Martin Taylor

Research interests

Partial differential equations, general relativity, kinetic theory.

Conferences

• I co-organised a Münster--Imperial Day in PDE with Gustav Holzegel and Christian Seis.  The event place at the University of Münster on 8th October 2024.
  
• I co-organised a workshop and summer school on Nonlinear Waves and Fluids with Mahir Hadžić and Arick Shao. The workshop took place at University College London from 24--27th June 2024.
  

Seminars

I am a co-organiser of:

• London PDE seminar;
• London analysis and probability seminar.
  

Publications

• Quasilinear wave equations on Kerr black holes in the full subextremal range |a|<M (with M. Dafermos, G. Holzegel, I. Rodnianski), 99 pages;
• Inverse modified scattering and polyhomogeneous expansions for the Vlasov--Poisson system (with V. Schlue), 48 pages;
  
• Future stability of expanding spatially homogeneous FLRW solutions of the spherically symmetric Einstein--massless Vlasov system with spatial topology R$$³, J. Math. Phys. 65, no. 2 (2024), 22 pages;
  
• Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes (with M. Dafermos, G. Holzegel, I. Rodnianski), 99 pages;
• Lectures on the nonlinear stability of the Schwarzschild family of black holes, 46 pages;
  
• The nonlinear stability of the Schwarzschild family of black holes (with M. Dafermos, G. Holzegel, I. Rodnianski), 513 pages;
• The nonlinear stability of the Schwarzschild family of black holes, Oberwolfach Reports, Vol. 15, Issue 3 (2018), 2157--2251;
  
• Global stability of Minkowski space for the Einstein--Vlasov system in the harmonic gauge (with H. Lindblad), Arch. Ration. Mech. Anal. 235 (2020) 517--633;
• The global nonlinear stability of Minkowski space for the massless Einstein--Vlasov system, Ann. PDE 3:9 (2017), 177 pages;
• Packing twelve spherical caps to maximize tangencies (with L. Flatley, F. Theil and A. Tarasov), JCAM 254:220--225 (2013).  (See also the webpage).

Lecture notes

• I gave a mini course on the nonlinear stability of the Schwarzschild family of black holes in April 2022 as part of the General Relativity Program at the Center of Mathematical Sciences and Applications, Harvard University.  Lecture notes are available here.  Recordings of the lectures are available online: Lecture 1, Lecture 2, Lecture 3, Lecture 4.
  
• I have lectured the Riemannian geometry course at Imperial College London several times.  Lecture notes are available here.
  

Talks

• Singularities in fluids and general relativity, Workshop on black holes, naked singularities, shocks and implosions, National University of Singapore, 6--10th January 2025;
  
• Analysis seminar, Stony Brook University, 13th December 2024;
  
• Advances in PDEs in Physics and Materials Science, University of Crete, 29--31st May 2024;
  
• General relativity and PDE seminar, University of Leipzig, 10th May 2024;
  
• Analysis seminar, University of Edinburgh, 24th January 2024;
  
• Universe community seminar, Imperial College London, 16th January 2024;
• Analysis seminar, Stony Brook University, 12th December 2023;
  
• Nonlinear aspects of general relativity workshop, Princeton Center for Theoretical Astrophysics, Princeton University, 10--13th October 2023;
  
• Hyperbolic PDEs and nonlinear evolution problems workshop, MATRIX, Mathematics Research Institute, University of Melbourne, 18--29th September 2023;
• Singularities and patterns in evolution equations workshop, University of Bath, 4--8th September 2023;
  
• Department of mathematics and applied mathematics colloquium, University of Crete, 3rd May 2023;
  
• Kings and Queens of gravity workshop, King's College London and Queen Mary University of London, 29--31st March 2023;
  
• PDE and applied math seminar, UC Davis, (online), 9th February 2023;
  
• Department of mathematics colloquium, Stony Brook University, 15th December 2022;
  
• International conference on geometric analysis and hyperbolic equations, Guangxi Center for Mathematical Research, Nanning, (online), 10--17th December 2022;
• London geometry and topology seminar, Imperial College London, 18th November 2022;
  
• Analysis seminar, University of Leeds, 16th November 2022;
  
