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BEGIN:VEVENT
SUMMARY:Hans Ringström (KTH Stockholm)
DTSTART;VALUE=DATE-TIME:20201001T133000Z
DTEND;VALUE=DATE-TIME:20201001T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/1
DESCRIPTION:Title:
On highly anisotropic big bang singularities\nby Hans Ringström (KTH
Stockholm) as part of JoMaReC - Joint Online Mathematical Relativity Collo
quium\n\n\nAbstract\nIn cosmology\, the universe is typically modelled by
spatially homogeneous and isotropic solutions to Einstein’s equations. H
owever\, for large classes of matter models\, such solutions are unstable
in the direction of the singularity. For this reason\, it is of interest t
o study the anisotropic setting. \n\nThe purpose of the talk is to describ
e a framework for studying highly anisotropic singularities. In particular
\, for analysing the asymptotics of solutions to linear systems of wave eq
uations on the corresponding backgrounds and deducing information concerni
ng the geometry.\n\nThe talk will begin with an overview of existing resul
ts. This will serve as a background and motivation for the problem conside
red\, but also as a justification for the assumptions defining the framewo
rk we develop. Following this overview\, the talk will conclude with a rou
gh description of the results.\n
LOCATION:https://researchseminars.org/talk/jomarec/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Galloway (University of Miami)
DTSTART;VALUE=DATE-TIME:20201105T143000Z
DTEND;VALUE=DATE-TIME:20201105T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/2
DESCRIPTION:Title:
Initial data rigidity results\nby Greg Galloway (University of Miami)
as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\n
Abstract\nWe present several rigidity results for initial data sets motiva
ted by the positive mass theorem. An important step in our proofs is to es
tablish conditions that ensure that a marginally outer trapped surface is
“weakly outermost”. A rigidity result for Riemannian manifolds with a
lower bound on their scalar curvature is included as a special case. Rele
vant background on marginally outer trapped surfaces will be discussed. Th
is talk is based on joint work with Michael Eichmair and Abraão Mendes.\n
LOCATION:https://researchseminars.org/talk/jomarec/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lydia Bieri (University of Michigan\, Ann Arbor)
DTSTART;VALUE=DATE-TIME:20201203T143000Z
DTEND;VALUE=DATE-TIME:20201203T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/3
DESCRIPTION:Title:
New structures in gravitational radiation\nby Lydia Bieri (University
of Michigan\, Ann Arbor) as part of JoMaReC - Joint Online Mathematical Re
lativity Colloquium\n\n\nAbstract\nGravitational waves are transporting in
formation from faraway regions of the Universe. A new era began with the f
irst detection of gravitational waves by Advanced LIGO in September 2015\,
and since then several events have been recorded by the LIGO/VIRGO collab
oration. New challenges await us to unravel the interesting interplay betw
een physics\, astrophysics and mathematics. Most studies so far have been
devoted to sources like binary black hole mergers or neutron star mergers\
, or generally to sources that are stationary outside of a compact set. We
describe these systems by asymptotically-flat manifolds solving the Einst
ein equations. These sources have in common that far away their gravitatio
nal field decays fast enough towards Minkowski spacetime. In particular\,
far away from the source\, the decay behavior can be described by a term t
hat is homogeneous of degree -1 and lower order terms. I will present new
results on gravitational radiation for sources that are not stationary out
side of a compact set\, but whose gravitational fields decay more slowly t
owards infinity. A panorama of new gravitational effects opens up when del
ving deeper into these more general spacetimes. In particular\, whereas th
e former sources produce memory effects that are of purely electric parity
(permanent displacement only)\, the latter in addition generate memory of
magnetic type\, thus allowing for rotation in the system. These new effec
ts emerge naturally from the Einstein equations.\n
LOCATION:https://researchseminars.org/talk/jomarec/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harvey Reall (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210204T143000Z
DTEND;VALUE=DATE-TIME:20210204T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/4
DESCRIPTION:Title:
Well-posed formulation of Lovelock and Horndeski theories\nby Harvey R
eall (University of Cambridge) as part of JoMaReC - Joint Online Mathemati
cal Relativity Colloquium\n\n\nAbstract\nLovelock theories are the most ge
neral diffeomorphism invariant theories of gravity in higher dimensions wi
th second order equations of motion. Horndeski theories are the most gener
al diffeomorphism invariant theories of gravity coupled to a scalar field
in four dimensions with second order equations of motion. In this talk I w
ill discuss well-posedness of the initial value problem for these theories
. Previous work has shown that (generalised) harmonic gauge does not give
a well-posed initial value problem. I will describe recent work with Aron
Kovacs in which we introdued a modification of harmonic gauge that does gi
ve a well-posed initial value problem provided that the theory remains “
weakly coupled”. Our modified harmonic gauge may also have applications
in conventional GR.\n
LOCATION:https://researchseminars.org/talk/jomarec/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton University)
DTSTART;VALUE=DATE-TIME:20210304T143000Z
DTEND;VALUE=DATE-TIME:20210304T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/5
DESCRIPTION:Title:
On naked singularities in Einstein equations\nby Igor Rodnianski (Prin
ceton University) as part of JoMaReC - Joint Online Mathematical Relativit
