Topics in Geometry: Discrete Geometry: Incidence Theorems and their Applications

The course focuses on algebraic methods in geometric incidence problems. Most topics fall under one of these three themes: (1) Kakeya type problems: packing lines in different directions (2) Szemeredi-Trotter type problems: Counting incidences between lines/points/curves etc. (3) Sylvester-Gallai type problems: finding structure in point sets with many local dependencies (e.g., many collinear triples). Applications in theoretical computer science are also discussed.