BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hans Ringström (KTH Stockholm) DTSTART:20201001T133000Z DTEND:20201001T143000Z DTSTAMP:20260422T225927Z 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:20201105T143000Z DTEND:20201105T153000Z DTSTAMP:20260422T225927Z 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:20201203T143000Z DTEND:20201203T153000Z DTSTAMP:20260422T225927Z 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:20210204T143000Z DTEND:20210204T153000Z DTSTAMP:20260422T225927Z 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:20210304T143000Z DTEND:20210304T153000Z DTSTAMP:20260422T225927Z 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:20210401T133000Z DTEND:20210401T143000Z DTSTAMP:20260422T225927Z 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:20210506T133000Z DTEND:20210506T143000Z DTSTAMP:20260422T225927Z 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:20210603T133000Z DTEND:20210603T143000Z DTSTAMP:20260422T225927Z 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:20210701T133000Z DTEND:20210701T143000Z DTSTAMP:20260422T225927Z 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:20211007T133000Z DTEND:20211007T143000Z DTSTAMP:20260422T225927Z 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:20220602T133000Z DTEND:20220602T143000Z DTSTAMP:20260422T225927Z 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:20211104T143000Z DTEND:20211104T153000Z DTSTAMP:20260422T225927Z 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:20211202T143000Z DTEND:20211202T153000Z DTSTAMP:20260422T225927Z 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:20220203T143000Z DTEND:20220203T153000Z DTSTAMP:20260422T225927Z 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:20220505T133000Z DTEND:20220505T143000Z DTSTAMP:20260422T225927Z 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:20220407T133000Z DTEND:20220407T143000Z DTSTAMP:20260422T225927Z 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:20220303T143000Z DTEND:20220303T153000Z DTSTAMP:20260422T225927Z 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:20220707T133000Z DTEND:20220707T143000Z DTSTAMP:20260422T225927Z 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:20220901T133000Z DTEND:20220901T143000Z DTSTAMP:20260422T225927Z 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:20221006T133000Z DTEND:20221006T143000Z DTSTAMP:20260422T225927Z 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:20221103T143000Z DTEND:20221103T153000Z DTSTAMP:20260422T225927Z 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:20221201T143000Z DTEND:20221201T153000Z DTSTAMP:20260422T225927Z 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:20230202T143000Z DTEND:20230202T153000Z DTSTAMP:20260422T225927Z 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:20230302T143000Z DTEND:20230302T153000Z DTSTAMP:20260422T225927Z 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:20230406T133000Z DTEND:20230406T143000Z DTSTAMP:20260422T225927Z 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:20230504T133000Z DTEND:20230504T143000Z DTSTAMP:20260422T225927Z 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:20230601T133000Z DTEND:20230601T143000Z DTSTAMP:20260422T225927Z 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:20230706T133000Z DTEND:20230706T143000Z DTSTAMP:20260422T225927Z 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:20231102T143000Z DTEND:20231102T153000Z DTSTAMP:20260422T225927Z 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:20231207T143000Z DTEND:20231207T153000Z DTSTAMP:20260422T225927Z 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:20240201T143000Z DTEND:20240201T153000Z DTSTAMP:20260422T225927Z 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:20240307T143000Z DTEND:20240307T153000Z DTSTAMP:20260422T225927Z 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:20240404T133000Z DTEND:20240404T143000Z DTSTAMP:20260422T225927Z 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:20240502T133000Z DTEND:20240502T143000Z DTSTAMP:20260422T225927Z 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:20240606T133000Z DTEND:20240606T143000Z DTSTAMP:20260422T225927Z 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 BEGIN:VEVENT SUMMARY:Carsten Gundlach (University of Southampton) DTSTART:20241003T140000Z DTEND:20241003T150000Z DTSTAMP:20260422T225927Z UID:jomarec/36 