3 citations · 6 across the 4 of their papers we have counts for
7 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…