31 citations · 144 across the 14 of their papers we have counts for
16 papers
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…
On large externally definable sets in NIP
Martin Bays, Omer Ben-Neria, Itay Kaplan +1
We study cofinal systems of finite subsets of . We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a questi…
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…
Density of compressible types and some consequences
Martin Bays, Itay Kaplan, Pierre Simon
We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension…
Incidence bounds in positive characteristic via valuations and distality
Martin Bays, Jean-François Martin
We prove distality of quantifier-free relations on valued fields with finite residue field. By a result of Chernikov-Galvin-Starchenko, this yields Szemerédi-Trotter-like incidence…
Definability in the group of infinitesimals of a compact Lie group
Martin Bays, Ya'acov Peterzil
We show that for a simple compact Lie group, the infinitesimal subgroup is bi-intepretable with a real closed valued field. We deduce that for an infinite definabl…
Projective geometries arising from Elekes-Szabó problems
Martin Bays, Emmanuel Breuillard
We generalise the Elekes-Szabó theorem to arbitrary arity and dimension and characterise the complex algebraic varieties without power saving. The characterisation involves certain…
Pseudo-exponential maps, variants, and quasiminimality
Martin Bays, Jonathan Kirby
We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilber's pseudo-exponential function. In particular we construct pseudo-exponential m…
Model Theory of Compact Complex Manifolds with an Automorphism
Martin Bays, Martin Hils, Rahim Moosa
Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex man…
Universal covers of commutative finite Morley rank groups
Martin Bays, Bradd Hart, Anand Pillay
We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More gen…
Excellence and uncountable categoricity of Zilber's exponential fields
Martin Bays, Jonathan Kirby
We prove that Zilber's class of exponential fields is quasiminimal excellent and hence uncountably categorical, filling two gaps in Zilber's original proof.
A Note on Divisible Points of Curves
Martin Bays, Philipp Habegger
Let be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3. We partially answer a question posed by Levin on points…
Quasiminimal structures and excellence
Martin Bays, Bradd Hart, Tapani Hyttinen +2
We show that the excellence axiom in the definition of Zilber's quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies…
Some Definability Results in Abstract Kummer Theory
Martin Bays, Misha Gavrilovich, Martin Hils
Let be a semiabelian variety over an algebraically closed field, and let be an irreducible subvariety not contained in a coset of a proper algebraic subgroup of . We sho…
A Schanuel property for exponentially transcendental powers
Martin Bays, Jonathan Kirby, A. J. Wilkie
We prove the analogue of Schanuel's conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transc…
Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic
Martin Bays, Boris Zilber
We show that algebraic analogues of universal group covers, surjective group homomorphisms from a -vector space to with "standard kernel", are determined u…