Research

Broadly, I am interested in partial differential equations arising in mathematical physics. I am particularly interested in nonlinear wave equations, the geometry and physics of asymptotic structures of spacetimes and fields, scattering theory, the structure of (null, spacelike, timelike) infinity, and the regularity properties of fields arising in general relativity.

Publications

Papers

1. G. Taujanskas
   Wave map null form estimates via Peter–Weyl theory
   Submitted (2023) [arXiv].
2. G. Taujanskas, J. A. Valiente Kroon
   Controlled regularity at future null infinity from past asymptotic initial data: massless fields
   Submitted (2023) [arXiv].
3. J.-P. Nicolas, G. Taujanskas
   Conformal scattering of Maxwell potentials
   To appear in Ann. Inst. Fourier [arXiv].
4. G. Taujanskas
   Large data decay of Yang–Mills–Higgs fields on Minkowski and de Sitter spacetimes
   J. Math. Phys. 60 (12), pp. 121504 (2019) [arXiv] [Journal].
5. G. Taujanskas
   Conformal scattering of the Maxwell-scalar field system on de Sitter space
   J. Hyperbolic Differ. Equ. 16 (04), pp. 743-791 (2019) [arXiv] [Journal].

Proceedings

1. G. Taujanskas, J. A. Valiente Kroon
   Introduction: At the interface of asymptotics, conformal methods, and analysis in general relativity
   Phil. Trans. R. Soc. A 382: 20230048 (2024) [Journal].
   
2. G. Taujanskas
   Scattering of Maxwell potentials on curved spacetimes
   Ghent Methusalem Colloquium: Extended Abstracts 2021/2022, pp. 57-64 (2024) [arXiv] [Journal].

Edited Volumes

1. At the interface of asymptotics, conformal methods and analysis in general relativity
   Edited by G. Taujanskas and J. A. Valiente Kroon
   Phil. Trans. R. Soc. A 382 (2267) (2024) [Journal].
   Proceedings for the conference of the same title, which took place at the Royal Society in London on 9–10 May 2023. Contributors: J. Borthwick, H. Friedrich, E. Gasperin, Y. Herfray, P. Hintz, L. Kehrberger, M. Mars, M. Minucci, M. M. A. Mohamed, J.-P. Nicolas, R. Panosso Macedo, R. Penrose, G. Taujanskas, P. Tod, J. A. Valiente Kroon

PhD Thesis

• Conformal scattering and analysis of asymptotic properties of gauge theories in general relativity
  Oxford University Research Archive (2020) [ORA].

Some Notes

• Kähler manifolds and the Calabi conjecture.
• The Ward correspondence and stationary axisymmetric spacetimes.

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