Homepage of Dr. Athanasios Chatzikaleas

Research Interests

I am interested in Mathematical General Relativity, with a particular focus on the Anti-de Sitter solution of the Einstein equations. My research centers on two main 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) 

The Ioannina Winter School

I have the great pleasure of co-organizing the Ioannina Winter School together with my dear friends Andreas Savas-Halilaj (University of Ioannina, Greece) and Konstantinos Zemas (University of Bonn, Germany). The school is an annual event that brings together students and researchers from across Greece to meet in Ioannina and explore exciting topics in Geometric Analysis and General Relativity. 

At the school, we offer mini-courses designed to provide students and participants with in-depth introductions to cutting-edge results in the field. However, the program is not just about lectures: these mini-courses on campus are mainly there to kick off the discussions. A big part of the experience happens outside the classroom (by the lake in Ioannina or on walks through the nearby villages of Zagorochoria) where we continue our mathematical conversations in a more informal setting. 

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 Muenster

4. Spring 2025, Riemannian Geometry, EPFL

5. Fall 2025, Foundations of Mathematical Analysis, National and Kapodistrian University of Athens

6. Fall 2025, Geometric Analysis, National and Kapodistrian University of Athens
   You can download the Lecture Notes (in Greek, updated version: November 2025).
   
   

You can download the Exam Sheet and Solutions (both in Greek) for the undergraduate course "Complex Analysis 1" for the supplementary examination period on 21/11/2025.

Seminars on 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).