y Colloquium\n\n\nAbstract\nI will describe recent and ongoing work with Y
. Shlapentokh-Rothman on a construction of solutions to the Einstein vacuu
m equations corresponding to a naked singularity forming from a regular p
ast. The talk will focus on a new geometric phenomenon\, corresponding to
twisting of null geodesics\, new type of self-similarity\, dynamical appro
ach to the problem\, and on the comparisons with the naked singularity sol
utions constructed by Christodoulou for the spherically symmetric Einstein
-scalar field model.\n
LOCATION:https://researchseminars.org/talk/jomarec/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martín Reiris (Universidad de la República\, Montevideo)
DTSTART;VALUE=DATE-TIME:20210401T133000Z
DTEND;VALUE=DATE-TIME:20210401T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/6
DESCRIPTION:Title:
New results on compact Cauchy horizons of smooth vacuum spacetimes\nby
Martín Reiris (Universidad de la República\, Montevideo) as part of JoM
aReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nCauc
hy horizons are rather unique and peculiar objects that have been studied
for decades. In this talk I will first review old and new breakthroughs on
the subject by Isenberg and Moncrief\, and by Petersen and Rácz\, and th
en discuss joint recent work together with I. Bustamante where it is prove
d that non-degenerate compact Cauchy horizons on smooth vacuum spacetimes
(shortly CHs) have indeed constant non-zero temperature. It then follows b
y the work of Petersen and Petersen-Rácz that CHs are Killing horizons\,
and by the work of Beig-Chruściel-Schoen that such objects are non-gener
ic on the initial data (in agreement with the Cosmic Censorship conjecture
). A null-orbital and topological classification of CHs will also be comme
nted.\n
LOCATION:https://researchseminars.org/talk/jomarec/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lan-Hsuan Huang (University of Conneticut)
DTSTART;VALUE=DATE-TIME:20210506T133000Z
DTEND;VALUE=DATE-TIME:20210506T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/7
DESCRIPTION:Title:
Existence of static vacuum extensions\nby Lan-Hsuan Huang (University
of Conneticut) as part of JoMaReC - Joint Online Mathematical Relativity C
olloquium\n\n\nAbstract\nThe study of static vacuum Riemannian metrics ari
ses naturally in general relativity and differential geometry. A static va
cuum metric produces a static spacetime by a warped product\, and it is re
lated to scalar curvature deformation and gluing. The well-known Uniquenes
s Theorem of Static Black Holes says that an asymptotically flat\, static
vacuum metric with black hole boundary must belong to the Schwarzschild fa
mily. In contrast to the rigidity phenomenon\, R. Bartnik conjectured that
there are asymptotically flat\, static vacuum metric realizing certain ar
bitrarily specified boundary data. I will discuss recent progress toward t
his conjecture. It is based on joint work with Zhongshan An. \n \nIn the s
econd part of the talk (if time permits)\, I will discuss related topics i
n the non-time-symmetric case. In many ways\, a stationary vacuum initial
data set is a generalization of a static vacuum metric. However\, from the
point of view of deforming the dominant energy condition\, we discover th
at a “ground state” initial data set need not be stationary vacuum but
can sit in a null dust spacetime with a global Killing vector field\, suc
h as the pp-waves. This part is based on joint work with Dan Lee.\n
LOCATION:https://researchseminars.org/talk/jomarec/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Chruściel (University of Vienna)
DTSTART;VALUE=DATE-TIME:20210603T133000Z
DTEND;VALUE=DATE-TIME:20210603T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/8
DESCRIPTION:Title:
The hyperbolic positive energy theorem\nby Piotr Chruściel (Universit
y of Vienna) as part of JoMaReC - Joint Online Mathematical Relativity Col
loquium\n\n\nAbstract\nI will review the notion of mass of asymptotically
locally hyperbolic manifolds\, and sketch the proof of positivity of the e
nergy for manifolds with spherical conformal infinity.\n\nTalk based on jo
int work with Erwann Delay in arXiv: 1901.05263 [math.DG]\n
LOCATION:https://researchseminars.org/talk/jomarec/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Moschidis (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20210701T133000Z
DTEND;VALUE=DATE-TIME:20210701T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/9
DESCRIPTION:Title:
The instability of Anti-de Sitter spacetime for the Einstein-scalar field
system\nby Georgios Moschidis (University of California\, Berkeley) as
part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAb
stract\nThe AdS instability conjecture provides an example of weak turbule
nce appearing in the dynamics of the Einstein equations in the presence of
a negative cosmological constant. The conjecture claims the existence of
arbitrarily small perturbations to the initial data of Anti-de Sitter spac
etime which\, under evolution by the vacuum Einstein equations with reflec
ting boundary conditions at conformal infinity\, lead to the formation of
black holes after sufficiently long time. In this talk\, I will present a
rigorous proof of the AdS instability conjecture in the setting of the sph
erically symmetric Einstein-scalar field system. The construction of the u
nstable initial data will require carefully designing a family of initial
configurations of localized matter beams and estimating the exchange of en
ergy taking place between interacting beams over long periods of time\, as
well as estimating the decoherence rate of those beams. I will also discu
ss possible paths for extending these ideas to the vacuum case.\n
LOCATION:https://researchseminars.org/talk/jomarec/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihalis Dafermos (Princeton University and University of Cambridge
