Lecture notes
Notes will usually be posted the day before lecture.
Lecture 1 (May 7): introduction [pdf] [one]

Lecture 2 (May 9): graph spectrum [pdf] [one]

Lecture 3 (May 14): Cheeger's inequality [pdf] [one]

Lecture 4 (May 16): higher order Cheeger's inequality [pdf] [one]

Lecture 5 (May 21)

Lecture 6 (May 23): improved Cheeger's inequality [pdf] [one]

Lecture 7 (May 28): random walks [pdf] [one]

Lecture 8 (May 30): local graph partitioning [pdf] [one]

Lecture 9 (June 4): expander graphs [pdf] [one]

Lecture 10 (June 6):

Lecture 11 (June 11): high dimensional expanders [pdf] [one]

Lecture 12 (June 13):

Lecture 13 (June 18): higher order random walks [pdf] [one] (expanded on Aug 11)

Lecture 14 (June 20): spectral sparsification [pdf] [one]

Lecture 15 (June 25)

Lecture 16 (June 27)

Lecture 17 (July 4): linearsized spectral sparsification [pdf] [one]

Lecture 18 (July 9): interlacing polynomials [pdf] [one] (expanded on July 10)

Lecture 19 (July 11)

Lecture 20 (July 16): bipartite Ramanujan graphs [pdf] [one]

Lecture 21 (July 18): Weaver's conjecture [pdf] [one]

Lecture 22 (July 23): strongly Rayleigh measure [pdf] [one]

Lecture 23 (July 30)

Lecture 24 (Aug 1)
