Maxime Van de Moortel

I am an Assistant Professor (tenure-track) in the Mathematics departement at Rutgers University. I am originally from France.

My research is currently supported by the NSF Grant DMS-2247376.

Vita:
  • Curriculum Vitae (last update: January 2024)
  • Google Scholar

    • Mailing Address:
    Rutgers University
    Department of Mathematics
    Hill Center - Busch Campus
    110 Frelinghuysen Road
    Piscataway, NJ 08854-8019, USA
    USA

    Office: Hill Center 432
    E-mail: maxime.vandemoortel AT rutgers DOT edu

    Research Interests: Partial Differential Equations, General Relativity, Mathematical Physics

  • Most of my research concerns the analysis of the black hole interior -- namely the region beyond the event horizon -- which is closely linked to the Strong Cosmic Censorship Conjecture. The PDE aspect of this conjecture involves nonlinear dispersive estimates and finite-time singularity formation, together with connections to Lorentzian Geometry.
  • I have worked on establishing late-time asymptotics for wave-type equations on the black hole exterior, a question of independent interest also motivated by the aforementioned problems in the black hole interior. Lately, I have been particularly interested in the asymptotics of the Klein--Gordon equation on a black hole.
  • I am also interested in low-regularity solutions for quasilinear wave equations and related questions in General Relativity such as the interaction of impulsive gravitational waves.

    • Publications:

    1. (With Dejan Gajic) Late-time tails for scale-invariant wave equations with a potential and the near-horizon geometry of null infinity, preprint (29pp)

    2. (With Yakov Shlapentokh-Rothman) Polynomial time decay for solutions of the Klein-Gordon equation on a subextremal Reissner-Nordström black hole, preprint (76pp)

    3. (With Federico Pasqualotto & Yakov Shlapentokh-Rothman) The asymptotics of massive fields on stationary spherically symmetric black holes for all angular momenta, preprint (41pp)

    4. (With Warren Li) Kasner inversions and fluctuating collapse inside hairy black holes with charged matter, preprint (100pp)

    5. Violent nonlinear collapse in the interior of charged hairy black holes, preprint (38pp)

    6. (With Jonathan Luk) Nonlinear interaction of three impulsive gravitational waves II: The wave estimates, Annals of PDE, 9:10, 2023.

    7. (With Christoph Kehle) The null contraction singularity at the Cauchy horizon of dynamical black holes, in preparation.

    8. (With Christoph Kehle) Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry, preprint (79pp) To appear in Analysis & PDE.

    9. (With Jonathan Luk) Nonlinear interaction of three impulsive gravitational waves I: Main result and the geometric estimates, preprint (79pp)

    10. Mass inflation and the C2-inextendibility of spherically symmetric charged scalar field dynamical black holes, Commun. Math. Phys., 382, 1263–1341, 2021.

    11. The breakdown of weak null singularities inside black holes, Duke Mathematical Journal, 172 (15), 2957-3012, 2023.

    12. Charged scalar fields on black hole space-times. Ph.D. Thesis, University of Cambridge, 2019.

    13. Decay of weakly charged solutions for the spherically symmetric Maxwell-Charged-Scalar-Field equations on a Reissner-Nordström exterior space-time, Ann. Sci. Éc. Norm. Supér., 55. no. 2, 283–404, 2022.

    14. Stability and instability of the sub-extremal Reissner-Nordström black hole interior for the Einstein-Maxwell-Klein-Gordon equations in spherical symmetry, Commun. Math. Phys., 360, 103–168, 2018.

    Expository:

    The breakdown of weak null singularities inside black holes, Oberwolfach Report, pages 2252-2255.

    PhD students:

  • Weihao Zheng: 2022-present.

    • I am currently looking for motivated PhD students. If you are interested in working in Hyperbolic PDEs/General Relativity, and are already admitted to the graduate program at Rutgers University, feel free to reach out.

    Hyperbolic & Dispersive PDE Seminar:

    With Avy Soffer, I organize the weekly Hyperbolic & Dispersive PDE Seminar at Rutgers University, every Thursday from 3:50 pm to 4:50 pm in Hill 705.

    Please visit the seminar website here.

