Martin Bays

Since October 2023, I am the Departmental Lecturer in Logic at Oxford University.

Current teaching

B1.2 Set Theory; lecture notes

Papers

An asymmetric version of Elekes-Szabó via group actions with Tingxiang Zou; talk
Elekes-Szabó for collinearity on cubic surfaces with Jan Dobrowolski and Tingxiang Zou; talk; talk
On large externally definable sets in NIP with Omer Ben-Neria, Itay Kaplan, and Pierre Simon; published in J. Inst. Math. Jussieu;
Density of compressibility and some consequences with Itay Kaplan and Pierre Simon; published in JEMS; overview talk; detailed talk
Elekes-Szabó for groups, and approximate subgroups in weak general position with Jan Dobrowolski and Tingxiang Zou; published in Discrete Analysis; talk
Incidence bounds in positive characteristic via valuations and distality with Jean-François Martin; published in Annales Henri Lebesgue; (source); talk (source)
Definability in the infinitesimal subgroup of a compact Lie group with Kobi Peterzil; published in Confluentes Mathematici; source; slides from Padua (source); notes from Paris
Projective geometries arising from Elekes-Szabó problems with Emmanuel Breuillard; published in Ann. Sci. Ec. Norm. Super.; source; slides from Oxford (source).
Pseudo-exponential maps, variants, and quasiminimality with Jonathan Kirby; published in Algebra and Number Theory; notes from Manchester; erratum.
Model Theory of Compact Complex Manifolds with an Automorphism with Martin Hils and Rahim Moosa; notes from Paris; published in the Transactions of the AMS.
Universal covers of commutative finite Morley rank groups with Bradd Hart and Anand Pillay; notes from Edinburgh; notes from MSRI; notes on Manin kernel example; published in the Journal of the IMJ. Scans of citation [Ser00]; Erratum.
A Note on Divisible Points of Curves with Philipp Habegger, published in the Transactions of the AMS; talk.
Excellence and uncountable categoricity of Zilber's exponential fields with Jonathan Kirby (not intended for publication; essentially superseded by PEMVQ).
Quasiminimal structures and excellence with Bradd Hart, Tapani Hyttinen, Meeri Kesälä and Jonathan Kirby, published in the Bulletin of the London Mathematical Society.
Some Definability Results in Abstract Kummer Theory with Misha Gavrilovich and Martin Hils; published in International Mathematical Research Notices
Covers of Multiplicative Groups of Algebraically Closed Fields of Arbitrary Characteristic with Boris Zilber; published in the Bulletin of the London Mathematical Society.
A Schanuel property for exponentially transcendental powers with Jonathan Kirby and A.J. Wilkie; published in the Bulletin of the London Mathematical Society.

The published versions of the above papers are mathematically identical to the latest arxiv versions, except in rare cases (explained in the arxiv version notes) where the arxiv version contains fixes to errors in the published version. The published versions always use the same numbering as the arxiv versions.

My DPhil thesis

Categoricity results for exponential maps of 1-dimensional algebraic groups & Schanuel Conjectures for Powers and the CIT, written at Oxford under the supervision of Boris Zilber.

Lecture notes

Introductory Set Theory (Oxford, HT25)
Introductory Logic (Oxford, MT24)
Geometric group theory (Bass-Serre theory) (Münster, WS22/23)
Model theory (Münster, WS19/20) (deutsche Version)
Geometric Stability Theory (corrected version of a chapter in Lectures in Model Theory, Münster Lectures in Mathematics); source.
Elementary combinatorics (McMaster, Winter 2015)
Truth and provability (McMaster, Fall 2012)

Old Teaching

Oxford:
- B1.1 Logic; lecture notes