| 1 | Introduction to communication complexity, protocol partition and tiling, clique vs independent set. | KN97 (§ 1.1, 1.2, 2.2, 2.3), Juk12 (§ 3.2, 4.4) |
| 2 | Fooling set and rectangle size bound, rank bound, comparison of two techniques, non-determinism. | KN97 (§ 1.3, 1.4, 2.1, 2.5), DHS96 |
| 3 | More on non-determinism, $P = NP \cap coNP$, Separation of $P$ and $NP \cap coNP$, $UP$, Decision tree and composed functions. | KN97 (§ 2.3 - 2.5), Juk11 (§ 13.4), GPW15 |
| 4 | Simulation theorem (I): Hitting distribution for $GH$, The simulation algorithm. | GPW15, CKLM17 |
| 5 | Simulation theorem (II): Thickness and its properties, The simulation algorithm. | GPW15, CKLM17 |
| 6 | Randomization: Zero-error, one-sided error, $EQ$ function and separations, Private coin vs public coin. | KN97 (§ 3.1 - 3.3) |
| 7 | Protocol for $GT, DISJ_{nk}$, Distributional complexity, Yao’s minimax principle. | KN97 (§ 3.4), HW07 |
| 8 | Discrepancy: lower bound for $IP_n, GT_n$; Disjointness under product distribution. | KN97 (§ 3.5), CP10, BW16 |
| 9 | Disjointness under product distribution: Lower bound and upper bound. | CP10, BFS86 |
| 10 | Corruption bound, Razborov’s hard distribution for $DISJ_n$, Index function. | KN97 (§ 4.6), CP10, GW16 |
| 11 | Information theory primer, Index function lower bound, Information complexity. | RY18 (§ 6.1 - 6.4), BJKS04, JKS03 |
| 12 | Direct sum of information complexity, Lower bound for $DISJ_n$. | RY18 (§ 6.1 - 6.4), BJKS04, JKS03, Bra17, BR11 |
| 13 | Asymmetric communication complexity, Richness method, Index function and lopsided $DISJ$, Application in data-structure. | KN97 (§ 4.3), MNWS98 |
| 14 | Lecture by Jakob Nordström (I). Proof systems, Proof complexity and communication complexity, (Critical) block sensitivity. | HN12, Notes |
| 15 | Lecture by Jakob Nordström (II). Communication complexity of lifted search problem. | HN12, Notes |