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Hire Dr. Jack B.

France

Mathematician | Geometric Analysis, PDEs, and Mathematical Physics

Profile Summary

I am a mathematician specialising in differential geometry, partial differential equations, and mathematical physics. My work explores the deep connections between geometry and analysis, with applications ranging from Lorentzian and Cartan geometries to asymptotic methods in general relativity and field theory. I have published around 15 peer-reviewed papers in leading journals such as Annales de l’Institut Fourier, Nonlinearity, Classical and Quantum Gravity, and Transactions of the AMS. My experience spans advanced analytical techniques and a broad range of problems including inverse problems as well as conceptual frameworks in theoretical physics, allowing me to bridge rigorous mathematics with physical intuition. On Kolabtree, I offer collaboration and consulting on projects involving complex differential equations, geometric modelling, and theoretical frameworks in physics or engineering. I’m also available for scientific writing, editing, and peer-review support for research papers and grant proposals. My approach combines clarity, precision, and conceptual insight, with a focus on delivering high-quality, well-structured work tailored to both academic and applied contexts.

Subject Matter Expertise

• ★ Mathematical Physics
• ★ Differential Equations
• ★ Geometry
• ☆ Particle Physics
• ☆ Quantum Mechanics
• ☆ Relativity Theory
• ☆ Applied Mathematics
• ☆ Group Theory
• ☆ Pure Mathematics
• ☆ Algebra
• ☆ Calculus
• ☆ Mathematical Analysis
• ☆ Topology
• ☆ Integral Equations

Services

• Writing
• Research

Writing Technical Writing, Creative Writing, Audio Transcription, General Proofreading & Editing, Translation

Research Fact Checking, Scientific and Technical Research, Systematic Literature Review

Work Experience

Maître de conférences

Université Paris Cité

September 2025 - Present

Post-doctorant

McGill University

January 2023 - August 2025

Post-doctorat

Université Bourgogne Franche-Comté

September 2021 - December 2022

ATER

Université de Bretagne Occidentale

October 2020 - August 2021

Education

PhD (Mathematics)

Université de Bretagne Occidentale

October 2017 - July 2021

Diplôme d'ingénieur

École centrale de lille

September 2012 - September 2016

M.Sc (Master of Science)

Lunds Universitet

August 2014 - June 2016

Certifications

• Certification details not provided.

Publications

JOURNAL ARTICLE

Jack Borthwick, Maël Chantreau, Yannick Herfray (2025). Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity . Classical and Quantum Gravity.

Jack Borthwick, Eric Gourgoulhon, Jean-Philippe Nicolas (2025). Peeling at extreme black hole horizons . Journal of Hyperbolic Differential Equations.

Jack Borthwick, Yannick Herfray (2025). Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds . Geometriae Dedicata.

Borthwick, Jack, Herfray, Yannick (2025). Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds . Geometriae Dedicata.

Jack Borthwick, Niky Kamran (2024). Boundary Rigidity, and Non-Rigidity, of Projective Structures . The Journal of Geometric Analysis.

Jack Borthwick, Yannick Herfray (2024). Asymptotic symmetries of projectively compact order one Einstein manifolds . Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

Borthwick, Jack, Chang, Xiaojun, Jeanjean, Louis, Soave, Nicola (2024). BOUNDED PALAIS-SMALE SEQUENCES WITH MORSE TYPE INFORMATION FOR SOME CONSTRAINED FUNCTIONALS . Transactions of the American Mathematical Society.

Borthwick, Jack, Chang, Xiaojun, Jeanjean, Louis, Soave, Nicola (2024). BOUNDED PALAIS-SMALE SEQUENCES WITH MORSE TYPE INFORMATION FOR SOME CONSTRAINED FUNCTIONALS . Transactions of the American Mathematical Society.

Jack Borthwick, Xiaojun Chang, Louis Jeanjean, Nicola Soave (2023). Normalized solutions of L 2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities . Nonlinearity.

Jack A. Borthwick(2023). Scattering theory for Dirac fields near an extreme Kerr–de Sitter black hole . Annales de l'Institut Fourier. 73. (3). p. 919--997. Cellule {MathDoc}/{CEDRAM}

Borthwick, Jack A. (2023). Scattering theory for Dirac fields near an extreme Kerr-de Sitter black hole . Annales de l'Institut Fourier.

Jack Borthwick, Nabile Boussaïd, Thierry Daudé(2023). Inverse Regge poles problem on a warped ball . Inverse Problems and Imaging. 0. (0). p. 0--0. American Institute of Mathematical Sciences ({AIMS})

Borthwick, Jack, Gourgoulhon, Eric, Nicolas, Jean-Philippe (2023). Peeling at extreme black hole horizons . ArXiv.

Borthwick, Jack, Kamran, Niky (2023). Boundary rigidity, and non-rigidity, of projective structures . ArXiv.

Borthwick, Jack, Chang, Xiaojun, Jeanjean, Louis, Soave, Nicola (2023). Normalized solutions of <i>L</i> <SUP>2</SUP>-supercritical NLS equations on noncompact metric graphs with localized nonlinearities . Nonlinearity.

