4 papers
math.CO2025
An asymmetric version of Elekes-Szabó via group actions
Martin Bays, Tingxiang Zou
We consider when finite families of bounded degree polynomials, or more generally of bounded complexity finite-to-finite correspondences on …
math.CO2025
Non-expansion in polynomial automorphisms of
Martin Bays, Tingxiang Zou
We treat the higher-dimensional Elekes-Szabó problem in the case of the action of Aut(C^2) on C^2.
math.LO2025
Elekes-Szabó for collinearity on cubic surfaces
Martin Bays, Jan Dobrowolski, Tingxiang Zou
We study the orchard problem on cubic surfaces. We classify possibly reducible cubic surfaces $X\subseteq \mathbb{P}^3(\C)$ with smooth components on which there exist families of…
math.CO2024
A group-action Szemerédi-Trotter theorem and applications to orchard problems in all characteristics
Yifan Jing, Tingxiang Zou
We establish a group-action version of the Szemerédi-Trotter theorem over any field, extending Bourgain's result for the group . As an Elekes-Szabó-type applica…