UBC Discrete Math Seminar: Olivine Silier

  • Date: 03/28/2023
  • Time: 16:00
Olivine Silier, UC Berkeley

University of British Columbia


A Proto Inverse Szemerédi-Trotter Theorem


A point-line incidence is a point-line pair such that the point is on the line. The Szemer\'edi-Trotter theorem says the number of point-line incidences for n (distinct) points and lines in R^2 is tightly upperbounded by O(n^{4/3}). We advance the inverse problem: we geometrically characterize `sharp' examples which saturate the bound by proving the existence of a nice cell decomposition we call the \textit{two bush cell decomposition}. The proof crucially relies on the crossing number inequality from graph theory and has a traditional analysis flavor.


Our two bush cell decomposition also holds in the analogous point-unit circle incidence problem. This constitutes an important step towards obtaining an ϵ improvement in the unit-distance problem. (Ongoing work with Nets Katz)


No background required, all welcome!

Other Information: 

Location: ESB 4127

Time: 4pm Pacific