)
DTSTART;VALUE=DATE-TIME:20211007T133000Z
DTEND;VALUE=DATE-TIME:20211007T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/10
DESCRIPTION:Title: The black hole stability problem in general relativity\nby Mihalis Da
fermos (Princeton University and University of Cambridge) as part of JoMaR
eC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nI will
review the current status of the black hole stability problem in general
relativity and discuss joint work Holzegel\, Rodnianski and Taylor.\n
LOCATION:https://researchseminars.org/talk/jomarec/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Isenberg (University of Oregon)
DTSTART;VALUE=DATE-TIME:20220602T133000Z
DTEND;VALUE=DATE-TIME:20220602T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/11
DESCRIPTION:Title: Stability of AVTD behavior for polarized T^2-symmetric space-times\nb
y Jim Isenberg (University of Oregon) as part of JoMaReC - Joint Online Ma
thematical Relativity Colloquium\n\n\nAbstract\nOne of the most effective
tools for proving that Strong Cosmic Censorship holds for a family of cosm
ological solutions of Einstein’s equations is to verify that these solut
ions all exhibit Asymptotically Velocity Term Dominated (AVTD) behavior in
a neighborhood of their Big Bang singularities. After presenting some bac
kground history of known results and conjectures concerning the behavior o
f the gravitational field near the Big Bang in cosmological solutions of E
instein’s equations\, we discuss recent work with Ellery Ames\, Florian
Beyer\, and Todd Oliynyk in which we prove that polarized T^2-Symmetric va
cuum solutions in a neighborhood of Kasner solutions all exhibit AVTD beha
vior close to the initial singularity. We also discuss our very recent ext
ension of these results to the case of non-vanishing cosmological constant
.\n
LOCATION:https://researchseminars.org/talk/jomarec/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Graf (University of Tübingen)
DTSTART;VALUE=DATE-TIME:20211104T143000Z
DTEND;VALUE=DATE-TIME:20211104T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/12
DESCRIPTION:Title: Singularity theorems in low regularity\nby Melanie Graf (University o
f Tübingen) as part of JoMaReC - Joint Online Mathematical Relativity Col
loquium\n\n\nAbstract\nThe singularity theorems of R. Penrose and S. Hawki
ng from the 1960s show that a spacetime satisfying certain physically reas
onable curvature and causality conditions cannot be causal geodesically co
mplete. Despite their great success these classical theorems still have so
me drawbacks\, one of them being that they require smoothness of the metri
c while in many physical models the metric is less regular. In my talk I w
ill present work on singularity theorems based on distributional energy co
nditions for metrics that are merely continuously differentiable – a reg
ularity where one still has existence but not uniqueness for solutions of
the geodesic equation. We will see that an approximation-based approach to
the low-regularity issue is closely linked to establishing singularity th
eorems under weakened energy conditions and while the improvements necessa
ry are still entirely straightforward in the present case\, attempting to
lower the regularity further would require some new methods.\n
LOCATION:https://researchseminars.org/talk/jomarec/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Czimek (Brown University)
DTSTART;VALUE=DATE-TIME:20211202T143000Z
DTEND;VALUE=DATE-TIME:20211202T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/13
DESCRIPTION:Title: The characteristic gluing problem of general relativity\nby Stefan Cz
imek (Brown University) as part of JoMaReC - Joint Online Mathematical Rel
ativity Colloquium\n\n\nAbstract\nIn this talk we introduce and solve the
characteristic gluing problem for the Einstein vacuum equations. We prove
that obstructions to characteristic gluing come from an infinite-dimension
al space of conservation laws along null hypersurfaces for the linearized
equations at Minkowski. We show that this obstruction space splits into an
infinite-dimensional space of gauge-dependent charges and a 10-dimensiona
l space of gauge-invariant charges. We identify the 10 gauge-invariant cha
rges to be related to the energy\, linear momentum\, angular momentum and
center-of-mass of the spacetime. Based on this identification\, we explain
how to characteristically glue a given spacetime to a suitably chosen Ker
r black hole spacetime. As corollary we get an alternative proof of the Co
rvino-Schoen spacelike gluing to Kerr. Moreover\, we apply our characteris
tic gluing method to localise characteristic initial data along null hyper
surfaces. In particular\, this yields a new proof of the Carlotto-Schoen s
pacelike localization where our method yields no loss of decay\, thus reso
lving an open problem in this direction. We also outline further applicati
ons. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Prin
ceton).\n
LOCATION:https://researchseminars.org/talk/jomarec/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Ling (Rutgers University)
DTSTART;VALUE=DATE-TIME:20220203T143000Z
DTEND;VALUE=DATE-TIME:20220203T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/14
DESCRIPTION:Title: On the discrete Dirac spectrum of a point electron in the zero-gravity Ke
rr-Newman spacetime\nby Eric Ling (Rutgers University) as part of JoMa
ReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nIn re
lativistic quantum mechanics\, the point spectrum of the Dirac hamiltonian
with a Coulomb potential famously agrees with Sommerfeld’s fine structu
re formula for the hydrogen atom. In the Coulomb approximation\, the proto
n is assumed to only have a positive electric charge. However\, the physic
al proton also appears to have a magnetic moment which yields a hyperfine
structure of the hydrogen atom that’s normally computed perturbatively.
