Okay, Dr. Madzola, are you there? Yes, just a moment please. Okay. It's me. Hello. La matina. Sorry, there is a. Okay. Okay. So good afternoon everybody. It's a very, it's a great pleasure for me to welcome all of you to this afternoon's ceremony for the awarding the 2021 Dirac medal and prize. As all of you here know, Dirac was one of the all time greats in theoretical physics. And also a good friend of the center. He visited ICTP on a number of occasions, and we even have a scholar Dirac named after him. And the prize is in his honor, given to measure breakthroughs in theoretical physics. And there's a dirac medal. We are very happy that they are medallist are Alessandra Bonanno from Max Planck Institute in Germany. And Amur from Institute, the scientific in France. France victorious from Princeton University in the US, and so to call ski from Caltech and Cornell University in the US. Dr. is joining us online and the other three dirac medallist are here. I'm also very happy that Dr. Micaela Mazzola is joining us here from Rome, representing the director general consulate from the Ministry of Research. ICTP is very grateful, as you probably know, ICTP is governed by a tripod agreement between the government of Italy, International Atomic Energy Agency and UNESCO. And we are very grateful for the, you know, unwavering support of the Italian government and for hosting us here. And as a scientific to give the scientific introduction to the to the winners of the dirac medal this year, we invited Professor Kip Thon from Caltech, who received the 2017 Nobel Prize. And I'm very glad that Kip has agreed to join us on this very important occasion. The medal has been given for establishing the predicted properties of gravitational waves in the curvature of space time produced when stars or black hole spiral together emerge. This achievement was essential for the Lego detection of gravitational waves from this energetic astronomical events. And the consistency of theory and observation is an impressive check of the accuracy of the general theory of relativity. And I think it's really truly a remarkable achievement of, let's say the 21st century physics that this extraordinary events were detected, the two black holes merging, for which the Nobel Prize was was awarded. The theoretical work of this year's dirac medalist was essential for interpreting the observations from the Lego collaboration, which is an unusually subtle experiment. And to really understand what it is that we are seeing one needs detailed waveforms about what it is that you expect. And I think it's really a marvelous tribute to the remarkable power of our theoretical understanding of nature, that by solving the Einstein's equations which were written 100 years ago, we are able to predict how the waves will look like. So, and the work of the this year's dirac medalist was absolutely essential for our ability to compute from these equations. So it has been said actually that this really opens a new era in astronomy, rather like Galileo's telescope that it's a new eye, a new window onto the universe. But unlike Galileo's telescope which human I can immediately process and see the images of the signal that we get from this Lego detector is something that requires this very abstract processing via the Einstein's equation. And this is what the middle is about. And I think if you look at the history we were actually just discussing before this ceremony the very interesting history of the discovery of the gravitational waves it's a truly remarkable. The ups and downs and skepticism in the community, even about the existence of black holes, the possibility of detecting it, and the role of the scientific community as a whole I mean I think it's really a collaboration of between analytical methods, numerical methods, analytical relativists, observational breakthroughs, and also many inspiring sort of guiding lights, you know, putting you know come in a forcing the community to say that this problem is important. And oftentimes quite serious hesitations and the criticisms from rest of the community, and keep on it certainly one of the people I think therefore his most ideally suited to talk, tell us a bit about this very interesting history and the path to the discovery of the gravitational gravitational waves and the contributions of the direct Middle East. So I'm very happy that keep is here to tell us about it. So I will give now the floor to Dr. Micaela Majola for the remarks as a representative of the government of Italy. Thank you. Thank you, Chair. Estimated Chairman, members of the ICTP, dear all, let me first create the ICTP director at this lab with the organizer of this special event and all of you in the audience on behalf of General Regi Consoli, general director of the internalization department of the ministry of the university and research in Italy. Thank you for allowing the ministry to contribute to this important ceremony to appoint this edition of the Iraq Middle. The ministers as always appreciated the excellent scientific performances of the ICTP, a distinguished international center that we are honored to host in our country, especially in this beautiful city of Trieste. ICTP contributes to Italy and Trieste as a reference for science in Europe and the worldwide. I am particularly sorry not to be in this beautiful city in person, but unfortunately, as you know, it is a very intense work period in Italy, especially for the project of PNRR that you know. ICTP distinguished activities is based not only on the well-recognized worldwide high level formation and across virtualization among different research fields, but also on prize and distinguished scientific science 1985 for assigning the Dira Middle. We are here to give the person of the Dira Middle 2021 to Alessandra Bonanno, Stevo D'Amour, Franci Pertorius, who won this prize with Sol Tewkorskis, I'm sorry for my pronunciation with this surname, who will be connected in line for the outstanding theoretical contribution to the understanding of the gravitation. They significantly contributed to writing such a beautiful page of physics and human knowledge. I hope the audience and the other winners allow me to congratulate Alessandra Bonanno more especially. She represents one more extraordinary example of what our school and university can contribute to forming. She got her master's and doctorate degrees in Pisa, is my city, or not, confirming that Italian high-level information is of value. She has then chosen to work between France, Swiss, Germany and USA. We understand that this fits very well with intrinsic international character of science. So we're represented here at ICTP, but we hope Alessandra still feels our Italian roots. Let me also stress that our country has a historical and actual weakness in the field of gravitational wave detection. It started in the late 50s under Eduardo Amaldipush with the cryogenic antennas. Then it continued with Alberto Giazzotto, one of the inspiring founders of interfered metric detection in Pisa. Actually, during the time Alessandra was studying there, they may, and maybe he was inspired here too. We hope it will continue. If our account trying to re-host as a very interesting, the third generation high-stand telescope detector in Saus and Aptos, Sardinia. We hope that this work possible. Saus and Aptos region shows an exceptional low seismic and entropic noise, and is I need an ideal territory to host such an ambition project as E.T. We then count in Alessandra and our semantic colleagues to continue this necessary and fruitful collaboration between trailers and experimentals on such a fascinating research can hopefully help in our country to be at the forefront of the gravitational science. Therefore, I wish you a successful event. And again, our personal and institutional congratulations to the TIRAC medalists 2021. Thank you very much. Thank you very much, Dr. E.Mazzola. I now request Professor Kip Thorn to say a few words. You may remember actually he visited ICTP about three years ago. He gave a beautiful colloquium on this topic. So I request him to give an introduction to the pioneering contributions of the 2021 medalists. Thank you very much. It's a great honor to be here with you today. I wish I could be there in person. It was not possible. So I'm remote from the United States. Let me share my screen with you. Let me make sure I get the right one. Then I'm going to bring up my slides. Okay. Can you see those slides? Okay. I trust. Okay. So, according to the laws of physics, there are just two types of waves that can be produced in the distant universe and traveled across the great reaches of intergalactic space to Earth, bringing us information about what's far away. Electromagnetic waves and gravitational waves. It was Galileo, of course, 400 years ago who built a small optical telescope pointed at Jupiter, discovered Jupiter's four largest moons, and in the process created modern instrument based electromagnetic astronomy. It was LIGO on September 14, 2015 with data analysis jointly from the LIGO collaboration and the Virgo collaboration that discovered gravitational waves from colliding black holes and thereby created gravitational wave astronomy. It was very important in developing the foundations for this that we know already by about 19, very early on, what the expected strongest sources of gravitational waves would be. And it was that knowledge then that underpinned the work of our medalists. It became clear by about 1980 that the strongest sources would be binary neutron stars to neutron stars orbiting each other, spiraling together as they emit gravitational waves colliding and merging. The binary black holes, neutron stars made of course from almost pure nuclear matter, the binary black holes made from pure warped space and time, the spiral together merged and collided and produced a great burst of gravitational waves and that of course was what was seen. Now, there were three components of R&D that required in order to have the great success of LIGO. At first the experiment, a gravitational wave interferometer largely conceived by Ray Weiss at MIT which consisted of two mirrors that hang from overhead supports four kilometers apart that along one arm of an L and two similar mirrors along the other arm of an L. When the gravitational waves came by, they would push these mirrors apart while squeezing those together and then at the next half cycle, push these apart while squeezing those together. And those motions, the difference in changing difference in arm length was monitored using laser interferometry. The R&D for these interferometers began in 1972 by 1987 LIGO project was initiated in the United States and not long thereafter the Virgo project initiated by as a French and Italian collaboration. And then 1994 the construction of the LIGO interferometers began and 21 years later the first detection of gravitational waves. The second component of R&D that was required with the knowledge of the waveforms to feed into data analysis. The gravitational waveform is a plot of the gravitational wave strain, which is the fractional change in arm length in the interferometer as a function of time. And plotting up then as a stretch, plotting down as a squeeze of the arm and the oscillatory stretching and squeezing is the gravitational waveform that we very much needed in order to be able to feed into the data analysis for searching for the gravitational waves in the gravity wave interferometer data. In 1989, a decision was made by the LIGO director that the waveform computations would be carried out outside of the LIGO project. This decision was motivated to a great degree by an underappreciation of how crucial the waveforms would be and how extremely difficult it would be to compute them. A few days ago Barry Barish, the LIGO director who most responsible for LIGO's success, said to me, how very lucky we were that despite the lack of close coordination with the LIGO project, waveforms are ready in time for LIGO's first detection of gravitational waves. Actually, it wasn't luck. It was due to the dedication, the cleverness and the perseverance of our four direct medalists and their collaborators.  The first stage, the early stage, the two objects orbit around each other, gradually spiraling together as they emit gravitational waves which carry off orbital energy. The merger, collision and merger of the two objects and the ring down the final object sort of like the ringing of a bell. In the 1980s, as we were planning for LIGO, I speculated as to what the waveforms would be in this sort of a cartoon. And in spiral waveforms, which we already by then had some understanding what they would be the ring down waveforms at the end and the merger waveforms which I thought and hope would be rather complex. And the merger waveforms could only be carried out, deduced from supercomputer simulations, and we believe at that time. They merger in the ring down for a binary black binary neutron star occurred gravitational wave frequencies that are so high above one kilohertz that the LIGO noise is bad there. And there's not much hope, at least there was not in those that era of actually seeing those waves so the R&D for the binary neutron stars focused on the in spiral waves. The binary black holes at the gravitational the gravity, the merger ring down where gravitational wave frequencies we expected below one kilohertz where the noise is low so the focus for binary black holes was on all three stages and that was where almost all of the energy went in the early years of planning for LIGO and Virgo gravity wave observations.  