Ryan Unger

Department of Mathematics, Princeton University
Fine Hall, Princeton, NJ 08540
email: runger [at] math.princeton.edu

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I'm a 5th year PhD student at Princeton University, advised by Mihalis Dafermos.
I'm interested in general relativity, nonlinear wave equations, and scalar curvature geometry.
Here is my CV (updated 02/19/24).

Starting in Fall 2024, I will be an NSF Postdoctoral Fellow at Stanford University and a Miller Fellow at UC Berkeley (on leave until 2025).

I received my undergrad degree from the University of Tennessee, where I was mentored by Alexandre Freire.

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Papers

1. Extremal black hole formation as a critical phenomenon (2024)
   with Christoph Kehle
   arXiv:2402.10190

2. Event horizon gluing and black hole formation in vacuum: the very slowly rotating case (2023)
   with Christoph Kehle
   submitted
   arXiv:2304.08455

3. Gravitational collapse to extremal black holes and the third law of black hole thermodynamics (2022)
   with Christoph Kehle
   to appear in J. Eur. Math. Soc. (arXiv:2211.15742)

4. Noncompact fill-ins of Bartnik data (2022)
   with Dan A. Lee and Martin Lesourd
   J. Geom. Anal. 34:102 (2024) (arXiv:2211.06280)

5. Density and positive mass theorems for incomplete manifolds (2022)
   with Dan A. Lee and Martin Lesourd
   Calc. Var. Partial Differential Equations 62 (2023) (arXiv:2201.01328)

6. Density and positive mass theorems for initial data sets with boundary (2021)
   with Dan A. Lee and Martin Lesourd
   Comm. Math. Phys. 395.2 (2022) (arXiv:2112.12017)

7. The positive mass theorem with arbitrary ends (2021)
   with Martin Lesourd and Shing-Tung Yau
   to appear in J. Differential Geom. (arXiv:2103.02744)

8. Positive scalar curvature on noncompact manifolds and the Liouville theorem (2020)
   with Martin Lesourd and Shing-Tung Yau
   to appear in Comm. Anal. Geom. (arXiv:2009.12618)

Talks