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                * Princeton Discrete Math Seminar *
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Date: Thursday 29th November, 2.00 in Fine Hall 224
 
Speaker: Josh Zahl (UCLA)

Title: A Szemeredi-Trotter theorem in R^4

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.

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Next week: TBA

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