Research

I am a differential topologist that studies geometric structures. The questions I consider are often of the form: “What is the homotopy type of the space of all geometric structures of class X on a given manifold M?“

This is a rather broad question, since it can be posed in any geometric setting you like. I mostly spend my time thinking about:

  • h-Principle. This is the subfield of Differential Topology that studies the question above. I am particularly interested in developing techniques that are general and not geometry-specific. Some keywords: wrinkling, jiggling, convex integration, removal of singularities, non-local h-principle.
  • Contact and Symplectic Topology. These two geometries (which are closely related to one another) have been studied topologically for a long time. I am interested in how ideas from this setting can be generalised to other geometries. Some keywords: overtwistedness, looseness, pseudoholomorphic curves.
  • Tangent distributions. This is a large family of geometric structures that generalise contact structures (namely, they are subbundles of the tangent bundle, which I often assume to satisfy some notion of non-integrability). Some keywords: horizontal submanifolds, Engel structures, (2,3,5)-distributions, (4,6)-distributions, Cartan distribution in jet space.
  • Poisson Geometry and Foliation Theory. These are the theories of involutive bivectors and distributions, respectively. Some keywords: symplectic foliation, contact foliation, Lie algebroid, transverse geometry, b^k algebroid.

Furthermore, I am very interested in Sub-Riemannian Geometry (as the field that studies distributions from a geometric perspective), and Homotopy Theory (concretely, its relation to h-principle).

Preprints

  • The h-principle fails for prelegendrians in corank 2 fat distributions. arXiv:2511.17780 (with E. Fernández and W. Zhou)
  • Engel CR submanifolds of C3. arXiv:2509.11488 (with E. Fernández and W. Zhou)
  • Jiggling: an h-principle without homotopical assumptions. arXiv:2501.13627 (with A. Fokma and L.E. Toussaint)
  • b^k-algebroids and the variety of foliation jets. arXiv:2508.20241  (with F. Bischoff and A. Witte). This was extracted from the earlier paper arXiv:2311.17045 and expanded.
  • Wrinkling and Haefliger structures. arXiv:2309.15715 (with A. Fokma and L.E. Toussaint)
  • Classification of tangent and transverse knots in bracket-generating distributions. arXiv:2210.00582 (with F.J. Martínez Aguinaga)
  • Wrinkling h-principles for integral submanifolds of jet spaces. arXiv:2112.14720 (with L.E. Toussaint)
  • Convex integration with avoidance and hyperbolic (4,6) distributions. arXiv:2112.14632 (with F.J. Martínez Aguinaga)

Accepted/published articles

Expository writing

My PhD thesis