Synopsis for Combinatorial Geometry

Happy Ending theorem, empty convex polygons. Caratheodory's theorem, Radon's lemma, Helly's theorem, Tverberg's theorem. Crossing number lemma, Szemeredi-Trotter theorem, sum-product estimates, unit distance problem, distinct distances problem. Frankl-Wilson theorem, disproof of Borsuk's conjecture. Borsuk-Ulam theorem, Ham-sandwich theorem, Necklace theorem, Kneser's conjecture. Davenport-Schinzel sequences. 

The area of combinatorial geometry is one of the most important and diverse branches of modern combinatorics. In this course, we will study a broad range of topics from this area, from early theorems up to modern developments. 

1. Jiri Matousek, Lectures on discrete geometry, Graduate Texts in Mathematics, 212, Springer-Verlag, New York, 2002. 2. Jiri Matousek, Using the Borsuk-Ulam theorem: lectures on topological methods in combinatorics and geometry, Universitext, Springer-Verlag, Berlin, 2003.