Volker Schlue

Volker Schlue Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie
4 Place Jussieu
75005 Paris


I am currently a postdoc in the Laboratoire Jacques-Louis Lions at Université Pierre et Marie Curie (Paris 6), where I work with Jérémie Szeftel. My research interests are in problems related to mathematical general relativity.

I received my Ph.D. in 2012 as a student of Mihalis Dafermos in Cambridge. Since then I have been a Postdoctoral Fellow at the University of Toronto, and at the Mathematical Sciences Research Institute in Berkeley. In Toronto, I worked with Spyros Alexakis, while at MSRI, I was mentored by Hans Lindblad. In 2014 I was also a Visiting Postdoctoral Research Associate at Princeton, and last year a postdoctoral laureate of the Fondation Sciences Mathématiques de Paris.

Curriculum Vitae: CV.

Upcoming Talks

Recent Talks

  1. PDE Seminar, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Lisbon, Portugal, June 15, 2016.
  2. Analysis and PDE seminar, Imperial College, London, May 13, 2016.
  3. Oberseminar Geometrische Analysis, Universität Tübingen, February 12, 2016.
  4. Conference in Mathematical General Relativity, Tsinghua Sanya International Mathematics Forum in Sanya, Hainan, China, January 5-9, 2016. [Poster]
  5. Geometric Analysis and Partial Differential Equations Seminar, University of Cambridge, November 2, 2015.
  6. Dynamics of Self-Gravitating Matter, Workshop, Institute Henri Poincaré, Paris, October 26-29, 2015. [Poster]
  7. Vienna Relativity Seminar, University of Vienna, (and additional talk in the Geometric Analysis and Physics joint seminar of the University of Vienna and the University of Technology), Vienna, October 22, 2015.
  8. Mathematical Aspects of General Relativity, Workshop, Mathematisches Forschungsinstitut Oberwolfach, July 12-18, 2015. [Extended abstract, Preliminary report]
  9. Session A1: Mathematical General Relativity, GRG conference: A Centennial Perspective, Penn State, June 8, 2015.
  10. International Conference on Black Holes, Fields Institute, Toronto, June 2, 2015. [Video]
  11. Colloquium, University of Miami, February 2, 2015. [Slides]
  12. Mathematical Problems in General Relativity, Simons Center for Geometry and Physics, January 21, 2015. [Video]
  13. more ...


  1. Decay of linear waves on higher dimensional Schwarzschild black holes,
    Analysis & PDE 6-3 (2013), 515--600.

    Published version: [pdf] (screen) [pdf] (printing)

    In this paper I prove several decay statements for solutions to the wave equation on Schwarzschild black hole spacetimes in all dimensions. While the quantitative decay rates had been established in the 3+1-dimensional case, c.f. Luk (2009), the main interest in this paper lies in its method of proof, which uses and extends the "new physical-space approach to decay" of Dafermos and Rodnianski (2009).

  2. Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies,
    Communications in Mathematical Physics: Volume 334, Issue 2 (2015), 977--1023.

    Published version: Springer, arXiv: 1207.6055v2

    In this paper I develop the global study of linear waves on Kerr de Sitter spacetimes. I am particularly interested here in the so-called cosmological region that is bounded in the past by the cosmological horizons and to the future by a spacelike hypersurface at infinity. It is shown that the expansion of that region provides a stability mechanism that manifests itself in a global redshift effect; moreover this effect persists in a large class of expanding cosmologies near the Schwarzschild de Sitter geometry. Global boundedness and decay results are obtained when our estimates are combined with earlier work concerning the stationary region by Dafermos and Rodnianski (2007) and Dyatlov (2010).

  3. (with Spyros Alexakis and Arick Shao) Unique continuation from infinity for linear waves, Advances in Mathematics 286 (2016) 481-544.

    Published version: Elsevier, arXiv: 1312.1989
    Video: Banff, Geometry and Inverse problems workshop (Spyros Alexakis).

    We explore in this paper the question if solutions to wave equations are completely determined from their radiation towards infinity. We are led to show that if the radiation fields of two solutions to a wave equation with suitably fast decaying coefficients conincide to all orders on suitable parts of null infinity, then these solutions indeed coincide in a neighborhood of infinity. The size of this neighborhood depends strongly on the geometry of the asymptotically flat background spacetime; in particular we find that a positive mass of the spacetime works strongly in our favor.

  4. (with Spyros Alexakis) Non-existence of time-periodic vacuum space-times, Journal of Differential Geometry, to appear, 63 pages.

    arXiv: 1504.04592
    Video: Simons Center for Geometry and Physics (Volker Schlue)
    Cf. Oberwolfach Report: Extended abstract, 3 pages.

    In this paper we address an older question in general relativity: Is it possible for an isolated self-gravitating relativistic system to be in periodic motion? We prove that any asymptotically flat spacetime, which is assumed to be time-periodic and a solution to the Einstein vacuum equations far away from the sources, must be stationary, at least near infinity. Thus genuinely time-periodic solutions do not exist. This problem has been repeatedly studied, first by Papapetrou [Annalen der Physik, 1957], and most recently by Bicak, Scholz and Tod [arXiv:1003.3402], whose approach yields a symmetry "at infinity". Our proof relies crucially on the uniqueness results for linear waves obtained in our previous [3.] for the extension of this symmetry to the spacetime.

  5. Decay of the Weyl curvature in expanding black hole cosmologies, 124 pages.

    arXiv: 1610.04172

    This paper is the first in a series on the non-linear stability problem of the expanding region of Schwarzschild de Sitter cosmologies. Recently Hintz and Vasy (2016) proved the non-linear stability of Kerr de Sitter black hole exteriors on a domain bounded by the cosmological horizon. This paper approaches the characteristic initial value problem beyond the cosmological horizon. From my paper [2.] - which developed the relevant linear theory - we cannot expect the solutions to converge to the Kerr de Sitter geometry at future null infinity, but merely to a nearby geometry which is however a priori unknown. Here we show - under assumptions which are consistent with this expectation - that nonetheless the Weyl curvature of spacetime decays uniformly towards the future boundary at infinity. One expects this to be an essential part of a global existence result for the Einstein equations with positive cosmological constant in this region.


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