DESCRIPTION:Title: The interplay of mathematics and numerics in understanding naked singular ity formation in critical collapse\nby Carsten Gundlach (University of Southampton) as part of JoMaReC - Joint Online Mathematical Relativity Co lloquium\n\n\nAbstract\nI will give an overview of numerical evidence that codimension one-sets of smooth initial data for matter coupled to GR form naked singularities - from scalar fields and fluids in spherical symmetry \, where the evidence is strong\, to vacuum GR\, where the evidence is sti ll confusing\, but at least now beginning to be agreed by independent code s. Can one hope to prove some form of this naked singularity conjecture? I n the last ten years or so\, there has been considerable mathematical prog ress on the existence and stability of smooth self-similar blowup solution s in dispersive PDEs\, and on naked singularity formation in GR. I will hi ghlight some of these papers that particularly interest me as steps on the way to a future proof of naked singularity formation from codimension-one smooth initial data.\n LOCATION:https://researchseminars.org/talk/jomarec/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhongshan An (University of Michigan\, Ann Arbor) DTSTART:20241107T143000Z DTEND:20241107T153000Z DTSTAMP:20260422T225927Z UID:jomarec/37 DESCRIPTION:Title: Einstein manifolds with boundary\nby Zhongshan An (University of Mich igan\, Ann Arbor) as part of JoMaReC - Joint Online Mathematical Relativit y Colloquium\n\n\nAbstract\nWe will talk about existence of Einstein metri cs on manifolds with boundary\, while prescribing the induced conformal me tric and mean curvature of the boundary. In dimension 3\, this becomes the existence of conformal embeddings of surfaces into constant sectional cur vature space forms\, with prescribed mean curvature. We will show existenc e of such conformal emebeddings near generic Einstein background. We will also discuss the existence question in higher dimensions\, where things be come more subtle and a non-degenerate boundary condition is used to constr uct metrics with nonpositive Einstein constant.\n LOCATION:https://researchseminars.org/talk/jomarec/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hintz (ETH Zurich) DTSTART:20241205T143000Z DTEND:20241205T153000Z DTSTAMP:20260422T225927Z UID:jomarec/38 DESCRIPTION:Title: Gluing small black holes along timelike geodesics\nby Peter Hintz (ET H Zurich) as part of JoMaReC - Joint Online Mathematical Relativity Colloq uium\n\n\nAbstract\nSuppose we are given a globally hyperbolic spacetime $ (M\,g)$ solving the Einstein vacuum equations\, and a timelike geodesic in M. I will explain how to construct\, on any compact subset of M\, a solut ion geps of the Einstein vacuum equations which is approximately equal to g far from the geodesic but near any point along the geodesic approximatel y equal to the metric of a Kerr black hole with masseps. As an application \, we can construct spacetimes which describe the merger of a very light b lack hole with a unit mass black hole\, followed by the relaxation of the resulting single black hole to its equilibrium (Kerr or Kerr-de Sitter) st ate.\n LOCATION:https://researchseminars.org/talk/jomarec/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Brendle (Columbia University) DTSTART:20250306T143000Z DTEND:20250306T153000Z DTSTAMP:20260422T225927Z UID:jomarec/39 DESCRIPTION:Title: Systolic inequalities and the Horowitz-Myers conjecture\nby Simon Bre ndle (Columbia University) as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nI will discuss joint work with Pei-Ke n Hung on the\nHorowitz-Myers conjecture in dimension at most 7. Our appro ach 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 inequal ity\nrelates the systole of the boundary to the mean curvature of the\nbou ndary.\n LOCATION:https://researchseminars.org/talk/jomarec/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Suhr (Ruhr-University Bochum) DTSTART:20250206T143000Z DTEND:20250206T153000Z DTSTAMP:20260422T225927Z UID:jomarec/40 DESCRIPTION:Title: Optimal Transport in Lorentzian Geometry\nby Stefan Suhr (Ruhr-Univer sity Bochum) as part of JoMaReC - Joint Online Mathematical Relativity Col loquium\n\n\nAbstract\nIn recent years the theory of optimal transportatio n has made an impact on Lorentzian geometry\, mainly through synthetic def initions of timelike Ricci curvature bounds for Lorentzian manifolds and L orentzian length spaces. But there are also other aspects of Lorentzian op timal transport relevant to general relativity. I will give an overview of the basic ideas of Lorentzian optimal transport and recent results. Furth er I will indicate some open problems in this context.