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BEGIN:VEVENT
SUMMARY:Hans Ringström (KTH Stockholm)
DTSTART:20201001T133000Z
DTEND:20201001T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/1
DESCRIPTION:Title: On highly anisotropic big bang singularities\nby Hans Ringströ
m (KTH Stockholm) as part of JoMaReC - Joint Online Mathematical Relativit
y Colloquium\n\n\nAbstract\nIn cosmology\, the universe is typically model
led by spatially homogeneous and isotropic solutions to Einstein’s equat
ions. However\, for large classes of matter models\, such solutions are un
stable in the direction of the singularity. For this reason\, it is of int
erest to study the anisotropic setting. \n\nThe purpose of the talk is to
describe a framework for studying highly anisotropic singularities. In par
ticular\, for analysing the asymptotics of solutions to linear systems of
wave equations on the corresponding backgrounds and deducing information c
oncerning the geometry.\n\nThe talk will begin with an overview of existin
g results. This will serve as a background and motivation for the problem
considered\, but also as a justification for the assumptions defining the
framework we develop. Following this overview\, the talk will conclude wit
h a rough description of the results.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Galloway (University of Miami)
DTSTART:20201105T143000Z
DTEND:20201105T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/2
DESCRIPTION:Title: Initial data rigidity results\nby Greg Galloway (University of
Miami) as part of JoMaReC - Joint Online Mathematical Relativity Colloquiu
m\n\n\nAbstract\nWe present several rigidity results for initial data sets
motivated by the positive mass theorem. An important step in our proofs i
s to establish conditions that ensure that a marginally outer trapped surf
ace is “weakly outermost”. A rigidity result for Riemannian manifolds
with a lower bound on their scalar curvature is included as a special case
. Relevant background on marginally outer trapped surfaces will be discus
sed. This talk is based on joint work with Michael Eichmair and Abraão Me
ndes.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lydia Bieri (University of Michigan\, Ann Arbor)
DTSTART:20201203T143000Z
DTEND:20201203T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/3
DESCRIPTION:Title: New structures in gravitational radiation\nby Lydia Bieri (Univ
ersity of Michigan\, Ann Arbor) as part of JoMaReC - Joint Online Mathemat
ical Relativity Colloquium\n\n\nAbstract\nGravitational waves are transpor
ting information from faraway regions of the Universe. A new era began wit
h the first detection of gravitational waves by Advanced LIGO in September
2015\, and since then several events have been recorded by the LIGO/VIRGO
collaboration. New challenges await us to unravel the interesting interpl
ay between physics\, astrophysics and mathematics. Most studies so far hav
e been devoted to sources like binary black hole mergers or neutron star m
ergers\, or generally to sources that are stationary outside of a compact
set. We describe these systems by asymptotically-flat manifolds solving th
e Einstein equations. These sources have in common that far away their gra
vitational field decays fast enough towards Minkowski spacetime. In partic
ular\, far away from the source\, the decay behavior can be described by a
term that is homogeneous of degree -1 and lower order terms. I will prese
nt new results on gravitational radiation for sources that are not station
ary outside of a compact set\, but whose gravitational fields decay more s
lowly towards infinity. A panorama of new gravitational effects opens up w
hen delving deeper into these more general spacetimes. In particular\, whe
reas the former sources produce memory effects that are of purely electric
parity (permanent displacement only)\, the latter in addition generate me
mory of magnetic type\, thus allowing for rotation in the system. These ne
w effects emerge naturally from the Einstein equations.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harvey Reall (University of Cambridge)
DTSTART:20210204T143000Z
DTEND:20210204T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/4
DESCRIPTION:Title: Well-posed formulation of Lovelock and Horndeski theories\nby H
arvey Reall (University of Cambridge) as part of JoMaReC - Joint Online Ma
thematical Relativity Colloquium\n\n\nAbstract\nLovelock theories are the
most general diffeomorphism invariant theories of gravity in higher dimens
ions with second order equations of motion. Horndeski theories are the mos
t general diffeomorphism invariant theories of gravity coupled to a scalar
field in four dimensions with second order equations of motion. In this t
alk I will discuss well-posedness of the initial value problem for these t
heories. Previous work has shown that (generalised) harmonic gauge does no
t give a well-posed initial value problem. I will describe recent work wit
h Aron Kovacs in which we introdued a modification of harmonic gauge that
does give a well-posed initial value problem provided that the theory rema
ins “weakly coupled”. Our modified harmonic gauge may also have applic
ations in conventional GR.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Rodnianski (Princeton University)
DTSTART:20210304T143000Z
DTEND:20210304T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/5
DESCRIPTION:Title: On naked singularities in Einstein equations\nby Igor Rodniansk
i (Princeton University) as part of JoMaReC - Joint Online Mathematical Re
lativity Colloquium\n\n\nAbstract\nI will describe recent and ongoing work
with Y. Shlapentokh-Rothman on a construction of solutions to the Einstei
n vacuum equations corresponding to a naked singularity forming from a re
gular past. The talk will focus on a new geometric phenomenon\, correspond
ing to twisting of null geodesics\, new type of self-similarity\, dynamica
l approach to the problem\, and on the comparisons with the naked singular
ity solutions constructed by Christodoulou for the spherically symmetric E
instein-scalar field model.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martín Reiris (Universidad de la República\, Montevideo)
DTSTART:20210401T133000Z
DTEND:20210401T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/6
DESCRIPTION:Title: New results on compact Cauchy horizons of smooth vacuum spacetimes<
/a>\nby Martín Reiris (Universidad de la República\, Montevideo) as part
of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstrac
t\nCauchy horizons are rather unique and peculiar objects that have been s
tudied for decades. In this talk I will first review old and new breakthro
ughs on the subject by Isenberg and Moncrief\, and by Petersen and Rácz\,
and then discuss joint recent work together with I. Bustamante where it i
s proved that non-degenerate compact Cauchy horizons on smooth vacuum spac
etimes (shortly CHs) have indeed constant non-zero temperature. It then fo
llows by the work of Petersen and Petersen-Rácz that CHs are Killing hori
