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.

I'm on the move: in Fall 2025, I'll be doing a short term postdoc at the University of Toronto, sponsored by Spyros Alexakis. In January 2026, I'll be starting as a tenure track Assistant Professor at the University of North Carolina at Chapel Hill.

Here is my CV

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

Research

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

Papers

Complex harmonic maps and rank 2 higher Teichmüller theory (2025). Joint with Christian El Emam. Submitted.
Local asymptotics for Hitchin's equations and high energy harmonic maps (2025). Joint with Peter Smillie. Submitted.
On Hitchin's equations for cyclic G-Higgs bundles (2024). Joint with Ognjen Tošić. Submitted.
Holomorphic dependence for the Beltrami equation in Sobolev spaces (2024). Joint with Christian El Emam. Submitted.
Complex affine spheres and a Bers theorem for SL(3,C) (2024). Joint with Christian El Emam. Submitted.
Minimal diffeomorphisms with L^1 Hopf differentials (2023). International Mathematics Research Notices 13 (2024), 10088-10103. 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. Commentarii Mathematici Helvetici 100 1 (2025), 93-121. https://doi.org/10.4171/CMH/582.
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.

Talks, notes, etc.

Lecture notes for an online mini-course, "Minimal surfaces in symmetric spaces and Labourie's Conjecture," at the conference Zero mean curvature surfaces at ICTS Bengaluru.
Hitchin representations and minimal surfaces, online talk for the Joint Seminar on Teichmüller theory and Related topics (2022).

Upcoming talks

July 1 - 5, 2025: Higgs bundles and harmonic maps, conference at the University of Kiel.

Teaching and Organization

Organization

University of Luxembourg Geometry and Topology seminar.
Workshop on Convexity and 3d Geometry, August 19 - 20, 2024.
Metrics on higher Teichmüller spaces, August 28 - September 1, 2023.

Past courses

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

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