Nathaniel Sagman's Homepage

In July 2026, I plan to start as a tenure track Assistant Professor at the University of North Carolina at Chapel Hill. In the meantime, while applying for a visa, I'm teaching remotely for UNC.

Here is my CV.

You can contact me at: nathaniels1729(at)gmail(dot)com or nsagman(at)unc(dot)edu.

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

Domination between non-Fuchsian representations and anti-de Sitter geometry (2025). Joint with Farid Diaf and Abderrahim Mesbah. Submitted.
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. To appear in Mathematische Annalen.
On Hitchin's equations for cyclic G-Higgs bundles (2024). Joint with Ognjen Tošić. Advances in Mathematics (2025). Journal.
Holomorphic dependence for the Beltrami equation in Sobolev spaces (2024). Joint with Christian El Emam. To appear in Proceedings of the American Mathematical Society.
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 (2024). Journal.
Non-convexity of extremal length (2023). Annales Fennici Mathematici (2023). Journal.
Minimal surfaces and the new main inequality (2022). Joint with Vladimir Merković. Annales Fennici Mathematici (2024). Journal.
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 (2025). Journal.
Spaces of harmonic surfaces in non-positive curvature (2021). Mathematische Zeitschrift (2023). Journal.
Almost strict domination and anti-de Sitter 3-manifolds (2021). Journal of Topology (2024). Journal.

A factorization theorem for harmonic maps (2020). Journal of Geometric Analysis (2021). Journal.

Infinite energy equivariant harmonic maps, domination, and anti-de Sitter 3-manifolds (2019). Journal of Differential Geometry (2023). Journal.

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.
Two talks on minimal surfaces and Labourie's Conjecture.

Upcoming talks

Geometric structures and stability conference, February 16-27, ICTS, Bengaluru, India.
BRIDGe - Building Research Interconnections in Dynamics and Geometry conference, July 12-18, Virginia.

Teaching and Organization

Past conferences

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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