\n LOCATION:https://researchseminars.org/talk/jomarec/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergiu Klainerman (Princeton University) DTSTART:20250403T133000Z DTEND:20250403T143000Z DTSTAMP:20260422T225927Z UID:jomarec/41 DESCRIPTION:Title: On the legacy of Y. Choquet-Bruhat (1923-2025)\nby Sergiu Klainerman (Princeton University) as part of JoMaReC - Joint Online Mathematical Rela tivity Colloquium\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/jomarec/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Mars (University of Salamanca) DTSTART:20250508T134000Z DTEND:20250508T143000Z DTSTAMP:20260422T225927Z UID:jomarec/42 DESCRIPTION:Title: Null geometry and applications to existence of spacetimes\nby Marc Ma rs (University of Salamanca) as part of JoMaReC - Joint Online Mathematica l Relativity Colloquium\n\n\nAbstract\nNon-null hypersurfaces can be easil y viewed as geometric objects detached from the spacetime where they are e mbedded. This process of "detachment" is more complicated in the case of n ull hypersurfaces. In this talk I will introduce the notion of "null manif old"\, together with related concepts such as "ruled null manifold" or "me tric hypersurface data"\, as a way to study null hypersurfaces from a full y detached point of view. With this framework at hand\, I will then discus s three applications related to existence of spacetimes. Specifically\, I will present a detached version of the characteristic initial value proble m\, a general analysis of transverse expansions across a null hypersurface and an existence and asymptotic uniqueness result of $\\Lambda$-vacuum sp acetimes from data on a (detached) non-degenerate Killing horizon. The thr ee applications are joint work with Gabriel Sánchez Pérez.\n\nwill be st reamed from the GAPs conference at IMAG https://www.birs.ca/events/2025/5- day-workshops/25w5397\n LOCATION:https://researchseminars.org/talk/jomarec/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Warren Li (Stanford University) DTSTART:20251002T133000Z DTEND:20251002T143000Z DTSTAMP:20260422T225927Z UID:jomarec/44 DESCRIPTION:Title: Progress towards the BKL Proposal\nby Warren Li (Stanford University) as part of JoMaReC - Joint Online Mathematical Relativity Colloquium\n\n\ nAbstract\nAround 50 years ago\, physicists Belinski\, Khalatnikov and Lif shitz provided heuristics describing the behaviour of near-singularity sol utions to the Einstein equations as spacelike\, local and oscillatory. Vag uely speaking\, they suggest that dynamics corresponding to different spat ial points on the singularity decouple and resemble a chaotic cascade of s o-called “Kasner epochs”. In this talk\, we present a mathematical for mulation of this “BKL Conjecture” and progress towards the conjecture in the case of Gowdy symmetric spacetimes.\n LOCATION:https://researchseminars.org/talk/jomarec/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaela Wutte (Arizona State University) DTSTART:20250605T133000Z DTEND:20250605T143000Z DTSTAMP:20260422T225927Z UID:jomarec/45 DESCRIPTION:Title: Hyperbolic Mass in 2+1 Dimensions\nby Raphaela Wutte (Arizona State U niversity) as part of JoMaReC - Joint Online Mathematical Relativity Collo quium\n\n\nAbstract\nSolutions to general relativity with a negative cosmo logical constant have received significant attention due to the conjecture d AdS/CFT correspondence\, a particularly well-understood example of which is exhibited in 2+1 dimensions.\n\nI will review known vacuum solutions t o general relativity with a negative cosmological constant in 2+1 dimensio ns and discuss the difficulties in defining mass\, which are resolved via minimisation using a positive energy theorem. I will present a gluing theo rem for vacuum time-symmetric general-relativistic initial data sets in tw o spatial dimensions. By gluing two given time-symmetric vacuum initial da ta sets at conformal infinity\, we obtain new time-symmetric vacuum initia l data sets. I will sketch the derivation of the mass formulae of the resu lting manifolds. Our gluing theorem yields complete manifolds with any mas s aspect function\, which are smooth except for one conical singularity.