zons\, and by the work of Beig-Chruściel-Schoen that such objects are no
n-generic on the initial data (in agreement with the Cosmic Censorship con
jecture). A null-orbital and topological classification of CHs will also b
e commented.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lan-Hsuan Huang (University of Conneticut)
DTSTART:20210506T133000Z
DTEND:20210506T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/7
DESCRIPTION:Title: Existence of static vacuum extensions\nby Lan-Hsuan Huang (Univ
ersity of Conneticut) as part of JoMaReC - Joint Online Mathematical Relat
ivity Colloquium\n\n\nAbstract\nThe study of static vacuum Riemannian metr
ics arises naturally in general relativity and differential geometry. A st
atic vacuum metric produces a static spacetime by a warped product\, and i
t is related to scalar curvature deformation and gluing. The well-known Un
iqueness Theorem of Static Black Holes says that an asymptotically flat\,
static vacuum metric with black hole boundary must belong to the Schwarzsc
hild family. In contrast to the rigidity phenomenon\, R. Bartnik conjectur
ed that there are asymptotically flat\, static vacuum metric realizing cer
tain arbitrarily specified boundary data. I will discuss recent progress t
oward this conjecture. It is based on joint work with Zhongshan An. \n \nI
n the second part of the talk (if time permits)\, I will discuss related t
opics in the non-time-symmetric case. In many ways\, a stationary vacuum i
nitial data set is a generalization of a static vacuum metric. However\, f
rom the point of view of deforming the dominant energy condition\, we disc
over that a “ground state” initial data set need not be stationary vac
uum but can sit in a null dust spacetime with a global Killing vector fiel
d\, such as the pp-waves. This part is based on joint work with Dan Lee.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piotr Chruściel (University of Vienna)
DTSTART:20210603T133000Z
DTEND:20210603T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/8
DESCRIPTION:Title: The hyperbolic positive energy theorem\nby Piotr Chruściel (Un
iversity of Vienna) as part of JoMaReC - Joint Online Mathematical Relativ
ity Colloquium\n\n\nAbstract\nI will review the notion of mass of asymptot
ically locally hyperbolic manifolds\, and sketch the proof of positivity o
f the energy for manifolds with spherical conformal infinity.\n\nTalk base
d on joint work with Erwann Delay in arXiv: 1901.05263 [math.DG]\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Moschidis (University of California\, Berkeley)
DTSTART:20210701T133000Z
DTEND:20210701T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/9
DESCRIPTION:Title: The instability of Anti-de Sitter spacetime for the Einstein-scalar
field system\nby Georgios Moschidis (University of California\, Berke
ley) as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\
n\n\nAbstract\nThe AdS instability conjecture provides an example of weak
turbulence appearing in the dynamics of the Einstein equations in the pres
ence of a negative cosmological constant. The conjecture claims the existe
nce of arbitrarily small perturbations to the initial data of Anti-de Sitt
er spacetime which\, under evolution by the vacuum Einstein equations with
reflecting boundary conditions at conformal infinity\, lead to the format
ion of black holes after sufficiently long time. In this talk\, I will pre
sent a rigorous proof of the AdS instability conjecture in the setting of
the spherically symmetric Einstein-scalar field system. The construction o
f the unstable initial data will require carefully designing a family of i
nitial configurations of localized matter beams and estimating the exchang
e of energy taking place between interacting beams over long periods of ti
me\, as well as estimating the decoherence rate of those beams. I will als
o discuss possible paths for extending these ideas to the vacuum case.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihalis Dafermos (Princeton University and University of Cambridge
)
DTSTART:20211007T133000Z
DTEND:20211007T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/10
DESCRIPTION:Title: The black hole stability problem in general relativity\nby Mih
alis Dafermos (Princeton University and University of Cambridge) as part o
f JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\
nI will review the current status of the black hole stability problem in g
eneral relativity and discuss joint work Holzegel\, Rodnianski and Taylor.
\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Isenberg (University of Oregon)
DTSTART:20220602T133000Z
DTEND:20220602T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/11
DESCRIPTION:Title: Stability of AVTD behavior for polarized T^2-symmetric space-times
\nby Jim Isenberg (University of Oregon) as part of JoMaReC - Joint On
line Mathematical Relativity Colloquium\n\n\nAbstract\nOne of the most eff
ective tools for proving that Strong Cosmic Censorship holds for a family
of cosmological solutions of Einstein’s equations is to verify that thes
e solutions all exhibit Asymptotically Velocity Term Dominated (AVTD) beha
vior in a neighborhood of their Big Bang singularities. After presenting s
ome background history of known results and conjectures concerning the beh
avior of the gravitational field near the Big Bang in cosmological solutio
ns of Einstein’s equations\, we discuss recent work with Ellery Ames\, F
lorian Beyer\, and Todd Oliynyk in which we prove that polarized T^2-Symme
tric vacuum solutions in a neighborhood of Kasner solutions all exhibit AV
TD behavior close to the initial singularity. We also discuss our very rec
ent extension of these results to the case of non-vanishing cosmological c
onstant.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Graf (University of Tübingen)
DTSTART:20211104T143000Z
DTEND:20211104T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/12
DESCRIPTION:Title: Singularity theorems in low regularity\nby Melanie Graf (Unive
rsity of Tübingen) as part of JoMaReC - Joint Online Mathematical Relativ
ity Colloquium\n\n\nAbstract\nThe singularity theorems of R. Penrose and S
. Hawking from the 1960s show that a spacetime satisfying certain physical
ly reasonable curvature and causality conditions cannot be causal geodesic
ally complete. Despite their great success these classical theorems still
have some drawbacks\, one of them being that they require smoothness of th
e metric while in many physical models the metric is less regular. In my t
alk I will present work on singularity theorems based on distributional en
ergy conditions for metrics that are merely continuously differentiable
– a regularity where one still has existence but not uniqueness for solu
tions of the geodesic equation. We will see that an approximation-based ap
proach to the low-regularity issue is closely linked to establishing singu
larity theorems under weakened energy conditions and while the improvement
s necessary are still entirely straightforward in the present case\, attem
