Tim Santens

I am a Herschel-Smith postdoctoral fellow at the university of Cambridge.

Before that I was a PhD student under the supervision of Arne Smeets (KU Leuven) and Daniel Loughran (U Bath) at KU Leuven.

My research focuses on rational points on varieties, a subject lying at the intersection of algebraic geometry and number theory. I use geometric, algebraic and analytic techniques in my work. More particularly, some of my research interests are:

Brauer-Manin obstruction
Counting problems related to rational points
Rational and integral points on stacks

Contact:

Address: Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WB

Email: ts996[at]cam.ac.uk

Articles:

Integral points on affine quadric surfaces. [Arxiv], Journal de Théorie des Nombres de Bordeaux, 2022.
Diagonal quartic surfaces with a Brauer-Manin obstruction. [Arxiv], [Magma code], Compositio Mathematica, 2023.

Preprints:

The Brauer-Manin obstruction for stacky curves. [Arxiv].
Manin's conjecture for integral points on toric varieties. [Arxiv].
Malle's conjecture and Brauer groups of stacks, with Daniel Loughran. [Arxiv]
Local solubility of generalised Fermat equations, with Peter Koymans, Ross Paterson and Alec Shute. [Arxiv].
Counting points on some genus zero Shimura curves, with Tyler Genao, Tristan Phillips, Fredderick Saia and John Yin. [Arxiv].
Serre's question on thin sets in projective space, with Tijs Buggenhout, Raf Cluckers and Floirs Vermeulen. [Arxiv].