By 1972, we knew that quiescent black holes are described by Roy Kerr's solution of the Einstein field equations. In 1972, the same year as Ray Weiss initiated R&D for these interferometers, Salty Kolsky as a graduate student at Caltech, deduced the equations for weak perturbations of black holes and brought them into a simple, easily usable form. This was actually quite a tour de force a number of other people were struggling to do this. Many of us had begun to suspect that this would not be possible. But in fact, he succeeded, and he thereby initiated and he working together with his fellow student, Bill Press did much of this early work, initiated the study of the Quasi normal modes of oscillation of a black hole. That is the ring down waves that LIGO and Virgo would ultimately see. And also the study of the waves from a small body, for example, a small black hole orbiting a large black hole, which would also play an important role in the work I'll describe today. The in spiral waves, the waveforms were computed by the post Newtonian approximation. The basic idea was to expand the metric of spacetime and Einstein's equations in powers of the Newtonian gravitational potential, which is of the same magnitude as the orbital speed squared. At first order in this expansion, one has Newton's theory of gravity. Second order is what was called the first post Newtonian order at order 2.5. One software the first time rate the effects of radiation reaction back on the source, and so forth higher and higher orders a variety of new physical effects and new influences on the waveforms. Building on earlier work of Einstein, Chandra Sarkar and others, Tebo D'Amour led a successful major effort in the 1980s and 90s to carry the expansion to high enough order to meet LIGO's future needs. To achieve this D'Amour reformulated the post Newtonian expansion and he developed ways to re-sum the expansion, so as to make it more accurate. This work was tremendously complex with pitfalls that D'Amour circumvented elegantly. Major contributions were also made by D'Amour's former student, Luc Blanchet and by Balaiar, Gerhard Schaefer and others. The merger waveforms we expected to be computed from numerical relativity simulations of the binary black holes. These simulations are extremely difficult. One reason is that one must be evolved black holes, which themselves are made for warped space time as they move through space with time passing. So just think about that and how difficult and different from any other computational work that had been done before this must have been. And the merger creates in fact a wild storm in the shape of space and time and the rate of flow of time in the vicinity of the black hole horizon, which had to be dealt with. The early history of numerical relativity began in 1959 with foundations laid in John Wheeler's Princeton University group by Charles and Mr. Richard Lindquist and Susan Haugh. In the 1960s and 70s, Bess DeWitt spearheaded and Larry Sperr had successfully had a success in computing the head-on collisions of non-spinning black holes. The 1980s and 90s were devoted to developing techniques for evolving, orbiting, colliding black holes and these techniques were developed by many people. But already finally by 1999 it was not, nobody had succeeded in putting all these techniques together so as to evolve even non-spinning black holes through even just one orbit around each other. There was great frustration and I was beginning to be worried as to whether or not the numerical relativity would succeed. In 1999, Alessandra Buannano and Thibaut Delmore came to the rescue. They invented a method called the effective one-body method. A method in which they were computing the waveforms from inspiring and merging binaries. In this method they re-expressed the orbital motion of non-spinning binary black holes in terms of the motion of a particle around a spherical central body. The metric of the central body was determined by the binary black holes mass ratio in a very clever way that was informed by a resummed post-Newtonian expansion of the binary black hole orbit. From this EOB model, Buannano and Delmore computed the analytic binary black hole in spiral waveform. And then with the aid of Tchaikovsky's perturbation methods they deduced the approximate analytical waveform for the binary black holes very late in spiral. It's inward plunge, it's collision, it's merger, it's vibrational ring down. The approximate merger waveform was very simple, amazingly. A very smooth transition for in spiral to ring down, not at all what I had hoped for and expected. And we now know I think in retrospect that this was because the wild oscillations of space and time were occurring very near the horizon. And the gravitational waves from those were largely going down the black hole, the merged black hole, and not coming off for us to see, unfortunately. By the early 2000s, approximately 15 numerical relativity research groups were trying to simulate the binary black hole in spiral merger and ring down. These simulations were absolutely essential because we did not know how accurate the approximate EOB waveforms were. And still in the early 2000s, not a single orbit had been simulated successfully. In 2005, Franz Pretorius, a postdoc at Caltech, wrote the logjam working alone with a code that he wrote largely single-handedly, though borrowing key ideas from others. Franz's brilliance, lay in identifying which tools and in what combination and with what kinds of interfacing would be capable of surmounting the obstacles. The combination of techniques that he adopted was very different from the approaches being used by all the major groups struggling to do so, do these simulations in these 15 numerical relativity research groups. The waveform that he found for identical binary black holes, non-spinning orbiting around each other, colliding and merging, had this very simple form. The early parts of this waveform, the stretch and squeeze as a function of time are due to just transient waves associated with the way he set his initial conditions. But by this point, the in spiral waves were the correct prediction and very believable. The merger waves, a very smooth transition to the bringing down waves at the end. And this waveform was in good agreement with the Buonano and D'Amore effective one body predictions, which surprised me to some degree because I really was, well, it was just amazing how brilliant Buonano and D'Amore had been in developing their approximate waveform and pulling it off with success. The LIGO data analysis was going to require codes that could simulate mass ratios of one to one up to 10 to one, vectorial spins on the holes with representing wide range of magnitudes and directions. And this corresponds to seven non-trivial parameters and the accuracies needed to be known with confidence. The code had to be fast enough and robust enough to keep up with the LIGO observations. And it was Saul Tkulski who created and led a large collaboration that had constructed the spectral Einstein code, which by 2014 was 10 times faster and 10 times more accurate than any other code. Most importantly, SPEC used pseudo spectral methods and was based on mathematical formulation that is strongly hyperbolic. These two features guaranteed that SPEC should converge exponentially rapidly as the coordinate grid was refined. Verification of this gave confidence in the code's accuracy and the exponential convergence made the code 10 times faster and more accurate than any of the other competing codes. The data analysis required generating however 100,000 waveforms on the fly for different parameters and comparing with incoming data by a matched filtering. From 2006 onward, Buonanno conceived and led an effort toward this. She and her students and postdocs extended the EOB to spinning black holes, as did D'Amore in parallel. They tuned the EOB by adjusting it to fit hundreds of SXS numeric relativity simulations thereby creating the combined EOBNR formalism. And they then joined the LIGO scientific collaboration and from 2009 onward, they participated in making EOBNR the foundation for LIGO's EOBNR waveforms. EOBNR waveform template family and data analysis pipeline capable of the 100,000 waveform computations on the fly in a very short periods of time. LIGO's first discovery on 14 September 2015 involved data analysis carried out by combined LIGO Virgo teams using primarily two data analysis pipelines. EOBNR and one called IMR Phenom, which was conceived and developed largely by Jith, Hanum, and Husha and colleagues. And it was a separate pipeline that combined the EOB-inspiral waveforms of Buonanno and D'Amore, which had been informed by numerical relativity. And combined those Inspiral waveforms with numerical relativity merger and ringdown waveforms in a different manner than Buonanno had done. The detection paper showed a comparison of the actual template waveforms in gray that best fit the observations with a SXS numeric relativity waveform and verified that the numerical relativity waveforms were indeed beautifully reproduced by the templates that had been built by Buonanno and her collaborators. The initial black hole, as one saw from the observations comparing the waveforms, had masses of 29 and 36 solar masses for a total of 65 solar masses. The final black hole was 62 solar masses. Three solar masses went into gravitational waves and the distance to this source was 1.3 billion light years, all deduced by comparing the waveforms with the observations. Buonanno then led the effort to do a series of remarkable tests of general relativity with these observations. She coordinated the data analysis for this and she co-led the writing of the paper with a thousand authors.  And Ilaigo and Virgo will turn back on next spring with improved sensitivity at the level that they should be seeing binary black hole mergers at a rate of about one a day, which is really impressive. I congratulate Alessandro Buonanno, Timo D'Amore, Frans Pertorius and Saul Tekulski on their very well-deserved Dirac medals, and I thank you. Thank you very much, Kip, for this wonderful summary of the contributions of the medalists. Okay, Dr. Amatsalo, thank you for your presence. I understand you have to leave. Now, we will follow this up by the awarding of the medals. And then there will be lectures by the four medalists, followed by question and answer session. And then we will also inaugurate, that is, we have now started this new ICTP Dirac medalist exhibit in our staircase, the photo exhibition of Dirac medalists in the Leonardo building. So that will be at the end of this session. So we begin with the awarding of the medals, please. So, Saul, we are trying to, we'll try to give it to you remotely. Thank you. Thank you. Congratulations. And now we can move to the talks by the Dirac medalist, I request Alessandro Buonanno to give a talk here. Okay, good afternoon. I'm very honored to have just received the Dirac medal. I also wanted to say that I was here at ICTP 20 years ago, attending as a graduate student in July of that year, the cosmology school. So I'm very delighted to be here again. Okay. Okay, so let's start. So, we just heard from Kip Torn, seven almost seven years ago, the LIGO and VIEGO collaboration observed for the first time a gravitational wave from the collision of two black holes. And, sorry, since then, 85 more binary black holes have been observed by LIGO and VIEGO. These are two neutron stars, and they even mixed binaries formed by neutron star and black holes. And in this plot here, you see the distribution of the black holes detected by LIGO and VIEGO in blue. You can appreciate the spread in mass, this is in mass in solar masses, between five and 90 solar masses, the component black holes. And some of the neutron stars detected by LIGO and VIEGO in orange. So, Kip Torn reminded us beautifully the importance of the prediction, the theoretical prediction of the waves, why we are interested in predicting the waves. And one of the reasons is that through the waves we can learn about the properties of the source that has emitted the waves. So, from the frequency evolution, we can infer the masses of the binary. If we know the amplitude, measure the amplitude and the masses, we can infer the distance of the binary with respect to the earth. From the time of arrivals, the amplitude and the phase of the detector, we can reconstruct the sky location. And if we can observe modulations of the amplitude, in the amplitude and the phase, we can actually learn whether the binary was moving on a circular orbit or eccentric, whether the black holes were rotating as they were inspiring around each other. And if we can compare the wave form to deviation from general relativity, we can probe gravity. So this means we need to solve the two body problem very accurately. And for many years, this problem has been a tackle between parallel between the analytical relativity effort and the numerical relativity effort until actually 2005 with a breakthrough by Franz Pretorius. And just to say, briefly about the analytical techniques. So we heard about post Newtonian theory, which is applicable. One does an expansion of the Einstein equations in powers of you oversee, which is also intertwined with the GM over RC square the strength. And one can do an expansion of the Einstein equation in post minkoskin theory is an expansion in G, which is valid for a large separation and but not expanded in velocities also important for master for fast emotion. And finally, one can do also an expansion of the Einstein equation in the mass ratio, the gravitational self force. So as I keep was summarizing briefly. I started working in this in this field that when I was a post doc at IHS, and one of the motivation of our work was can be summarizing this question, can the two body dynamics and the radiation of arbitrary mass ratio binary black holes be reduced with a simple mapping from the results of test body limit or the so called problem it. And following this motivation, we brought the way that he would have moved the first paper where we met the two body dynamics in the dynamics of an effective body, which move in a deformed space time at the time the partial space time because we were considering non spinning objects, and this mapping, which was also inspired by results in quantum field theory led to a resumption of the Hamiltonian and also the binding energy, the post Newtonian results through this simple formula here. In 1999 I moved to Caltech in naturally the group of keep torn and at the time we completed actually the second paper where we provided also the dynamics and of the spiral up to the planche. The way for me, which the full way for me including also the merger ring down, which was actually estimated semi analytically with some based on results at the time known at the time, and I want to emphasize for example just within the model we could estimate the final mass and final spin of the black hole and deduce the quasi normal modes that then could be actually match the glue simply with imposing the continuation of the waveform analytic continuation between the inspired planche and the merger ring down. Okay, so since then, a lot of work has been done, especially since the breakthrough from transporatarios in 2005 to improve the theory part of the ob but also to complete through numerical relativity simulations. And so I want the moment to spend a slide just to emphasize the main steps. So, originally if you compare the waveform without any information from numerical relativity you will have some differences after a certain number of cycles as you can see in this upper panel, but then you include higher order corrections in, for