pting to lower the regularity further would require some new methods.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Czimek (Brown University)
DTSTART:20211202T143000Z
DTEND:20211202T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/13
DESCRIPTION:Title: The characteristic gluing problem of general relativity\nby St
efan Czimek (Brown University) as part of JoMaReC - Joint Online Mathemati
cal Relativity Colloquium\n\n\nAbstract\nIn this talk we introduce and sol
ve the characteristic gluing problem for the Einstein vacuum equations. We
prove that obstructions to characteristic gluing come from an infinite-di
mensional space of conservation laws along null hypersurfaces for the line
arized equations at Minkowski. We show that this obstruction space splits
into an infinite-dimensional space of gauge-dependent charges and a 10-dim
ensional space of gauge-invariant charges. We identify the 10 gauge-invari
ant charges to be related to the energy\, linear momentum\, angular moment
um and center-of-mass of the spacetime. Based on this identification\, we
explain how to characteristically glue a given spacetime to a suitably cho
sen Kerr black hole spacetime. As corollary we get an alternative proof of
the Corvino-Schoen spacelike gluing to Kerr. Moreover\, we apply our char
acteristic gluing method to localise characteristic initial data along nul
l hypersurfaces. In particular\, this yields a new proof of the Carlotto-S
choen spacelike localization where our method yields no loss of decay\, th
us resolving an open problem in this direction. We also outline further ap
plications. This is joint work with S. Aretakis (Toronto) and I. Rodniansk
i (Princeton).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Ling (Rutgers University)
DTSTART:20220203T143000Z
DTEND:20220203T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/14
DESCRIPTION:Title: On the discrete Dirac spectrum of a point electron in the zero-gra
vity Kerr-Newman spacetime\nby Eric Ling (Rutgers University) as part
of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract
\nIn relativistic quantum mechanics\, the point spectrum of the Dirac hami
ltonian with a Coulomb potential famously agrees with Sommerfeld’s fine
structure formula for the hydrogen atom. In the Coulomb approximation\, th
e proton is assumed to only have a positive electric charge. However\, the
physical proton also appears to have a magnetic moment which yields a hyp
erfine structure of the hydrogen atom that’s normally computed perturbat
ively. Aiming towards a non-perturbative approach\, Pekeris in 1987 propos
ed taking 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 w
ell within the naked singularity sector which possess closed timelike loop
s. In 2014 Tahvildar-Zadeh showed that the zero-gravity limit of the Kerr-
Newman spacetime (zGKN) produces a flat but topologically nontrivial space
time that’s no longer plagued by closed timelike loops. In 2015 Tahvilda
r-Zadeh and Kiessling studied the hydrogen problem with Dirac’s equation
on the zGKN spacetime and found that the hamiltonian is essentially self-
adjoint and contains a nonempty discrete spectrum. In this talk\, we show
how their ideas can be extended to classify the discrete spectrum complete
ly and relate it back to the known hydrogenic Dirac spectrum but yielding
hyperfine-like and Lamb shift-like effects.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Sormani (City University of New York)
DTSTART:20220505T133000Z
DTEND:20220505T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/15
DESCRIPTION:Title: Towards a Spacetime Intrinsic Flat Convergence\nby Christina S
ormani (City University of New York) as part of JoMaReC - Joint Online Mat
hematical Relativity Colloquium\n\n\nAbstract\nIn order to define a s
pacetime intrinsic flat convergence\, Carlos Vega and I defined th
e null distance to convert spacetimes endowed with regular cosmologic
al times into metric spaces. Currently Anna Sakovich and I have been
exploring the properties of these metric spaces. We can prove t
hat one can recover the causal structure from the null distance and t
he cosmological time. We can prove that a distance-preserving time-preserv
ing bijection between the spacetimes endowed with a null distance is in fa
ct a Lorentzian isometry under suitable conditions. Next we will prove t
here are biLipschitz charts so that we may view the spacetimes endowed wit
h the null distance as integral current spaces. This allows us to rigorous
ly define the spacetime intrinsic flat convergence for spacetimes
that arise as the future maximal developments of initial\ndata set
s. For more information about intrinsic flat convergence see https://site
s.google.com/site/intrinsicflatconvergence/\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Wald (University of Chicago)
DTSTART:20220407T133000Z
DTEND:20220407T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/16
DESCRIPTION:Title: The memory effect and infrared divergences\nby Robert Wald (Un
iversity of Chicago) as part of JoMaReC - Joint Online Mathematical Relati
vity Colloquium\n\n\nAbstract\nThe “memory effect” is the permanent re
lative displacement of test particles after the passage of gravitational r
adiation. It is associated with both the propagation of massive bodies out
to timelike infinity (“ordinary memory”) or the propagation of radiat
ion out to null infinity (“null memory”). The memory effect can be cha
racterized by the failure of the shear tensor at order 1/r to return to ze
ro at late times\, even though it is “pure gauge.” Closely analogous e
ffects 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 frequencies. This gives rise to infrared divergences (i.e.\, infinite
numbers of “soft” gravitons/photons) in the quantum field theory descr
iption if one attempts to describe these states as vectors in the usual Fo
ck Hilbert space representation. To obtain a mathematically sensible quant
um scattering theory\, one must allow states with nonvanishing memory in t
he “in” and “out” Hilbert spaces. An elegant solution to this prob
lem in massive quantum electrodynamics was given by Kulish and Fadeev\, wh
o constructed a Hilbert space of incoming/outgoing charged particle states
that are “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 prima
ry underlying reason is that the “dressing” contributes to null memory
\, thereby invalidating the construction of eigenstates of large gauge cha
rges. In quantum gravity\, there does not appear to be any choice of (sepa
rable) Hilbert space of incoming/outgoing states that can accommodate all
scattering states. Thus\, we argue that scattering should be described at
the level of algebraic incoming/outgoing states rather than attempting to
artificially restrict states to a particular Hilbert space.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zoe Wyatt (University of Cambrdige)
DTSTART:20220303T143000Z
DTEND:20220303T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/17
DESCRIPTION:Title: Global Stability of Spacetimes with Supersymmetric Compactificatio
