Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Martin Bays is active.

Publication


Featured researches published by Martin Bays.


Bulletin of The London Mathematical Society | 2014

Quasiminimal structures and excellence

Martin Bays; Bradd Hart; Tapani Hyttinen; Meeri Kesälä; Jonathan Kirby

We show that the excellence axiom in the definition of Zilbers quasiminimal excellent classes is redundant, in that it follows from the other axioms. This substantially simplifies a number of categoricity proofs.


Bulletin of The London Mathematical Society | 2011

Covers of multiplicative groups of algebraically closed fields of arbitrary characteristic

Martin Bays; Boris Zilber

An automatic degaussing circuit for a color picture tube (CPT) capable of automatically degaussing the CPT when a power conservation mode is released in a monitor having a power conservation function. The degaussing circuit includes a degaussing coil for eliminating electromagnetic waves produced from the CPT, a power conservation mode detecting section for detecting the release of the power conservation mode in accordance with a power conservation mode signal of the CPT inputted thereto and providing a degaussing control signal for controlling the operation of the degaussing coil if the release of the power conservation mode is detected, and a degaussing coil driving section for driving the degaussing coil for a predetermined time in accordance with the degaussing control signal when the power conservation mode is released.


Bulletin of The London Mathematical Society | 2010

A Schanuel property for exponentially transcendental powers

Martin Bays; Jonathan Kirby; A. J. Wilkie

We prove the analogue of Schanuels conjecture for raising to the power of an exponentially transcendental real number. All but countably many real numbers are exponentially transcendental. We also give a more general result for several powers in a context which encompasses the complex case.


Algebra & Number Theory | 2018

Pseudo-exponential maps, variants, and quasiminimality

Martin Bays; Jonathan Kirby

We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilbers pseudo-exponential function. In particular we construct pseudo-exponential maps of simple abelian varieties, including pseudo-


Transactions of the American Mathematical Society | 2014

A note on divisible points of curves

Martin Bays; Philipp Habegger

\wp


Transactions of the American Mathematical Society | 2017

Model theory of compact complex manifolds with an automorphism

Martin Bays; Martin Hils; Rahim Moosa

-functions for elliptic curves. We show that the complex field with the corresponding analytic function is isomorphic to the pseudo-analytic version if and only the appropriate version of Schanuels conjecture is true and the corresponding version of the strong exponential-algebraic closedness property holds. Moreover, we relativize the construction to build a model over a fairly arbitrary countable subfield and deduce that the complex exponential field is quasiminimal if it is exponentially-algebraically closed. This property asks only that the graph of exponentiation have non-trivial intersection with certain algebraic varieties but does not require genericity of these points. Furthermore Schanuels conjecture is not required as a condition for quasiminimality.


International Mathematics Research Notices | 2014

Some Definability Results in Abstract Kummer Theory

Martin Bays; Misha Gavrilovich; Martin Hils

Let C 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 on C for which a non-trivial power lies again on C . Our results have connections to Zilbers Conjecture on Intersections with Tori and yield to methods arising in transcendence theory and the theory of o-minimal structures.


arXiv: Logic | 2013

Excellence and uncountable categoricity of Zilber's exponential fields

Martin Bays; Jonathan Kirby

Motivated by possible applications to meromorphic dynamics, and generalising known properties of difference-closed fields, this paper studies the theory CCMA of compact complex manifolds with a generic automorphism. It is shown that while CCMA does admit geometric elimination of imaginaries, it cannot eliminate imaginaries outright: a counterexample to 3-uniqueness in CCM is exhibited. Finite-dimensional types are investigated and it is shown, following the approach of Pillay and Ziegler, that the canonical base property holds in CCMA. As a consequence the Zilber dichotomy is deduced: finite-dimensional types of SU-rank one are either one-based or almost internal to the fixed field. In addition, a general criterion for stable embeddedness in TA (when it exists) is established, and used to determine the full induced structure of CCMA on projective varieties, simple nonalgebraic complex tori, and simply connected nonalgebraic strongly minimal manifolds.


Journal of The Institute of Mathematics of Jussieu | 2018

UNIVERSAL COVERS OF COMMUTATIVE FINITE MORLEY RANK GROUPS

Martin Bays; Bradd Hart; Anand Pillay


arXiv: Logic | 2015

Some pseudo-analytic functions on commutative algebraic groups

Martin Bays; Jonathan Kirby

Collaboration


Dive into the Martin Bays's collaboration.

Top Co-Authors

Avatar

Jonathan Kirby

University of East Anglia

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Rahim Moosa

University of Waterloo

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Philipp Habegger

Technische Universität Darmstadt

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Anand Pillay

University of Notre Dame

View shared research outputs
Researchain Logo
Decentralizing Knowledge