Nathaniel Sagman's Homepage

I'm a postdoc in Jean-Marc Schlenker's research group at the University of Luxembourg. I completed my PhD at Caltech in June 2022, under the supervision of Vlad Marković. Before Caltech, I received my BSc from McGill University in June 2017.

Here is my CV.

You can contact me at: nathaniels1729(at)gmail(dot)com.

Research

I work in differential geometry and (geometric, complex) analysis. My research is currently focused on harmonic maps, (higher) Teichmüller theory, Higgs bundles, and hyperbolic and anti-de Sitter geometry.

Papers

On a Bers Theorem for SL(3,C) (2024). Joint with Christian El Emam. Submitted.
Local asymptotics for Hitchin's equations and high energy harmonic maps (2023). Joint with Peter Smillie.
Minimal diffeomorphisms with L^1 Hopf differentials (2023). International Mathematics Research Notices (2024). https://doi.org/10.1093/imrn/rnae049.
Non-convexity of extremal length (2023). Annales Fennici Mathematici, 48 2 (2023), 691–702. https://doi.org/10.54330/afm.138339.
Minimal surfaces and the new main inequality (2022). Joint with Vladimir Merković. Annales Fennici Mathematici, 49 1 (2024), 99-117. https://doi.org/10.54330/afm.143716.
Unstable minimal surfaces in symmetric spaces of non-compact type (2022). Joint with Peter Smillie. Submitted.
Unstable minimal surfaces in R^n and in products of hyperbolic surfaces (2022). Joint with Vladimir Merković and Peter Smillie. To appear in Commentarii Mathematici Helvetici.
Spaces of harmonic surfaces in non-positive curvature (2021). Mathematische Zeitschrift 304 8 (2023). https://doi.org/10.1007/s00209-023-03268-9.
Almost strict domination and anti-de Sitter 3-manifolds (2021). Journal of Topology 17 1 (2024). https://doi.org/10.1112/topo.12323.

A factorization theorem for harmonic maps (2020). Journal of Geometric Analysis 31 (2021), 11714-11740 . https://doi.org/10.1007/s12220-021-00699-w.

Infinite energy equivariant harmonic maps, domination, and anti-de Sitter 3-manifolds (2019). Journal of Differential Geometry 124 3 (2023), 553-598. https://doi.org/10.4310/jdg/1689262064.

Other writing

Higher Teichmüller spaces and Labourie's conjecture (2023). A preliminary version of a chapter for the proceedings of the workshop on "Minimal surfaces in symmetric spaces and Labourie's conjecture."
Harmonic maps of Riemann surfaces and Applications in Geometry (2022). My PhD thesis.

Recorded talk

Hitchin representations and minimal surfaces, for the Joint Seminar on Teichmüller theory and Related topics (2022).

Upcoming talks

July 15-19, 2024: Cetraro, Italy, Conference in honour of Dick Canary.
September 2-6, 2024: ICTS Bengaluru, Zero mean curvature surfaces (online mini-course).

Teaching and Organization

Organization

University of Luxembourg Geometry and Topology seminar.
Metrics on higher Teichmüller spaces, August 28 - September 1, 2023.

Past courses

Complex geometry (masters level), Winter 2023.
Basic Analysis , Fall 2023.
Analyse Fonctionnelle, Winter 2024.

Past learning seminars

Reading seminar on Higgs bundles, 2023-2024., Luxembourg.

Geometrization for Haken manifolds, Fall 2018, Caltech.
The Atiyah-Singer Index Theorem, Winter 2020, Caltech.