In-Person Talk 

The Szemerédi–Trotter theorem can be considered as the fundamental theorem of geometric incidences. This combinatorial theorem has an unusually wide variety of applications, and is used in combinatorics, theoretical computer science, harmonic analysis, number theory, model theory, and more. Surprisingly, hardly anything is known about the structural question - characterizing the cases where the theorem is tight. We present such structural results for the case of cartesian products. This is a basic survey talk and does not require previous knowledge of the field. Joint work with Olivine Silier. This is also a shameless advertisement of the speaker's new book "Polynomial Methods and Incidence Theory."