ns\nby Zoe Wyatt (University of Cambrdige) as part of JoMaReC - Joint
Online Mathematical Relativity Colloquium\n\n\nAbstract\nSpacetimes with c
ompact directions which have special holonomy\, such as Calabi-Yau spaces\
, play an important role in supergravity and string theory. In this talk I
will discuss a recent work with Lars Andersson\, Pieter Blue and Shing-Tu
ng Yau\, where we show the global\, nonlinear stability a spacetime which
is a cartesian product of a high dimensional Minkowski space with a compac
t Ricci flat internal space with special holonomy. This stability result i
s related to a conjecture of Penrose concerning the validity of string the
ory. Our proof uses the intersection of methods for quasilinear wave and K
lein-Gordon equations\, and so towards the end of the talk I will also com
ment more generally on coupled wave–Klein-Gordon equations.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Körber (University of Vienna)
DTSTART:20220707T133000Z
DTEND:20220707T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/18
DESCRIPTION:Title: Uniqueness of large area-constrained Willmore spheres in initial d
ata sets\nby Thomas Körber (University of Vienna) as part of JoMaReC
- Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nThe Hawki
ng mass of an area-constrained Willmore sphere is a useful quasi-local mea
sure for the strength of the gravitational field of an initial data set fo
r the Einstein field equations. If the scalar curvature satisfies certain
asymptotic assumptions\, the asymptotic region of such an initial data set
is foliated by large area-constrained Willmore spheres with non-negative
Hawking mass. It has been conjectured that these are the only such spheres
. In this talk\, I will present a proof of this conjecture for all large a
rea-constrained Willmore spheres with non-negative Hawking mass and outer
radius less than the logarithm of the inner radius. This is joint work wit
h Michael Eichmair\, Jan Metzger\, and Felix Schulze.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badri Krishnan (Radboud University Nijmegen)
DTSTART:20220901T133000Z
DTEND:20220901T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/19
DESCRIPTION:Title: A quasi-local view of black hole mergers\nby Badri Krishnan (R
adboud University Nijmegen) as part of JoMaReC - Joint Online Mathematical
Relativity Colloquium\n\n\nAbstract\nIn this talk I will summarize recent
progress and open mathematical problems in understanding black hole merge
rs quasi-locally\, i.e. by using marginally trapped surfaces instead of ev
ent horizons.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcus Khuri (Stony Brook University)
DTSTART:20221006T133000Z
DTEND:20221006T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/20
DESCRIPTION:Title: Level Set Methods in Mathematical GR\nby Marcus Khuri (Stony B
rook University) as part of JoMaReC - Joint Online Mathematical Relativity
Colloquium\n\n\nAbstract\nWe will review recent developments concerning t
he use of level set techniques associated with solutions to elliptic equat
ions\, in particular spacetime harmonic functions\, and their application
to positive mass theorems and comparison geometry.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Natário (Instituto Superior Técnico)
DTSTART:20221103T143000Z
DTEND:20221103T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/21
DESCRIPTION:Title: Relativistic elasticity and compactness bounds\nby José Natá
rio (Instituto Superior Técnico) as part of JoMaReC - Joint Online Mathem
atical Relativity Colloquium\n\n\nAbstract\nAfter reviewing the basics of
relativistic elasticity theory\, I will introduce a general framework to s
tudy spherically symmetric self-gravitating elastic bodies systematically
within general relativity\, and apply it to investigate compactness bounds
in this context.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Columbia University)
DTSTART:20221201T143000Z
DTEND:20221201T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/22
DESCRIPTION:Title: Physical-space estimates on black hole perturbations\nby Elena
Giorgi (Columbia University) as part of JoMaReC - Joint Online Mathematic
al Relativity Colloquium\n\n\nAbstract\nMost works on the analysis of the
wave equation on Kerr black holes rely on a combination of the vector fiel
d method and Fourier decomposition\, with the notable exception of a gener
alized vector field method introduced by Andersson-Blue. Their method allo
ws for commutation with second order differential operators entirely in ph
ysical-space by supplementing the Killing vector fields with the Carter op
erator of Kerr to obtain a local energy decay identity at the level of thr
ee derivatives of the solution for sufficiently small |a|. I this talk I w
ill describe the main ideas of Andersson-Blue's method and explain its adv
antages in two recent applications where physical space-estimates have bee
n crucial: the linear stability of Kerr-Newman black hole to coupled gravi
tational-electromagnetic perturbations and our proof of the non-linear sta
bility of the slowly rotating Kerr family with Klainerman-Szeftel.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémie Szeftel (Sorbonne Université)
DTSTART:20230202T143000Z
DTEND:20230202T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/23
DESCRIPTION:Title: The nonlinear stability of Kerr for small angular momentum\nby
Jérémie Szeftel (Sorbonne Université) as part of JoMaReC - Joint Onlin
e Mathematical Relativity Colloquium\n\n\nAbstract\nI will introduce the c
elebrated black hole stability conjecture according to which the Kerr fami
ly of metrics are stable as solutions to the Einstein vacuum equations of
general relativity. I will then discuss the history of this problem\, incl
uding a recent work on the resolution of the black hole stability conjectu
re for small angular momentum.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert J. McCann (University of Toronto)
DTSTART:20230302T143000Z
DTEND:20230302T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/24
DESCRIPTION:Title: A nonsmooth approach to Einstein's theory of gravity\nby Rober
t J. McCann (University of Toronto) as part of JoMaReC - Joint Online Math
ematical Relativity Colloquium\n\n\nAbstract\nWhile Einstein's theory of g
ravity is formulated in a smooth setting\, the celebrated singularity theo
rems of Hawking and Penrose describe many physical situations in which thi
s smoothness must eventually breakdown. In positive-definite signature\, t
here is a highly successful theory of metric and metric-measure geometry w
hich includes Riemannian manifolds as a special case\, but permits the ex
traction of nonsmooth limits under dimension and curvature bounds analogou
s to the energy conditions in relativity: here sectional curvature is refo
rmulated through triangle comparison\, while Ricci curvature is reformula
ted using entropic convexity along geodesics of probability measures. This
lecture explores recent progress in the development of an analogous theor