example, unknown post Newtonian terms, and you can feed them from numerical relativity and improve the agreement. And this is done for one way for, but then basically you repeat this for many numerical relativity way for me here represented in the space of the combination of the spins in the binary and the symmetric mass ratio. So this is an example of a calibration that we did to prepare for the like of your go first run and then improvement for the subsequent runs. So, you basically calibrate the model in this point of the parameter space where you have very accurate numerical relativity and they were taken from the sxx catalog and notice also very low mass ratio. We also use actually equation for the way from for the inspiring down obtained by solving the so called it's your cost equation. And so we did this work at a so called s for spin your BNR waveforms. And this is actually the template bank that was used in the light go runs. You can see at the low masses plane post Newtonian templates were used for binary neutron stars, but for masses above three solar masses, we form for a neutron star black or binary black or you needed to include also the merger in down. Now, this is not the only family that is used for like going Virgo inference analysis, keep ton was actually referring to the inspire a merger in down phenomenological way from mainly developed by a G and mark an arm and Sasha USA. There is another also version of the you'll be way for models. There was been the mainly developed by Alexander Naga, the board of Moore and the Sebastian of the notesy and more recently also numerical relativity way for more than interpolating directly. Sorry, way from obtain interpolating directly numerical relativity way from have been also developed the so called in our surrogate way forms. Okay, so now if you actually just to explain why this way for my important to what we learn by using them and not something you know less accurate. To make quick examples, the first one, the 14 of August 2019, the Lego and we go collaboration observe a binary with a puzzling companion, the primary black hole, the primary object is certainly black hole because as a mass 23 times the mass of the sun, but a smaller object that we don't know is a black collar neutron star, because the neutron star maximum mass for standard equation of status around the 2.1 2.2. And in this case was around 2.6 dollar masses so it was very important actually to nail down that value. And I want also to emphasize that because of the very large mass ratio in the binary this event, which is here is represented through this visualization and was also very rich in the emission of gravitational waves higher harmonics that could be also observed. And so you see here, the different actually harmonics pull out here, this appears nine second before merger, and then for second before merger you start seeing maybe not very well from the plot. And then from the screen at the l equal four m equal four and then the l equal five m equal five very close to merger around the one second. Now, to explain the importance of the way for models that this is the posterior distribution of the secondary mass, and you can see the two different way for models, you'll be an iron phenomenon, and only when you include the higher harmonics when you include the precession P. This is a much tighter distribution and compute the mass of measure the mass of the secondary with larger accuracy. The other example I wanted to make is the largest binary black hole observed by Lago and Virgo the 21st of May 2019. This is also a numerical relativity simulation that was produced for the event. The reality of this is also that the mass especially of the primary lays in a lies in a region where we should not expect the black holes because of the pairing stability supernova.  I wanted also to refer to the application of the way for more therefore for example test of general relativity, and here I want to refer to two examples. So the first one from the inspirational part of the signal, the phase can be expanded in post Newtonian terms and this coefficient depend on physical effects, we can allow this coefficient to be different from the value predicted by general relativity. We can look at whether we see deviation, we don't see any deviation actually on this parameter but we can use the result to put a bound on the post Newtonian parameters that are in this plot here. And I want to focus on the minus one PM parameter which is a describe the dipole emission would not be there in general relativity will be there in some scholar tensor theory. And just to emphasize we the first neutral sub black hole, we put a bound at the level of 10 to the minus three, we the first binary neutron star a bound around 10 to the minus five. For the higher post Newtonian parameter, we have to rely on binary black holes in spirals, and you see here, they bound for different actually events, and then they combine by bound, you know some of these parameters today are at the level of 10% The second example I wanted to make is to understand the properties of the remnant that forms after two black holes to compact object dark compact object merge and here in general relativity. We expected that the remnant black hole relaxes to the solution of care and emits quasi normal modes, and this was possible actually to observe at least measure the dominant ones. And to know this ratio that we have in the major in down is not very high to actually measure higher harmonics for the ring down. And just an example, the deviation in the frequency and decay time or the quasi normal mode of the dominant mode, you see here the posterior distribution that encompassed zero, which means that GR is still not evaluated. Okay. So, now I want to talk a moment about the next few years. All binary systems are everywhere. The results of Gaia have told us that there are 1.3 millions of binary systems at one kiloparsec around the, you know, from the earth, okay. Now, not all these binary system form, you know, end up in a black hole binaries or neutron star binaries, but certainly a large portion and one of the important questions astrophysicists are interested is understand what are the formation scenarios of the binaries that we are seeing with LIGO in Virgo. And in order to extract this information, it's important, for example, to measure properties like eccentricity, or the spin magnitude or the spin precession. And also, if we can extract the signatures of the astrophysical environment of the system, knowing whether the binary was actually a triple system that was a third body, or it was in a discord gas, we can also unveil the formation scenario. Now, let me say that the binary that we observe with LIGO in Virgo in this spectrum of the mass of the black holes is actually in this region here, the stellar mass black hole, or even in the very instability gap. But there are actually black holes with much larger mass in our universe, think about the black hole at the center of our galaxy. This is actually the largest black hole known today. So these black holes we want to measure with gravitational waves, and the black holes at the center, the core of the galaxy are very important. They play a very important role. They have a symbiotic relationship with the galaxy, and they ultimately influence also the growth of structures in our universe.  Okay, so we are going actually to open a new frequency band in the next decade, and have the possibility to observe these other classes of black holes. So we expect new facilities on the ground, the cosmic explorer in the US, and the Einstein telescope in Europe, they will improve the sensitivity with respect to LIGO and Virgo by one or two order of magnitude, actually improving especially at low frequency, which will allow to bring in the black holes with even larger masses, hundreds, several hundreds and thousands of solar masses, and these black holes could be seen up to a distance of 10 in redshift or 20, when the universe was 10 or 20 times smaller. Now I want a moment to impress you about the kind of system, but how many we are going to see and the signal to noise ratio. There will be few tens of binary black holes that can be seen for 10 minutes we signal to noise ratio larger than 1000 and 20,000 binary black holes that we signal to noise ratio larger than 100 binary neutron star can also be observed and this will be very important with very large signal to noise ratio to kneel down the equation of state of neutron stars. The signal will be much more complicated. We will observe intermediate mass ratio in spirals. This is the dynamics, the orbits at one Earth's and then at 10 Earth's so much more complicated. In the next decade, we will see also a new interface, well, the first interferometer in space Lisa supposed to be launched in 2035, which will open the frequency band around the the medias and allow to see new sources, extremist ratio in spirals that you see here, supermassive black holes at the center of galaxy merging with very large signal to noise ratio white dwarf binaries in our galaxy. And with much larger signal to noise ratio, we will perhaps see that the possibility to observe or discover new fundamental particles like ultralight boson forming boson clouds around the black holes and rotating and emitting gravitational waves. And with with very with is a large signal to noise ratio might probe more the horizon, understanding whether it's really, you know, an absorbing surface and not has no reflectivity. So now, in order to take advantage of these detectors in the next decade, and even in the next actually a few years, we need actually to continue to improve the way for models and merge together or use together all the different calculations that I was describing before. And in fact, we will need maybe two or more order of magnitude of improvement in accuracy, depending on the parameter space. And now we can do this by extending post Newtonian calculations today they are known in the conservative part at 4pm, but even the dissipative parties almost completed now at 4pm. We can do also calculation in post minkowski and theory. The expectation is that perhaps for really the next decade we will need up to 6pm or seven post minkowski and order. And for that to gain accuracy will be important to combine these different approximation within the F31 body framework, perhaps in novel ways to gain more effectively. And we also will need a numerical relativity simulation with larger accuracy, and also extend them in the region more extreme in the parameters the large mass ratio spins and eccentricity. So I think that Walter Koski will touch on this topic. And perhaps we think also we need to rethink the strategy of the two body problem in GR and beyond, and unify the description of bound and unbound orbits and I think also people will touch on this in his presentation. The first as you've been our model was actually developed in 2007 2009 was used for the first template bank in line with Virgo. Today we have the fifth generation and want to show you just as an example the improvement with respect to the previous generation that was used in the last year. This is in preparation of the new run. This is the so-called unfaithfulness, the match with numerical relativity waveform. Many of them after the calibration unfaithfulness zero here means basically that the two match perfectly. So you see here 10 to the minus two 10 to the minus three. There are gaps in numerical relativity waveform, although we have a much larger covering today with the SXX 442 line spin waveforms. And another interesting thing today we could also add uncertainty on the waveform models and basically the uncertainty that come from the calibration to numerical relativity will be important when we do parameter estimation. Now, the other example I wanted to make include eccentricity. Many people are working on it in preparation of the new run. This is an example of a real analysis of the second event of the Lagoon Vigo collaboration with a waveform with eccentricity and spin effects. And you can see a mild, you know, the posterior distribution picking around the very small value of the eccentricity. The eccentric waveforms also allow to go in the limit of dynamical capture. So these are events that maybe are less likely to be seen with Lagoon Vigo but nevertheless is good to have waveform models. And I want to emphasize there are many groups that are working on that, not just us. And one just comment I wanted to make, if you put together the different approximation methods. This is just the, this is just the peripheral distance, sorry, as a function of the eccentricity. There is actually an advantage of posmincosky and we respect to post Newtonian when you add eccentricity and so it will be important for example to push this posmincosky and calculation at higher order as people have are already doing today. So they're also quite important. So I have just to plot to show in fact the improvement also posmincosky and calculation. So this is the scattering angle that can be computed in numerical relativity, and these are the different approximations in the posmincosky and today known at 4pm. And for the bound case one can compare this calculation to the binding energy again computed in numerical relativity, and this is the improvement at different posmincosky and orders. And I should say, this is not the end of the story there are some subtleties in using the for posmincosky and for computing binding energy so for the bound case and I'm sure also that people that more will talk more about this. I cannot finish my talk without actually mentioning another important results in analytical calculation from the gravitational cell force. The gravitational cell force has been now computed for quasi circular orbits and non spinning. And the amazing thing is that although this approximation which is an expansion in the mass ratio should be valid for very large mass ratio. When you compare to a numerical relativity simulation on mass ratio 10, the second order cell force agrees very well with numerical relativity, even just a few cycles before merger. The gravitational spectrum has been open with LIGO and Virgo and soon also LIGO India and actually Kagra also already joined the collaboration Lisa and will be there in the next decade that I talked about Einstein cosmic telescope and cosmic explorer. There are also these other experiments here, and I won't since there are young people here in the audience. Actually, looking more into the future, there is the possibility going into 2050 so just thinking about the mission after Lisa in the next few years. There will be a selection as part of the ISA Voyage 2050 team between gravitational wave and cosmic microwave background radiation that could bring a new detector in space either in the desi earths or in the micro earths. And I want to conclude by thanking all the people we do my work actually in the last 15 years starting from the postdoc and graduate student at the University of Maryland, and then also a day I, and also many collaborators. My group also at the eye, and of course, the LIGO and Virgo and Kagra collaboration and all the agency that funded it and so thank you for this for your attention. Thank you. Okay. It is great honor and especially great pleasure to be awarded the direct medal here at the CTP, because actually, I met the rack here in probably in this building in July 1979. I wanted to find a photograph of this was during the second Marcel Wassmann meeting organized by Abdul Salam and remove Fini. And the only picture I could find was, I does not really work this thing. Yes, now it works. I'm listening to young. Okay, so you can see direct just on the side, but a few days later direct attended the Linda meeting in the same month of July.  