I am a PhD candidate at the Utrecht Geometry Centre under the supervision of Dr. Álvaro del Pino Gómez. 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: MSc in Mathematics, Radboud University Nijmegen
Publications
- Douwe Hoekstra, Florian Zeiser. “Poisson cohomology of 3D Lie algebras.” Journal of Geometry and Physics 191 (2023). arXiv:2211.04122
Teaching
- Lecturer for Proofs in Mathematics (Utrecht University, Fall 2025)
- TA for Analysis in several variables (Utrecht University, Summer 2025)
- TA for Topology and Geometry (Utrecht University, Spring 2025)
- TA for Introduction to Topology (Utrecht University, Winter 2024)
- TA for Calculus B (Radboud University Nijmegen, Spring 2024)
- TA for Group Theory (Radboud University Nijmegen, Spring 2024)
- TA for Poisson Geometry (Radboud University Nijmegen, Fall 2023)
- TA for Functional Analysis (Radboud University Nijmegen, Fall 2021)
Notes
- Matrix Lie Groups: Notes my colleague Sven Holtrop and I wrote for the Utrecht Summer School on Geometry in 2025
- Differentiable Stacks Seminar III: Notes I wrote for the seminar on differentiable stacks 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
These are my contact details.- d.hoekstra [at] uu.nl: Primary email at Utrecht University
- math [at] dhoekstra.xyz: Private email address
Work Address
Hans Freudenthal buildingRoom 8.04
Budapestlaan 6
3584 CD Utrecht
The Netherlands