| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Sylvester-Gallai Theorem, Scott's Problem about the Number of Distinct Slopes in the Plane | Problem set 1 out |
| 2 | Scott's Problem about the Number of Distinct Directions in Three-space | |
| 3 | Motzkin-Rabin Theorem on Monochromatic Lines | |
| 4 | Szemerédi-Trotter Theorem (Two Equivalent Formulations), Crossing Lemma | |
| 5 | Unit Distances, Unit Area Triangles, Beck's Two Extremities Theorem, Weak Dirac Conjecture | Problem set 1 due Problem set 2 out |
| 6 | Crossing Lemma for Multigraphs, Minimum Number of Distinct Distances | |
| 7 | Pach-Sharir Theorem on Incidences of Points and Combinatorial Curves | |
| 8 | Various Crossing Numbers, Embedding Technique | |
| 9 | More on Crossing Numbers Sum vs. Product Sets |
Problem set 2 due Problem set 3 out |
| 10 | Lipton-Tarjan and Gazit-Miller Separator Theorems | |
| 11 | Cutting Circles into Pseudo-segments, Lenses, Transversal and Packing Numbers, d-intervals | |
| 12 | Intersection Reverse Sequences | |
| 13 | Arrangements, Levels, Lower Envelopes, Davenport-Schinzel Sequences | Problem set 3 due Problem set 4 out |
| 14 | Davenport-Schinzel Sequences of Order 3 | |
| 15 | Complexity of the First k-levels, Clarkson-Shor Technique, Cutting Lemma | |
| 16 | Proof of Cutting Lemma, Simplicial Partitions | |
| 17 | Spanning Trees with Low Stabbing Numbers | Problem set 4 due Problem set 5 out |
| 18 | k-levels, k-sets, Halving Lines | |
| 19 | VC-dimension and ε-nets | |
| 20 | Optimal ε-approximations, Links to Discrepancy Theory | |
| 21 | Binary Space Partitions | Problem set 5 due Problem set 6 out |
| 22 | Geometric Graphs and Forbidden Subgraphs | |
| 23 | Zig-zag and Alternating Paths for Disjoint Segments | |
| 24 | Crossing-free Hamiltonian Cycles and Long Monochromatic Paths | Problem set 6 due |
| 25 | Pseudo-triangulations and Art Gallery Problems |