Aiming towards a non-perturbative approach\, Pekeris in 1987 proposed taki
ng the Kerr-Newman spacetime with its ring singularity as a source for the
proton’s electric charge and magnetic moment. Given the proton’s mass
and electric charge\, the resulting Kerr-Newman spacetime lies well withi
n the naked singularity sector which possess closed timelike loops. In 201
4 Tahvildar-Zadeh showed that the zero-gravity limit of the Kerr-Newman sp
acetime (zGKN) produces a flat but topologically nontrivial spacetime that
’s no longer plagued by closed timelike loops. In 2015 Tahvildar-Zadeh a
nd Kiessling studied the hydrogen problem with Dirac’s equation on the z
GKN spacetime and found that the hamiltonian is essentially self-adjoint a
nd contains a nonempty discrete spectrum. In this talk\, we show how their
ideas can be extended to classify the discrete spectrum completely and re
late it back to the known hydrogenic Dirac spectrum but yielding hyperfine
-like and Lamb shift-like effects.\n
LOCATION:https://researchseminars.org/talk/jomarec/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Sormani (City University of New York)
DTSTART;VALUE=DATE-TIME:20220505T133000Z
DTEND;VALUE=DATE-TIME:20220505T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/15
DESCRIPTION:Title: Towards a Spacetime Intrinsic Flat Convergence\nby Christina Sormani
(City University of New York) as part of JoMaReC - Joint Online Mathematic
al Relativity Colloquium\n\n\nAbstract\nIn order to define a spacetim
e intrinsic flat convergence\, Carlos Vega and I defined the null
distance to convert spacetimes endowed with regular cosmological time
s into metric spaces. Currently Anna Sakovich and I have been explo
ring the properties of these metric spaces. We can prove that on
e can recover the causal structure from the null distance and the cosm
ological time. We can prove that a distance-preserving time-preserving bij
ection between the spacetimes endowed with a null distance is in fact a Lo
rentzian isometry under suitable conditions. Next we will prove there ar
e biLipschitz charts so that we may view the spacetimes endowed with the n
ull distance as integral current spaces. This allows us to rigorously def
ine the spacetime intrinsic flat convergence for spacetimes that a
rise as the future maximal developments of initial\ndata sets. For
more information about intrinsic flat convergence see https://sites.googl
e.com/site/intrinsicflatconvergence/\n
LOCATION:https://researchseminars.org/talk/jomarec/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Wald (University of Chicago)
DTSTART;VALUE=DATE-TIME:20220407T133000Z
DTEND;VALUE=DATE-TIME:20220407T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/16
DESCRIPTION:Title: The memory effect and infrared divergences\nby Robert Wald (Universit
y of Chicago) as part of JoMaReC - Joint Online Mathematical Relativity Co
lloquium\n\n\nAbstract\nThe “memory effect” is the permanent relative
displacement of test particles after the passage of gravitational radiatio
n. It is associated with both the propagation of massive bodies out to tim
elike infinity (“ordinary memory”) or the propagation of radiation out
to null infinity (“null memory”). The memory effect can be characteri
zed by the failure of the shear tensor at order 1/r to return to zero at l
ate times\, even though it is “pure gauge.” Closely analogous effects
occur in electromagnetism\, where the vector potential at order 1/r fails
to return to zero even though it is “pure gauge.” In both cases\, the
Fourier transform of the radiative field has divergent behavior at low fre
quencies. This gives rise to infrared divergences (i.e.\, infinite numbers
of “soft” gravitons/photons) in the quantum field theory description
if one attempts to describe these states as vectors in the usual Fock Hilb
ert space representation. To obtain a mathematically sensible quantum scat
tering theory\, one must allow states with nonvanishing memory in the “i
n” and “out” Hilbert spaces. An elegant solution to this problem in
massive quantum electrodynamics was given by Kulish and Fadeev\, who const
ructed a Hilbert space of incoming/outgoing charged particle states that a
re “dressed” with radiative fields of corresponding memory\, so as to
yield vanishing large gauge charges at spatial infinity. However\, we show
that this type of construction fails in quantum gravity. The primary unde
rlying reason is that the “dressing” contributes to null memory\, ther
eby invalidating the construction of eigenstates of large gauge charges. I
n quantum gravity\, there does not appear to be any choice of (separable)
Hilbert space of incoming/outgoing states that can accommodate all scatter
ing states. Thus\, we argue that scattering should be described at the lev
el of algebraic incoming/outgoing states rather than attempting to artific
ially restrict states to a particular Hilbert space.\n
LOCATION:https://researchseminars.org/talk/jomarec/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Wyatt (University of Cambrdige)
