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 |
Calendar
Course Info
Topics
Learning Resource Types
assignment
Problem Sets