Floris Vermeulen

I'm currently a postdoc in Münster working with Prof. Franziska Jahnke. Before that, I was a PhD student at the algebra section at KU Leuven under supervision of Prof. Raf Cluckers. I am broadly interested in the following topics:

Tame non-Archimedean geometry, Hensel minimality and motivic integration.
The geometry of curves, scrollar invariants, and syzygies.
Rational points on varieties, curves over finite fields, and point-counting.
Number theory and successive minima.

Email: florisvermeulen dot math at gmail.com

Publications

Dimension growth for affine varieties, available at IMRN or arxiv. International Mathematics Research Notices, Volume 2024, Issue 15, August 2024, Pages 11464–11483.
A Pila-Wilkie theorem for Hensel minimal curves, together with Victoria Cantoral-Farfán, Kien Huu Nguyen, and Mathias Stout, JMT or arxiv. Journal of Model Theory, Vol. 3, No. 1 (2024), pp. 119–145.
Hensel minimality II: Mixed characteristic and a diophantine application, together with Raf Cluckers, Immanuel Halupczok and Silvain Rideau-Kikuchi, arxiv. Forum of Mathematics, Sigma, 11, E89. doi:10.1017/fms.2023.91.
Hensel minimality: Geometric criteria for ℓ-h-minimality, JML or arxiv. Journal of Mathematical Logic (2023) DOI: 10.1142/S0219061324500016.
Curves of fixed gonality with many rational points, available at jntb, Journal de théorie des nombres de Bordeaux, Volume 35 (2023) no. 1, pp. 135-149.
Arithmetically equivalent number fields have approximately the same successive minima, available at JNT or arxiv. Journal of Number Theory, 249 (2023), 119-130.
Scrollar invariants, syzygies and representations of the symmetric group, together with Wouter Castryck and Yongqiang Zhao, available at crelle or arxiv. Journal für die reine und angewandte Mathematik, 796 (2023), 117-159.
On abelian covers of the projective line with fixed gonality and many rational points, together with Xander Faber, available at IJNT or arxiv. International Journal of Number Theory (IJNT), vol. 18, no. 10, pp. 2211-2216, year 2022. Erratum.
Points of bounded height on curves and the dimension growth conjecture over Fq[t], available at BLMS or arxiv. Bulletin of the London Mathematical Society, volume 54 issue 2, pp. 635-654 (2022).
Lifting low-gonal curves for use in Tuitman's algorithm, with Wouter Castryck, available at link or arxiv. Accompanying magma code can be found at link. Proceedings of ANTS-XIV, MSP Open Book Series 4, pp. 109-125 (2020).

Preprints

Scrollar invariants, syzygies and representations of the symmetric group II, arxiv.
Improvements on dimension growth results and effective Hilbert's irreducibility theorem, together with Raf Cluckers, Pierre Dèbes, Yotam Hendel and Kien Huu Nguyen, arxiv. To appear in Forum of Mathematics, Sigma.
Almost real closed fields with real analytic structure, with Kien Huu Nguyen and Mathias Stout, arxiv.
Motivic Mellin Transforms, with Raf Cluckers, François Loeser and Kien Huu Nguyen, arxiv.
A geometric determinant method and geometric dimension growth, with Tijs Buggenhout and Yotam Hendel, arxiv.
Serre's question on thin sets in projective space, with Tijs Buggenhout, Raf Cluckers and Tim Santens, arxiv.
Counting rational points on transcendental curves in valued fields, arxiv. To appear in the proceedings of the CIRM Thematic Month "Singularites, Differential Equations, and Transcendence".

Other

My PhD thesis under supervision of Raf Cluckers.

My master thesis on lifting curves of low gonality under supervision of Wouter Castryck.