In the past I did research in universal algebra studying the first and second order properties of De Morgan algebras and De Morgan functions.
DPhil Thesis
Ax-Schanuel Type Inequalities in Differentially Closed Fields, University of Oxford, April 2017.
Papers (ordered by category)
Expository papers
- Complex solutions of polynomial equations on the unit circle, 2024. Preprint
- Exponential sums equations and the Exponential Closedness conjecture (with Francesco Gallinaro), 2024. Preprint
Unlikely intersections/Zilber-Pink
- Modular Zilber-Pink for geometrically generic varieties (with Sebastian Eterović and Guy Fowler), 2025. Preprint
- Multiplicative relations among differences of singular moduli (with Sebastian Eterović and Guy Fowler), Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2024).
- The Existential Closedness and Zilber-Pink Conjectures, Model Theory (2024).
- A note on unlikely intersections in Shimura varieties (with Chris Daw), The Journal of Number Theory (2024).
- Weak Modular Zilber-Pink with Derivatives, Mathematische Annalen (2021).
- Some remarks on atypical intersections, Proceedings of the AMS (2021).
Existential Closedness
- Equations involving the modular j-function and its derivatives (with Sebastian Eterović and Vincenzo Mantova), To appear in Crelle's Journal (2025).
- Algebraic types in Zilber's exponential field (with Jonathan Kirby), Model Theory (2024).
- The Existential Closedness and Zilber-Pink Conjectures, Model Theory (2024).
- A geometric approach to some systems of exponential equations (with Jonathan Kirby and Vincenzo Mantova), International Mathematics Research Notices (2021).
- A closure operator respecting the modular j-function (with Sebastian Eterović and Jonathan Kirby), Israel Journal of Mathematics (2022).
- Blurrings of the j-function (with Jonathan Kirby), Quarterly Journal of Mathematics (2021).
- Differential Existential Closedness for the j-function (with Sebastian Eterović and Jonathan Kirby), Proceedings of the AMS, 149:4 (2021), pp. 1417-1429.
- Existentially closed De Morgan algebras, Algebra Universalis, 81:4 (2020).
Model theory of differential fields
- Adequate predimension inequalities in differential fields, Annals of Pure and Applied Logic (2021).
- Differential Existential Closedness for the j-function (with Sebastian Eterović and Jonathan Kirby), Proceedings of the AMS, 149:4 (2021), pp. 1417-1429.
- Ax-Schanuel and strong minimality for the j-function, Annals of Pure and Applied Logic, 172:1 (2021).
- Ax-Schanuel for linear differential equations, Archive for Mathematical Logic, 57 (2018), pp. 629-648.
- Definability of derivations in the reducts of differentially closed fields, The Journal of Symbolic Logic, 82:4 (2017), pp. 1252-1277.
Model theory (other)
- Independence relations for exponential fields (with Robert Henderson, Mark Kamsma, Jonathan Kirby), Annals of Pure and Applied Logic (2023).
- A closure operator respecting the modular j-function (with Sebastian Eterović and Jonathan Kirby), Israel Journal of Mathematics (2022).
History of mathematics
- The mathematical work of Anania Shirakatsi, 2024. Preprint
Universal algebra
- Existentially closed De Morgan algebras, Algebra Universalis, 81:4 (2020).
- Characterization of zigzag De Morgan functions, Discrete Math. Algorithms Appl., 8 (2016), no. 2.
- A functional completeness theorem for De Morgan functions (with Yu. Movsisyan), Discrete Applied Mathematics, 162 (2014), pp. 1-16.
- Boole-De Morgan algebras and quasi-De Morgan functions (with Yu. Movsisyan), Communications in Algebra, 42:11 (2014), pp. 4757-4777.
- Super-De Morgan functions and free De Morgan quasilattices (with Yu. Movsisyan), Central European Journal of Mathematics, 12 (2014), no. 12, pp. 1749-1761.
- Super-Boolean functions and free Boolean quasilattices (with Yu. Movsisyan), Discrete Math. Algorithms Appl, 6 (2014), no. 2.