y in Lorentzian signature\, whose ultimate goal is to provide a nonsmooth
theory of gravity.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lindblad Petersen (KTH Stockholm)
DTSTART:20230406T133000Z
DTEND:20230406T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/25
DESCRIPTION:Title: Wave equations in subextremal Kerr-de Sitter spacetimes\nby Ol
iver Lindblad Petersen (KTH Stockholm) as part of JoMaReC - Joint Online M
athematical Relativity Colloquium\n\n\nAbstract\nIn 2013\, Vasy proved tha
t solutions to linear wave equations in Kerr-de Sitter spacetimes have asy
mptotic expansions in quasinormal modes up to an exponentially decaying te
rm\, assuming the angular momentum of the black hole satisfies certain bou
nds. This 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 talk\, we extend Vasy's result to the full subextremal range of Kerr-
de Sitter spacetimes\, by removing the restrictions on the angular momentu
m of the black hole. The proof is based on a new Fredholm setup and a new
analysis of the trapping of photons around a Kerr-de Sitter black hole. Th
is is joint work with Andras Vasy.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ettore Minguzzi (University of Florence)
DTSTART:20230504T133000Z
DTEND:20230504T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/26
DESCRIPTION:Title: Abstract Lorentzian metric spaces and their Gromov-Hausdorff conve
rgence\nby Ettore Minguzzi (University of Florence) as part of JoMaReC
- Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nA defini
tion for `bounded Lorentzian metric space' is presented and discussed. Thi
s is an abstract notion of Lorentzian metric space that is sufficiently ge
neral to comprise compact causally convex subsets of globally hyperbolic (
smooth) spacetimes\, and causets.\nIt is shown that a generalization of th
e Gromov-Hausdorff distance and convergence can be applied to these spaces
. Furthermore\, two additional axioms of timelike connectedness and existe
nce of maximizers\, which are stable under GH-convergence\, lead to suitab
le notions of Lorentzian pre-length and length spaces. Similarly\, section
al curvature bounds stable under GH-convergence can be introduced. A (pre)
compactness theorem is also mentioned and its limitations are discussed. T
alk based on joint work with Stefan Suhr (Bochum).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Virginia Agostiniani (University of Trento)
DTSTART:20230601T133000Z
DTEND:20230601T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/27
DESCRIPTION:Title: A Green’s function proof of the positive mass theorem and relate
d topics\nby Virginia Agostiniani (University of Trento) as part of Jo
MaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nIn
this talk\, we will explore the role of harmonic and p-harmonic functions
in establishing fundamental geometric inequalities in mathematical relativ
ity\, such as the positive mass theorem and the Penrose inequality. We wil
l introduce new monotonicity formulas along the level flow of these functi
ons\, which provide simple proofs for these inequalities. Additionally\, w
e will discuss how these formulas can be used to characterize the nonnegat
ivity of the scalar curvature\, suggesting a synthetic notion of this conc
ept applicable in non-smooth contexts.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cécile Huneau (École Polytechnique)
DTSTART:20230706T133000Z
DTEND:20230706T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/28
DESCRIPTION:Title: High frequency solutions in general relativity and the Burnett’s
conjecture\nby Cécile Huneau (École Polytechnique) as part of JoMaR
eC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nIn thi
s talk\, I will review some works in collaboration with Jonathan Luk on th
e behaviour of high frequency solutions to the Einstein equations. In the
eighties\, the physicist Burnett conjectured that the adherence of the sol
utions to the Einstein equations\, converging strongly at the level of the
metric\, and with boudedness assumptions at the level of derivative of th
e metric\, are the solutions to the Einstein-massless Vlasov equations. I
will focus on the resolution of this conjecture with the additionnal assum
ption of a translation symmetry\, and explain how to approximate a solutio
n to the Einstein-Vlasov equations by vacuum solutions.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Huisken (University of Tübingen)
DTSTART:20231102T143000Z
DTEND:20231102T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/29
DESCRIPTION:Title: Some observations on quasi-local mass and quasi-local radius\n
by Gerhard Huisken (University of Tübingen) as part of JoMaReC - Joint On
line Mathematical Relativity Colloquium\n\n\nAbstract\nThe lecture examine
s 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
-conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Schoen (University of California\, Irvine)
DTSTART:20231207T143000Z
DTEND:20231207T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/30
DESCRIPTION:Title: How minimal hypersurface and MOTS singularities affect relativity
theorems\nby Rick Schoen (University of California\, Irvine) as part o
f JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\
nSome theorems in relativity work directly only in low dimensions because
of the possibility of singularities in area minimizing hypersurfaces and M
OTS. These include both Riemannian and spacetime positive mass theorems as
well as the Riemannian Penrose inequality. In some cases the singularitie
s are relatively easy to work around and in others they present significan
t problems to overcome. This will be a general lecture which will attempt
to give perspective and more clarity to this issue.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyros Alexakis (University of Toronto)
DTSTART:20240201T143000Z
DTEND:20240201T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/31
DESCRIPTION:Title: Squeezing a fixed amount of gravitational energy to arbitrarily sm
all scales\, in U(1) symmetry\nby Spyros Alexakis (University of Toron
to) as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n
\n\nAbstract\nWe discuss a construction of polarized U(1) space-times of a
“fixed size”\, where the initial data contains a given amount η>0 of
incoming gravitational energy which is allowed to be supported at arbitra
rily small scales\, without affecting the time of existence. More speciali
zed examples can be constructed where any chosen fraction of this initial
incoming energy can stay focused along a null geodesic\, in the U(1) pictu
re. We discuss the relationship of this result with one direction of Thorn
e’s hoop conjecture. The work relies on a special structure of the Einst
ein equations in this symmetry class\, a new re-scaling of the equations a
nd large-time control\, along with a new local Klainerman-Sobolev estimate
. Time permitting\, some comparisons of the result and the methods with la
rge-data constructions for the Einstein equations over the last decade wil
