Geometric Combinatorics

Calendar

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