- De Morgan functions and free De Morgan algebras (with Yu. Movsisyan), Demonstr. Math., 47 (2014), no. 2, pp. 271-283.
- Subdirectly irreducible algebras with hyperidentities of the variety of De Morgan algebras (with Yu. Movsisyan), Journal of Contemporary Mathematical Analysis, 48 (2013), no. 6, pp. 241-246.
- Algebras with hyperidentities of the variety of De Morgan algebras (with Yu. Movsisyan), Journal of Contemporary Mathematical Analysis, 5 (2013), no. 5, pp. 233-240.
- Hyperidentities of De Morgan algebras (with Yu. Movsisyan), Logic Journal of the IGPL, 20(2012), pp. 1153-1174.
Papers (ordered chronologically)
Preprints
- Modular Zilber-Pink for geometrically generic varieties (with Sebastian Eterović and Guy Fowler), 2025. Preprint
- Exponential sums equations and the Exponential Closedness conjecture (with Francesco Gallinaro), 2024. Preprint
- Complex solutions of polynomial equations on the unit circle, 2024. Preprint
Publications
- Equations involving the modular j-function and its derivatives (with Sebastian Eterović and Vincenzo Mantova), To appear in Crelle's Journal (2025).
- Multiplicative relations among differences of singular moduli (with Sebastian Eterović and Guy Fowler), Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2024).
- Algebraic types in Zilber's exponential field (with Jonathan Kirby), Model Theory (2024).
- The Existential Closedness and Zilber-Pink Conjectures, Model Theory (2024).
- A note on unlikely intersections in Shimura varieties (with Chris Daw), The Journal of Number Theory (2024).
- Independence relations for exponential fields (with Robert Henderson, Mark Kamsma, Jonathan Kirby), Annals of Pure and Applied Logic (2023).
- A closure operator respecting the modular j-function (with Sebastian Eterović and Jonathan Kirby), Israel Journal of Mathematics (2022).
- A geometric approach to some systems of exponential equations (with Jonathan Kirby and Vincenzo Mantova), International Mathematics Research Notices (2021).
- Adequate predimension inequalities in differential fields, Annals of Pure and Applied Logic (2021).
- Blurrings of the j-function (with Jonathan Kirby), Quarterly Journal of Mathematics (2021).
- Weak Modular Zilber-Pink with Derivatives, Mathematische Annalen (2021).
- Some remarks on atypical intersections, Proceedings of the AMS (2021).
- Differential Existential Closedness for the j-function (with Sebastian Eterović and Jonathan Kirby), Proceedings of the AMS, 149:4 (2021), pp. 1417-1429.
- Ax-Schanuel and strong minimality for the j-function, Annals of Pure and Applied Logic, 172:1 (2021).
- Existentially closed De Morgan algebras, Algebra Universalis, 81:4 (2020).
- Ax-Schanuel for linear differential equations, Archive for Mathematical Logic, 57 (2018), pp. 629-648.
- Definability of derivations in the reducts of differentially closed fields, The Journal of Symbolic Logic, 82:4 (2017), pp. 1252-1277.
- Characterization of zigzag De Morgan functions, Discrete Math. Algorithms Appl., 8 (2016), no. 2.
- A functional completeness theorem for De Morgan functions (with Yu. Movsisyan), Discrete Applied Mathematics, 162 (2014), pp. 1-16.
- Boole-De Morgan algebras and quasi-De Morgan functions (with Yu. Movsisyan), Communications in Algebra, 42:11 (2014), pp. 4757-4777.
- Super-De Morgan functions and free De Morgan quasilattices (with Yu. Movsisyan), Central European Journal of Mathematics, 12 (2014), no. 12, pp. 1749-1761.
- Super-Boolean functions and free Boolean quasilattices (with Yu. Movsisyan), Discrete Math. Algorithms Appl, 6 (2014), no. 2.
- De Morgan functions and free De Morgan algebras (with Yu. Movsisyan), Demonstr. Math., 47 (2014), no. 2, pp. 271-283.
