Homepage of Dr. Athanasios Chatzikaleas

General Relativity

Weekly seminars on General Relativity and related topics are hosted at Sorbonne Université (LJLL), University of Muenster (WWU) and Ecole Polytechnique Fédérale de Lausanne (EPFL). 

Research Interests

I am interested in the analysis of non-linear Partial Differential Equations in General Relativity. Specifically, my work concentrates around the following two directions:

1. Islands of stability and the construction of time-periodic solutions to Einstein's equations near the Anti-de-Sitter spacetime.

2. Unique continuation for asymptotically Anti-de-Sitter spacetimes.

Publications and Preprints

1. Athanasios Chatzikaleas, Roland Donninger and Irfan Glogic. On blowup of co-rotational wave maps in odd space dimensions. Journal of Differential Equations. 263:8 (2017), 5090–5119. ArXiv Journal

2. Athanasios Chatzikaleas and Roland Donninger. Stable blowup for the cubic wave equation in higher dimensions. Journal of Differential Equations. 266:10 (2019), 6809–6865. ArXiv Journal

3. Athanasios Chatzikaleas. On the Fourier Analysis of the Einstein-Klein-Gordon System: Growth and Decay of the Fourier Constants. Annales Henri Poincaré (2023). ArXiv Journal

4. Athanasios Chatzikaleas. On time periodic solutions to the conformal cubic wave equation on the Einstein cylinder. Journal of Mathematical Physics 61(11):111505, 32, 2020. ArXiv Journal

5. Athanasios Chatzikaleas and Jacques Smulevici. Non-linear periodic waves on the Einstein cylinder. Analysis & PDE 17 (7), 2311-‌2378, 2024. ArXiv Journal

6. Athanasios Chatzikaleas and Arick Shao. A gauge-invariant unique continuation criterion for waves in asymptotically anti-de Sitter spacetimes. Communications in Mathematical Physics. 395, 521–570, 2022. ArXiv Journal

7. Athanasios Chatzikaleas and Jacques Smulevici. Time periodic solutions and Nekhoroshev stability to non-linear massive Klein-Gordon equations in Anti-de Sitter. arXiv:2304.12784. ArXiv

8. Athanasios Chatzikaleas and Jacques Smulevici. Null coordinates for quasi-periodic (1+1)-dimensional wave operators on the circle with applications to reducibility. arXiv:2502.04826. ArXiv

Collaborators

1. Jacques Smulevici, Sorbonne Université (Pierre et Marie Curie)

2. Arick Shao, Queen Mary University

Downloads

1. Curriculum vitae 

2. Research Statement

3. PhD Thesis (University of Bonn)

4. Master Thesis (University of Crete) 

Teaching

1. Fall 2021, General Relativity and the Analysis of Black Hole Spacetimes, University of Muenster

2. Fall 2022, Non-linear wave equations, University of Muenster

3. Fall 2023, Differential geometry, University of Munster

4. Spring 2025, Riemannian geometry, EPFL

Mini-courses

1. Hawking's Singularity Theorem, 15th Panhellenic Geometry Conference, University of Ioannina, Greece.                                            You can download the Lecture Notes and Slides.

2. Riemannian Penrose Inequality, Variational Problems in Geometric analysis & General Relativity, University of Ioannina, Greece.      You can download the Slides.