Grigorios Fournodavlos, Assistant Professor

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

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.

Teaching

This Fall (2022) I am teaching a basic course of ODEs.

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 Igor Rodnianski and Jared Speck) Stable Big Bang formation for Einstein's equations: The complete sub-critical regime, to appear in Journal of AMS, arXiv:2012.05888
  2. (with Spyros Alexakis) Stable space-like singularity formation for axi-symmetric and polarized near-Schwarzschild black hole interiors, arXiv:2004.00692
  3. (with Jonathan Luk) Asymptotically Kasner-like singularities, to appear in Amer. J. Math., arXiv:2003.13591
  4. (with Jacques Smulevici) On the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, arXiv:1912.07338
  5. Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant, J. Math. Phys. 63 (2022), no. 3, 032502, 23pp. pdf
  6. (with Jacques Smulevici) The initial boundary value problem in General Relativity: the umbilic case, Int. Math. Res. Not. (2021), online. pdf
  7. (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
  8. (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
  9. (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, pp. 379-400. pdf
  10. (with Volker Schlue) On 'hard stars' in general relativity, Ann. Henri Poincaré 20 (2019), Issue 7, pp 2135-2172. pdf
  11. (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
  12. On the backward stability of the Schwarzschild black hole singularity, Comm. Math. Phys. 345 (2016), Issue 3, pp 923-971. pdf
  13. (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
  14. (with Vassili Nestoridis) Generic approximation of functions by their Padé approximants, J. Math. Anal. Appl. 408 (2013), no. 2, 744-750. pdf
  15. 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

  • 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, 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.
  • Seminar on Mathematical General Relativity, 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)