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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 applicati…
math.CO2024
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.NT2024
Lang-Weil Type Estimates in Finite Difference Fields
Martin Hils, Ehud Hrushovski, Jinhe Ye +1
We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower…