Counting; Pigeon hole principle and resolution refutation lower bound; Matching and Hall's theorem.

Basic method; Lovaz local lemma and its constructive proof; Linearity of Expectation; The deletion method; The entropy function; Random walks and randomized algorithm for CNF formulas

Basic properties of graph spectrum; Cheeger's inequality and approximation of graph expansion; Expander graphs and applications to superconcentrators and pseudorandomness; Error correcting codes and expander codes; Small set expansion, Unique Games Conjecture and Hardness of approximation.

Sum product theorem, Szemeredi-Trotter theorem, Kakeya set problem and applications to randomness extractors.

Homework 1

Robin Moser and Gabor Tardos. A constructive proof of the general lovĂˇsz local lemma.

James R. Lee, Shayan Oveis Gharan and Luca Trevisan. Multi-way spectral partitioning and higher-order Cheeger inequalities.

Shayan Oveis Gharan and Luca Trevisan. Approximating the Expansion Profile and Almost Optimal Local Graph Clustering.

Adam Marcus, Daniel A. Spielman and Nikhil Srivastava. Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees.

Joshua Batson, Daniel A. Spielman and Nikhil Srivastava. Twice-Ramanujan Sparsifiers.

Klim Efremenko. 3-query locally decodable codes of subexponential length.

Zeev Dvir, Parikshit Gopalan and Sergey Yekhanin. Matching vector codes.

A. Bhowmick, Z. Dvir, and S. Lovett. New Bounds for Matching Vector Families.