Grigorios Fournodavlos

I am an Assistant Professor in the Department of Mathematics & Applied Mathematics at the University of Crete. I am also a member of the Institute for Applied and Computational Mathematics at FORTH, and a member of the Crete Center for Therotical Physics.

Mailing Address:
Department of Mathematics & Applied Mathematics
University of Crete
Voutes Campus, 70013 Heraklion
GREECE

Office: E-314
E-mail: gfournodavlos AT uoc DOT gr
Timios Stavros

Research Interests

Analysis, partial differential equations, differential geometry. More specifically, I am interested in the mathematical analysis of differential equations with a geometric background, like the Einstein equations in the context of the classical theory of general relativity. One of my main goals is to understand the nature of singularities that are typically found in the interior of black holes or at the Big Bang.

Project SINGinGR

In 2022, I received funding (ERC starting grant) from the European Research Council to support my research program.

PhD and postdoc positions are currently available. Interested candidates can apply by sending me their CV.

Scientific Events

Aspects of Cosmology, Mathematics and Physics, 25 – 27 September, 2024.

Mathematics of General Relativity and Fluids, SLMath Summer School hosted at FORTH, 22 July – 2 August, 2024. (See here for the local website and program.)

Modern Trends in Gravity and Black Holes, 17 – 22 June, 2024.

PDE in Physics and Materials Science, 29 – 31 May, 2024.

Cretan Waves, a workshop in geometric hyperbolic PDE, 9 – 13 October, 2023.

Public talk by Mihalis Dafermos on the course of determinism in classical physics (in Greek), 17 May, 2023. online video.

Teaching

This semester I am teaching Calculus III. For past teaching see here.

Seminars

I am an organizer of the Joint online Mathematical Relativity Colloquium (JoMaReC). To receive notifications for upcoming colloquia, you are invited to subscribe to our newsletter.

Seminar of Differential Equations and Numerical Analysis at the Department of Mathematics & Applied Mathematics. If you wish to give a talk, please send me an email.

Preprints and Publications

  1. (with Volker Schlue) Stability of the expanding region of Kerr de Sitter spacetimes, arXiv:2408.02596
  2. (with Elliot Marshall and Todd A. Oliynyk) Future stability of perfect fluids with extreme tilt and linear equation of state p=c2sr for the Einstein-Euler system with positive cosmological constant: The range 1/3 < c2s < 3/7, arXiv:2404.06789
  3. (with Spyros Alexakis) Stable space-like singularity formation for axi-symmetric and polarized near-Schwarzschild black hole interiors, arXiv:2004.00692
  4. (with Jacques Smulevici) On the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, arXiv:1912.07338
  5. (with Vassili Nestoridis and Spyros Pasias) A logarithmic characterization of Arakelian sets, Lobachevskii J. Math. 45 (2024), Issue 8, 3522-3528. pdf
  6. (with Jonathan Luk) Asymptotically Kasner-like singularities, Amer. J. Math. 145 (2023), no. 4, 1183-1272 pdf
  7. (with Igor Rodnianski and Jared Speck) Stable Big Bang formation for Einstein's equations: The complete sub-critical regime, J. Amer. Math. Soc. 36 (2023), 827-916. pdf
  8. (with Jacques Smulevici) The initial boundary value problem in General Relativity: the umbilic case, Int. Math. Res. Not. 2023 (2023), Issue 5, 3790-3807. pdf
  9. Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant, J. Math. Phys. 63 (2022), no. 3, 032502, 23pp. pdf
  10. (with Jacques Smulevici) The initial boundary value problem for the Einstein equations with totally geodesic boundary, Comm. Math. Phys. 385 (2021), no. 3, 1615-1653. pdf
  11. (with Jan Sbierski) Generic blow-up results for the wave equation in the interior of a Schwarzschild black hole, Arch. Ration. Mech. Anal. 235 (2020), Issue 2, 927-971. pdf
  12. (with Artur Alho and Anne T. Franzen) The wave equation near flat Friedman-Lemaître-Robertson-Walker and Kasner Big Bang singularities, J. Hyperbolic Differ. Equ. 16 (2019), no. 2, 379-400. pdf
  13. (with Volker Schlue) On 'hard stars' in general relativity, Ann. Henri Poincaré 20 (2019), Issue 7, pp 2135-2172. pdf
  14. (with Ilias Chenn and Israel Michael Sigal) The effective dynamics of the volume preserving mean curvature flow, J. Stat. Phys. 172 (2018), no. 2, 458-476. pdf
  15. On the backward stability of the Schwarzschild black hole singularity, Comm. Math. Phys. 345 (2016), Issue 3, pp 923-971. pdf
  16. (with Spyros Alexakis and Dezhong Chen) Singular Ricci solitons and their stability under the Ricci flow, Comm. Partial Differential Equations 40 (2015), no. 12, 2123-2172. pdf
  17. (with Vassili Nestoridis) Generic approximation of functions by their Padé approximants, J. Math. Anal. Appl. 408 (2013), no. 2, 744-750. pdf
  18. On a characterization of Arakelian sets, Izv. Nats. Akad. Nauk Armenii Mat. 47 (2012), no. 6, 3-18. pdf