And actually, I was lucky and bold enough to come and ask a question to direct any even answer so I was one of the lucky people to hear a few words from direct who was you know, usually not answering or just yes no. Anyway, I want to motivate going in the same direction as part of the talk of Alessandra. Alessandra, give some glimpses of the new methods and why the new theoretical methods link to scattering are interesting so just to repeat points already made so Alessandra beautiful we explain and keep explain that there are several parts of the way from the in spiral late in spiral where the resumption using effective one body allows to push up to merger but the full confirmed knowledge of merger came after the numerical breakthrough and then the the ring down of the black hole resumption is used at several levels in EOB both in the conservative dynamics described by an Hamiltonian and in the radiation reaction force. So what are we talking about we are talking about. We have a space time diagram where time goes up and spaces horizontal of two black holes here represented by the horizons the surface of the two black holes, moving around each other for hundreds of million of years emitting gravitational radiation with a back effect of gravitational reaction on the motion which makes them get closer go faster and ultimately merge. So the mathematical problem is we should solve Einstein equations which are explicitly written here. The methods which have been employed up to now in the actual data analysis of like go via go was a combination of methods developed over many years already mentioned post Newtonian post minkowski and multipolar post minkowski and developed in particular with Luke Blanchet and Balagh higher, but also other methods with an important complementary with numerical activity. And I want to emphasize that new methods have been developed over the last years and are being developed. And I want to talk about 2040 method developed with Donato beanie and Andrea Geralico Donato is here, and but I want to talk about scattering. So, although we are talking about the bound state problem, our concepts and methods coming often from quantum theory about scattering problem can be useful. Now, this new angle of attack on the two body dynamics, meaning, let's using the scattering where you have two bodies which come from infinity which cross at a distance at some impact parameter and then come out at a different angle, the idea that it could be a useful complement to things was emphasized in this paper. And in particular, in this paper, I urged, first I mentioned that the work of I'm a teacher following I'm going to discuss more, and I was urging amplitude experts to use their novel techniques to compute the two loop scattering amplitudes of scalar masses at the third post minkowski and approximation. This idea was then pushed forward by Chang Rothstein and so on. So actually, the idea to use quantum scattering amplitude to extract essentially the interaction potential, the gravitational interaction potential between two bodies had been first developed by Corinal Desi I mean proposed by Corinal Desi in the 50s. And the Japan I mean he was actually was the first one to reach in 71 by using pharma diagrams, the result that had been obtained by Lawrence and Rossi 1917 so you see, did not appear from outside as being a super efficient way of doing post Newtonian but the breakthrough was obtained by Danieli Amati here who was here in at CISA so in this building, no. He's here Danieli. And Marcello Ciafalone and Gabriele Veneziano in the long term project whose idea was to understand at the quantum level. What happens in ultra energy collision of particles to see when you create black holes and to understand the unitarity question of forming black holes, but a side product of the results was using sophisticated regi group of techniques was to compute at the two loop level. See the scattering angle as of two massless particle or two ultra energy particles. The economy phase being essentially the exponent of the scattering amplitude or the, the, the, the, the, the radial action essentially, and then so this was work done in around 1990. So after this new techniques, actually, coming from string theory, the fact that string theory is telling us that gravity is like the square of young meals or Maxwell is, which has been generalized within QFT by three burn. So here I understand, and many people. The idea is, one can use all those techniques to go beyond what can be done by other methods. Let me also quickly mentioned that here we are talking about using quantum scattering effect of two particles so you have to quantum particles states in the Hilbert space that scatter, but you are interested actually in the classical limit of this, and one can also do the computation purely at the classical level, except that in the old days when we did that in 1980s we were blocked by the computation of integrals and beyond one loop we did not know how to compute integrals we stopped, but recently inherited from quantum field theories, beautiful integration techniques as a lot in particular the group of our portal to, to reproduce the results of others that I will describe now, just a few words about the effective one body approach. So it was, as Alessandra already motivated, it was historically motivated by work by Bresin, Edward Bresin, Claudie Tixon, and Jean-Zine Justin, which was a quantum scattering resumption of a conical resumption in QED, but that they said that one can instead of having a two body problem maybe one can have an effective Coulomb problem to describe this. So this idea was transcribed within gravity, and the idea is instead of describing a two body system for bound states as being two particles going around and having an Hamiltonian of interaction, you replace that by some particle of mass mu, the effective mass mu like Newton, moving in some effective space time metric with fin slayer corrections and the idea which is looks like a much simpler condition, but you have to find what is the effective metric and what are these corrections which are equivalent to this more complicated things. So originally the effective one body approach was done for bound states, but then the idea in 2016-18 was to say but the same idea can be done directly if you don't have bound state observables like the radial action and the Borsamerfeld, the Launay Hamiltonian, but you have scattering data. So you know the real scattering angle, classical scattering angle of two particles coming with some energy and angular momentum, and you know the scattering angle as a function of energy and angular momentum. So basically you can identify this to the deflection angle of an effective particle of mass mu moving, satisfying some generalized mass shell condition of this type. And I have shown then that if you have the information say in expanded manner for the scattering angle, you can use this information by simple formulas and interpret this in terms of an effective energy dependent potential. Like this term is a potential in one of our square plus one of our cube, et cetera, we function of energy, and all this can be easy in one to one correspondence with the other thing. And then I applied this to the result of Amati Chafaloni-Venediano who had computed at the two loop level, third order in G, what was the scattering angle of two massless particle, very energetic massless particle coming in and scattering because of the gravitational interaction. They had found a result which had a nice expansion of this type. And then I could say, okay, this result is equivalent some Hamiltonian in UB description. Everything looked nice, okay. But then prompted by what I had said because I had urge and I discussed personally with Zibern saying, okay, please, I know that you can do it. So please do it. And they did it. The group of Zibern with many people here. It was a big effort. They succeeded in getting a third order in Newton's interaction using directly, I mean, precisely not find my diagrams but their double copy with et cetera, and integration techniques they computed this. And then they could compute at the same level of approximation as Amati Chafaloni-Venediano, what is the scattering angle but now for particles of finite mass, not massless particle, but finite mass. And the big surprise was that if you take their answer, and then you take the limit where the masses go to zero, fixing the energy so they go faster and faster, you know, at smaller and so it should reproduce the result of Amati Chafaloni-Venediano, but it did not because there was a logarithmic term coming from an arc-sinch which is somewhere here. Yes, from this arc-sinch. And then actually there was no energy limit of the result of Zibern so it created some doubts and confusion. At some point we said maybe there is something not fully correct, in which case Zibern said, okay, let's immediately bet a bottle of wine. We still have to drink it because of the pandemic and we will share it, because actually thanks to extra work with Donato and also work with Aguru and we could check that Zibern was correct. Therefore, there was no doubt that their formula was correct, but still there was a big puzzle. And this puzzle it took actually three years to understand why there was a discrepancy between the finite mass calculation at two loops of Zibern and the Amati Chafaloni massless scattering result. The result was that hidden in the computation of the group of Zibern was an assumption that one was not computing the full physical scattering angle, including the back action of radiation, the fact that this system emits a lot of gravitons and therefore this should have an effect on the scattering, but this was essentially what in classical physics you would call the Fokker-Wieler-Feinman time-symmetric interaction with time-symmetric greens function. And using a result derived with Donato-Dini and which was preceded, actually that's all work with Natalie Derweil, about radiative corrections linked to angular momentum loss. So the fact that in the collision you emit gravitons and these gravitons take away part of the angular momentum of the system and also energy. But what is crucial here is angular momentum is crucial. And this was understood from two different ways. One was a quantum calculation due to Paolo di Vecca, Carlo Eisenberg, Rodolfo Russo and Gabriele Venetiano, where they could relate what was implicit in the calculation of Amati Chafaloni-Venetiano, which is, I mean, an explicit that actually there was a link between the real part and the imaginary part of the angular angle, which means between losses of unitaryity, not of unitaryity, but of the 2-2-2 sector, a link to radiation effects at the quantum level, and they could relate this in this paper of Paolo di Vecca to the soft radiation emitted spectrum and the Weinberg famous soft graviton thing. And independently, I could show by a very simple calculation taking only one line that using the formula with Donato, this can be obtained from the angular momentum loss. But so now we have at the cubic order in G, there is a complete understanding of the scattering, but there is more than this, using quantum field theory techniques to very beautiful techniques to compute complicated integrals. Those authors were able to compute at cubic order something which had been written down by Kovacs and Kipthorn many years ago in the form of some integrals that nobody could compute and still today nobody can compute these integrals in the time domain, but they were computed recently by going to Fourier space with this nice formula, one could also have the radiated, so it's both the momentum transfer, the delta P mu of each particle and the radiated momentum. And recent work by other authors fully confirms these results, but now the frontier is at the next level okay using quantum scattering amplitudes at three loop, which means fourth order in the Newtonian interaction so you see it's described by diagrams here where you have three loops as you can see here, and if you count the number of square root of G at each point in this diagram you will find that this is a G4. So, at this G4 level, again the group of Zeeber was able to compute part of it, which is using only the gravitons, which have momentum comparable to the distance to the impact parameters so called potential gravitons and still you see how this quantum field theory technology allows to get very complicated, I mean, I know that by standards of Pierpaolo, Astoria and others this is not so sophisticated, but still LE2 and then, ah, but then you have elliptic integrals, complete elliptic and so on, E and K, okay, so this is a certain level of sophistication. But then this answer is incomplete and with Donato using our Tutti-Futti method that I did not describe, we could compute at the 6 p.m. level what is the post-Newtonian expanded contribution to G4 coming from radiating effects because what happens is when you have two world lines that interact by gravitons most of the scattering is due to gravitons which have momentum comparable to the inverse impact parameter, okay, but part of the answer comes from gravitons which are nearly radiated away, okay, very soft, I mean, soft gravitons which are called radiation type gravitons that you need to include and this is linked to a classical effect that was first understood by Luc Blanchet and myself in 1988 that in the interaction between the two bodies, they are part of the interaction which is non-local in time because it is