l also be presented.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Teixeira da Costa (Princeton University\, University of Cambr
idge)
DTSTART:20240307T143000Z
DTEND:20240307T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/32
DESCRIPTION:Title: The Teukolsky equation on Kerr in the full subextremal range\n
by Rita Teixeira da Costa (Princeton University\, University of Cambridge)
as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\
nAbstract\nThe Teukolsky equation is one of the fundamental equations gove
rning linear gravitational perturbations of the Kerr black hole family as
solutions to the vacuum Einstein equations. I will discuss joint work with
Yakov Shlapentokh-Rothman (Toronto)\, where we show that solutions arisin
g from suitably regular initial data decay inverse polynomially in time. O
ur proof holds for the entire subextremal range of Kerr black hole paramet
ers (|a| < M).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Lee (City University of New York)
DTSTART:20240404T133000Z
DTEND:20240404T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/33
DESCRIPTION:Title: The equality case of the positive mass theorem\nby Dan Lee (Ci
ty University of New York) as part of JoMaReC - Joint Online Mathematical
Relativity Colloquium\n\n\nAbstract\nWe will review the equality case of t
he positive mass theorem for initial data sets and discuss its proof in th
e general (not necessarily spin) setting. This is joint work with Lan-Hsua
n Huang.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Kehle (ETH Zürich)
DTSTART:20240502T133000Z
DTEND:20240502T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/34
DESCRIPTION:Title: Retiring the third law of black hole thermodynamics\nby Christ
oph Kehle (ETH Zürich) as part of JoMaReC - Joint Online Mathematical Rel
ativity Colloquium\n\n\nAbstract\nExtremal black holes are special types o
f black holes which have exactly zero temperature. I will present a proof
that extremal black holes form in finite time in gravitational collapse of
charged matter. In particular\, this construction provides a definitive d
isproof of the "third law" of black hole thermodynamics. We also show that
extremal black holes take on a central role in gravitational collapse\, g
iving rise to a new conjectural picture of "extremal critical collapse." T
his is joint work with Ryan Unger (Princeton).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Valiente Kroon (Queen Mary University of London)
DTSTART:20240606T133000Z
DTEND:20240606T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/35
DESCRIPTION:Title: BMS-supertranslation charges at the critical sets of null infinity
\nby Juan Valiente Kroon (Queen Mary University of London) as part of
JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nF
or asymptotically flat spacetimes\, a conjecture by Strominger states that
asymptotic BMS-supertranslations and their associated charges at past nul
l infinity can be related to those at future null infinity via an antipoda
l map at spatial infinity. We analyse the validity of this conjecture usin
g Friedrich's formulation of spatial infinity\, which gives rise to a regu
lar initial value problem for the conformal field equations at spatial inf
inity. We show that for a generic class of asymptotically Euclidean and r
egular initial data\, BMS-supertranslation charges are not well-defined at
the critical sets where null infinity meets spatial infinity unless the i
nitial data satisfies an extra regularity condition. We also show that giv
en initial data that satisfy the regularity condition\, BMS-supertranslati
on charges at the critical sets are fully determined by the initial data a
nd that the relation between the charges at past null infinity and those a
t future null infinity directly follows from our regularity condition. Thi
s is joint work with Mariem Magdy Ali Mohamed and Kartik Prabhu.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Gundlach (University of Southampton)
DTSTART:20241003T140000Z
DTEND:20241003T150000Z
DTSTAMP:20260424T235147Z
UID:jomarec/36
DESCRIPTION:Title: The interplay of mathematics and numerics in understanding naked s
ingularity formation in critical collapse\nby Carsten Gundlach (Univer
sity of Southampton) as part of JoMaReC - Joint Online Mathematical Relati
vity Colloquium\n\n\nAbstract\nI will give an overview of numerical eviden
ce that codimension one-sets of smooth initial data for matter coupled to
GR form naked singularities - from scalar fields and fluids in spherical s
ymmetry\, where the evidence is strong\, to vacuum GR\, where the evidence
is still confusing\, but at least now beginning to be agreed by independe
nt codes. Can one hope to prove some form of this naked singularity conjec
ture? In the last ten years or so\, there has been considerable mathematic
al progress on the existence and stability of smooth self-similar blowup s
olutions in dispersive PDEs\, and on naked singularity formation in GR. I
will highlight some of these papers that particularly interest me as steps
on the way to a future proof of naked singularity formation from codimens
ion-one smooth initial data.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhongshan An (University of Michigan\, Ann Arbor)
DTSTART:20241107T143000Z
DTEND:20241107T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/37
DESCRIPTION:Title: Einstein manifolds with boundary\nby Zhongshan An (University
of Michigan\, Ann Arbor) as part of JoMaReC - Joint Online Mathematical Re
lativity Colloquium\n\n\nAbstract\nWe will talk about existence of Einstei
n metrics on manifolds with boundary\, while prescribing the induced confo
rmal metric and mean curvature of the boundary. In dimension 3\, this beco
mes the existence of conformal embeddings of surfaces into constant sectio
nal curvature space forms\, with prescribed mean curvature. We will show e
xistence of such conformal emebeddings near generic Einstein background. W
e will also discuss the existence question in higher dimensions\, where th
ings become more subtle and a non-degenerate boundary condition is used to
construct metrics with nonpositive Einstein constant.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Hintz (ETH Zurich)
DTSTART:20241205T143000Z
DTEND:20241205T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/38
DESCRIPTION:Title: Gluing small black holes along timelike geodesics\nby Peter Hi
ntz (ETH Zurich) as part of JoMaReC - Joint Online Mathematical Relativity
Colloquium\n\n\nAbstract\nSuppose we are given a globally hyperbolic spac
etime $(M\,g)$ solving the Einstein vacuum equations\, and a timelike geod
esic in M. I will explain how to construct\, on any compact subset of M\,
a solution geps of the Einstein vacuum equations which is approximately eq
ual to g far from the geodesic but near any point along the geodesic appro
ximately equal to the metric of a Kerr black hole with masseps. As an appl
ication\, we can construct spacetimes which describe the merger of a very
light black hole with a unit mass black hole\, followed by the relaxation
of the resulting single black hole to its equilibrium (Kerr or Kerr-de Sit
