3 papers
math.AG2026
Approximating parametric suprema for constructible and power-constructible functions
Tijs Buggenhout, Mathias Stout, Lisa Vandebrouck
We prove that one may approximate parametric suprema of constructible and power-constructible functions using functions within the same class. This resolves a conjecture by Adiceam…
math.NT2026
A geometric determinant method and geometric dimension growth
Tijs Buggenhout, Yotam I. Hendel, Floris Vermeulen
We study a geometric version of the dimension growth conjecture. While it is closely related in spirit to themes arising in geometric Manin's conjecture, it applies in greater gene…
math.NT2026
Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Per Salberger +2
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least . For degrees and we improve the known boun…