• Topics in general relativity seminar, University of Münster, 3rd May 2022;
  
• PDE seminar, Penn State University, 13th April 2022;
  
• General relativity conference, Center of Mathematical Sciences and Applications, Harvard University, 4--8th April 2022;
  
• Aspects of gravity, mathematics and physics, École Polytechnique, Paris, 21--22nd March 2022;
• Mathematical perspectives of gravitation beyond the vacuum regime, Erwin Schrödinger Institute, Vienna, 14--18th February 2022;
  
• Frontiers in analysis of kinetic equations, Isaac Newton Institute, Cambridge, 10--14th January 2022;
  
• Mathematical and numerical aspects of gravitation, IPAM, University of California Los Angeles, 25--29th October 2021;
  
• Brussels, Oxford, Warwick, London (B.O.W.L.) online geometry seminar, 5th October 2021;
  
• Mathematical physics research group seminar, Rutgers University, 30th September 2021;
  
• Mathematical general relativity and hyperbolic PDE seminar, (online), 20th August 2021;
  
• Relativity seminar, University of Oxford, 1st June 2021;
  
• Black Hole Initiative colloquium, Harvard University, 20th April 2021;
• International conference on geometric analysis and hyperbolic equations, Guangxi Center for Mathematical Research, Nanning, 16--20th December 2019;
• Gravity seminar, University of Southampton, 28th November 2019;
• London analysis and probability seminar, University College London, 10th October 2019;
• Institut Mittag-Leffler Seminar, Stockholm, 3rd October 2019;
• MAFRAN Days, University of Cambridge, 1--5th July 2019;
• Pure mathematics seminar, University of Melbourne, 24th May 2019;
• General relativity and geometric analysis seminar, Columbia University, New York, 26th April 2019;
• Analysis and PDE seminar, UC Berkeley, 22nd April 2019;
• Geometry seminar, Stanford University, 17th April 2019;
• The Gravity Initiative inaugural meeting, Princeton University, 6--8th March 2019;
• 9th Central European Relativity Seminar, Kraków, 14--16th February 2019;
• Analysis and PDE seminar, University of Kentucky, 20th November 2018;
• Gravity Initiative lunch, Princeton University, 1st October 2018;
• Mathematical general relativity, Mathematisches Forschungsinstitut Oberwolfach, 5--11th August 2018;
• UK network on hyperbolic equations and related topics, University of Edinburgh, 27th April 2018;
• Recent trends in PDE, King's College London, 8--11th January 2018;
• DAMTP Friday GR seminar, University of Cambridge, 24th November 2017;
• Partial differential equations seminar, Instituto Superior Técnico, Lisbon, 2nd November 2017;
• MAFRAN Days, University of Cambridge, 25--27th September 2017;
• Analysis and PDE seminar, Johns Hopkins University, Baltimore, 28th August 2017;
• Analysis and applied mathematics seminar, University of Toronto, 23rd August 2017;
• Geometric transport equations in general relativity, Erwin Schrödinger Institute, Vienna, 20--24th February 2017;
• Séminaire de physique-mathématique, Institut Fourier, Grenoble, 14th November 2016;
• Geometry and analysis seminar, Queen Mary University of London, 27th September 2016;
• Analysis seminar, Princeton University, 18th April 2016;
• Analysis seminar, UPenn, Philadelphia, 12th April 2016;
• Analysis and PDE seminar, Johns Hopkins University, Baltimore, 4th April 2016;
• Relativity seminar, Universität Wien, Vienna, 17th December 2015;
• PDE CDT lunchtime seminar, University of Oxford, 15th October 2015;
• Weekly seminar on general relativity, Institut Henri Poincaré, Paris, 7th October 2015;
• Recent progress in collisionless models, Imperial College London, 7--11th September 2015;
• Pure analysis and PDE seminar, Imperial College London, 8th May 2015;
• Geometric analysis seminar, Imperial College London, 7th May 2015.

Recorded talks

• The nonlinear stability of the Schwarzschild family of black holes, Black Hole Initiative Colloquium, Harvard University, 20th April 2021.

Email

martin.taylor [at] imperial.ac.uk.