DTSTART;VALUE=DATE-TIME:20220303T143000Z
DTEND;VALUE=DATE-TIME:20220303T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/17
DESCRIPTION:Title: Global Stability of Spacetimes with Supersymmetric Compactifications\
nby Zoe Wyatt (University of Cambrdige) as part of JoMaReC - Joint Online
Mathematical Relativity Colloquium\n\n\nAbstract\nSpacetimes with compact
directions which have special holonomy\, such as Calabi-Yau spaces\, play
an important role in supergravity and string theory. In this talk I will d
iscuss a recent work with Lars Andersson\, Pieter Blue and Shing-Tung Yau\
, where we show the global\, nonlinear stability a spacetime which is a ca
rtesian product of a high dimensional Minkowski space with a compact Ricci
flat internal space with special holonomy. This stability result is relat
ed to a conjecture of Penrose concerning the validity of string theory. Ou
r proof uses the intersection of methods for quasilinear wave and Klein-Go
rdon equations\, and so towards the end of the talk I will also comment mo
re generally on coupled wave–Klein-Gordon equations.\n
LOCATION:https://researchseminars.org/talk/jomarec/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Körber (University of Vienna)
DTSTART;VALUE=DATE-TIME:20220707T133000Z
DTEND;VALUE=DATE-TIME:20220707T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/18
DESCRIPTION:Title: Uniqueness of large area-constrained Willmore spheres in initial data set
s\nby Thomas Körber (University of Vienna) as part of JoMaReC - Joint
Online Mathematical Relativity Colloquium\n\n\nAbstract\nThe Hawking mass
of an area-constrained Willmore sphere is a useful quasi-local measure fo
r the strength of the gravitational field of an initial data set for the E
instein field equations. If the scalar curvature satisfies certain asympto
tic assumptions\, the asymptotic region of such an initial data set is fol
iated by large area-constrained Willmore spheres with non-negative Hawking
mass. It has been conjectured that these are the only such spheres. In th
is talk\, I will present a proof of this conjecture for all large area-con
strained Willmore spheres with non-negative Hawking mass and outer radius
less than the logarithm of the inner radius. This is joint work with Micha
el Eichmair\, Jan Metzger\, and Felix Schulze.\n
LOCATION:https://researchseminars.org/talk/jomarec/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badri Krishnan (Radboud University Nijmegen)
DTSTART;VALUE=DATE-TIME:20220901T133000Z
DTEND;VALUE=DATE-TIME:20220901T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/19
DESCRIPTION:Title: A quasi-local view of black hole mergers\nby Badri Krishnan (Radboud
University Nijmegen) as part of JoMaReC - Joint Online Mathematical Relati
vity Colloquium\n\n\nAbstract\nIn this talk I will summarize recent progre
ss and open mathematical problems in understanding black hole mergers quas
i-locally\, i.e. by using marginally trapped surfaces instead of event hor
izons.\n
LOCATION:https://researchseminars.org/talk/jomarec/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcus Khuri (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20221006T133000Z
DTEND;VALUE=DATE-TIME:20221006T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/20
DESCRIPTION:Title: Level Set Methods in Mathematical GR\nby Marcus Khuri (Stony Brook Un
iversity) as part of JoMaReC - Joint Online Mathematical Relativity Colloq
uium\n\n\nAbstract\nWe will review recent developments concerning the use
of level set techniques associated with solutions to elliptic equations\,
in particular spacetime harmonic functions\, and their application to posi
tive mass theorems and comparison geometry.\n
LOCATION:https://researchseminars.org/talk/jomarec/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Natário (Instituto Superior Técnico)
DTSTART;VALUE=DATE-TIME:20221103T143000Z
DTEND;VALUE=DATE-TIME:20221103T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/21
DESCRIPTION:Title: Relativistic elasticity and compactness bounds\nby José Natário (In
stituto Superior Técnico) as part of JoMaReC - Joint Online Mathematical
Relativity Colloquium\n\n\nAbstract\nAfter reviewing the basics of relativ
istic elasticity theory\, I will introduce a general framework to study sp
herically symmetric self-gravitating elastic bodies systematically within
general relativity\, and apply it to investigate compactness bounds in thi
s context.\n
LOCATION:https://researchseminars.org/talk/jomarec/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Columbia University)
DTSTART;VALUE=DATE-TIME:20221201T143000Z
DTEND;VALUE=DATE-TIME:20221201T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/22
DESCRIPTION:Title: Physical-space estimates on black hole perturbations\nby Elena Giorgi
(Columbia University) as part of JoMaReC - Joint Online Mathematical Rela
tivity Colloquium\n\n\nAbstract\nMost works on the analysis of the wave eq
uation on Kerr black holes rely on a combination of the vector field metho