Corrigendum: Maximal Kerr–de Sitter spacetimes (2018 Class. Quantum Grav. 35 215006) <head> <META HTTP-EQUIV="Refresh" CONTENT="0;URL=/servlet/useragent"> </head> . Classical and Quantum Gravity.

Borthwick, Jack A (2022). Projective differential geometry and asymptotic analysis in General Relativity . ArXiv.

Borthwick, Jack, Chang, Xiaojun, Jeanjean, Louis, Soave, Nicola (2022). Normalized solutions of <italic>L</italic>²-supercritical NLS equations on noncompact metric graphs with localized nonlinearities . ArXiv.

Borthwick, Jack (2022). Maximal Kerr-de Sitter spacetimes (vol 35, 215006, 2018) . Classical and Quantum Gravity.

Borthwick, Jack A (2022). Projective differential geometry and asymptotic analysis in General Relativity . ArXiv.

Borthwick, Jack, Boussaid, Nabile, Daude, Thierry (2022). Inverse Regge poles problem on a warped ball . ArXiv.

Borthwick, Jack, Chang, Xiaojun, Jeanjean, Louis, Soave, Nicola (2022). Normalized solutions of <italic>L</italic>²-supercritical NLS equations on noncompact metric graphs with localized nonlinearities . ArXiv.

Jack Borthwick(2018). Maximal Kerr–de Sitter spacetimes . Classical and Quantum Gravity. 35. (21). p. 215006. {IOP} Publishing

Borthwick, Jack (2018). Maximal Kerr-de Sitter spacetimes . Classical and Quantum Gravity.

WORKING PAPER

Jack Borthwick, Eric Gourgoulhon, Jean-Philippe Nicolas(2023). Peeling at extreme black hole horizons . arXiv

Jack Borthwick, Niky Kamran(2023). Boundary rigidity, and non-rigidity, of projective structures . arXiv

Bounded Palais-Smale sequences with Morse type information for some constrained functionals @unpublished{borthwick:hal-03850019, TITLE = {{Bounded Palais-Smale sequences with Morse type information for some constrained functionals}}, AUTHOR = {Borthwick, Jack and Chang, Xiaojun and Jeanjean, Louis and Soave, Nicola}, URL = {https://hal.archives-ouvertes.fr/hal-03850019}, NOTE = {working paper or preprint}, YEAR = {2022}, MONTH = Nov, HAL_ID = {hal-03850019}, HAL_VERSION = {v1}, } .

Inverse Regge poles problem on a warped ball @unpublished{borthwick:hal-03622618, TITLE = {{Inverse Regge poles problem on a warped ball}}, AUTHOR = {Borthwick, Jack and Boussa{\"i}d, Nabile and Daud{\'e}, Thierry}, URL = {https://hal.archives-ouvertes.fr/hal-03622618}, NOTE = {working paper or preprint}, YEAR = {2022}, MONTH = Mar, HAL_ID = {hal-03622618}, HAL_VERSION = {v1}, } .

Projective differential geometry and Asymptotic Analysis in General Relativity @unpublished{borthwick:hal-03598907, TITLE = {{Projective differential geometry and Asymptotic Analysis in General Relativity}}, AUTHOR = {Borthwick, Jack}, URL = {https://hal.archives-ouvertes.fr/hal-03598907}, NOTE = {working paper or preprint}, YEAR = {2022}, MONTH = Mar, KEYWORDS = {Projective differential geometry ; tractor calculus ; projective compactifications}, PDF = {https://hal.archives-ouvertes.fr/hal-03598907/file/bmf_proj.pdf}, HAL_ID = {hal-03598907}, HAL_VERSION = {v1}, } .

DISSERTATION THESIS

Analytical and projective scattering on spacetimes with positive cosmological constant @phdthesis{borthwick:tel-03652254, TITLE = {{Analytical and projective scattering on spacetimes with positive cosmological constant}}, AUTHOR = {Borthwick, Jack}, URL = {https://tel.archives-ouvertes.fr/tel-03652254}, NUMBER = {2021BRES0055}, SCHOOL = {{Universit{\'e} de Bretagne occidentale - Brest}}, YEAR = {2021}, MONTH = Jul, KEYWORDS = {Projective exterior tractor calculus ; Asymptotic analysis ; Extreme Kerr-de Sitter black hole ; Dirac {\'e}quation ; Projective compactification ; Proca {\'e}quation ; Analyse asymptotique ; Trous noirs Kerr-de Sitter extr{\^e}me ; {\'E}quation de Dirac ; Com-pactifications projectives ; {\'E}quation de Proca ; Calcul ext{\'e}rieur pour les tracteurs projectifs}, TYPE = {Theses}, PDF = {https://tel.archives-ouvertes.fr/tel-03652254/file/These-2021-MATHSTIC-Mathematiques_et_leurs_interactions-BORTHWICK_Jack.pdf}, HAL_ID = {tel-03652254}, HAL_VERSION = {v1}, } .