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. Systems of Wave Equations on Asymptotically de Sitter Vacuum Solutions in All Even Spatial Dimensions, in preparation.
2. Nonlinear Scattering Theory for Asymptotically de Sitter Vacuum Solutions in All Even Spatial Dimensions, submitted, arXiv:2410.01558.
3. Scattering for the Wave Equation on de Sitter Space in All Even Spatial Dimensions, submitted, arXiv:2309.07342.
4. Extensions of Lorentzian Hawking–Page Solutions with Null Singularities, Spacelike Singularities, and Cauchy horizons of Taub–NUT type, submitted, 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