| 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 |
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| 3 |
Motzkin-Rabin Theorem on Monochromatic Lines |
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| 4 |
Szemerédi-Trotter Theorem (Two Equivalent Formulations), Crossing Lemma |
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| 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 |
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| 7 |
Pach-Sharir Theorem on Incidences of Points and Combinatorial Curves |
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| 8 |
Various Crossing Numbers, Embedding Technique |
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| 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 |
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| 11 |
Cutting Circles into Pseudo-segments, Lenses, Transversal and Packing Numbers, d-intervals |
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| 12 |
Intersection Reverse Sequences |
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| 13 |
Arrangements, Levels, Lower Envelopes, Davenport-Schinzel Sequences |
Problem set 3 due
Problem set 4 out |
| 14 |
Davenport-Schinzel Sequences of Order 3 |
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| 15 |
Complexity of the First k-levels, Clarkson-Shor Technique, Cutting Lemma |
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| 16 |
Proof of Cutting Lemma, Simplicial Partitions |
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| 17 |
Spanning Trees with Low Stabbing Numbers |
Problem set 4 due
Problem set 5 out |
| 18 |
k-levels, k-sets, Halving Lines |
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| 19 |
VC-dimension and ε-nets |
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| 20 |
Optimal ε-approximations, Links to Discrepancy Theory |
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| 21 |
Binary Space Partitions |
Problem set 5 due
Problem set 6 out |
| 22 |
Geometric Graphs and Forbidden Subgraphs |
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| 23 |
Zig-zag and Alternating Paths for Disjoint Segments |
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| 24 |
Crossing-free Hamiltonian Cycles and Long Monochromatic Paths |
Problem set 6 due |
| 25 |
Pseudo-triangulations and Art Gallery Problems |
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