Seminar

Dvir's algebraic solution of the Kakeya problem in finite fields in 2008 triggered dramatic progress in incidence geometry. Extensive work since then has revealed that algebraic varieties play a crucial role in incidence geometric problems: in principle, point-line incidences are truly many when the lines cluster on low-degree varieties. Guth has recently exploited such ideas to improve on the restriction problem, a harmonic analytic problem with point-tube incidence flavour. In this talk, we will present the basic algebraic techniques used in such settings, and discuss their potential to yield results in other harmonic analytic problems.