Spyros Alexakis

I am a Professor at the
Department of Mathematics,
University of Toronto.

Curriculum Vitae (pdf)
Contact me (remove spam defence)

UofT Analysis/Applied Math Seminar
Our seminar meets on Fridays from 1-2PM, in BA6183.

Thematic program on the Centennary of Einstein's equations at the Fields Institute

In May and June 2015 I co-organized a thematic program at the Fields Institute in Toronto, on the occasion of the 100 years of Einstein's equations (jointly with M. Dafermos (Princeton), L. Lehner (Perimeter), H. Pfeiffer (CITA, Toronto) and E. Poisson (Guelph)). As part of this, we organized a conference on Black holes from June 1--5 2015, bringing together leading researchers in this field, from both mathematics and physics communities. The videos of all lectures are available here .
The event also featured an outstanding public lecture by Clifford Will. Maybe the ideal way to introduce a layman to basic concepts in this subject.
The thematic program also included many focus weeks, on Constraint equations and Mass-momentum inequalities, Perturbation Methods, Black Hole stability, Singularities, and Non-linear waves. Links to the slides of those lectures will be available soon.

RESEARCH

I am interested in General Relativity and Geometric Analysis. I also like Inverse problems.

(Please note that the preprints posted here have some small differences from the published versions.)

The Penrose inequality on perturbations of the Schwarzschild exterior , (50 pp), arXiv:1506.06400

Non-existence of time-periodic vacuum spacetimes. (joint with V. Schlue), to appear in Jour. Diff Geom. (62pp) , arXiv:1504.04592

Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles. (joint with K. Hirachi), 44pp , arXiv:1501.02463

On the profile of energy concentration at blow-up points for sub-conformal focusing nonlinear waves. (joint with A. Shao),
to appear in Trans. Amer. Math. Soc (17pp), arXiv:1412.6844

Global uniqueness theorems for linear and nonlinear waves. (joint with A. Shao), Jour. Functional Anal, 269 (2015), no. 11, 3458--3499, arXiv:1412.1537

Unique continuation from infinity for linear waves. (joint with V. Schlue and A. Shao), Advances in Math. 286, (2016), 481--544, arXiv:1312.1989

Bounds on the Bondi Energy by a Flux of Curvature. (joint with A. Shao) To appear in Jour. Eur. Math. Soc. (52pp), arXiv.org/1308.4170.

Singular Ricci solitons and their stability under the Ricci flow. (joint with D. Chen and G. Fournodavlos) Comm. P.D.E. 40 (2015), no. 12, 2123--2172, arXiv.org/1304.6449.

Rigidity of stationary black holes with small angular momentum on the horizon. (joint with A. Ionescu and S. Klainerman) Duke Math. J. 163 (2014), no. 14, 2603--2615. arXiv.org/1304.0487.

On the Geometry of Null Cones to Infinity Under Curvature Flux Bounds. (joint with A. Shao) Classical Quantum Gravity 31 (2014), no. 19, 195012, 62 pp. arxiv.org/1303.1260.

Complete Willmore surfaces in H3 with bounded energy: boundary regularity and bubbling. (joint with R. Mazzeo) Jour. Diff. Geometry 101, no. 3 (2015) 369--422. arXiv:1204.4955.

The decomposition of Global Conformal invariants. Annals of Mathematics Studies, 182. Princeton University Press, Princeton, NJ, 2012. x+449 pp.
An earlier version of this book (divided into six papers) is on arXiv, arXiv:0912.3765, arXiv:0912.3764 , arXiv:0912.3761, arXiv:0912.3757, arXiv:0912.3755, arXiv:0711.1685.

The decomposition of global conformal invariants IV: A proposition on local Riemannian invariants . Adv. Math. 225 (2010), no. 2, 515--597. arXiv:arXiv:0912.3761.

The Decomposition of Global Conformal Invariants: Some Technical Proofs. II . Pacific J. Math. 260 (2012), no. 1, 1--88. arXiv:0912.3764.

The Decomposition of Global Conformal Invariants: Some Technical Proofs. I . SIGMA Symmetry Integrability Geom. Methods Appl. 7 (2011), Paper 019, 41 pp. arXiv:0912.3757.

Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces. (joint with A. Ionescu and S. Klainerman) Comm. Math. Phys. 299 (2010), no. 1, 89--127. arXiv:0904.0982.

Hawking's local rigidity theorem without analyticity. (joint with A. Ionescu and S. Klainerman) Geom. Funct. Anal. 20 (2010), no. 4, 845--869. arXiv:0902.1173.

Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds. (Joint with R. Mazzeo) Comm. Math. Phys. 297 (2010), no. 3, 621--651. arXiv:0802.2250.

Unique continuation for the vacuum Einstein equations . arXiv:0902.1131.

On conformally invariant differential operators . arXiv:0608771.

On the decomposition of global conformal invariants II. Adv. Math. 206 (2006), no. 2, 466--502. arXiv:0509572.

On the decomposition of global conformal invariants I. Ann. of Math. (2) 170 (2009), no. 3, 1241--1306. arXiv:0509571.

On conformally invariant differential operators in odd dimensions. Proc. Natl. Acad. Sci. USA 100 (2003), no. 8, 4409--4410

Video presentations of some of the papers above.

Non-existence of time-periodic vacuum space-times. A lecture at the Simons center by Volker Schlue.

Reconstruction of waves from radiation fields, and some nonlinear applications. A lecture at Banff by me.

Unique continuation from infinity for linear waves. A lecture at UofT by me.

Willmore surfaces in H3: Boundary regularity and Bubbling. A lecture at Banff by me.

Singular Ricci solitons and their stability under the Ricci flow. A lecture at the Fields Institute by Greg Fournodavlos.

The decomposition of global conformal invariants. A lecture at IAS by Charles Fefferman.

Teaching 2014-2015.

MAT1060HF: Partial Differential Equations I
Graduate-level course, Fall 2014.
More information on the course is available here and on Blackboard.

Current Students

Gregorios Fournodavlos

Tracey Balehowsky (joint with A. Nachman)

Ali Feiz (joint with A. Nachman)

Webpages of Collaborators

Arick Shao
Volker Schlue
Rafe Mazzeo
Alexandru Ionescu
Sergiu Klainerman
Kengo Hirachi