I am a 4th year PhD student in the Mathematics Department at Princeton University. My advisor is Igor Rodnianski.

My research interests are partial differential equations, general relativity, and nonlinear wave equations. I am currently working on self similar solutions of the Einstein vacuum equations. I am also interested in the weak cosmic censorship conjecture and examples of naked singularities.

Publications

1. Discretely self-similar exterior-naked singularities for the Einstein-scalar field system, with Christoph Kehle, arXiv:2412.09540.
2. Systems of Wave Equations on Asymptotically de Sitter Vacuum Spacetimes in all even spatial dimensions, submitted, arXiv:2411.16655.
3. Nonlinear scattering theory for asymptotically de Sitter vacuum solutions in all even spatial dimensions, submitted, arXiv:2410.01558.
4. Scattering for the wave equation on de Sitter space in all even spatial dimensions, submitted, arXiv:2309.07342.
5. Extensions of Lorentzian Hawking–Page solutions with null singularities, spacelike singularities, and Cauchy horizons of Taub–NUT type, Ann. Henri Poincarè (online first) (2024), arXiv:2209.06134.

Talks

• Elaine Hubbard PDE Seminar, Georgia Institute of Technology, November 2024

• Analysis Seminar, University of Toronto, November 2024

• Princeton Gravity Initiative Workshop, flash talk, March 2024

• Princeton Graduate Student Seminar, February 2024

• Mathematical GR and Hyperbolic PDE Seminar, online talk, March 2023

• Princeton Graduate Student Seminar, February 2023

Education

PhD in Mathematics, Princeton University, September 2021 - Present

Advisor: Igor Rodnianski

MASt in Mathematics, University of Cambridge, Trinity College, October 2020 - July 2021

Part III Essay: The Existence of Naked Singularities and Their Instability (supervised by Mihalis Dafermos)

BA in Mathematics, Princeton University, September 2016 - June 2020

Senior Thesis: Global Stability for Weak Null Wave Equations with Multi-localized Initial Data. (advised by Sergiu Klainerman)

Here is my complete resume.

Seminar

I organize the weekly Princeton-Cambridge Joint General Relativity Seminar. Please contact me if you would like to join the seminar.

Teaching

During Fall 2024 I am a TA for MAT 335 Analysis II: Complex Analysis.

During Summer 2024, I was an instructor for the SLMath Summer School “Mathematics of General Relativity and Fluids”.

Previously, I was a preceptor for MAT 175 Mathematics for Economics/Life Sciences, MAT 201 Multivariable Calculus and TA for MAT 335 Analysis II: Complex Analysis, MAT 425 Analysis III: Integration Theory and Hilbert Spaces.

Contact

You can email me at: cicortas [at] princeton.edu