Welcome to my webpages !

I am a Lecturer in the School of Mathematics and Statistics at the University of Melbourne.

My research interests are in partial differential equations, geometry and analysis.

In 2012, I obtained my Ph.D. from the University of Cambridge as a student of Mihalis Dafermos. Prior to joining the University of Melbourne in 2018, I held postdoctoral fellowships at the University of Toronto, MSRI, Berkeley, and most recently Sorbonne Université, Paris. Please refer to my curriculum vitae for a detailed academic history.

• New position in Melbourne: Lecturer in Analysis

  The School of Mathematics at the University of Melbourne has opened another position in Analysis, and is encouraging applications from any area of partial differential equations, and geometric analysis. A more detailed position description, and information about the application process can be found here: https://careers.pageuppeople.com/422/ci/en/job/900382/lecturer-in-analysis https://www.mathjobs.org/jobs?joblist-534-14133 I have recently joined the School myself, and would be happy to answer any informal inquiries, about …

  9 September, 2019

Past Talks

1. ACGRG10, 10th Australasian Conference on General Relativity and Gravitation, Australasian Society for General Relativity and Gravitation, Victoria University of Wellington, New Zealand, December 9-13, 2019
2. AustMS 2019 (Talks in Sessions: Geometric Analysis and PDE; Harmonic and Semi-Classical Analysis), 63rd Annual Meeting of the Australian Mathematical Society, Monash University, Australia, December 3-6, 2019
3. Session D41, DEA 2019, AGH University of Science and Technology, Kraków, Poland, September 19, 2019



4. Seminar, Institut Mittag-Leffler, Sweden, September 12, 2012
5. Mathematical Physics Seminar, University of Melbourne, Australia, May 14, 2019
6. Pure Mathematics Seminar, University of Melbourne, Australia, May 3, 2019
7. Analysis, PDE, and Geometry Seminar, Monash University, Australia, April 30, 2019
8. Probing the Earth and the Universe with Microlocal Analysis, BIRS, Banff, Canada, April 14 – 19, 2019.
9. Topology and Geometry Seminar, University of Sydney, Australia, March 11, 2019
10. Mathematical General Relativity Seminar, Sorbonne Université, Paris, October 29, 2018.
11. Analysis Seminar, Imperial College, London, October 26, 2018.
12. PDE Seminar, CAMGSD, Técnico, Lisbon, Portugal, September 19, 2018.
13. Conference on Mathematical General Relativity, Institut Henri Poincaré, Paris, May 28-June 1, 2018.
14. Seminar/Forum, University of Melbourne, December 7, 2017.
15. CMC Seminar, Korea Institute for Advanced Study, Seoul, December 4, 2017.
16. Mathematical General Relativity Seminar, Sorbonne Université, Paris, November 20, 2017.
17. General Relativity and Geometric Analysis Reading Seminar, Columbia University, New York, April 21, 2017.
18. Institut Fourier, Grenoble, March 2, 2017.
19. Analysis and PDE Seminar, Stanford University, January 9, 2017.
20. Geometry and Analysis Seminar, Queen Mary University of London, December 6, 2016.
21. Mathematical General Relativity Seminar, Sorbonne Université, Paris, November 21, 2016.
22. Séminaire Laurent Schwartz, Institut des Hautes Études Scientifiques, Paris, October 18, 2016.
23. PDE Seminar, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Técnico, Lisbon, Portugal, June 15, 2016.
24. Analysis and PDE seminar, Imperial College, London, May 13, 2016.
25. Oberseminar Geometrische Analysis, Universität Tübingen, February 12, 2016.
26. Conference in Mathematical General Relativity, Tsinghua Sanya International Mathematics Forum in Sanya, Hainan, China, January 5-9, 2016.



27. Geometric Analysis and Partial Differential Equations Seminar, University of Cambridge, November 2, 2015.
28. Dynamics of Self-Gravitating Matter, Workshop, Institute Henri Poincaré, Paris, October 26-29, 2015.
29. 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.
30. Mathematical Aspects of General Relativity, Workshop, Oberwolfach, July 12-18, 2015.
31. Session A1: Mathematical General Relativity, GRG conference: A Centennial Perspective, Penn State, June 8, 2015.
32. International Conference on Black Holes, Fields Institute, Toronto, June 2, 2015.
33. Colloquium, University of Miami, February 2, 2015.
34. Mathematical Problems in General Relativity, Simons Center for Geometry and Physics, January 21, 2015.
35. Analysis and PDEs Seminar, Johns Hopkins University, March 10, 2014.
36. Analysis Seminar, Princeton University, March 3, 2014.
37. Nonlinear Wave Equations and General Relativity Workshop, University of Oxford, January 13-14, 2014.
38. Geometry Seminar, Stanford University, November 11, 2013.
39. MSRI Postdoc Seminar, Evans Hall, University of California, Berkeley, October 25, 2013.
40. MGR Programmatic Seminar, MSRI, Berkeley, October 1, 2013.



