Home page
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. I am a member of the Analysis group.
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.
Past Talks
 MUMS Lecture, Melbourne Uni Maths & Stats Society, online talk, October 17, 2020
 Pacific Rim Conference in Mathematics, Session: PDE: Inviscid Fluid Mechanics and General Relativity, online hosted by UC Berkeley, August 1011, 2020.
 ACGRG10, 10th Australasian Conference on General Relativity and Gravitation, Australasian Society for General Relativity and Gravitation, Victoria University of Wellington, New Zealand, December 913, 2019
 AustMS 2019 (Talks in Sessions: Geometric Analysis and PDE; Harmonic and SemiClassical Analysis), 63rd Annual Meeting of the Australian Mathematical Society, Monash University, Australia, December 36, 2019
 Session D41, DEA 2019, AGH University of Science and Technology, Kraków, Poland, September 19, 2019
 Seminar, Institut MittagLeffler, Sweden, September 12, 2012
 Mathematical Physics Seminar, University of Melbourne, Australia, May 14, 2019
 Pure Mathematics Seminar, University of Melbourne, Australia, May 3, 2019
 Analysis, PDE, and Geometry Seminar, Monash University, Australia, April 30, 2019
 Probing the Earth and the Universe with Microlocal Analysis, BIRS, Banff, Canada, April 14 – 19, 2019.
 Topology and Geometry Seminar, University of Sydney, Australia, March 11, 2019
 Mathematical General Relativity Seminar, Sorbonne Université, Paris, October 29, 2018.
 Analysis Seminar, Imperial College, London, October 26, 2018.
 PDE Seminar, CAMGSD, Técnico, Lisbon, Portugal, September 19, 2018.
 Conference on Mathematical General Relativity, Institut Henri Poincaré, Paris, May 28June 1, 2018.
 Seminar/Forum, University of Melbourne, December 7, 2017.
 CMC Seminar, Korea Institute for Advanced Study, Seoul, December 4, 2017.
 Mathematical General Relativity Seminar, Sorbonne Université, Paris, November 20, 2017.
 General Relativity and Geometric Analysis Reading Seminar, Columbia University, New York, April 21, 2017.
 Institut Fourier, Grenoble, March 2, 2017.
 Analysis and PDE Seminar, Stanford University, January 9, 2017.
 Geometry and Analysis Seminar, Queen Mary University of London, December 6, 2016.
 Mathematical General Relativity Seminar, Sorbonne Université, Paris, November 21, 2016.
 Séminaire Laurent Schwartz, Institut des Hautes Études Scientifiques, Paris, October 18, 2016.
 PDE Seminar, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Técnico, Lisbon, Portugal, June 15, 2016.
 Analysis and PDE seminar, Imperial College, London, May 13, 2016.
 Oberseminar Geometrische Analysis, Universität Tübingen, February 12, 2016.
 Conference in Mathematical General Relativity, Tsinghua Sanya International Mathematics Forum in Sanya, Hainan, China, January 59, 2016.
 Geometric Analysis and Partial Differential Equations Seminar, University of Cambridge, November 2, 2015.
 Dynamics of SelfGravitating Matter, Workshop, Institute Henri Poincaré, Paris, October 2629, 2015.
 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.
 Mathematical Aspects of General Relativity, Workshop, Oberwolfach, July 1218, 2015.
 Session A1: Mathematical General Relativity, GRG conference: A Centennial Perspective, Penn State, June 8, 2015.
 International Conference on Black Holes, Fields Institute, Toronto, June 2, 2015.
 Colloquium, University of Miami, February 2, 2015.
 Mathematical Problems in General Relativity, Simons Center for Geometry and Physics, January 21, 2015.
 Analysis and PDEs Seminar, Johns Hopkins University, March 10, 2014.
 Analysis Seminar, Princeton University, March 3, 2014.
 Nonlinear Wave Equations and General Relativity Workshop, University of Oxford, January 1314, 2014.
 Geometry Seminar, Stanford University, November 11, 2013.
 MSRI Postdoc Seminar, Evans Hall, University of California, Berkeley, October 25, 2013.
 MGR Programmatic Seminar, MSRI, Berkeley, October 1, 2013.
 Miami Waves, FRG workshop, University of Miami, December 1821, 2012.
 Analysis Seminar, Princeton University, November 19, 2012.
 Analysis and Applied Mathematics Seminar, University of Toronto, October 5, 2012.
 Mathematical Aspects of General Relativity, MFO, Oberwolfach, July 29 – August 4, 2012.
 Recent Developments in Gravity, NEB 15 Conference, TEI Crete, Chania, June 2023, 2012.
 King’s Lunchtime Seminar, King’s College, Cambridge, May 4, 2012.
 Do we understand gravity?, IOP Gravitational Physics Group, IOP, London, September 16, 2011.
 Geometric Analysis Seminar, AEI Institute, PotsdamGolm, April 11, 2011.
Online Talks
 Black holes and the expanding universe (general audience talk aimed at undergraduates), organised by Melbourne Uni Maths & Stats Society and LunchMaths at Monash University, October 17, 2020
 Expanding black hole cosmologies: On the stability problem for Kerr de Sitter spacetimes, talk in PDE session at the Pacific Rim conference, UC Berkeley, August 2020
 Scattering from infinity for semilinear wave equations with weak null condition, talk in workshop at Banff International Research Station, April 2019
 Nonexistence of timeperiodic vacuum spacetimes, talk in workshop at Simons Center for Geometry and Physics, January 2015
Preprints