    Joint Princeton-Rutgers Seminar on Analysis of Fluids:

    With Alexandru Ionescu, YanYan Li, Zheng-Chao Han and Dennis Kriventsov, we organize the bi-semesterly Joint Princeton-Rutgers Seminar on Analysis of Fluids.

    Conference Talks:

  • May 2024: 126th Statistical Mechanics Conference, Plenary Speaker, Rutgers University.
  • October 2023: Workshop on Nonlinear Aspects of General Relativity, Princeton University.
  • June 2023: Singularities and Curvature in General Relativity, Radboud University, Nijmegen, Netherlands.
  • May 2023: Singularity formation in general relativity and dispersive PDEs', ICMS, Edinburgh, UK.
  • May 2023: 124th Statistical Mechanics Conference, Rutgers University.
  • July 2022: 23rd International Conference on General Relativity and Gravitation, GR23, Beijing, China.
  • May 2022: Black Hole Initiative Conference, "Beyond the Horizon", Harvard University.
  • April 2022: General Relativity Program Conference, CMSA, Harvard University.
  • August 2021: Mathematical aspects of General Relativity, Oberwolfach Workshop.
  • March 2021: AMS Sectional Meeting, Brown University (online).
  • June 2020: Conference on Mathematical General Relativity, Institut Henri Poincaré (postposned due to Covid 19).
  • September 2019: AMS Sectional Meeting, University of Wisconsin-Madison.
  • April 2018: AMS Sectional Meeting, Portland State University.
  • March 2018: OxBridge PDE Conference, University of Cambridge.
  • April 2017: ICMS joint CDT Colloquium, University of Edinburgh.

    • Seminars:

  • April 2024: Analysis and PDE Seminar, Stanford University.
  • March 2024: PDE Seminar, Brown University.
  • February 2024: Analysis and PDE Seminar, Yale University.
  • December 2023: High Energy Theory Seminar, Mitchell Institute, Texas A&M University.
  • June 2023: PDE Seminar, University of Crete, Heraklion.
  • April 2023: PDE Seminar, Brown University.
  • March 2023: Analysis Seminar, PennState.
  • January 2023: Mathematical Physics Seminar, Rutgers University.
  • January 2023: Math-Phys Research Group Online Seminar, Rutgers University.
  • August 2022: Center for Gravitation and Cosmology Seminar, Yangzhou University.
  • May 2022: Partial Differential Equations CDT seminar, University of Oxford.
  • April 2022: PDE seminar, University of Minnesota.
  • March 2022: Analysis and Partial Differential Equations Seminar, John Hopkins University.
  • March 2022: Analysis and PDE Seminar, University of Kentucky.
  • February 2022: Gravity Seminar, University of Southampton.
  • February 2022: Colloquium, Department of Mathematics, Oregon State University.
  • January 2022: Colloquium, Department of Mathematics, Vanderbilt University.
  • December 2021: Special Colloquium, Rutgers University.
  • December 2021: VandyGRAF Colloquium, Vanderbilt University.
  • December 2021: General Relativity & Geometric Analysis seminar, Columbia University.
  • February 2021: Pure Analysis and PDEs seminar, joint Imperial College London/ University College London.
  • January 2021: Analysis and PDE Seminar, Stanford.
  • January 2021: Séminaire Analyse et EDP, Cergy-Pontoise University.
  • December 2020: Mathematical GR and Hyperbolic PDE Seminar (online).
  • November 2020: Junior GR Seminar, Princeton University.
  • October 2020: Analysis seminar, Caltech.
  • October 2020: Analysis and PDE seminar, UC Berkeley.
  • April 2020: PDE seminar, Brown University.
  • March 2020: Gravity initiative seminar, Princeton University.
  • October 2019: Mathematical Physics seminar, Rutgers University.
  • November 2018: Cambridge Center for Analysis Seminar, University of Cambridge.
  • November 2018: Junior Analysis Seminar, Imperial College London.
  • November 2018: DAMTP Friday General Relativity Seminar, University of Cambridge.
  • October 2018: Analysis Seminar, Princeton University.
  • September 2018: Mathematical Relativity Seminar, Instituto Superior Tecnico, Universidade de Lisboa.
  • March 2018: Seminar on General Relativity, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie.
  • May 2017: Student analysis seminar, Stanford University.

