Publications and Preprints

Publications

Shimura varieties, André-Oort: 

[1]  ``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: 

[2] ``Unlikely intersections of curves with algebraic subgroups in semiabelian varieties",  Selecta Math. (2023) 29:18 (with Fabrizio Barroero and Lars Kühne) Link to arXiv.

[3] “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: 

[4] ``Height coincidences in products of the projective line", Math. Z. (2023), 304:26 (with Myrto Mavraki and Robert Wilms) Link to arXiv.

[5] ``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.

[6]  ``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. 

[7] ``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. 

Manin-Mumford and applications: 

[8] “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.

[9] “Relative Manin-Mumford in additive extensions”. Trans. Amer. Math. Soc. 371 (2019), no. 9, 6463–6486.  Link to pdf .

[10] “Pell’s equation in polynomials and additive extensions”, Q.J.Math. 68 (2017), no. 4, 1335–1355.

Effectivity: 

[11] “Pfaffian definitions of Weierstrass elliptic functions”, Math. Ann. (2021) 379:825-864  (with Gareth Jones). Link to pdf.

New proofs of classical theorems: 

[12] ``A short note on Manin-Mumford", International Journal of Number Theory Vol. 19, No. 01, pp. 223-227 (2023) Link to arXiv . 

[13] ``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:

[14]   ``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. 

Preprints

[15] ``On the dynamical Bogomolov conjecture for families of split rational maps" (with Myrto Mavraki) Link to arXiv 

[16] ``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 

[17] ``On the Manin-Mumford Theorem for Algebraic Groups", (with Immanuel van Santen) Link to arXiv 

Notes

``Explicit Riemann mappings for hedgehogs" Link to pdf