Douwe Hoekstra

I am a PhD candidate at the Utrecht Geometry Centre under the supervision Dr. Álvaro del Pino Gomez. My work focusses on the h-principle and in particular convex integration as a method to prove h-principles.

My interests lie more generally within the field of geometric/differential topology. The line between geometric topology, differential topology and differential geometry is blurry and the different fields have an important interplay, but at its simplest I am interested in the interplay between the geometric structure on a manifold and the underlying topology of the manifold (or other spaces associated to the geometric structure). To name a few examples in this spirit:

The de Rham isomorphism theorem
Morse functions
Myers' theorem: complete Riemannian manifolds with positive Ricci curvature are compact
Smale-Hirsch immersion theorem & Smale's sphere eversion.

See the contact section for information on how to get in touch.

Education

2021 – 2024: MSc in Mathematics, Radboud University Nijmegen.
2018 – 2021: BSc in Mathematics, Radboud University Nijmegen.
2018 – 2021: BSc in Physics, Radboud University Nijmegen.

Publications

D.H. and Florian Zeiser, "Poisson cohomology of 3D Lie algebras". In: Journal of Geometry and Physics 191 (2023). arXiv:2122.04122.

Teaching

TA for Analysis in several variables (Summer 2025, Utrecht University).
TA for Topology and Geometry (Spring 2025, Utrecht University).
- Here are some notes reviewing notions from point-set topology I have written for this course.
TA for Introduction to Topology (Winter 2024, Utrecht University).
TA for Calculus B (Spring 2024, Radboud University Nijmegen).
TA for Group Theory (Spring 2024, Radboud University Nijmegen).
TA for Poisson Geometry (Fall 2023, Radboud University Nijmegen).
TA for Functional Analysis (Fall 2021, Radboud University Nijmegen).

Notes

Here are the notes on matrix Lie groups my colleague Sven Holtrop and I wrote together for the Utrecht Summer School on Geometry.
Here are the notes on stacks for the differentiable stacks seminar I took part in.

Ancillary activities

I am one of the organizers of the Friday Fish seminar at the Utrecht Geometry Centre. Check out the webpage of the seminar to see what we are up to.

Contact

You can reach me at math [at] dhoekstra.xyz or at my work mail, d.hoekstra [at] uu.nl.

My work address is:

Hans Freudenthal building
Room 8.04
Budapestlaan 6
3584 CD Utrecht
The Netherlands

Other web presence

You can also find me here online: