31 citations · 144 across the 14 of their papers we have counts for
12 papers · 1 filter
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…
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…
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.
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…
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…