 Okay, dear colleagues, fellow scientists, and distinguished guests, I'm very pleased to welcome you to this important ceremony because of COVID situation. We are in this hybrid event, but at least I'm happy that we are holding it in the Boudinich Hall. And many of you might remember this location. So created the ICTP prize today, we are going to recognize an award ceremony for this very important prize created in 1982, which recognizes young scientists under 40 years from developing countries who work and live in those countries and who have made outstanding and original contributions to physics. And the prize includes a sculpture, a certificate and a cash award. So since its establishment, ICTP has awarded over 46 young scientists from over 15 countries. And each year the ICTP prize is given in the honor of a distinguished scientist who has made, you know, path-breaking contributions in the field in which the prize is given. Today we celebrate the 2019 ICTP prize award in the honor of the great Indian astrophysicist, Subramanya Chandrasekhar, who all of you know as the person who is famous for the Chandrasekhar limit. And I'm very pleased to present this award to Dr. Basudev Dasagukta from the Tata Institute of Fundamental Research in Mumbai, India and Dr. Subrat Raju at the International Center for Theoretical Physics, also a branch of Tata Institute of Fundamental Research in Bengaluru in India. And Basudev, in fact, was a post-doc, he has a long association with ICTP and Subrat has been a close colleague in a field very close to mine. So we had to postpone this celebration because of the pandemic, but I invite the winners of this award, Basudev Dasagukta and Subrat Raju to visit our ICTP campus in the future, whenever we will be able to host them safely. And it will be my pleasure to meet them in person and maybe talk some physics and introduce them to the campus and the faculty. Usually it's a very nice ceremony and you know there is a dinner and interaction with students. So this cannot happen this time, but we can postpone it and we can hold it in the future. So today's ceremony will be co-hosted by Professor Ashok Sen, who himself is a very distinguished physicist from India, close colleague and he has been on the steering in the Scientific Council of ICTP for many years. And he will introduce the winners and will formally give them the floor for the scientific talk. Before starting, let me remind you that this event is live streamed on the ICTP website and is available on the YouTube channel. And on this important occasion, I'm also pleased to launch the new ICTP welcome video, which we will watch shortly. It's a short video clip. After the talks of the two prize winners, there will be some questions and answers which will be moderated by my colleague, Professor Viladaro. He's also a member of the high energy physics section and he was also a member of the selection panel for this prize. And I invite guests to write their questions in the chat so that we can take them systematically. So without further ado, let's see the new video of ICTP welcome video and please enjoy the ceremony. Humans have always been curious. Why is the world the way it is? How does the world work? What does the future hold? The excitement of new ideas, passionate pursuit of new knowledge, expending the horizons of all. These belong to everyone. The Abdul Salam International Center for Theoretical Physics has a unique mission that supports research excellence in physics and mathematics and the nurturing of sustainable science for all. ICTP's founder, the Nobel Laureate Abdul Salam, believed that science is the common heritage of all humanity. The center supports researchers from less advantaged countries and works to remove barriers they may face. Here, everyone speaks one common language, science. Basic and applied research are both vital for society, from fundamental particles to black holes, from climate change to quantum computing. ICTP's vibrant atmosphere of collaboration opens doors. The exchanges and global scientific networks built here create fertile ground for new discoveries. These connections encourage brain gain. ICTP's training and education programs support scientists throughout their careers. They share their knowledge with students and enriching the global community of researchers. ICTP, where outstanding scientists explore the frontiers of knowledge, build capacity and promote bright minds. A community united by the power of science. Okay, thank you. I welcome Professor Ashok Sen for the scientific introduction of the first prize winner in alphabetical orders. Vasudev, Ashok, please go ahead. You're muted. Am I audible? Okay, so first of all, I'd like to thank ICTP for giving me this honor of introducing to you two outstanding theoretical physicists, Vasudev Dasgupta and Subrat Raju. So the way I'm going to do it is that I'll first read out Vasudev's citation, then I'll say a few words about his work, and then I'll hand it over to Atish for the prize ceremony. And after that, I think Vasudev can give his talk, and then I'll repeat the same thing for Subrat. So first, I'm going to read the citation of Vasudev. Vasudev Dasgupta was recognized for his innovative theoretical contributions to nutrient and dark matter physics, especially to the understanding of collective nutrient oscillations. So I'll now give a slightly longer introduction to Vasudev's work. So Vasudev is a professor at the Trata Institute of Fundamental Research in Mumbai. He has made important contributions to the field of collective nutrient of flavor evolution in extreme astrophysical environments, such as those in supernovae, by taking into account the effect of interactions among all three nutrient flavors. This improved our understanding of these spectacular and phenomenological events. His work on dark matter, in particular the dependence of the dark matter relic density, on the mass and annihilation cross-section of the dark matter particle, produced crucial input for the interpretation of ongoing direct search experiments. His new ideas on this subject improved our understanding of the possible nature and properties of this obscure form of matter. Okay, I'll now hand it over to Atish to give the award. Okay, so Vasudev, I hope you can see this and you can sort of switch hand and accept this award