19. March 16 (GC)
20. March 18 (HZ)
21. March 23 (HZ)
22. March 25 (Krystal Guo)
23. March 30 (GC)
24. April 1 and notes (CG)

## Exercises and Problems

Exercises: Continuous

Exercises: Discrete

## Resources: pdfs

1. Many of the lectures will based on the following drafts of books:
2. Nathan Lindzey has set up a zulip channel for the course; for discussing the exercises for example. He says "This is the only chat software that I'm aware of that renders TeX. Students and participants might find it handy for discussing problem sets or research remotely amongst themselves." (And if you've read this, you now know as much about zulip as I do.)
3. Visualizations of some continuous walks. (Prepared by Nathan Benedetto ProenÃ§a.)
4. Some material on linear algebra.

## Resources: code

1. sage minicourse: given by Krystal Guo.
2. sage practice: examples of using sage to work with graphs.

## Content and Outline

Some of the topics covered:

1. motivation
2. Physics
3. arc-reversal walks
4. representation theory for two reflections
5. Grover
6. face-vertex walks
7. bipartite walks and Hamiltonians
8. graph isomorphism failures
9. real states (periodicity, state transfer, ratio condition)
10. pst on Laplacians of trees
11. strongly cospectral vertices and symmetries
12. uniform mixing
13. orthogonal polynomials
14. pretty good state transfer
15. fractional revival
16. average mixing, average states