d and Fourier decomposition\, with the notable exception of a generalized
vector field method introduced by Andersson-Blue. Their method allows for
commutation with second order differential operators entirely in physical-
space by supplementing the Killing vector fields with the Carter operator
of Kerr to obtain a local energy decay identity at the level of three deri
vatives of the solution for sufficiently small |a|. I this talk I will des
cribe the main ideas of Andersson-Blue's method and explain its advantages
in two recent applications where physical space-estimates have been cruci
al: the linear stability of Kerr-Newman black hole to coupled gravitationa
l-electromagnetic perturbations and our proof of the non-linear stability
of the slowly rotating Kerr family with Klainerman-Szeftel.\n
LOCATION:https://researchseminars.org/talk/jomarec/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémie Szeftel (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20230202T143000Z
DTEND;VALUE=DATE-TIME:20230202T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/23
DESCRIPTION:Title: The nonlinear stability of Kerr for small angular momentum\nby Jéré
mie Szeftel (Sorbonne Université) as part of JoMaReC - Joint Online Mathe
matical Relativity Colloquium\n\n\nAbstract\nI will introduce the celebrat
ed black hole stability conjecture according to which the Kerr family of m
etrics are stable as solutions to the Einstein vacuum equations of general
relativity. I will then discuss the history of this problem\, including a
recent work on the resolution of the black hole stability conjecture for
small angular momentum.\n
LOCATION:https://researchseminars.org/talk/jomarec/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert J. McCann (University of Toronto)
DTSTART;VALUE=DATE-TIME:20230302T143000Z
DTEND;VALUE=DATE-TIME:20230302T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/24
DESCRIPTION:Title: A nonsmooth approach to Einstein's theory of gravity\nby Robert J. Mc
Cann (University of Toronto) as part of JoMaReC - Joint Online Mathematica
l Relativity Colloquium\n\n\nAbstract\nWhile Einstein's theory of gravity
is formulated in a smooth setting\, the celebrated singularity theorems of
Hawking and Penrose describe many physical situations in which this smoot
hness must eventually breakdown. In positive-definite signature\, there is
a highly successful theory of metric and metric-measure geometry which in
cludes Riemannian manifolds as a special case\, but permits the extractio
n of nonsmooth limits under dimension and curvature bounds analogous to th
e energy conditions in relativity: here sectional curvature is reformulate
d through triangle comparison\, while Ricci curvature is reformulated usi
ng entropic convexity along geodesics of probability measures. This lectur
e explores recent progress in the development of an analogous theory in Lo
rentzian signature\, whose ultimate goal is to provide a nonsmooth theory
of gravity.\n
LOCATION:https://researchseminars.org/talk/jomarec/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lindblad Petersen (KTH Stockholm)
DTSTART;VALUE=DATE-TIME:20230406T133000Z
DTEND;VALUE=DATE-TIME:20230406T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/25
DESCRIPTION:Title: Wave equations in subextremal Kerr-de Sitter spacetimes\nby Oliver Li
ndblad Petersen (KTH Stockholm) as part of JoMaReC - Joint Online Mathemat
ical Relativity Colloquium\n\n\nAbstract\nIn 2013\, Vasy proved that solut
ions to linear wave equations in Kerr-de Sitter spacetimes have asymptotic
expansions in quasinormal modes up to an exponentially decaying term\, as
suming the angular momentum of the black hole satisfies certain bounds. Th
is was the first step towards the proof of non-linear stability for slowly
rotating Kerr-de Sitter black holes by Hintz and Vasy in 2018. In this ta
lk\, we extend Vasy's result to the full subextremal range of Kerr-de Sitt
er spacetimes\, by removing the restrictions on the angular momentum of th
e black hole. The proof is based on a new Fredholm setup and a new analysi
s of the trapping of photons around a Kerr-de Sitter black hole. This is j
oint work with Andras Vasy.\n
LOCATION:https://researchseminars.org/talk/jomarec/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ettore Minguzzi (University of Florence)
DTSTART;VALUE=DATE-TIME:20230504T133000Z
DTEND;VALUE=DATE-TIME:20230504T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/26
DESCRIPTION:Title: Abstract Lorentzian metric spaces and their Gromov-Hausdorff convergence<
/a>\nby Ettore Minguzzi (University of Florence) as part of JoMaReC - Join
t Online Mathematical Relativity Colloquium\n\n\nAbstract\nA definition fo
r `bounded Lorentzian metric space' is presented and discussed. This is an
abstract notion of Lorentzian metric space that is sufficiently general t
o comprise compact causally convex subsets of globally hyperbolic (smooth)
spacetimes\, and causets.\nIt is shown that a generalization of the Gromo