if you can. Thank you very much. And the citation and the certificate is here. I point it to the citation and here is the award. Thank you. So congratulations Vasudev. Thank you. I suggest that instead of going directly to Vasudev's talk, we can finish the award ceremony. We will go next to Surat and then we will have the talks by Vasudev and Surat one after another. Ashok, I will hand it over to you again to introduce Surat. Okay, thank you. Okay, so what I'll do now is to read the Surat citation. Surat Raju was cited for his new insights into the holographic description of black hole interiors for clarifying the nature of subtle non-local effects in quantum gravity and for contributions to the study of ADSTFD correspondence. So here is a slightly longer description. So Surat Raju is a professor at the International Center for Theoretical Sciences at Bangalore. His research has spanned a wide range of topics in string theory and quantum field theory, including his recent work on black hole information problem in flat spacetime. But perhaps his most remarkable contribution is a series of papers with Kiryakos Papadodimus on the construction of interior modes of black holes in anti-disseter space in the dual gauge theory description. Earlier work on this topic suggested that such modes cannot be constructed, leading to the proposal of a firewall at the black hole horizon. The work of Papadodimus and Raju showed how we could evade the Nogo theorems and give explicit construction of the interior modes. One surprising feature of that construction was that it depends on the details of the micro state of the black hole and not just on its macroscopic description. While this met with resistance initially, by now most practitioners in the field have accepted this as inevitable. So I hand it over to this for the award. Okay. So Surat, congratulations. Actually Surat's work, I'm myself, I'm more closely familiar with, and this was a very important breakthrough together with my colleague here at Kiryakos who was also at ICTP. So congratulations, Surat, and you can stretch your hands and accept this award. Thank you. Thank you. Thank you. Thank you very much Ashok for the kind words and attention. Thank you. Okay. Yeah, usually this very nice Boudinich Hall is full and it's a very lively interaction, but we will make do with this virtual interaction. So now I will pass it on to Basu to give his talk. I will now go and sit in the audience so that I can watch it more on the screen. And Professor Laduro will moderate the questions. Thank you and congratulations Basu and Surat and thank you very much Ashok for your time. Thank you. Thank you very much. Thank you. Thank you. So could I start? Yes please. It's a real pleasure to be awarded this very prestigious prize. I have been a postdoc at ICTP not very long ago, but more importantly I started my physics career as a student at TIFR and one of the first places I visited was ICTP as a summer school student in 2005. ICTP holds a very warm place in my heart and it's a real, real pleasure and an honor to be recognized by one's alma mater. This prize I feel very fortunate as a representative of our community of astroparticle physicists. And so I'm really happy that the work in this area is being recognized and I feel particularly privileged to be chosen as the representative. I would like to personally thank all of my mentors, my collaborators and my students. There are so many that I probably wouldn't be able to name all of them, but I would be remiss if I did not in particular thank my dear friend and collaborator Alessandro Mirizzi who would certainly have been with me there today had it been held in person. But thank you Alessandro for your friendship and your collaborating with me. So with that, I would like to start my talk. I'm going to talk about some recent work that we have done in this area of collective neutrino oscillations. So perhaps a little bit too colorful is Dying Stars, Dancing Neutrinos and Us. And what I would like to tell you about is this idea that although a variety of different physical systems comprised of small individual units can exhibit collective behavior. So in Italy, certainly you have seen this phenomenon called murmuration of starlings where a huge flock of birds fly in a concerted fashion, as if it's one big, you know, organism. Similarly in biological systems, neurons can start firing in synchrony. There are known examples of fireflies that blink together, you know, in sync. But, and there are a variety of reasons for why such things happen. Typically this has to do with the fact that there are individual agents and they interact with their nearby neighbors through some, you know, interaction, and it also depends on how many of these agents you pack together in a volume. This has also become very interesting in some modern studies related to things like active matter. But here we are talking about a much simpler system. It's a system of neutrinos and neutrinos come in three kinds, electron neutrino, muon neutrino, tau neutrino, and they can transmute into each other. And electron neutrino after some time, it can be seen as a muon neutrino and this keeps happening back and forth, back and forth. Now this happens individually for each neutrino, but when you pack a lot of these neutrinos into a small volume, the high density, what one finds is that this dance of neutrino flavor, neutral neutrino oscillations becomes synchronized and it exhibits very interesting behavior, including certain instabilities. And one of the key things that happens with these neutrinos, which is, I think the most remarkable of all, is that this collective evolution is faster than the evolution of any individual agent. So if each neutrino was oscillating at some frequency, let's say once per one kilometer. If you put in a million of them in some box, small volume, let's say a centimeter cubes in size, these neutrinos oscillate at a rate that is a million times larger. So this collective oscillation frequency scales linearly with the number of agents. So this is what is called fast conversion, which means that in a high density environment, this evolution can be very rapid and occur on very small time scales and length scales, and that has a lot of physical impact. For example, it can be a reason why there is more efficient energy