MATH Seminar

Title: Rigidity of Extremal Point-Line Arrangements
Seminar: Combinatorics
Speaker: Hung-Hsun Hans Yu of Princeton University
Contact: Dr. Cosmin Pohoata, cosmin.pohoata@emory.edu
Date: 2024-10-25 at 10:00AM
Venue: MSC N306
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Abstract: It is a classical theorem by Szemerédi and Trotter that n points and m lines in the Euclidean plane form at most C(mn)^{2/3} + m + n incidences, and the bound is optimal up to the constant C. However, there is still no satisfactory description of configurations maximizing the number of incidences. As a small step toward such description, in this talk, I will show how to prove that the extremizers are rigid in some sense. This is based on joint work with Gabriel Currier and Jozsef Solymosi.