due to the fact that the gravitational waves was emitted very long ago by the system backscattered on the curvature of space time and then focus back on the system creating correlations over a very long time so we could compute this in a p.n. expanded way and this helped Zviber and his group to check their full, so they did compute the full answer including now these things, okay, but still there are puzzles, okay, we know that this thing does not include real back reaction effects of radiation, it is the part, it has included part of the radiative effects which are time symmetric in a sense which is surprising that radiative effects can also be time symmetric but it is and the part which is time symmetric and the square of the time, the symmetric effects enter actually at the G4, G5 and G6 level and as of today, there exists still puzzles and discrepancies between computations which are QFT based in EFT language due to UNS bloom line and his group and for fast to Rani where they computed some numbers and we have shown that these numbers should satisfy this constant but they do not satisfy this constant so it's an interesting situation where we have a beautiful tool which definitely will be an important part of progress in the future but they are conceptual puzzles and physicists love to have conceptual puzzles. Those conceptual puzzles are linked to the basic idea that when you have greens function which means propagation of gravitation between two world lines. You have different greens function depending at the classical level you could say, okay, if I am really talking about the physical effect I should use the retarded greens function. But if I want an effective action I should use the focus time symmetric greens function if I'm doing quantum calculation. And I use the usual in out formalism I have a five man greens function, which is actually linked to this plus radiative effects. Again, you have other things how to take into account radiation reaction effects and today, we don't know yet how to do it. So I just want to conclude by saying that, as Alessandra also insist I mean, emphasize analytical approaches to gravitational waves signal, play the cultural role in the past but is needed for future improvements. Now, over the last years, many ideas of the community coming from many things from early days of quantum field theory early days of string theory all those tools now combine together and allow us to compute effects beyond what can be computed by other methods but with puzzles. And the final word is what I said about the problem in physics, you know, that there are no important problems in physics which are definitely solve problems but they are always more or less important. Thank you. Thank you very much to go. And now I request to Professor Pretorius to give a stop. Thank you very much. I wanted to echo. Alessandra and Tivo in my honor and receiving this award, you know it's a great honor. And also I want to thank a lot of the people that you know some of them have been named as collaborators some haven't been named in the community as a whole, collaborated and contributed to the sort of the background of knowledge that we sort of built on to get to to this place. So again, thank you it's a great honor. So what I'm going to talk about today or some open questions or dynamics of black holes. So, what I'll give is a very brief reminder of what we do know about the theory of black holes. And then, you know, I guess most of this, the talks and the surprise has been on things that we do know about which I guess makes sense, you know, things to, to discoveries are not the unknown but I want to sort of ask the question, you know, given everything that we've learned about the dynamics of black holes or there's some open questions or open problems. So there are a couple of regimes that where I will say that they are, I think in my opinion something interesting, perhaps only of theoretical interest but some interesting open problems. And this relates to the perturbations the nonlinear perturbations of near extremal curve black holes, and the ultra relativistic limit of a binary of binary black interactions are very similar. So really, in spurts what Tivo spoke about. I'm going to be focusing on the small impact parameter case. What I want to know about black holes in very brief. I think our modern understanding of black holes came quite late in, you know, in understanding of Einstein's theory. I'd say, you know, what we think of black holes today at least how we understand them today was the knowledge logic came from what keeps on called the golden age of general relativity in the 60s and 70s. So that's I could have picked from, but I just mentioned a few of the key ones. So for instance, the generosity of singularities inside of black holes pen roses, famous singularity theorems. The uniqueness of no hair properties of isolated stationary black holes that was pioneered by Israel and completed by other authors. That was the astonishing result that for complicated equations as Einstein equations we have an exact analytical solution that we think described essentially every isolated black hole in the universe the curse solution, which was very much ties in with the black holes properties of black holes.  First, sort of noticed analogy with the laws of black of thermodynamics and the laws of black or mechanics and then in some sense putting a more real footing by Hawkins discovery of Hawkin radiation. It's very interesting, you know, just from a theoretical perspective but what really made made it so black hole so relevant and why we still studying black holes and dynamics today is kind of at the same time people realize that they actually are black holes in the universe. So the first stellar mass black can the black hole candidate sickness x one that was discovered around that time and quasars which were, which were discovered a bit earlier. But essentially the first or then it was realized in this time frame that you could understand the energetics of plays as quasars by appealing to a supermassive black holes being the central engine. And since then, you know, we've understood that we've learned a lot about the dynamics of binary black holes, which is either what this award is celebrating this year. And of course that I should in this new era of gravitational wave observation of the universe that that kept spoke to eloquently about and now Sandra and Tebow so essentially, you know, from the golden age tool. And in the last 20, 30 years now also got a very good understanding of the dynamics of pairs of black holes binary black holes. So, again, that brings me to the main topic of this question well what don't we know about dynamics of black holes today.  I'm thinking just asymptotically flat four dimensional space times. And my my bar for what no is is pretty low it's the physicist for just about understanding so the qualitative answers of what's going on. Of course if I said that the bar and say that theoretical gold standard of a mathematical proof that we don't really know. I'm not sure about black holes, mathematical relativists are, I think quite close to proving the nonlinear stability of the current solution, but that's that today is still an open problem at that level of rigor. So, I'm not nearly thinking of that level of rigor so just for these restrictions. What don't we know about black holes in classic relatively today. And again I mentioned these first two nonlinear perturbations of near extremal curve or extremal the generic outcome of ultra relativistic limit of black hole interactions. Then another top area that we also know very little about is the interior of a generic black hole form for gravitational collapse. And unfortunately I won't have time to say anything about that but that's also very interesting. There's a lot of interesting open questions there. Let me now describe these two, two cases and the rest of the talk is mostly going to be just motivating this that there are some interesting questions, and then just some wild speculations. So anyone can, you can criticize these as much as you want that's completely fine they just, you know, perhaps wild speculations. So what what is the motivation if you will for studying near extremal curve black holes, but one is pure theoretical interest. There's an off chance that these might be relevant to gravitational wave observations, if supermassive black holes or if there are some supermassive black holes that it's that's been near to maximum. Unfortunately, what I mean by near near extremal as you'll see later with some examples is, we need many nines. So perhaps like one or two point nine point nine nine is not going to be good enough for perhaps the 4059 so does nature spin up some supermassive black holes to such a high level. If they do, then extremist the best ratio in spirals with a back reaction is relatively small and it won't sort of kick it away from extra matter the unlike comparable mass mergers that that could be a test bed to observe some of these quantities but who knows if nature provides that. So why why might there be some interest something interesting in the in the nonlinear perturbation so we know what happens at the linear level that's thanks to Tickolsky, the Tickolsky equation and work by Tickolsky and press. And there's sort of two interesting things that happen with linear perturbations of extremal curve that suggests something interesting might happen at the nonlinear level. The first is that the damping time of the dawn was a normal mode, or family of quasi normal modes that goes to zero in the extreme limit. So these waves if you perturb in the extreme or black hole, the perturbation can sit around for a long time. Now the interesting property about perturbations are rotating black holes and these are in any rotation it doesn't have to be extremely near extremal, but they have this super radiance phenomenon. So if you if you excited black holes low frequency gravitational wave at a certain level you can extract rotation energy from black holes. The interesting thing is the onset of super radiance so sort of in a sense when the black hole at the linear level is acting like a perfect reflector. The onset of that to that frequency becomes equal to the onset of super radiance in the extreme limit so what these two frequencies that become commensurate in the extreme limit. And what that suggests is that conditions are actually favorable for some form of strong turbulent dynamics to occur on the horizon of near extremal black holes. So what is turbulence strong turbulence I really have very good answers a lot of people don't but at least this one one definition that I think perhaps, perhaps make make sense here. And one is, if you look at a nonlinear ringing system. It has weak turbulence weak turbulence is just mold coupling so beyond linear order modes are going to talk to each other it's going to be an exchange of energy that becomes strong. If on some relevant local dynamical time scale they can be a strong exchange of energy between between the modes. In terms of aerodynamics sometimes this is termed in terms of like the eddy turnover time scale, you can have strong to know strong turbulence if on an eddy time significant energy can be transferred to smaller or larger eddies depending on whether the turbulent cascade is directly indirect. So we know that at least for most of the kid times perhaps all but at least for sub extremal black holes, we don't have strong turbulence, because the system loses energy because it's not a quite sort of normal mode that was normal mode so it loses energy, and the rate of the case just too rapid for it to be much interaction. Well, let's let's get rid of the decay and can do that by going to the extreme limit so that's that's where the, so that one point. But then also you think well okay now you're disturbing a black hole there's going to be back reaction, if we have to be very close to extremality. The perturbation of a ring down mode in general in general you'd think would push it away from extremality if cosmic sensors should be satisfied and that is a big if but let's assume that it is satisfied. So you want to try to not want to limit the effects of back, back reaction. And so this onset of super radiance at least in terms of the parameters of black holes at leading where might be a good place to actually have less back reaction so these modes can sit around and actually interact in a non trivial fashion. Let me just give you a good but so one unrelated and then one perhaps related bit of evidence that they might be interesting things going on. So this, this bit of evidence actually now appeals to outside of this class that I've spoken about it's not asymptotically that space but asymptotically anti-decider space. And this comes from the gauge gravity dualities of string theory, which actually in certain situations in particular asymptotically anti-decider space makes very precise dictionary between black hole dynamics and hydrodynamics. And I think inspired by this people then thought well we know that fluid except it's from turbulence so black brains in anti-decider space should people look for it and they and they found that both from the gravitational wave perspective and on this holographic deal in the food perspective. This is a work by Adams Chesler and you that looks at perturbations of a black brain in asymptotically anti-decider space, and clearly you can see, you know, that's a very interesting turbulent dynamics that's unfolding there. Now this, this is actually is decaying and they factor out the overall decay, but these modes are interacting a very interesting passion. So back to the case. These authors have sort of speculated about, well is that possible incurred in asymptotically flat. And they try to come up with an effective Reynolds number to which might be an indication of when it might happen. And they sort of argue that yes it should, but you need I think at least four nines or higher to get to this support so point nine nine nine, nine, at least. So another interesting thing. This is from work that I did with the least and for the Ramizana group. And this was we were just looking at super radian scattering and so here we had a black hole of point nine nine so this is kind of low in this thing but that's very challenging numerically go to high spin so this is a pretty low spin. We wanted to study the nonlinear effects in super radian so we took these clouds of gravitational energy with about 10% of the mass of the space time so we wanted to be quite nonlinear. So this information is going to show an example. So the blue is going to be the imploding gravitational wave