(with Hans Lindblad) Scattering from infinity for semi linear wave equations satisfying the null condition or the weak null condition, 53 pages (v2).
Publications

Decay of the Weyl curvature in expanding black hole cosmologies, Annals of PDE, (2022).
Springer SharedIt Enhanced PDF 1610.04172
YouTube, PRCM, UC Berkeley 
Optical functions in de Sitter, Journal of Mathematical Physics, 62 (8), 082501 (2021)

(with Grigorios Fournodavlos) On `hard stars’ in general relativity, Annales Henri Poincaré, 20(7), 21352172 (2019)

(with Spyros Alexakis) Nonexistence of timeperiodic vacuum spacetimes, J. Differential Geom. Volume 108, Number 1 (2018), 162.
Project Euclid 1504.04592
Simons Center for Geometry and Physics
Oberwolfach Report, 3 pages. 
(with with Spyros Alexakis and Arick Shao) Unique continuation from infinity for linear waves, Advances in Mathematics 286 (2016) 481544.
Elsevier 1312.1989
Banff International Research Station (by Spyros Alexis) 
Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies, Communications in Mathematical Physics: Volume 334, Issue 2 (2015), 977–1023.

Decay of linear waves on higher dimensional Schwarzschild black holes, Analysis & PDE 63 (2013), 515–600.
Theses

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

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 GravitationalWave Experiments, Phys. Rev. Letters (67), no 12, pp. 1486–1489, (1991)], 48 pages.
MSc Courses
Differential Geometry (MAST90143)
This course is offered biennially (every two years). I am teaching it for the first time in Semester 2, 2022.
Partial Differential Equations (MAST90133)
This course is offered biennially (every two years). I have taught it for the first time in Semester 2, 2021.
Measure Theory (MAST90012)
This course is offered biennially. I taught it in Semester 1, 2019.
Syllabus (2019), Course material (2019).
MSc Theses
If you are a student in the Master’s program of the School of Mathematics and currently looking for a supervisor, then the following topics give you an idea what I have currently in mind:
 Topics in relativistic elasticity. Flavour: Differential Geometry. Literature: Christodoulou & Kaelin (2012)
 Asymptotics for semilinear wave equations. Flavour: Functional Analysis, PDE. Literature: Luk (2012), Lindblad & Rodnianski (2003), Lindblad & Schlue (2020)
 Waves in de Sitter and Schwarzschild de Sitter. Flavour: General Relativity, PDE. Literature: Dafermos and Rodnianski (2008), Schlue (2012)
Lecture Notes
Undergraduate Courses
Calculus 2: Advanced (MAST10021)
This course is offered annually for first year students in Semester 2.
I have been teaching it every year since 2020 when it was first introduced.
FAQ about this course:
 What is the difference between Calculus 2: Advanced and Calculus 2?
I would say, while the topics covered in this course are broadly the same as in MAST10006 Calculus 2, the material is more “advanced” in the sense that you will see more proofs and concepts, and fewer examples with “ad hoc” solutions. Here we aim to strike a balance between the theoretical underpinnings of Calculus and its practical applications, which also prepares you to take other classes is mathematics & physics.  What is the difference between Calculus 2: Advanced and Accelerated Mathematics 2?
In comparison to Calculus 2 the course Accelerated Mathematics 2 proceeds quicker, but not at a deeper level. The idea of the new courses in the Advanced stream is to offer solid entry courses in mathematics, where the foundations of these subjects are developed with more care, and more emphasis on the underlying proofs is given, both in the presentation of the material, and the skills acquired by the student.  How do I enroll?
Please contact msmslcapprovals@ms.unimelb.edu.au for all questions related to enrollment.  Is there a book you recommend?
I like Spivak‘s “Calculus” which gives a beautiful introduction to Calculus at the intended level for this course. In fact, large parts of this course are based on Spivak‘s text. I also recommend Folland‘s “Advanced Calculus”.
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
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 JacquesLouis 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”