\n \nBased on joint work with P. T. Chruściel.\n LOCATION:https://researchseminars.org/talk/jomarec/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacques Smulevici (Sorbonne Université) DTSTART:20251106T143000Z DTEND:20251106T153000Z DTSTAMP:20260422T225927Z UID:jomarec/46 DESCRIPTION:Title: Non-linear waves and time-periodicity\nby Jacques Smulevici (Sorbonne Université) as part of JoMaReC - Joint Online Mathematical Relativity Co lloquium\n\n\nAbstract\nI will give an overview talk concerning the possib le existence and stability of solutions to non-linear wave equations which are periodic in time. Such solutions can arise in a variety of mathematic al models\, from fluid dynamics\, elasticity\, and general relativity\, wh ere in particular\, there were investigated numerically by Maliborski and Rostworowski (2013) for the Einstein-scalar-field model in spherically sym metry near the Anti-de-Sitter spacetime. \n\nI will start the presentation with some reminder concerning the linear wave equation on Anti-de-Sitter before presenting some results and methods for semi-linear wave equations. In a second part\, I will describe a recent construction of special coord inates for 1+1 Lorentzian metric on \\mathbb{R}\\times\\mathcal{S}^1 with time-periodic coefficients\, which is expected to be an essential step to extend the previous results to quasi linear wave equations.\n\nThis a join t work with Athanasios Chatzikaleas (National and Kapodistrian University of Athens ).\n LOCATION:https://researchseminars.org/talk/jomarec/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Annachiara Piubello (University of Copenhagen) DTSTART:20251204T143000Z DTEND:20251204T153000Z DTSTAMP:20260422T225927Z UID:jomarec/47 DESCRIPTION:Title: A geometric choice of asymptotically Euclidean coordinates via STCMC-foli ations\nby Annachiara Piubello (University of Copenhagen) as part of J oMaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nAs ymptotically Euclidean initial data sets (IDS) in General Relativity 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 hypersurfaces of constant spacetime mean curvature (STCMC)\, provided these hypersurface s satisfy certain geometric estimates\, some weak foliation properties\, a nd each surface exhibits generalized stability. Building on the work of Ce derbaum and Sakovich (2021)\, which established that every asymptotically Euclidean IDS has a unique STCMC foliation\, we conclude that the existenc e of such a foliation characterizes asymptotically Euclidean IDS. Furtherm ore\, we explore the connections to the center of mass and show why these coordinates seem well-adapted to describe this concept. This is joint work with O. Vičánek Martínez.\n LOCATION:https://researchseminars.org/talk/jomarec/47/ END:VEVENT BEGIN:VEVENT SUMMARY:David Maxwell (University of Alaska\, Fairbanks) DTSTART:20260205T143000Z DTEND:20260205T153000Z DTSTAMP:20260422T225927Z UID:jomarec/48 DESCRIPTION:Title: Einstein-fluid initial data\nby David Maxwell (University of Alaska\, Fairbanks) as part of JoMaReC - Joint Online Mathematical Relativity Coll oquium\n\n\nAbstract\nFluids are a standard matter source for gravitation\ , going back to the early days of general relativity. Nevertheless\, const ructing initial data for this family of matter models is surprisingly nuan ced. In this talk we describe a novel approach to building Einstein-fluid initial data based on a recently established phase-space technique for con structing non-vacuum initial data sets. Compared to prior approaches to wo rking with fluids\, the input parameters allow for more direct specificati on of physical quantities\, such as the number of particles in any given r egion. We focus on perfect fluids but also touch on extensions of these id eas\nto viscous models.