A Szemeredi-Trotter theorem in R^4

A Szemeredi-Trotter theorem in R^4

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Josh Zahli , UCLA
Fine Hall 224

The Szemeredi-Trotter 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 almost-sharp version of the Szemeredi-Trotter theorem for points and 2--flats 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.