Shimura varieties, André-Oort:
``Lower bounds for Galois orbits of special points on Shimura varieties: a point-counting approach", Math. Ann. (2023) 385:961-973 (with Gal Binyamini and Andrei Yafaev) Link to arXiv.
Semi-abelian varieties, Zilber-Pink:
``Unlikely intersections of curves with algebraic subgroups in semiabelian varieties", Selecta Math. (2023) 29:18 (with Fabrizio Barroero and Lars Kühne) Link to arXiv.
“Unlikely intersections in semi-abelian surfaces'' Algebra Number Theory 13 (2019), no. 6, 1455–1473 (with Daniel Bertrand) Link to pdf on arXiv .
Dynamical systems:
``On the dynamical Bogomolov conjecture for families of split rational maps" (with Myrto Mavraki) Link to arXiv, to appear in Duke Math. J..
``Lower bounds for the canonical height of a unicritical polynomial and capacity" (with Philipp Habegger) Forum of Mathematics, Sigma (2024), Vol. 12:e45 1–20, Link to article.
``Height coincidences in products of the projective line", Math. Z. (2023), 304:26 (with Myrto Mavraki and Robert Wilms) Link to arXiv.
``Polynomial dynamics and local analysis of small and grand orbits", Compositio Math. 159 (2023) 53-86 (working title: ``Polynomial dynamics and local analysis") Link to arXiv.
``Rational values of transcendental functions and arithmetic dynamics", J. Eur. Math. Soc. 24 (2022), 1567-1592 (with Gareth Boxall and Gareth Jones) link to arXiv.
Manin-Mumford and applications:
“A Manin-Mumford theorem for the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves” IMRN Vol. 2021, No. 21, pp. 16205-16228 (with Gareth Jones). Link to arXiv.
“Relative Manin-Mumford in additive extensions”. Trans. Amer. Math. Soc. 371 (2019), no. 9, 6463–6486. Link to pdf .
“Pell’s equation in polynomials and additive extensions”, Q.J.Math. 68 (2017), no. 4, 1335–1355.
Effectivity:
“Pfaffian definitions of Weierstrass elliptic functions”, Math. Ann. (2021) 379:825-864 (with Gareth Jones). Link to pdf.
``An effective Pila-Wilkie theorem for sets definable using Pfaffian functions, with some diophantine applications" (with Gal Binyamini, Gareth Jones and Margaret Thomas) Link to arXiv (to appear in J. Eur. Math. Soc.).
New proofs of classical theorems:
``A short note on Manin-Mumford", International Journal of Number Theory Vol. 19, No. 01, pp. 223-227 (2023) Link to arXiv .
``Counting rational points and lower bounds for Galois orbits”, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 3, 497–509 Link to arXiv .
Elliptic curves:
``Resultants and discriminants of multiplication polynomials for elliptic curves'' (with an appendix written jointly with J.K. Canci), Journal of Number Theory 149 (2014), 70-91.
``On the Manin-Mumford Theorem for Algebraic Groups", (with Immanuel van Santen) Link to arXiv
``Explicit Riemann mappings for hedgehogs" Link to pdf