    • Talks available online:

  • Across the horizon and beyond: the interior of dynamical black holes. 23rd International Conference on General Relativity and Gravitation, July 2022.
  • Black holes: the inside story of gravitational collapse. General Relativity CMSA Conference, Harvard University, April 2022.
  • The breakdown of weak null singularities inside black holes. Oberwolfach, September 2021.
  • Local existence for the ternary interaction of impulsive gravitational waves. Stanford, January 2021.

    • Teaching:

  • Spring term 2024: Course head and instructor for 16:640:507, Selected topics in Analysis (graduate), at Rutgers University.
  • Fall term 2023: Course instructor for 01:640:251, Multivariable Calculus, at Rutgers University.
  • Spring term 2023: Course instructor for 01:640:477, Mathematical Theory of Probability, at Rutgers University.
  • Fall term 2022: Course head and instructor for 16:640:507, Functional Analysis (graduate), at Rutgers University.
  • Spring term 2022: Course head and instructor for Math104, Calculus II, at Princeton University.
  • Fall term 2021: Course head and instructor for Math425, Analysis III: Integration Theory and Hilbert Spaces, at Princeton University.
  • Spring term 2021: Course head and instructor for Math104, Calculus II, at Princeton University.
  • Fall term 2020: Course instructor for Math104, Calculus II, at Princeton University.
  • Spring term 2020: Course head and instructor for Math429, Topics in Analysis: Distribution Theory, PDE & Basic Inequalities of Analysis, at Princeton University.
  • Fall term 2019: Course instructor for Math201, Multivariable Calculus, at Princeton University.
  • Michaelmas (Fall) term 2018: Course supervisor for the Part II class Probability and Measure, at the University of Cambridge.
  • Summer 2015: Teaching assistant, at Schiller University, Paris campus.

    • Positions:

  • September 2022-Present: Assistant Professor, Rutgers University, New Brunswick, United States.
  • September 2019-August 2022: Instructor, Princeton University, Princeton, United States.
  • May 2019-August 2019: Research Associate, Imperial College London, London, United Kingdom.

    • Education:

  • Ph.D. in Mathematics (2019): University of Cambridge.
  • MSc in Engineering (2016): CentraleSupélec.
  • Master 1 in Pure and Applied Mathematics (2015): Université Paris-Saclay.
  • BSc in Pure and Applied Mathematics (2014): Université Paris-Saclay.

    • Awards:

  • July 2023: National Science Foundation Grant DMS-2247376.
  • May 2022: Research Fellowship of the Royal Commission for the Exhibition of 1851 (declined).
  • September 2015-September 2019: EPSRC Ph.D. scholarship.
  • January 2017: Smith-Knight & Rayleigh-Knight Ph.D. dissertation prize.
  • July 2015: Centrale talents, awarded to the best students of CentraleSupélec for exceptional achievements.

    • Outreach Activities:

  • I volunteer in Clubes de Ciencia, a non-profit outreach association providing week-long workshops in STEM to local high-school students across Latin America, led by US-based instructors. I have designed a 40h intensive course intended as a first exposure to General Relativity: Gravity: from Newton’s Apple to the frontier of Black Holes. The course was first given from August 6th to August 12th 2023 in Oaxaca, Mexico.

    I have also given outreach talks to various audiences over the years:

  • August 2022: “Mathematical Analysis and black holes: the inside story", Research Glimpse Talks, Rutgers University.
  • April 2021: “The world according to Partial Differential Equations”, Propective Maths Major Talks, Princeton University.
  • February 2017: “An overview of mathematical general relativity: how wave equations enlighten the theory of Black Holes”, Kiddie Colloquium, Stanford University.
  • April 2016: “Space-time, waves and black holes: how determinism in General Relativity can be addressed by the theory of wave equations”, Research days talk at Robinson College, University of Cambridge.
  • September 2015: “Why should you love Maths?”, talk given at Notre-Dame high-school, Mantes-la-Jolie, France.
  • August 2015: “Why should you love Maths?”, talk given at Schiller University, Paris.