Website of Athanasios Chatzikaleas

1. 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:

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

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

2. Publications and Preprints

• 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

• 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

• 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

• 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

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

• 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

• 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

• 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

3. Collaborators

• Jacques Smulevici, Sorbonne Université (Pierre et Marie Curie)

• Arick Shao, Queen Mary University

4. Short CV

5. Downloads

• Curriculum vitae 

• Research Statement

• PhD Thesis (University of Bonn)

• Master Thesis (University of Crete) 

6. Organization of Conferences and Winter/Summer Schools

• Ioannina Winter School 2024: Geometric analysis & General Relativity
  Co-organizer together with Andreas Savas-Halilaj and Konstantinos Zemas
  December 16th, 2024 - December 20th, 2024
  University of Ioannina, Greece

• Ioannina Winter School 2025: Geometric analysis & General Relativity
  Co-organizer together with Andreas Savas-Halilaj and Konstantinos Zemas
  December 8th, 2025 - December 12th, 2025
  University of Ioannina, Greece

• Workshop and Summer School in Geometric Analysis
  Co-organizer together with Grigorios Fournodavlos and Andreas Savas-Halilaj
  August 31,2026 - September 4, 2026
  University of Ioannina, Greece

• Ioannina Winter School 2026: Geometric analysis & General Relativity
  Co-organizer together with Andreas Savas-Halilaj and Konstantinos Zemas
  December 14th, 2026 - December 18th, 2026
  University of Ioannina, Greece

7. The Ioannina Winter School 

8. Teaching

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

• Fall 2022, Non-linear Wave Equations, University of Muenster

• Fall 2023, Differential Geometry, University of Muenster

• Spring 2025, Riemannian Geometry, EPFL

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

• Fall 2025, Geometric Analysis, National and Kapodistrian University of Athens  

• Spring 2026, Complex Analysis 1, National and Kapodistrian University of Athens

9. Lecture Notes

• Lecture Notes on "Geometric Analysis", in Greek, 280 pages

• Lecture Notes on "Complex Analysis", in Greek, 466 pages

10. 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).