I am presently a research associate at Princeton. My research interests are in problems related to mathematical general relativity.
This year I am on leave from the University of Toronto where I am a postdoctoral fellow in the group of Spyros Alexakis. I have completed my Ph.D. in 2012 as a student of Mihalis Dafermos in Cambridge. Most recently, I spent a semester at MSRI in Berkeley.
Curriculum Vitae: CV.
- 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 13-14, 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.
- more ...
- Decay of linear waves on higher dimensional Schwarzschild black holes, Analysis & PDE 6-3 (2013), 515--600. DOI 10.2140/apde.2013.6.515.
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).
- Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies, arXiv:1207.6055v2, 45 pages.
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).
- (with Spyros Alexakis and Arick Shao) Unique continuation from infinity for linear waves, arXiv:1312.1989, 47 pages.
Videos: 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.
- Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes, Ph.D. Thesis, University of Cambridge (2012), available on DSpace, 223 pages.
- The asymptotics of the gravitational field and the memory effect, Diploma 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)], available as PDF here, 48 pages.
- General Relativity [153 pages; Chapter 1 - The equivalence principle and its consequences, Chapter 2 - Einstein's field equations in the presence of matter, Chapter 3 - Spherical Symmetry, Chapter 4 - Dynamical Formulation of General Relativity, Slow Motion Approximation, Gravitational Radiation]
- Differential Geometry, based on lectures by Demetrios Christodoulou. [incomplete, last update 01/08: Chapter 2]
- General Relativity (APM426, MAT1700, Winter 2013) at U of T: A course on general relativity theory for advanced undergraduates and beginning graduate students in mathematics and physics alike. Please refer to the Syllabus for details. Lectures are Wednesdays and Fridays at 10AM in MP 118. My office hours are Fridays 2PM - 4PM. Tutorials are offered Tuesdays 3PM - 4PM in BA 2185. The course covers Chapters 1 - 3 of my lecture notes, and is accompanied by the homework assignments: I,II,III,IV,V,VI.
- Multivariable Calculus (MAT235, Fall 2012 & Winter 2013) at U of T:
A course on vector calculus with applications in the natural sciences. We follow the Syllabus, but please check black board for frequent announcements. I teach the Thursday 6PM - 9PM session in MP 103, and my office hours are Tuesdays 4PM - 6PM. [Some nice complementary notes at the level of the course on Kepler's Laws can be found on Gilbert Weinstein's website.]
- PDE Tutorial (Fall 2012) at CCA: The lecture notes on Sobolev spaces by Willie Wong from the previous year may be useful for this course.
Other Interests and Writings
- I maintain an interest in photography. In recent years I mainly used a Mamiya RB67 for medium format film photography; see my collection of photos taken on trips to Italy, Israel and Korea. Currently, I am using a Fuji X100; follow my photostream on:
- I contributed to the development of the 8pen, a writing system for small devices which received some attention in the media. Here is a short note which describes some of the conceptual ideas behind the 8pen; see also this video, and these blog posts.
- An essay on entropy that I wrote as a student at King's for the John Rose prize, a yearly essay competition for the explanation of a scientific principle.
- In October 2012 I participated in the UNICEF Prof-in-a-box campaign, and my class raised funds for UNICEF Canada. (Photo)
- In July 2012 I graduated from Cambridge University. (Photo with Stefanos Aretakis)