The HADES seminar on Tuesday, October 4th will be at 3:30 pm in Room 740.

Speaker: Olivine Silier

Abstract: A point-line incidence is a point-line pair such that the point is on the line. The Szemerédi–Trotter theorem says the number of point-line incidences for $n$ (distinct) points and lines in ${\mathbb{R}}^2$ is tightly upperbounded by $O(n^{4/3})$. We advance the inverse problem: we geometrically characterize `sharp’ examples which saturate the bound using the cell decomposition and crossing lemma proofs of Szemerédi–Trotter. This result is also an important step towards obtaining an $ϵ$ improvement in the unit-distance problem. (Ongoing work with Nets Katz)

No background required, all welcome!