ter) state.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Brendle (Columbia University)
DTSTART:20250306T143000Z
DTEND:20250306T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/39
DESCRIPTION:Title: Systolic inequalities and the Horowitz-Myers conjecture\nby Si
mon Brendle (Columbia University) as part of JoMaReC - Joint Online Mathem
atical Relativity Colloquium\n\n\nAbstract\nI will discuss joint work with
Pei-Ken Hung on the\nHorowitz-Myers conjecture in dimension at most 7. Ou
r approach relies\non a new geometric inequality. For a Riemannian metric
on $B^2 \\times\nT^{n-2}$ with scalar curvature at least $-n(n-1)$\, this
inequality\nrelates the systole of the boundary to the mean curvature of t
he\nboundary.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Suhr (Ruhr-University Bochum)
DTSTART:20250206T143000Z
DTEND:20250206T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/40
DESCRIPTION:Title: Optimal Transport in Lorentzian Geometry\nby Stefan Suhr (Ruhr
-University Bochum) as part of JoMaReC - Joint Online Mathematical Relativ
ity Colloquium\n\n\nAbstract\nIn recent years the theory of optimal transp
ortation has made an impact on Lorentzian geometry\, mainly through synthe
tic definitions of timelike Ricci curvature bounds for Lorentzian manifold
s and Lorentzian length spaces. But there are also other aspects of Lorent
zian optimal transport relevant to general relativity. I will give an over
view of the basic ideas of Lorentzian optimal transport and recent results
. Further I will indicate some open problems in this context.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergiu Klainerman (Princeton University)
DTSTART:20250403T133000Z
DTEND:20250403T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/41
DESCRIPTION:Title: On the legacy of Y. Choquet-Bruhat (1923-2025)\nby Sergiu Klai
nerman (Princeton University) as part of JoMaReC - Joint Online Mathematic
al Relativity Colloquium\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Mars (University of Salamanca)
DTSTART:20250508T134000Z
DTEND:20250508T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/42
DESCRIPTION:Title: Null geometry and applications to existence of spacetimes\nby
Marc Mars (University of Salamanca) as part of JoMaReC - Joint Online Math
ematical Relativity Colloquium\n\n\nAbstract\nNon-null hypersurfaces can b
e easily viewed as geometric objects detached from the spacetime where the
y are embedded. This process of "detachment" is more complicated in the ca
se of null hypersurfaces. In this talk I will introduce the notion of "nul
l manifold"\, together with related concepts such as "ruled null manifold"
or "metric hypersurface data"\, as a way to study null hypersurfaces from
a fully detached point of view. With this framework at hand\, I will then
discuss three applications related to existence of spacetimes. Specifical
ly\, I will present a detached version of the characteristic initial value
problem\, a general analysis of transverse expansions across a null hyper
surface and an existence and asymptotic uniqueness result of $\\Lambda$-va
cuum spacetimes from data on a (detached) non-degenerate Killing horizon.
The three applications are joint work with Gabriel Sánchez Pérez.\n\nwil
l be streamed from the GAPs conference at IMAG https://www.birs.ca/events/
2025/5-day-workshops/25w5397\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Warren Li (Stanford University)
DTSTART:20251002T133000Z
DTEND:20251002T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/44
DESCRIPTION:Title: Progress towards the BKL Proposal\nby Warren Li (Stanford Univ
ersity) as part of JoMaReC - Joint Online Mathematical Relativity Colloqui
um\n\n\nAbstract\nAround 50 years ago\, physicists Belinski\, Khalatnikov
and Lifshitz provided heuristics describing the behaviour of near-singular
ity solutions to the Einstein equations as spacelike\, local and oscillato
ry. Vaguely speaking\, they suggest that dynamics corresponding to differe
nt spatial points on the singularity decouple and resemble a chaotic casca
de of so-called “Kasner epochs”. In this talk\, we present a mathemati
cal formulation of this “BKL Conjecture” and progress towards the conj
ecture in the case of Gowdy symmetric spacetimes.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaela Wutte (Arizona State University)
DTSTART:20250605T133000Z
DTEND:20250605T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/45
DESCRIPTION:Title: Hyperbolic Mass in 2+1 Dimensions\nby Raphaela Wutte (Arizona
State University) as part of JoMaReC - Joint Online Mathematical Relativit
y Colloquium\n\n\nAbstract\nSolutions to general relativity with a negativ
e cosmological constant have received significant attention due to the con
jectured AdS/CFT correspondence\, a particularly well-understood example o
f which is exhibited in 2+1 dimensions.\n\nI will review known vacuum solu
tions to general relativity with a negative cosmological constant in 2+1 d
imensions and discuss the difficulties in defining mass\, which are resolv
ed via minimisation using a positive energy theorem. I will present a glui
ng theorem for vacuum time-symmetric general-relativistic initial data set
s in two spatial dimensions. By gluing two given time-symmetric vacuum ini
tial data sets at conformal infinity\, we obtain new time-symmetric vacuum
initial data sets. I will sketch the derivation of the mass formulae of t
he resulting manifolds. Our gluing theorem yields complete manifolds with
any mass aspect function\, which are smooth except for one conical singula
rity.\n\nBased on joint work with P. T. Chruściel.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacques Smulevici (Sorbonne Université)
DTSTART:20251106T143000Z
DTEND:20251106T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/46
DESCRIPTION:Title: Non-linear waves and time-periodicity\nby Jacques Smulevici (S
orbonne Université) as part of JoMaReC - Joint Online Mathematical Relati
vity Colloquium\n\n\nAbstract\nI will give an overview talk concerning the
possible existence and stability of solutions to non-linear wave equation
s which are periodic in time. Such solutions can arise in a variety of mat
hematical models\, from fluid dynamics\, elasticity\, and general relativi
ty\, where in particular\, there were investigated numerically by Malibors
ki and Rostworowski (2013) for the Einstein-scalar-field model in spherica
lly symmetry near the Anti-de-Sitter spacetime. \n\nI will start the prese
ntation with some reminder concerning the linear wave equation on Anti-de-
Sitter before presenting some results and methods for semi-linear wave equ
ations. In a second part\, I will describe a recent construction of specia
l coordinates for 1+1 Lorentzian metric on \\mathbb{R}\\times\\mathcal{S}^
1 with time-periodic coefficients\, which is expected to be an essential s
tep to extend the previous results to quasi linear wave equations.\n\nThis
a joint work with Athanasios Chatzikaleas (National and Kapodistrian Univ
