A SzemerediTrotter theorem in R^4
A SzemerediTrotter theorem in R^4

Josh Zahli , UCLA
Fine Hall 224
The SzemerediTrotter theorem states that m points and n lines in the plane can have at most O(m^{2/3}n^{2/3}+m+n) incidences. This theorem has seen a number of generalizations, including a theorem of Toth that obtains the same result for (complex) points and lines in the complex plane. In this talk I will discuss an almostsharp version of the SzemerediTrotter theorem for points and 2flats in R^4 that yields Toth's theorem as a corollary. This new result combines the discrete polynomial partitioning technique of Guth and Katz with some topological arguments involving the crossing number inequality.