Previous Positions

  • Research Associate Scholar at Princeton University, 2021-2022. (Supervisor: Igor Rodnianski.)
  • Postdoctoral Researcher at the Sorbonne Université, 2018-2021. (Supervisor: Jacques Smulevici.)
  • Research Associate at the University of Cambridge, 2016-2018. (Supervisor: Mihalis Dafermos.)

    • Education

  • PhD in Mathematics (2016), University of Toronto. Advisor: Spyros Alexakis
  • MSc in Mathematics (2012), University of Toronto.
  • BSc in Mathematics (2010), National and Kapodistrian University of Athens.

    • Past and Upcoming Talks

  • "Black holes, naked singularities, shocks and implosions", National University of Singapore, 6-10 January, 2025.
  • Colloquium, Department of Physics, University of Crete, 10 October, 2024.
  • "Hyperbolic Differential Equations and Calculus of Variations", FORTH, 17-19 July, 2024.
  • Mini-course in "Nonlinear Waves and Fluids", University College London, 24-27 June, 2024.
  • "Gravitational physics and its mathematical analysis", SwissMAP Research Station, 2-7 June, 2024.
  • Mathematical General Relativity seminar, Sorbonne Université, Paris, May 2, 2024.
  • General Relativity seminar, University of Leipzig, 8 December, 2023.
  • "Hyperbolic PDEs and Nonlinear Evolution Problems", MATRIX, Melbourne, 18-29 September, 2023.
  • "Singularity Formation in General Relativity and Dispersive PDEs", ICMS Bayes Centre, Edinburgh, 29 May - 02 June 2023.
  • Geometric Analysis and PDE seminar, DPMMS, University of Cambridge, 13 March, 2023.
  • General Relativity seminar, University of Münster, 8 November, 2022.
  • "Stability and Instability in General Relativity", Clay research conference, University of Oxford, 26-30 September, 2022.
  • 23rd International Conference on General Relativity and Gravitation (GR23), Beijing, China, July 3-8, 2022
  • Black Hole Initiative Colloquium, Harvard University, 18 April, 2022. online video
  • "Hyperbolic Differential Equations in Geometry and Physics", MATRIX, Melbourne, 4-8 April, 2022.
  • "Aspects of Gravity, Mathematics and Physics", Ecole Polytechnique, 21-22 March, 2022.
  • Geometry, Analysis & Gravitation seminar, Department of Mathematics, Queen Mary University of London, 27 January, 2022.
  • General Relativity & Geometric Analysis seminar, Department of Mathematics, Columbia University, 5 November, 2021.
  • "New Trends in Geometric PDEs", University of Münster, 1-5 November, 2021.
  • "Mathematical and Numerical Aspects of Gravitation", IPAM, 25-29 October, 2021. online video
  • Seminar series at the Vanderbilt Initiative for Gravity, Waves and Fluids, 22 October, 2021.
  • "Mathematical Aspects of General Relativity", Mathematisches Forschungsinstitut Oberwolfach, 29 August - 4 September, 2021.
  • International Congress of Mathematical Physics, Geneva, 2-7 August, 2021.
  • Relativity seminar, Department of Physics, University of Vienna, 20 May, 2021.
  • Seminar in the course "Hidden symmetries of gravitation" (given by prof. Marc Henneaux), Collège de France, 19 May, 2021. online video
  • Mathematical Relativity seminar, Department of Mathematics, Instituto Superior Técnico, 13 May, 2021.
  • Analysis & PDE seminar, Department of Mathematics, Stanford University, 2 April, 2021.