\n LOCATION:https://researchseminars.org/talk/jomarec/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilbert Weinstein (Ariel University\, Israel) DTSTART:20260305T143000Z DTEND:20260305T153000Z DTSTAMP:20260422T225927Z UID:jomarec/49 DESCRIPTION:Title: The mass angular momentum inequality\nby Gilbert Weinstein (Ariel Uni versity\, Israel) as part of JoMaReC - Joint Online Mathematical Relativit y Colloquium\n\n\nAbstract\nIn this talk\,I will discuss our recent result . Either there is a counterexample to black hole uniqueness\, or the follo wing statement holds. Axisymmetric\, complete\, simply connected\, maximal initial data sets for the Einstein equations of nonnegative energy densit y with ends that are either asymptotically flat or asymptotically cylindri cal\, admit an ADM mass lower bound given by the square root of total angu lar momentum. Moreover\, equality is achieved only for a constant time sli ce of an extreme Kerr spacetime. The proof is based on a novel flow of sin gular harmonic maps with hyperbolic plane target\, under which the renorma lized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solution s to the linearized harmonic map equations.\n\nThis is joint work with Qin g Han\, Marcus Khuri\, and Jingang Xiong.\n LOCATION:https://researchseminars.org/talk/jomarec/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariem Magdy (Perimeter Institute and Fields Institute\, Canada) DTSTART:20260402T133000Z DTEND:20260402T143000Z DTSTAMP:20260422T225927Z UID:jomarec/50 DESCRIPTION:Title: Estimates for spinor fields using the space-spinor formalism\nby Mari em Magdy (Perimeter Institute and Fields Institute\, Canada) as part of Jo MaReC - Joint Online Mathematical Relativity Colloquium\n\n\nAbstract\nI w ill discuss recent work on estimates for spinor fields obeying first-order equations\, formulated within the space–spinor framework. The approach is motivated by the positive commutator method presented in the work of P. Hintz and A. Vasy\, originally designed for tensor fields satisfying seco nd-order equations. In this talk\, I will outline how these ideas can be a dapted to the spinorial setting and how the resulting estimates fit natura lly into the first-order structure of the equations.\n LOCATION:https://researchseminars.org/talk/jomarec/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Roya Mohayaee (Sorbonne University\, France) DTSTART:20260507T133000Z DTEND:20260507T143000Z DTSTAMP:20260422T225927Z UID:jomarec/51 DESCRIPTION:Title: Optimal Transport theory and its applications in cosmology\nby Roya M ohayaee (Sorbonne University\, France) as part of JoMaReC - Joint Online M athematical Relativity Colloquium\n\n\nAbstract\nI will begin with a conci se review of the fundamental ideas underlying optimal transport theory\, b efore illustrating how these concepts naturally emerge in cosmological con texts and provide a powerful framework for addressing the problem of cosmo logical reconstruction. I will then highlight how optimal transport extend s beyond its analytical utility in handling big data\, and demonstrate int riguing connections with certain theories of modified gravity.\n LOCATION:https://researchseminars.org/talk/jomarec/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Sánchez (University of Granada\, Spain) DTSTART:20260604T133000Z DTEND:20260604T143000Z DTSTAMP:20260422T225927Z UID:jomarec/52 DESCRIPTION:Title: Globally hyperbolic spacetimes-with-timelike-boundary: global splitting\, asymptotically AdS spacetimes and null-convexity\nby Miguel Sánchez (University of Granada\, Spain) as part of JoMaReC - Joint Online Mathemat ical Relativity Colloquium\n\n\nAbstract\nGlobally hyperbolic spacetimes w ith a timelike boundary model spacetimes with naked singularities distribu ted on a timelike hypersurface\, potentially admitting conditions on both the boundary and a Cauchy hypersurface. Typically\, the boundary can serve as: (1) a cut-off for the system under consideration\, or (2) a conformal completion of the spacetime\, as in the case of asymptotically Anti-de Si tter spacetimes.\n\nFirst\, we will review some of their general propertie s\, including those related to causality\, the existence of global orthogo nal splittings\, and the relationship between the properties of the bounda ry and the interior of the spacetime. Then\, we will focus on the null-con vexity of the boundary. This is a natural assumption satisfied by asymptot ically AdS spacetimes\, which implies that the interior of the spacetime r etains most of the geometric properties of the boundaryless case\, such as being causally simple with a Hausdorff space of lightlike geodesics.\n\nB ased in joint work with L. Aké and JL. Flores (arxiv: 1808.04412) and wit h J. Herrera (arxiv: 2506.09032).\n LOCATION:https://researchseminars.org/talk/jomarec/52/ END:VEVENT END:VCALENDAR