- Subdirectly irreducible algebras with hyperidentities of the variety of De Morgan algebras (with Yu. Movsisyan), Journal of Contemporary Mathematical Analysis, 48 (2013), no. 6, pp. 241-246.
- Algebras with hyperidentities of the variety of De Morgan algebras (with Yu. Movsisyan), Journal of Contemporary Mathematical Analysis, 5 (2013), no. 5, pp. 233-240.
- Hyperidentities of De Morgan algebras (with Yu. Movsisyan), Logic Journal of the IGPL, 20(2012), pp. 1153-1174.
Talk slides
- Modular Existential Closedness with Derivatives, Model theory and tame expansions of topological fields, Naples, 16 July 2025.
- Modular Zilber-Pink with Derivatives, Unlikely Intersections in arithmetic and dynamical systems, Warwick, 2 July 2025.
- A remark on unlikely intersections, Manchester Pure Mathematics Colloquium, Manchester, 8 December 2023.
- Multiplicative relations among differences of singular moduli, Manchester Number Theory seminar, Manchester, 28 November 2023.
- The Existential Closedness with Derivatives conjecture for the j-function, Logic Colloquium, Milan, Italy, 7 June 2023.
- Modular Existential Closedness and Zilber-Pink with Derivatives, LYMoTS, University of Manchester, 27 January 2023.
- A remark on unlikely intersections, Pure mathematics seminar, University of Reading, 25 May 2022.
- A geometric approach to some systems of exponential equations, Models and Sets, University of Leeds, 9 June 2021.
- A geometric approach to certain systems of exponential equations, Logic seminar, Università degli Studi della Campania Luigi Vanvitelli, 11 March 2021.
- Blurrings of the j-function, Manchester Logic seminar, University of Manchester, 25 November 2020.
- Introduction to o-minimality and applications, LMS Online Lecture Series: An Excursion Into Model Theory and Its Applications, 24 November 2020.
- Blurrings of the j-function, Berkeley Model Theory seminar, UC Berkeley, 16 June 2020.
- Introduction to the Zilber-Pink conjecture, Number Theory learning seminar, UC Berkeley, 15 April 2020.
- Strongly minimal sets in j-reducts of differentially closed fields, SEEMOD, Imperial College London, London, 11 December 2019.
- A remark on atypical intersections, UEA pure mathematics seminar, Norwich, 11 November 2019.
- Functional Modular Zilber-Pink with Derivatives, Oxford Logic Seminar, Oxford, 7 November 2019.
- Ax-Schanuel and strongly minimal sets in j-reducts of differentially closed fields, ASL North American Annual Meeting, Macomb, IL, 16 May 2018.
Research projects
University of Manchester
From 2023 to 2028 I will be working on the research project "Model theory, Diophantine geometry, and automorphic functions" supported by EPSRC Open Fellowship EP/X009823/1 and Dame Kathleen Ollerenshaw Fellowship (PI: Vahagn Aslanyan). The main aim of this project is to make progress on two major problems at the boundary between model theory, complex geometry, and number theory – the Existential Closedness and Zilber-Pink conjectures for automorphic functions together with their derivatives – and explore the connections between them.
PhD projects. I am looking for PhD students to work with me on the Existential Closedness and/or related topics. I have advertised a PhD project called "The Existential Closedness problem for exponential and automorphic functions". If you are interested in this or would like to work with me on a different topic (e.g. differential algebra), please get in touch.
University of Leeds
From 2022 to 2023 I worked on the project "Model theory, Diophantine geometry, and modular functions" supported by the Leverhulme Early Career Fellowship ECF-2022-082 (PI: Vahagn Aslanyan). This is now incorporated into the above project.
University of East Anglia
From 2019 to 2022 I was a postdoc on the project "Exponentially Algebraically Closed Fields" supported by the EPSRC Standard Grant EP/S017313/1 (PI: Jonathan Kirby). The aim of this project was to make progress on the Exopnential Algebraic Closedness conjecture.