as measured by this new and Penrose scalar size zero, and then the red is going to be the scattered wave. And it's just to illustrate, and that little mantos thing here. That's the apparent horizon that's spinning. And as you see as a gravitational waves interact actually started to notice the spin. And that's because now it's actually symmetric so you don't see the spin but that the gravitational wave deforms the horizon. So here comes the imploding wave interacts with a black hole it starts to perturb the black hole, and now we get this, this way that's probably getting outwards. I mean you can't see that it's super radian from this this animation but this this is sort of the example we looked at. Well, what was interesting about the study was actually not the super radiance or the sub radiance but the thing that happened when we sort of tuned the frequency of the waves to the quasi normal mode frequency of this black hole. So you know properties of the dynamical horizon of the, that was a function of time, and incidentally, this kind of this sort of jaggedy behavior. So over there that's just where we're when it was really dynamical the apparent horizon, the finder had trouble finding the parent horizon so that's a failure of the parent horizon finder. So the irreducible mass here in this middle panel that does increase even for dynamic horizon so it's not a artifact of coordinates so that's just a messy code thing. What this is supposed to show is okay the the super radian case the black curve, and you can see the mass of the black hole does decrease after the interaction, as does the spin, but the area increases as is consistent. A sub radiant case here, where it absorbs essentially that you know 10% of the energy, but then the interesting thing is that is the quasi normal mode case where you can at least from this parameter this, this picture doesn't look like that with the least amount of changes happening to the black hole. And incidentally this kind of quantitatively says how far away we are from extramality so again at extramality these two frequencies the black and the red should be told to go to one, but you see they quite different, not just 1% like you think from being a spin off point 99. And now if we look at the properties of the horizons like that that all the formed white sphere that you saw. Here's what I'm what I'm meaning why this is the interesting frequency this quasi normal mode frequency. So in terms of two measures of a ratio of the proper to equatorial circumference of the horizon. And yeah this is the intrinsic curvature of the horizon. So in the straight lines this would be for extremal black holes so again you can see by the difference between the lines and think how far from extremal we are to begin with even at point 99. But we can see that the largest perturbation of this horizon is occurring at this quasi normal mode frequency. So again extrapolating to the case of extremal what that might suggest is that, you know, in some sense. Okay, so you can see even at point 99 they did decay fast the waves are going to sit there for a long time.  That's going to be in this limit so if we put a wave onto the black hole we fine tune it to this quasi normal mode, and we take the limit to extra melody. It might be a set of measures zero but I think that's where you could get see some fireworks and perhaps break a black hole, and where we might get some turbulent dynamics. It's a crazy speculation, I don't know, but that's why we don't know this about this is an aspect of black hole that I'm sure we don't know anything about. Okay now let me just briefly mention about the scattering problem. So the motivation you're mostly theoretically interest. What got me interested in this, you know, a while ago was the possibility that you know in LHC credit could produce black holes. And the ideas were these inspired by large extra dimension scenarios that suggested that our usual sort of definition of the plonk scale is actually not correct if they are large extra dimensions. There should be a much lower true plonk scale. And if you collide fundamental particles efficiently above the scale.  Now unfortunately, at least you didn't find black holes that would have been astonishing. So that's essentially telling us at the plonk scale, even if they're all these kind of bizarre scenarios can't be at a TV that might be higher, but the naturalness arguments that argued for TV or perhaps now not so naturally, it's 10 or higher. But in any case that is one interesting possible observational motivation. And I'm thinking here about the very small impact parameter case. So perhaps these calculations also be of relevance into some of the work that he was speaking about but perhaps not in the small impact parameter case. So what I mean here by the altruistic problem, of course, is that in the center of mass frame the energy of the space time is dominated by the kinetic energy of these black holes. So the gamma factors are very, very large. So most of the energy is in kinetic energy. There's an infinite boost limit. So then you have to scale the masses to zero such as this product of M times gamma is finite. Then you actually so what in the finite boost limit become the sort of Lawrence contracted.  And say very little qualitatively for the small impact parameter range is known, except for the, except for the head on collision case when B is equal to zero. And here's just an example of a simulation this was worked with will East, where we had, where we actually didn't have black holes being the source of these plain waves but as I mentioned during the text for the insane words but one interesting thing about this altruistic measure limit is the source of the gravitational these these almost impulsive gravitational wave shouldn't matter that can be black holes that can be like in this animation that I'll show you actually now that's particles. And that's actually why you can, you know, you, if you're sufficiently above the plunge scale, you don't need quantum gravity it's purely a classical calculation because of this conjecture that matter doesn't matter. This is just it just the enchantimation so in the head on collision case these planes once collided they formed this black hole in the center.  And incidentally they they circling around that the dominant quasi normal mode frequency so the sort of a very geometric picture that shows you but like where the dominant quasi normal mode frequency comes from it's just geometric. That's geometric property of the black hole. Okay, so, so what are what are the open questions. One is cosmic censorship always satisfied with these small impact parameters we know it is for the head on collision case quasi circular sort of astrophysical inspirals it is. But again it is, that's kind of surprising that was cosmic censorship should be satisfied, you know in some of these most wild storms on space time dynamics as kept puts it. If it is possible to violate it in the binary problem, I suspect it will be in this altruistic limit, probably with some fine change impact parameters or they might be a range of impact parameters. Of course if it is violated at the point that it's violated we don't know what's going to happen to the future we need quantum gravity. If it satisfied the then they are perhaps then are the more interesting open questions because in principle we could answer this with classical gravity. One is, is the end state always either just one or two black holes so one black hole in the head on collision case, very large impact parameters it's going to be two black holes. But what happens in this intermediate intermediate case. And as I explained a little bit more perhaps will become apparent why I think that they might be more. What is the maximum energy and what is the maximum angular momentum that can be radiated the back of the envelope suggests it might be close to 100% energy, you might be able to form close to extremal black holes. But, you know, what are those numbers and if they not, you know, these, if they don't saturate the bounds what are the numbers. And actually as I mentioned more interesting the qualitative properties so it's really not those numbers that are going to be that interesting. But if they turn out to be either they saturate the bounds always some finite value I think the interesting questions going to be, what was the dynamics that led to that particular number those particular numbers. And just to reframe it I think the key question in this regard is, if we look at the threshold impact parameter between one black hole as a final state and two black holes perhaps more. So we tune the impact parameter to have threshold. What is the nature of that threshold. And now again just going into the regime of wild speculation but I think like this is kind of motivated by work that a Marty and then Benetiano collaborators did sort of and so to live sort of describe what happens in a large but finite collision case. So what is actually going on in these altruistic interactions. So again you've got most of the space time energies and kinetic energy. And what what what a sort of a Lawrence contracted Coulomb field essentially does it acts as a very strong gravitational lens. And the question is how does one of these strong gravitational lens lenses lens the other lens and vice versa. What it seems to be is that, you know, when that when they interact initially, some fraction and for small impact parameters probably most of the kinetic energies converted to gravitational radiation. It's very efficient. It's highly beamed, but it's also gets focused down. So in some sense, what this sort of suggests is after this initial interaction. The black holes are kind of separated there or gravitational waves have separated themselves from the seeds of these of the energy of the space time, and you now have two clouds of collapsing gravitational wave energy. And this really becomes after this initial interaction, not so much a scattering problem anymore, but a gravitational collapse problem. And if that's the case, then one would expect that this threshold is going to be a critical solution in the sense of chop to critical phenomena. In the case, then by fine shooting this impact parameter, because this critical solution is expected to be self similar and actually we don't know what the gravitational wave critical solution is exactly but we expect to be self similar. Then we should be able to radiate 100% of the energy at threshold. But then you know this also goes with this, this, this matter does not matter you know we had these two little black holes, imagine two black holes as the sources they arbitrarily small, you know in terms of their s mass relative to the total mass. Now they've created these huge clouds of gravitational wave energy, but now they've kind of been liberated from the space time, are they going to stick around in this collapsing space time or could they escape. If they can somehow escape, then this collapsing cloud could form a black hole and you'd have to black holes, moving apart so that could be a case where there's a three black hole in state. On the other hand, the strong focusing argument suggests that perhaps that one to two black hole threshold is actually not a critical collapse threshold, but instead it's a threshold of between one large black hole. In the essay a macroscopic but macroscopic relative to the initial rest masses, or two large macroscopic black holes so it's a one to two black hole threshold. And then their arguments and work by by various people that suggests that even though perhaps 100% of the kinetic energy is converted to gravitational waves. So half of it will essentially be trapped by either the single black or the two black holes, and the further that you make the impact parameter way far away from that, the less efficient this conversion from kinetic to gravitational wave energy would be. And that suggests that this would be the maximum and would be about 50% of the energy radiated. It's not quite so clear what that would imply for the angular momentum of the remnant. On the other hand, if this if this one to two threshold is not a critical threshold, but it is still gravitational collapse which is doing it. That means that some further impact parameter around these now to separately collapsing clouds, they will be chopped to it like critical behavior, presumably, and in that case in the same arguments as of the previous thing might hold. And you know if these two little black holes and separate from the critical solution that could be an example where there's a full black hole in state. There's collapsing clouds, and these two little black holes that managed to escape. And of course they know that we just been taking this to the, what would be implied for superplug scale scattering. Again, it doesn't matter that was fundamental particles or black holes, but it suggests that the possible end states might be more more interesting, not just a single black hole, which you're close to the plunge threshold will quickly walking evaporate that you could have two unbound particles, or two black holes and unbound particles. Again, all of this is just wild speculation but again, that these are open questions and I think there's a lot of interesting physics here even if it might not be extra for this city or experimentally relevant. So to conclude, you know, I think in the last few decades I've seen a significant progress in our understanding of the dynamics of black holes as governed by general activity. As both Alessandra and Tebo mentioned with respect to some astrophysical sources of gravitational waves, perhaps these qualitative questions have been answered, but the frontier is now accuracy and getting the relevant precision to actually take advantage of these, you know, almost astonishing experiments that that that might come up, not that like isn't astonishing. But for example that that 3G might see 150917 like black holes throughout the observable the universe is just mindboggling. But to be able to take advantage of that, we really need precision. And there's going to be a lot of work both numerically and analytically to get there. However, as my talk is focused on, there are some interesting areas of sort of parameter space or theory space with also unanswered questions, and also with interior structure which I didn't mention. And of course, this is not going to be as relevant. You know, if there was some observational signal that would be much more relevant but I think it's interesting enough that it's worth some fraction of the community's effort to explore. Thank you. Thank you very much, Franz. And Professor Tukolsky to give you the stock solution. Okay, can you see the slides. Yes, we can see the slides. Great. Okay. Just. Is that better. Yeah, that's better. Yeah. Okay, great. All right, so my, my talk is going to be a slightly different flavor from the previous ones. I'm going to be focusing on some computational questions. And, you know, in the past decades, computational physics has been applied, especially in astrophysics to many different kinds of examples.  