2 citations · 6 across the 12 of their papers we have counts for
13 papers
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.
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…
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 …
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…
The model theory of geometric random graphs
Omer Ben-Neria, Itay Kaplan, Tingxiang Zou
We study the logical properties of infinite geometric random graphs, introduced by Bonato and Janssen. These are graphs whose vertex set is a dense ``generic'' subset of a metric s…
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…
Elekes-Szabó for groups, and approximate subgroups in weak general position
Martin Bays, Jan Dobrowolski, Tingxiang Zou
We show that with a suitable weak notion of general position, the Elekes-Szabó condition on the group operation of a connected complex algebraic group characterises nilpotence of t…
Dimension and measure in pseudofinite H-structures
Alexander Berentein, Dario Garcia, Tingxiang Zou
We study H-structures associated to SU-rank 1 measurable structures. We prove that the SU-rank of the expansion is continuous and that it is uniformly definable in terms of the par…
Pseudofinite primitive permutation groups acting on one-dimensional sets
Tingxiang Zou
Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which sat…
Schlichting's Theorem for Approximate Subgroups
Tingxiang Zou
We prove Schlichting's theorem for approximate subgroups: if is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an in…
Pseudofinite difference fields and counting dimensions
Tingxiang Zou
We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinit…
Pseudofinite H-structures and groups definable in supersimple H-structures
Tingxiang Zou
In this paper we explore some properties of H-structures. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudo-finiteness.…
Classical and Relative Realizability
Jaap van Oosten, Tingxiang Zou
We show that every abstract Krivine structure in the sense of Streicher can be obtained, up to equivalence of the resulting tripos, from a filtered opca (A,A') and a subobject of 1…