  • Analysis seminar, Department of Mathematics, Aristotle University of Thessaloniki, 30 March, 2021.
  • Analysis seminar, Department of Mathematics, University of Toronto, 26 February, 2021.
  • Joint ICL/UCL Pure Analysis and PDEs seminar, Department of Mathematics, Imperial College London, 19 February, 2021.
  • Virtual seminar series, Princeton Gravity Initiative, 8 February, 2021.
  • Analysis and PDE seminar, Department of Mathematics, University of Berkeley, 23 November, 2020.
  • PDE seminar, Mathematical Institute, University of Oxford, 26 October, 2020.
  • Analysis seminar, Laboratoire Analyse Géométrie Modélisation, Cergy Paris Universté, 21 September, 2020.
  • Analysis seminar, Department of Mathematics, Princeton University, 31 August, 2020.
  • General Relativity seminar, CMSA, Harvard University, 22 June, 2020.
  • Séminaire de Physique Mathématique - EDP, Institut de Mathématiques de Bordeaux, 18 February, 2020.
  • Journée thématique "Evolution equations in General Relativity", Institut Fourier, Grenoble, 13 December, 2019.
  • Summer meeting of young researchers in mathematics, Department of Mathematics, University of Athens, 16-17 July 2019.
  • Three days' workshop in mathematical general relativity, Institut Camille Jordan, Lyon, April 15-17, 2019.
  • Mathematical General Relativity seminar, Sorbonne Université, Paris, November 19, 2018.
  • "Conference on Mathematical General Relativity and Nonlinear Wave Equations", Institut Henri Poincaré, Paris, May 28-June 1, 2018.
  • General Relativity seminar, DAMPT, University of Cambridge, November 17, 2017.
  • Geometry and Analysis seminar, Queen Mary University of London, September 26, 2017.
  • Séminaire de Relativité Générale Mathématique, IHES, May 22, 2017.
  • Analysis seminar, School of Applied Mathematical and Physical Science, National Technical University of Athens, December 2016.
  • 2016-17 Warwick EPSRC Symposium: Geometric PDEs, University of Warwick, December 2016.
  • PDE seminar, Department of Mathematics, Instituto Superior Técnico, October 28, 2016.
  • Mathematical Physics seminar, Department of Mathematics, Michigan State University, 2016.
  • Analysis seminar, Department of Mathematics, McMaster University, 2016.
  • Analysis seminar, Department of Mathematics, Princeton University, 2016.
  • Analysis seminar, Department of Mathematics, Imperial College of London, 2015.
  • Singularities in General Relativity, Fields Institute, June 15-18, 2015.
  • International Conference on Black Holes, Fields Institute, June 2, 2015. online video
  • Fields Geometric Analysis Colloquium, 2014. online video
  • Analysis seminar, Department of Mathematics, University of Western Ontario, 2013.
  • 6th World Congress of Nonlinear Analysts (WCNA), 2012.
  • Universal Functions and Hypercyclic Operators, Department of Mathematics, University of Crete, 2011.
  • Analysis Seminar, Department of Mathematics, University of Athens, 2011.
    • Πᾶσά τε ἐπιστήμη χωριζομένη δικαιοσύνης καὶ τῆς ἄλλης ἀρετῆς πανουργία, οὐ σοφία φαίνεται. (Πλάτωνος Μενέξενος)

    All knowledge cut off from rectitude and the rest of virtue has the look of low cunning, not wisdom. (Plato's Menexenus)