Nelson Schuback

Postdoctoral Researcher at the Jagiellonian University in Kraków

Institute of Mathematics, Jagiellonian University
Kraków, Poland

Email nelson.schuback@imj-prg.fr / nelson.schuback@uj.edu.pl

Office Room 2122, ul. Łojasiewicza 6, 30-348 Kraków

I recently completed my PhD at Sorbonne Université (IMJ-PRG) in Paris, supervised by Patrice Le Calvez.
I am now a postdoctoral researcher at the Institute of Mathematics of the Jagiellonian University in Kraków, Poland, as a member of Jan P. Boroński's team within the NCN Sonata Bis project on topological and dynamical properties of non-hyperbolic attractors.

My research interests lie at the interface of low-dimensional topology/geometry and dynamical systems.
I am currently working on the classification problem of Brouwer mapping classes, which are special elements of the mapping class group of the flute surface. My approach to this problem uses mostly techniques from Brouwer-Le Cavez foliations and hyperbolic geometry.

• Surface homeomorphisms
• Planar Foliations
• Brouwer theory
• Big mapping class groups

Publications & Preprints

1. An index theory for transverse trajectories Preprint, January 2026 — arXiv:2601.15651
2. An alternative approach to Homotopy Brouwer Theory Preprint, December 2025 — arXiv:2512.07510
3. Refined methods in Foliated Brouwer Theory Preprint, October 2025 — arXiv:2510.17616

Dissertations

1. A foliated viewpoint on homotopy Brouwer theory PhD dissertation — Sorbonne Université (IMJ-PRG), Paris, 2025. Supervised by Patrice Le Calvez theses.fr/2025SORUS597
2. A synthesis on classical Brouwer theory Master's dissertation — Institute of Mathematics and Statistics, University of São Paulo, 2021 doi:10.11606/D.45.2021.tde-30032022-114757

Talks

2025

• Un point de vue feuilleté sur la théorie de Brouwer homotopique Géométrie & Dynamique à Aussois, 8ème édition — Centre Paul Langevin, Aussois, France

2024

• What is rotation theory on surfaces? PhD Students' Seminar — IMJ-PRG, Paris, France
• Maryam Mirzakhani and non-Euclidean geometry Série "Un texte, un mathématicien 2024" — Lycée Blaise Pascal d'Orsay, France
• Isotopy classes of Brouwer homeomorphisms relative to r > 0 orbits GDT Dynamiques Sauvages — IMJ-PRG, Paris, France
• Isotopy classes of Brouwer homeomorphisms relative to r > 0 orbits Dynamical Systems Seminar — IMRL-UdelaR, Montevideo, Uruguay

2023

• Homotopy Brouwer theory meets transverse foliations Surfaces in Banyuls — Oceanological Observatory, Banyuls-sur-Mer, France
• Homological rotation set of Axiom A diffeomorphisms GDT Dynamiques Sauvages — IMJ-PRG, Paris, France
• Periodic orbits of Hamiltonian homeomorphisms on surfaces GDT Dynamiques Sauvages — IMJ-PRG, Paris, France

2019 – 2022

• Genericity of transverse homoclinic intersections for conservative surface diffeomorphisms GDT Dynamiques Sauvages — IMJ-PRG, Paris, France
• Applications of prime-ends rotation sets to conservative surface diffeomorphisms GDT Dynamiques Sauvages — IMJ-PRG, Paris, France
• C^k-linearization of non-resonant hyperbolic fixed points GDT Dynamiques Sauvages — IMJ-PRG, Paris, France
• On the Weinstein conjecture for overtwisted contact 3-manifolds Seminar on Symplectic Topology — IMPA, Brazil
• Positive entropy for torus homeomorphisms with rotation set of non-empty interior Topological Surface Dynamics course seminars — IME-USP, Brazil
• A non-ergodic minimal real-analytic conservative diffeomorphism Ergodic Theory course — IME-USP, Brazil

Teaching