v-Hausdorff distance and convergence can be applied to these spaces. Furth
ermore\, two additional axioms of timelike connectedness and existence of
maximizers\, which are stable under GH-convergence\, lead to suitable noti
ons of Lorentzian pre-length and length spaces. Similarly\, sectional curv
ature bounds stable under GH-convergence can be introduced. A (pre)compact
ness theorem is also mentioned and its limitations are discussed. Talk bas
ed on joint work with Stefan Suhr (Bochum).\n
LOCATION:https://researchseminars.org/talk/jomarec/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Virginia Agostiniani (University of Trento)
DTSTART;VALUE=DATE-TIME:20230601T133000Z
DTEND;VALUE=DATE-TIME:20230601T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/27
DESCRIPTION:Title: A Green’s function proof of the positive mass theorem and related topic
s\nby Virginia Agostiniani (University of Trento) as part of JoMaReC -
Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nIn this ta
lk\, we will explore the role of harmonic and p-harmonic functions in esta
blishing fundamental geometric inequalities in mathematical relativity\, s
uch as the positive mass theorem and the Penrose inequality. We will intro
duce new monotonicity formulas along the level flow of these functions\, w
hich provide simple proofs for these inequalities. Additionally\, we will
discuss how these formulas can be used to characterize the nonnegativity o
f the scalar curvature\, suggesting a synthetic notion of this concept app
licable in non-smooth contexts.\n
LOCATION:https://researchseminars.org/talk/jomarec/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cécile Huneau (École Polytechnique)
DTSTART;VALUE=DATE-TIME:20230706T133000Z
DTEND;VALUE=DATE-TIME:20230706T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/28
DESCRIPTION:Title: High frequency solutions in general relativity and the Burnett’s conjec
ture\nby Cécile Huneau (École Polytechnique) as part of JoMaReC - Jo
int Online Mathematical Relativity Colloquium\n\n\nAbstract\nIn this talk\
, I will review some works in collaboration with Jonathan Luk on the behav
iour of high frequency solutions to the Einstein equations. In the eightie
s\, the physicist Burnett conjectured that the adherence of the solutions
to the Einstein equations\, converging strongly at the level of the metric
\, and with boudedness assumptions at the level of derivative of the metri
c\, are the solutions to the Einstein-massless Vlasov equations. I will fo
cus on the resolution of this conjecture with the additionnal assumption o
f a translation symmetry\, and explain how to approximate a solution to th
e Einstein-Vlasov equations by vacuum solutions.\n
LOCATION:https://researchseminars.org/talk/jomarec/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Huisken (University of Tübingen)
DTSTART;VALUE=DATE-TIME:20231102T143000Z
DTEND;VALUE=DATE-TIME:20231102T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/29
DESCRIPTION:Title: Some observations on quasi-local mass and quasi-local radius\nby Gerh
ard Huisken (University of Tübingen) as part of JoMaReC - Joint Online Ma
thematical Relativity Colloquium\n\n\nAbstract\nThe lecture examines older
and newer concepts of quasi-local mass for one domain relative to another
\nas well as concepts of quasi-local radius in relation to the hoop-conjec
ture.\n
LOCATION:https://researchseminars.org/talk/jomarec/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schoen (University of California\, Irvine)
DTSTART;VALUE=DATE-TIME:20231207T143000Z
DTEND;VALUE=DATE-TIME:20231207T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/30
DESCRIPTION:Title: How minimal hypersurface and MOTS singularities affect relativity theorem
s\nby Rick Schoen (University of California\, Irvine) as part of JoMaR
eC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nSome t
heorems in relativity work directly only in low dimensions because of the
possibility of singularities in area minimizing hypersurfaces and MOTS. Th
ese include both Riemannian and spacetime positive mass theorems as well a
s the Riemannian Penrose inequality. In some cases the singularities are r
elatively easy to work around and in others they present significant probl
ems to overcome. This will be a general lecture which will attempt to give
perspective and more clarity to this issue.\n
LOCATION:https://researchseminars.org/talk/jomarec/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyros Alexakis (University of Toronto)
DTSTART;VALUE=DATE-TIME:20240201T143000Z
DTEND;VALUE=DATE-TIME:20240201T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/31
DESCRIPTION:Title: Squeezing a fixed amount of gravitational energy to arbitrarily small sca
les\, in U(1) symmetry\nby Spyros Alexakis (University of Toronto) as
part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbs
tract\nWe discuss a construction of polarized U(1) space-times of a “fix
ed size”\, where the initial data contains a given amount η>0 of incomi
ng gravitational energy which is allowed to be supported at arbitrarily sm
