19 citations · 53 across the 15 of their papers we have counts for
22 papers
Sum-product Phenomenon Via Dimension
Yuyan He, Sergei Starchenko
We show a sum-product phenomenon in fields equipped with abstract dimension theories, which simultaneously generalizes the dimensions in geometric theories and Hrushovski's coarse…
Combinatorics in one-based and related structures
Artem Chernikov, Sergei Starchenko
We consider some extremal combinatorial questions for bipartite graphs definable in stable one-based (and related) structures. We show that they satisfy both strong Erdős-Hajnal pr…
Limits of definable families and dilations in nilmanifolds
Ya'acov Peterzil, Sergei Starchenko
Let be a unipotent group and a family of subsets of , with definable in an o-minimal expansion of the real field. Given a l…
Model-theoretic Elekes-Szabó for stable and o-minimal hypergraphs
Artem Chernikov, Ya'acov Peterzil, Sergei Starchenko
A theorem of Elekes and Szabó recognizes algebraic groups among certain complex algebraic varieties with maximal size intersections with finite grids. We establish a generalization…
Zarankiewicz's problem for semilinear hypergraphs
Abdul Basit, Artem Chernikov, Sergei Starchenko +2
A bipartite graph with is semilinear if for some and the edge relation consists of th…
Peterzil-Steinhorn subgroups and -stabilizers in ACF
Moshe Kamensky, Sergei Starchenko, Jinhe Ye
We consider , a linear group defined over , an algebraically closed field. By considering as an embedded residue field of an algebraically closed valued field , we can…
O-minimal flows on nilmanifolds
Ya'acov Peterzil, Sergei Starchenko
Let be a connected, simply connected nilpotent Lie group, identified with a real algebraic subgroup of , and let be a lattice in , with $π:G\t…
Model-theoretic Elekes-Szabó in the strongly minimal case
Artem Chernikov, Sergei Starchenko
We prove a generalizations of the Elekes-Szabó theorem for relations definable in strongly minimal structures that are interpretable in distal structures.
Algebraic and o-minimal flows on complex and real tori
Ya'acov Peterzil, Sergei Starchenko
We consider the covering map of a compact complex torus. Given an algebraic variety we describe the topological closure of…
Cutting lemma and Zarankiewicz's problem in distal structures
Artem Chernikov, David Galvin, Sergei Starchenko
We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the p…
A note on o-minimal flows and the Ax--Lindemann--Weierstrass theorem for abelian varieties over
Ya'acov Peterzil, Sergei Starchenko
In this short note we present an elementary proof of the Ax-Lindemann-Weierstrass theorem for abelian and semi-abelian varieties. The proof uses ideas of Pila, Ullmo, Yafaev, Zanni…
Ramsey growth in some NIP structures
Artem Chernikov, Sergei Starchenko, Margaret E. M. Thomas
We investigate bounds in Ramsey's theorem for relations definable in NIP structures. Applying model-theoretic methods to finitary combinatorics, we generalize a theorem of Bukh and…
Definable regularity lemmas for NIP hypergraphs
Artem Chernikov, Sergei Starchenko
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hy…
Regularity lemma for distal structures
Artem Chernikov, Sergei Starchenko
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be…
Solvable Lie groups definable in o-minimal theories
Annalisa Conversano, Alf Onshuus, Sergei Starchenko
In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.
A note on the Erdős-Hajnal property for stable graphs
Artem Chernikov, Sergei Starchenko
In this short note we provide a relatively simple proof of the Erdős-Hajnal conjecture for families of finite (hyper-)graphs without the -order property. It was originally prove…
Topological groups, μ-types and their stabilizers
Ya'Acov Peterzil, Sergei Starchenko
We consider an arbitrary topological group definable in a structure , such that some basis for the topology of consists of sets definable in . To ea…
On forking and definability of types in some dp-minimal theories
Pierre Simon, Sergei Starchenko
We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.
Remarks on Tao's algebraic regularity lemma
Anand Pillay, Sergei Starchenko
We give a stability theoretic proof of the algebraic regularity lemma of Tao, making use of a lemma of Hrushovski. We also point out that the underlying results hold at the level o…
Vapnik-Chervonenkis density in some theories without the independence property, II
M. Aschenbrenner, A. Dolich, D. Haskell +2
We study the Vapnik-Chervonenkis (VC) density of definable families in certain stable first-order theories. In particular we obtain uniform bounds on VC density of definable famili…
Definability of restricted theta functions and families of abelian varieties
Ya'acov Peterzil, Sergei Starchenko
We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure $\Rae$.…
Some (non-)elimination results for curves in geometric structures
Serge Randriambololona, Sergei Starchenko
We show that the first order structure whose underlying universe is and whose basic relations are all algebraic subset of does not have quantifier elimina…