It wants to make some breakthroughs in astrophysics. And that's my feeling too. And we've already seen this example, several times this is from the detection paper, the first detection paper by the LIGO collaboration. On the right panel, you see the strain signal that was measured in the detector. And on the right hand side, the signal from Hanford, the red one has been superposed on the signal at Livingston. And you don't have to do any fancy data analysis to see by eye that, you know, these things match up. It's that's what that's how we know that this was a extraterrestrial event. It wasn't people slamming car doors in the parking lot, simultaneously two places, 2000 miles apart. Below that is the comparison. So the gray signal is the detected signal with a bit of smoothing done and the width of that shows the uncertainty of the measurement. And then superposed on that is a numerical waveform from our collaboration. And you can see that, again, without any fancy data analysis, it looks like a very good match. So that's what tells us that the signal came from black holes because the numerical simulation was done by choosing masses and spins that would give this fit and we know therefore using general relativity that it was black holes. All right, so that sounds great. But now I have to let you in on a dirty secret. For the past 60 years or so, the dominant algorithm that's been used in all fields to solve the underlying partial differential equations numerically is essentially unchanged. It's as if we've made no progress. This goes by different names, finite differencing or five volume methods, but this is what basically just about everybody solving these problems has used this particular technique. The first stirrings that maybe we should be thinking stretching our minds about other methods came in other fields came in mainly in terrestrial hydrodynamics. And we're interested in Einstein's equations and the key thing about Einstein's equations, if you're purely, you know, no matter in the problem just the vacuum Einstein's equations, the solutions are smooth. Right, we're assuming we're solving them in the observable part of the space time away from singularities, and you're not choosing crazy coordinates that have shock waves in them. So that suggests that we should use higher order numerical methods. Right, if you think of an underlying Taylor series approximation to the solution. If the solution is smooth your Taylor series goes on forever and you should adapt a numerical method to represent all those higher order pieces in your approximation, and that will give you a very efficient way of solving the equation. So, I'm not going to go into the details of I mean this is meant to show the difference. The first line is supposed to show finite differencing. So you have some numerical grid represented by the dots. And then by combining function values at those dots you know f of x plus h minus f of x divided by h approximates the derivative. You can use more and more points to h apart three h apart and so on, to get a higher order approximation. And the problem comes when you running to the boundary, either a physical boundary on the left hand side, or if you have two neighboring subdomains of your regime that you've put on a parallel computer on different processes. The boundary where they have to talk to each other. The finite difference methods run into problems you can't easily go to high order. One way around this is to use the spectral methods, which I've sort of represented below with an unequal space grid where you use all the interior points in a particular subdomain to get a high order approximation to the solution. The point is that a spectral approximation as you add more and more grid points converges exponentially fast for a smooth solution, right faster than any polynomial, which is what finite difference techniques do. This is why when we first started thinking about really trying to get good solutions for Einstein's equations numerically, it was this sort of information from other dynamics that suggested one should use spectral methods. Now the problem is, if you want to simulate neutron stars. Now you have matter you have fluids, they're smashing to each other, you get shock waves. Neutron stars are stars, they have surfaces, these are discontinuities and spectral methods don't work well when you have discontinuities you get Gibbs phenomena. And we would like to do, not just black hole physics, but we're going to learn a lot about the universe from neutron star physics as well when two neutron stars collide or when a neutron star and a black hole collide. In this era that's called multi messenger astronomy where we see these events, not just with gravitational waves, but also with throughout the electromagnetic spectrum and learn all kinds of things about nuclear physics about production of heavy elements. All kinds of interesting information. So as we look to the future. What are the challenges for our field.  As we've heard the LIGO signal to noise ratio continues to improve. We're looking forward to a new generation of detectors the ground based ones cosmic explorer the Einstein telescope, and then going to space detectors like Lisa where the signal to noise ratio will be more than 100 times probably. Collision of supermassive black holes, more than 100 times greater than even LIGO at its design sensitivity, which is still a few years away. So, we need higher accuracy, if we're going to get the full benefit of these precision experiments. The actual methods that that are very good now and adequate for LIGO's needs. Do not scale we won't be able to make use of the next generation of supercomputers to get accuracies. For example, for, let's take the example of Lisa. So we'll have the city will be in the situation where. We'll spend billions of dollars on the experiment. And then, you know, for lack of a few million dollars to support some black hole theorists doing these calculations. We won't be able to say to extract all the science to say whether in fact there are deviations from general activity in some very accurate uses. That's something which we really do need to be thinking about now. It's even worse for neutron stars. Even today. The accuracy of the neutron star simulations is not really adequate to the job if we really want to know just before the merger of two neutron stars. Look at that gravitational wave signal can we see evidence for the title deformation and how does it vary as we vary the equation of state. It's very iffy whether the numerical accuracy of these calculations is sufficient. And once again the current methods these finite difference methods will not work. They will not be able to take advantage of the next generation of supercomputers. And there are lots of reasons why this is true. I spoke about this fish, the non smoothness of the solutions, multiple time scales, the geometry changes. But then also we have multi physics we want to solve not only Einstein's equations we have a higher dynamics we want to put in magnetic fields neutrinos. All of these things make it difficult for the various pieces of the computer code, you're sort of limited by the slowest piece of the calculation, everything else has to wait to do that. So we have one proposed solution again it's not something that that we invented it comes again from mainly from applied mathematicians in the terrestrial hydrodynamics community. It's something called the discontinuous Galerkin algorithm DG. You don't have to know what it is it's a kind of a hybrid between spectral methods it has some of the advantages of spectral methods and the advantages of finite difference methods for handling sharks. I'm not claiming this is the only way forward but it's certainly a good candidate. So we're working on a new computer code we had a spec was our original spectral Einstein code. This sector is the new code. And so it has two key ingredients one is this DG algorithm which has not been used before in computational astrophysics alone in in numerical relativity. But also it's designed to take advantage of machines which will have millions of CPUs. Right so. So, and beginning graduate student today. By the time they graduate, they could log on to a national supercomputer and have access to a million cores. I'm pretty sure that that's on the horizon. I couldn't find a nice picture of a of a chip with even you know 10,000 cores he has one from 2012. The bottom left it says P you zero. That's processing unit number zero and if you go round clockwise on the bottom right you'll see P you 17. So there's 17 processes here. One of them is used for input and output so that leaves 30 they're 18 processes starting at zero. So that leaves you with 17. And this is advertised as a machine with 16 useful cores. And I'll leave you to think about why it actually has 17, but is advertised on 16. You can ask later if you can't figure that out. Anyway, that's what's coming up. So why is it so hard to run current codes on a million processes. I mean the way we parallelize is we divide up our domain you know the interior of the neutron star and the exterior where the gravitational waves travel into little subdomains. We assign each subdomain to its own CPU. And then we use a very standard software package MPI, which passes the messages back and forth. And we have this problem then that the load is on balance that the. We have to wait for the slowest processor to finish its computation maybe it's finding an apparent horizon, while the piece that's propagating the gravitational waves away that's already finished its little time step and it's waiting. Even the communication at these boundaries between the cells that's a very slow process, compared with doing arithmetic on the on the chips. So how are we going to get around that problem this. Everyone is using this MPI method. We have to change the way we parallelize our computer algorithms. We have to use what's called task based parallelism. So the top half of this diagram is a sort of a figure to show the conventional way we parallelize. So we can think of our algorithm is having a bunch of tasks, you know, compute the right hand side of the evolution equation for the Einstein for the metric. I do that arithmetic. And information from my neighbor about you know some some flux of energy and momentum that has to be added to the piece in the volume. Look for an apparent horizon. Propagate some nutrient all kinds of tasks that make up the algorithm. The idea is that as time goes on to the right some of these tasks finish earlier than others. But before you could take the next time step you have to wait for the slowest one to finish in task based parallelization. You put all the tasks into a queue. And then you have a pool of available CPUs. And every time one of them finishes a task, it gets sort of popped off the stack and you start up the next task that's ready to be executed. So the idea is you're always keeping the machine busy, all million cores are doing some useful piece of the algorithm. And if you can get this to work. This has the hope of taking advantage of the next generation of machines. So here's a simple example. This is a relativistic magneto hydrodynamics code that the part of the spectrum was a test case. One, some, you know, simple case of an analytically known vortex. And so time is moving to the right. And then what's vertically is sort of the percentage utilization of all the cores in the machine. And the color is different tasks different pieces of the algorithm.  But the, the white is idle, right. So you see at the beginning as the, the program starts up is some white that blue piece there is the initialization. And then the evolution starts. And then, you know, it's dominated by this red and this greenish colored tasks, those are computing the right hand sides and sending fluxes to neighbors. The black at the top is the overhead of the task management software. Right, it's a very complicated bookkeeping device to keep track of everything. But then you can see as you go along, sort of more than 90% of the machine is being used to do this. And then at the end we only did 10 time steps here, you can see the white as the cores become idle, and you end up you've completed everything. So in principle, we know how to do this. And the question is, can we get this to work for the full Einstein equations and then for the full Einstein equations with magnetic fields and nuclear physics and all the stuff that will make multi messenger astronomy work. And so here's an example of a more challenging one. This is a movie of the Kelvin Helmholtz instability. So this is a standard test case that we always do. So it's this instability occurs when you have a dense layer of material, say moving in one direction, and then a lighter fluid moving in the opposite direction. In this case, I'm going to have the lighter fluid both above and below. So there's no gravity in this problem is just the flows. And what happens at the interface is you get an instability. And you can see these curl, curls of sort of odyssey is being produced. And the challenge in this is to resolve all the fine scale structure. The little boxes that you can see are where we're using. So in the, in the center here, the standard DG algorithm is being used, getting a high order solution. But in order to resolve this fine structure with our discontinuities, the little boxes show a new algorithm being used. And I, as part of the thesis by my former graduate student, Niels Deppie, to be able to resolve those things. And if you didn't do that, all of that structure gets smeared out numerically. And when two neutron stars have been orbiting each other and they collide, they collide sort of shearing the surfaces. And this instability plays a crucial role in figuring out what happens to the remnants. Okay, so just to summarize, the way I would say it is after 60 years of finite differencing, doing the same thing, it really is time for us as a field to move on. We can't keep our heads in the sand, keep doing the same old thing, and then suddenly wake up tomorrow and realize there are these big machines out there, and we can't take advantage of that. Algorithms like this DG method are high order, and they're