41. Miami Waves, FRG workshop, University of Miami, December 18-21, 2012.
42. Analysis Seminar, Princeton University, November 19, 2012.
43. Analysis and Applied Mathematics Seminar, University of Toronto, October 5, 2012.



44. Mathematical Aspects of General Relativity, MFO, Oberwolfach, July 29 – August 4, 2012.
45. Recent Developments in Gravity, NEB 15 Conference, TEI Crete, Chania, June 20-23, 2012.
46. King’s Lunchtime Seminar, King’s College, Cambridge, May 4, 2012.
47. Do we understand gravity?, IOP Gravitational Physics Group, IOP, London, September 16, 2011.
48. Geometric Analysis Seminar, AEI Institute, Potsdam-Golm, April 11, 2011.

Online Talks

• Scattering from infinity for semi-linear wave equations with weak null condition, Banff International Research Station, April 2019
• Non-existence of time-periodic vacuum spacetimes, Simons Center for Geometry and Physics, January 2015

Preprints

• Optical functions in de Sitter, 93 pages.

  1910.05799

• (with Hans Lindblad) Scattering from infinity for semilinear models of Einstein’s equations satisfying the weak null condition, 34 pages.

  1711.00822
  Banff International Research Station

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

  1610.04172

Publications

1. (with Grigorios Fournodavlos) On `hard stars’ in general relativity, Annales Henri Poincaré, 20(7), 2135-2172 (2019)

   Springer   1710.00754

2. (with Spyros Alexakis) Non-existence of time-periodic vacuum space-times, J. Differential Geom. Volume 108, Number 1 (2018), 1-62.

   Project Euclid   1504.04592
   Simons Center for Geometry and Physics
   Oberwolfach Report, 3 pages.

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

   Elsevier   1312.1989
   Banff International Research Station (by Spyros Alexis)

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

   Springer   1207.6055v2

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

   MSP   PDF

Theses

• Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes, Ph.D. Thesis, University of Cambridge (2012), 223 pages.

  DSpace

• The asymptotics of the gravitational field and the memory effect, Dipl.phys. Thesis, ETH Zurich (2008), [expository, after D. Christodoulou, Nonlinear Nature of Gravitation and Gravitational-Wave Experiments, Phys. Rev. Letters (67), no 12, pp. 1486–1489, (1991)], 48 pages.

  PDF

Courses

2019

This semester I am teaching Measure Theory (MAST90012). Please refer to the Syllabus for details. Students who are enrolled in the course can access all course materials on LMS, and those who audit the class may find some of the material here.

Lecture Notes

General Relativity (2015)

Current position

Lecturer in Pure Mathematics (Analysis & Geometry), University of Melbourne

Education

Ph.D. in Pure Mathematics, University of Cambridge, 2012
Diploma in Physics, ETH Zürich, 2008

Curriculum Vitae (PDF)

Academic history

December 2018September 2015

Postdoctoral Researcher

Sorbonne Université

• Funding: ERC consolidator Grant 725589 EPGR, ERC advanced grant 291214 BLOWDISOL, Fondation Sciences Mathématiques de Paris
• Affiliation: Laboratoire Jacques-Louis Lions
• Supervisor: Jérémie Szeftel

July 2017May 2017

Research Associate

Imperial College London

• Supervisor: Gustav Holzegel

July 2014January 2014

Visiting Postdoctoral Research Associate

Princeton University

December 2013August 2013

Postdoctoral Fellow

Mathematical Sciences Research Institute, Berkeley

• Mentor: Hans Lindblad

July 2015August 2012

Postdoctoral Fellow

University of Toronto

• Supervisor: Spyros Alexakis

July 2012October 2008

Ph.D. in Pure Mathematics

University of Cambridge

• Advisor: Mihalis Dafermos
• Thesis title: “Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes”
• Department: Department of Pure Mathematics and Mathematical Statistics
• College: King’s College, Cambridge

April 2008October 2005

Diploma in Physics

ETH Zürich

• Diploma thesis advisor: Demetrios Christodoulou
• Thesis title:“The asymptotics of the gravitational field and the memory effect”