all scales\, without affecting the time of existence. More specialized exa
mples can be constructed where any chosen fraction of this initial incomin
g energy can stay focused along a null geodesic\, in the U(1) picture. We
discuss the relationship of this result with one direction of Thorne’s h
oop conjecture. The work relies on a special structure of the Einstein equ
ations in this symmetry class\, a new re-scaling of the equations and larg
e-time control\, along with a new local Klainerman-Sobolev estimate. Time
permitting\, some comparisons of the result and the methods with large-dat
a constructions for the Einstein equations over the last decade will also
be presented.\n
LOCATION:https://researchseminars.org/talk/jomarec/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Teixeira da Costa (Princeton University\, University of Cambr
idge)
DTSTART;VALUE=DATE-TIME:20240307T143000Z
DTEND;VALUE=DATE-TIME:20240307T153000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/32
DESCRIPTION:Title: The Teukolsky equation on Kerr in the full subextremal range\nby Rita
Teixeira da Costa (Princeton University\, University of Cambridge) as par
t of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstra
ct\nThe Teukolsky equation is one of the fundamental equations governing l
inear gravitational perturbations of the Kerr black hole family as solutio
ns to the vacuum Einstein equations. I will discuss joint work with Yakov
Shlapentokh-Rothman (Toronto)\, where we show that solutions arising from
suitably regular initial data decay inverse polynomially in time. Our proo
f holds for the entire subextremal range of Kerr black hole parameters (|a
| < M).\n
LOCATION:https://researchseminars.org/talk/jomarec/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Lee (City University of New York)
DTSTART;VALUE=DATE-TIME:20240404T133000Z
DTEND;VALUE=DATE-TIME:20240404T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/33
DESCRIPTION:Title: The equality case of the positive mass theorem\nby Dan Lee (City Univ
ersity of New York) as part of JoMaReC - Joint Online Mathematical Relativ
ity Colloquium\n\n\nAbstract\nWe will review the equality case of the posi
tive mass theorem for initial data sets and discuss its proof in the gener
al (not necessarily spin) setting. This is joint work with Lan-Hsuan Huang
.\n
LOCATION:https://researchseminars.org/talk/jomarec/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Kehle (ETH Zürich)
DTSTART;VALUE=DATE-TIME:20240502T133000Z
DTEND;VALUE=DATE-TIME:20240502T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/34
DESCRIPTION:Title: Retiring the third law of black hole thermodynamics\nby Christoph Keh
le (ETH Zürich) as part of JoMaReC - Joint Online Mathematical Relativity
Colloquium\n\n\nAbstract\nExtremal black holes are special types of black
holes which have exactly zero temperature. I will present a proof that ex
tremal black holes form in finite time in gravitational collapse of charge
d matter. In particular\, this construction provides a definitive disproof
of the "third law" of black hole thermodynamics. We also show that extrem
al black holes take on a central role in gravitational collapse\, giving r
ise to a new conjectural picture of "extremal critical collapse." This is
joint work with Ryan Unger (Princeton).\n
LOCATION:https://researchseminars.org/talk/jomarec/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Valiente Kroon (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20240606T133000Z
DTEND;VALUE=DATE-TIME:20240606T143000Z
DTSTAMP;VALUE=DATE-TIME:20240614T055526Z
UID:jomarec/35
DESCRIPTION:Title: BMS-supertranslation charges at the critical sets of null infinity\nb
y Juan Valiente Kroon (Queen Mary University of London) as part of JoMaReC
- Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nFor asym
ptotically flat spacetimes\, a conjecture by Strominger states that asympt
otic BMS-supertranslations and their associated charges at past null infin
ity can be related to those at future null infinity via an antipodal map a
t spatial infinity. We analyse the validity of this conjecture using Fried
rich's formulation of spatial infinity\, which gives rise to a regular ini
tial value problem for the conformal field equations at spatial infinity.
We show that for a generic class of asymptotically Euclidean and regular
initial data\, BMS-supertranslation charges are not well-defined at the cr
itical sets where null infinity meets spatial infinity unless the initial
data satisfies an extra regularity condition. We also show that given init
ial data that satisfy the regularity condition\, BMS-supertranslation char
ges at the critical sets are fully determined by the initial data and that
the relation between the charges at past null infinity and those at futur
e null infinity directly follows from our regularity condition. This is jo
int work with Mariem Magdy Ali Mohamed and Kartik Prabhu.\n
LOCATION:https://researchseminars.org/talk/jomarec/35/
END:VEVENT
END:VCALENDAR