local, they're confined, they only talk to nearest neighbors, they only need information from the nearest neighbors, whereas standard finite difference methods to make them higher order, you need to talk to your next to next to next to nearest neighbor, and it's very slow and doesn't scale very well. And then this question of being able to resolve the fine structure and the discontinuities in these high order methods. The technical name for that is using a limiter, it limits the Gibbs phenomenon. And the standard things that are in the literature are very bad, they don't work especially for relativistic cases. So this reminds me that I really want to echo what the other speakers have said. You know, this, you know, it's very flattering to be awarded something as prestigious as the direct medal and I'm very honored to be one of the recipients this year. But, you know, science is never done in a vacuum. And I want to acknowledge, you know, in this example is was my graduate students who played a key role, but just in general, all the great graduate students and postdocs that I've been privileged to work with have really been the people on whom this this huge enterprise really risks. So, just to encourage people who are interested in looking at this this code is open source you can go there and downloaded right after the ceremony today, and you can run the test problems read the documentation and get involved. Thank you very much. And thank you very much for this very interesting talks by the medallist. Now we have time for some questions. Thanks. Actually, I'm reading a question from somebody attending on on zoom. The question is that whether there are numerical methods. I don't know for which maybe for for Pretorius, are there any numerical methods to approximately solve Einstein's equations very close to the singularities. So in principle, the various methods of people I've developed will work at least from a numerical perspective, you know, whether it's finite difference or pseudo spectral. The problem approaching the singularity I think is largely one of choosing the correct coordinate system the correct gauge or if you let the dynamical coordinates that get you close enough to the singularity we can answer the questions that are that you're interested in. And for example, again, in, in, so that the question about what the singularity is in a black hole formed from gravitational collapse. You know that one of the big questions is, you know, is it sort of, it was probably some combination but these are sort of like a BKL type behavior approaching a certain region like in cosmological cosmological singularities.  But they have to get to that especially if we know that there is a piece that's associated with a kosher eyes and we have to evolve the entire infinity of the exterior space before we can get there. So the challenge is coming up with the time slicing that goes through infinity on the outside doesn't run too fast and fall into a BKL singularity on the interior. And sort of just nicely sidles up to what's going on. And in spherical symmetry. So with rise in an order and people have been able to do that that you can actually it's pretty straightforward you can essentially need to come up with a Penrose diagram. And you can do that in spherical symmetry but beyond spherical symmetry. There's not been much success. So I think that that's the big problem is finding a dynamical coordinate system to get close enough to the interesting part of the space. Any other question. There is one question in the back there. Professor team of the board. Now, you have shown several approximations. I mean, it's a series of that represents the quantity that is being calculated. Are we sure that this series are converging. I mean, looking at the coefficients and the coefficients look very strange. So actually we we know they are not converging from a general theorem of the materials to do. But approximately they have a radius of convergence. And that resumption methods, even if they are not converging, and they are asymptotic, one can boost the validity, the domain, and from the practical point of view. It's not so important whether they, they converge or not. Okay. So, like in qft where they are known not to converge and using paddy representations can improve and then allow quantities. But then how many terms you think would be necessary that you will be sure that the next term will not spoil the previous. Indeed, if one had only post nutrient information, probably it would be impossible to decide this we are in the lucky situation where we can compare to numerical data. Then when you combine the two. Usually you can with good physicist confidence know when some recent analytical expression is accurate. Two, three, four digits. Now if in the long term one needs phase accuracy of 10 minus four 10 minus five. So the question you are asking will become important and for Lisa type phisics for instance, in a flanagan and others have emphasized that you you cross some resonances and then, then you lose accuracy a lot. Okay. I'm not at all to exclude your question is saying we understand everything. Okay, it's a research problem and everybody is alert to the fact that and it's good. Yeah, to know that we don't know and that the series are delicate. Like when I said you know when I was motivated by the end body problem. When he got a price for having proven the theorem then he realized the theorem was wrong because somebody told him there was a mistake in there and then he understood that we enter very delicate areas of mathematics. Thank you. Thank you very much. Okay, there is one more question there. There is some discussion by Professor Bonanno on the possibility of gravitational waves from supermassive black holes. Was this from mergers and if yes, from Merger of two supermassive black holes and if yes, how likely is for two supermassive black holes to find each other for male binary and then merge. Yeah, I'm not sure and this to the question so the question is what what are the perspective to to see gravitational wave from supermassive black hole binaries. What process creates this gravitational wave Merger or something. It's, if you want is similar to the same is the same process for stellar mass binary black holes. So you have black holes million solar masses, originally at the core of the galaxies, then they end up in a bound state so they start to spiral in around each other. And then we get the signal in one of the plot I was showing in one year even depending on the masses, we might see the signal for an entire year so the spiral part, and then when they merge with each other, and then they're down. So we will see the whole process depending on the masses of the supermassive black holes. So the members of the binary are supermassive black holes and see both of them as well. These are sources for Lisa whether for the detector in space because it are signals in the milliards or around the milliards. They will already be merged at the frequency of like one vehicle so we don't see them. Thank you. Any other question. The audience. I'm Professor looking from Ukraine. I'm meeting scientists here to the moment. Thank you very much for very, very exciting presentations and the general question. The Einstein theory is based on hypothesis of space time continuum. All the solutions we are talking about. You applied the finite different methods, but assume that the space time is continued. In the, I think it was mentioned that the superplunk scale than meta is meta or not meta, but then my question. I think that investigation of such singularities like lake holes and what they're generating. The ways maybe to which extent to which scale this space time continuum is applicable, or it's maybe the you can point at the scale where we should consider a discrete model or something like this. Thank you. Alas, I'm afraid and. Please. We were discussing this is that from the theoretical physics point of view. One would need to have some modification of Einstein theory at kilometer scales to see something in like over a go. Even the most optimistic way of saying there could be something beyond gravity. I mean beyond Einstein gravity to derivatives is that maybe at the micron level, you could have something which will not be seen by like over. So I think, Alas, like we're go will not give us information about what happens on in the UV on very small scale. We are reasonably expected from theoretical physics solution. Sorry, that I thought maybe studying very more details and algorithms and physics. In this area, maybe you face some fundamental contradictory contradictions, which inspire to sink on modifications. So my question wasn't that. You mean modified. For me, not for me for young people are here. I think you have already answered the people you want to continue or. No, I think this is a great Lego logo is very great laboratory to learn about astrophysics and, but I think it does not access the scales where you have to go let's say higher derivative terms and beyond Einstein action or quantum gravity effects and that's, that's where you might see the discreteness and I don't think. I'm on your side, I thought just maybe pick up something. Thank you. Any, any other. Please go ahead. I should say that people are trying to think sort of out of the outside the box and come up with more outrageous suggestions where you might get away from this from a very small scale. Perhaps you can, I can say, like, for example, fuzz balls and things like that. But then also like what I was under mentioning a talk that despite the even if we don't anticipate that there's a lot of work trying to use gravitation wave detections to actually measure what's out there like these post Newtonian coefficients, constraining them to be zero like I think unusual happens like what you might suggest that the constraints is going to get stronger, but like I still very actively looking for something. And perhaps nature surprises our intuition and gives us something that's going to show up at significant at the kilometer scale. And, yeah, but people should be thinking about that I definitely agree. And people should be thinking about these things, and like I was looking for anomalies. So you want to comment maybe on, you know, possibilities of using like a for going beyond. Well, I think I was going to say basically what France already said, I think people are who are trying to do this test, they consider modified years of general relativity in which actually the scale is not the blank scale but that they might like open to the possibility that the scale could be of the order of kilometers and are trying just to see whether in, you know, the gravitational observation can say something about in that case. Now, perhaps theoretically this is. I don't know how to motivate but I think one has to be open minded and please say experimental bounds on this parameters that certainly is a very important thing to do. So do you want to comment on this question. Yeah, I mean I will just say that one of the challenges in trying to even with the current experiment to try to set bounds on these things is we don't really have a good framework. I mean what does it mean you know if I measure some parameter in a way for model, and I put a bound on it. Well, does that mean that certain theories are actually ruled out. We don't have a good theory of theories. We have some. There's certainly, you know, is work by Francis thought about these things and other people too. But so the one issue is we don't have a good way to associate any potential bounds that we find with a class of theories. Well, if you have a favorite theory which you think is going to make you famous because you're going to prove Einstein was wrong. You need to be able to calculate what the way forms are what what LIGO should see in your theory. And most theories that theorists have come up with actually you can't do that calculation. You are ill posed in a mathematical sense you can't there's no Koshy evolution problem that you can use to actually calculate. So people are you know in the old days before LIGO people could get away with coming up with some modified theory, checking that it agreed with the solar system tests of general relativity.  Well, you can't get away with that today. Thanks to LIGO, you have to be able to calculate what LIGO sees. And if you can't do that, your theory is not complete. So I think that these are challenges that people tend to not think about when asking about alternative theories of gravity. Alessandra, you want to comment. Yeah. Oh, maybe I just add, I fully agree with the soul. I just wanted to add that on one side. People are doing. So the kind of bounds that, for example, I was showing are more to be considered like null test in the sense it's not the absolute value of the bound that is really important is more to see how the bound would improve over time just to show that one has more sensitivity. But I fully agree that one should actually do calculations including numerical calculation in beyond the GR theories and this is very hard because many of them are not well posed. And but there are, you know, techniques method that people are trying to suggest to do that. So there is a lot of work actually all the work that we have done for GR, at some point, should be extended to non GR theories, which is immense. Okay, keep do you want to add something to do you have some thoughts on how future research in this field could, you know, take us beyond. Some of the concrete thoughts beyond my enthusiasm that this field is just taking off so marvelously. Thanks both to the theoretical work, the computational work and the observations. It is. I'm just so enthusiastic about the future. I really have nothing more to say than that. Okay. I think if there are no further questions I think let's thank all the speakers for wonderful. We all know that this is a very exciting field is just beginning to bloom and thank you very much for very inspiring talks. Thank you very much, Saul for joining us remotely and keep for being here with us and for this marvelous introduction to this work. I wish that both of you could join us for a nice Italian dinner, but maybe next time. I would like to also announce that please follow me after this. We are going to inaugurate the deduct exhibition. So you are the stars of the. We are starting at the ICTP this new deduct exhibit of the deduct medalist. And today is the inauguration so please, all of you requested to follow me, and you can take your time and look at the deduct medalist since the beginning. And so with this I do this session is closed but we will go to the dirac stairs. Thank you.