Martin Bays

Papers

• Non-expansion in polynomial automorphisms of C^2 with Tingxiang Zou;
• 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; version published in JEMS (CC-BY); 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); erratum.
• 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uncountable categoricity of Zilber's exponential fields with Jonathan Kirby (not intended for publication; essentially superseded by PEMVQ).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.

I avoid the use of LLMs, and commit to disclosing any use which contributes to my papers (none as of Sept 2026).

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, MT25)
• 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 MT24
  • B1.2 Set Theory HT25
• Münster:
  • Geometrische Gruppentheorie I WS 22/23
  • Logik II: Modelltheorie
  • Seminar SoSe22: Model theory and topological dynamics
  • Seminar WS21/22: Geometries, Hrushovski constructions, and ampleness
  • Seminar SoSe21: Model theory of pseudofinite structures
  • Seminar SoSe20: Hrushovski-Amalgamierung
  • Vorlesung über Small Cancellation Theorie
  • Seminar über einfachen Theorien
  • Logik II WS16/17
  • Seminar über Gruppen in o-minimale Strukturen
• McMaster

Misc

• Miscellaneous notes and talks
• Z75: a model theory meeting in Oxford 10-13 September 2024
• Spring SEEMOD meeting
• Special volume of Model Theory for Zilber's 75th
• MR reviews
• Other people's theses

Contact

Martin Bays
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Woodstock Road
Oxford
OX2 6GG
	

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