Discrete Analysis Seminar

The celebrated Elekes-Szabo theorem asserts that an irreducible algebraic set V in C^3 admits no power-saving if and only if it is in coordinatewise correspondence with a product of connected subgroups of powers of 1-dimensional complex algebraic groups. The result was recently generalized to C^n by Bays and Breuillard. On the other hand, little is known when the ambient field has character p. In this talk, I will talk about an Elekes-Szabo-type result for collinearity on a cubic surface in F_p with a quantitative bound, based on joint work with Tingxiang Zou.