ersity of Athens ).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annachiara Piubello (University of Copenhagen)
DTSTART:20251204T143000Z
DTEND:20251204T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/47
DESCRIPTION:Title: A geometric choice of asymptotically Euclidean coordinates via STC
MC-foliations\nby Annachiara Piubello (University of Copenhagen) as pa
rt of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstr
act\nAsymptotically Euclidean initial data sets (IDS) in General Relativit
y model instants in time for isolated systems. In this talk\, we show that
an IDS is asymptotically Euclidean if it admits a cover by closed hypersu
rfaces of constant spacetime mean curvature (STCMC)\, provided these hyper
surfaces satisfy certain geometric estimates\, some weak foliation propert
ies\, and each surface exhibits generalized stability. Building on the wor
k of Cederbaum and Sakovich (2021)\, which established that every asymptot
ically Euclidean IDS has a unique STCMC foliation\, we conclude that the e
xistence of such a foliation characterizes asymptotically Euclidean IDS. F
urthermore\, we explore the connections to the center of mass and show why
these coordinates seem well-adapted to describe this concept. This is joi
nt work with O. Vičánek Martínez.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Maxwell (University of Alaska\, Fairbanks)
DTSTART:20260205T143000Z
DTEND:20260205T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/48
DESCRIPTION:Title: Einstein-fluid initial data\nby David Maxwell (University of A
laska\, Fairbanks) as part of JoMaReC - Joint Online Mathematical Relativi
ty Colloquium\n\n\nAbstract\nFluids are a standard matter source for gravi
tation\, going back to the early days of general relativity. Nevertheless\
, constructing initial data for this family of matter models is surprising
ly nuanced. In this talk we describe a novel approach to building Einstein
-fluid initial data based on a recently established phase-space technique
for constructing non-vacuum initial data sets. Compared to prior approache
s to working with fluids\, the input parameters allow for more direct spec
ification of physical quantities\, such as the number of particles in any
given region. We focus on perfect fluids but also touch on extensions of t
hese ideas\nto viscous models.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilbert Weinstein (Ariel University\, Israel)
DTSTART:20260305T143000Z
DTEND:20260305T153000Z
DTSTAMP:20260424T235147Z
UID:jomarec/49
DESCRIPTION:Title: The mass angular momentum inequality\nby Gilbert Weinstein (Ar
iel University\, Israel) as part of JoMaReC - Joint Online Mathematical Re
lativity Colloquium\n\n\nAbstract\nIn this talk\,I will discuss our recent
result. Either there is a counterexample to black hole uniqueness\, or th
e following statement holds. Axisymmetric\, complete\, simply connected\,
maximal initial data sets for the Einstein equations of nonnegative energy
density with ends that are either asymptotically flat or asymptotically c
ylindrical\, admit an ADM mass lower bound given by the square root of tot
al angular momentum. Moreover\, equality is achieved only for a constant t
ime slice of an extreme Kerr spacetime. The proof is based on a novel flow
of singular harmonic maps with hyperbolic plane target\, under which the
renormalized harmonic energy is monotonically nonincreasing. Relevant prop
erties of the flow are achieved through a refined asymptotic analysis of s
olutions to the linearized harmonic map equations.\n\nThis is joint work w
ith Qing Han\, Marcus Khuri\, and Jingang Xiong.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariem Magdy (Perimeter Institute and Fields Institute\, Canada)
DTSTART:20260402T133000Z
DTEND:20260402T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/50
DESCRIPTION:Title: Estimates for spinor fields using the space-spinor formalism\n
by Mariem Magdy (Perimeter Institute and Fields Institute\, Canada) as par
t of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstra
ct\nI will discuss recent work on estimates for spinor fields obeying firs
t-order equations\, formulated within the space–spinor framework. The ap
proach is motivated by the positive commutator method presented in the wor
k of P. Hintz and A. Vasy\, originally designed for tensor fields satisfyi
ng second-order equations. In this talk\, I will outline how these ideas c
an be adapted to the spinorial setting and how the resulting estimates fit
naturally into the first-order structure of the equations.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roya Mohayaee (Sorbonne University\, France)
DTSTART:20260507T133000Z
DTEND:20260507T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/51
DESCRIPTION:Title: Optimal Transport theory and its applications in cosmology\nby
Roya Mohayaee (Sorbonne University\, France) as part of JoMaReC - Joint O
nline Mathematical Relativity Colloquium\n\n\nAbstract\nI will begin with
a concise review of the fundamental ideas underlying optimal transport the
ory\, before illustrating how these concepts naturally emerge in cosmologi
cal contexts and provide a powerful framework for addressing the problem o
f cosmological reconstruction. I will then highlight how optimal transport
extends beyond its analytical utility in handling big data\, and demonstr
ate intriguing connections with certain theories of modified gravity.\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Sánchez (University of Granada\, Spain)
DTSTART:20260604T133000Z
DTEND:20260604T143000Z
DTSTAMP:20260424T235147Z
UID:jomarec/52
DESCRIPTION:Title: Globally hyperbolic spacetimes-with-timelike-boundary: global spli
tting\, asymptotically AdS spacetimes and null-convexity\nby Miguel S
ánchez (University of Granada\, Spain) as part of JoMaReC - Joint Online
Mathematical Relativity Colloquium\n\n\nAbstract\nGlobally hyperbolic spac
etimes with a timelike boundary model spacetimes with naked singularities
distributed on a timelike hypersurface\, potentially admitting conditions
on both the boundary and a Cauchy hypersurface. Typically\, the boundary c
an serve as: (1) a cut-off for the system under consideration\, or (2) a c
onformal completion of the spacetime\, as in the case of asymptotically An
ti-de Sitter spacetimes.\n\nFirst\, we will review some of their general p
roperties\, including those related to causality\, the existence of global
orthogonal splittings\, and the relationship between the properties of th
e boundary and the interior of the spacetime. Then\, we will focus on the
null-convexity of the boundary. This is a natural assumption satisfied by
asymptotically AdS spacetimes\, which implies that the interior of the spa
cetime retains most of the geometric properties of the boundaryless case\,
such as being causally simple with a Hausdorff space of lightlike geodesi
cs.\n\nBased in joint work with L. Aké and JL. Flores (arxiv: 1808.04412)
and with J. Herrera (arxiv: 2506.09032).\n
LOCATION:https://stable.researchseminars.org/talk/jomarec/52/
END:VEVENT
END:VCALENDAR