transport in stars, which allows these stars to explode. It can change which elements are created in stars, and it also changes what kind of a signal we will observe from these stars. So that's what I'm going to tell you about. Now, let's take a few steps back. Those that are more than eight or 10 times the mass of our sun, at the end of their lives when they have burnt up all their hydrogen and helium fuel, they go through other stages of burning, eventually, the core of this star becomes made of iron and iron will undergo fusion nor fusion, fission nor fusion. And this iron core, once it becomes larger than the Chandrasekhar mass limit, which is about one and 1.4 times the mass of the sun, this iron core collapses. And once it reaches nuclear density after collapsing, it bounces back, and this bounce back creates a shock wave in the star, which explodes the star. So this is the rough idea of how stars explode as a supernova. But this picture has many detailed elements still missing and not completely understood. In particular, it is seen in very detailed calculations on the computer that the shock wave as it goes through the star, it breaks the nuclei, iron nuclei into protons and neutrons. And as a result, the shock wave loses energy, and it stops at some point. So this explosion should not happen. But there are neutrons being emitted from the dense inner part of the star, which deposits a little bit of energy behind the shock wave, and reenergizes the shock. This is called the neutrino mechanism. But this on the other hand does not work very well. So there are many unknown and uncertain aspects of this very, very old problem, how do stars explode? And neutrinos have a role to play here. And we have observed neutrinos from a star of this kind once before, that was in 1987. And we observed about 20 odd neutrinos. So what you see here on the horizontal axis is time. And on the vertical axis are four panels corresponding to four different experiments. And in each panel, the vertical axis tells you the energy of the neutrino that was observed. So all of these red vertical scratches are one neutrino each. And you can see that there are about 20 odd neutrinos seen across three or four detectors. And this meager amount of information was already enough to confirm for us the basic picture of how stars explode, that there are neutrinos that are emitted in this supernova explosion. So how many such neutrinos should be emitted? And they should have roughly energies of, you know, somewhere between 10 and 40 maybe and so on. But a lot more detailed information can be obtained from these stellar explosions. And in order to understand the signal that we will see from such an exploding star in future, we will need to understand what neutrinos do inside these stars. And this is the topic that I have worked on and that I would like to tell you a little bit more about. So just so that we are all on the same page, neutrino oscillations are the fact that if you start with a new to know one flavor, let's say electron neutrino. And this new to know is traveling along some direction. Make a measurement at some distance and ask what is the probability that I see this neutrino in the same flavor that it was initial. Let's say electron neutrinos. You will find that this probability oscillates sinusoidally with the travel distance. And what you see on your screen is this a cartoon for this phenomena with two different colors. And the point to be noted here is that these neutrinos with different energies, oscillate with different frequencies. So, and the frequency goes in inversely proportional to the energy. So this is standard neutrinos oscillations. And a bit more technically what this would be seen as is that this is a non stationary flavor is a non stationary quantum state, and the probability of seeing this non stationary quantum state oscillates sinusoidally with time or space. So this problem, while you can write it as a quantum mechanics problem, which I do here on the first equation that you see, can also be converted into a much simpler classical mechanics problem. By writing the density matrix in terms of the block vector, you represent each flavor state by this vector green colored vector that I'm showing you on the screen. The effect of the Hamiltonian is represented by this light gray vector, which I have labeled as B, and the time dependent oscillation of the survival probability is captured by the precession of this polarization vector P around this magnetic field vector B. So, initially it starts aligned along the z axis, and with time it goes on the tip of the vector goes on this circle, and you can see that therefore the probability of it being in the same state which is the projection along the z axis will keep changing sinusoidally with time and periodical. And the rate at which this would happen is related to the difference in the eigenvalues of the Hamiltonian, which in this case happens to be the mass squared difference divided by twice energy. So therefore this precession frequency depends on the neutrino energy. Now, all of this is changed by having some matter in the background. In particular, what happens is that neutrinos that we're traveling freely can forward scatter on electrons in the background or neutrinos in the background. And that changes their Hamiltonian. And this little bit of a change to the Hamiltonian can be written as a potential which then changes the way in which the neutrino changes its flavor over time. Okay, so this is the famous work of Mikhev's spin of a Wolfson's team when it applies to electrons in the background, for example, but same thing will happen when there are a lot of neutrinos in the background, each neutrino will impart a potential other neutrinos. Now the problem is suddenly more complicated because in order to solve the evolution for any one of the neutrinos, I need to know the state of the other neutrinos in the background. So instead of solving a one particle or one body quantum mechanics problem, I'm forced to solve the evolution of n quantum particles that are coupled to each other. So this problem suddenly becomes more complicated. But without going into the details, I want to first tell you what happens. So in this very strongly coupled neutrino gas, what happens is that the dynamics becomes collective that whereas before neutrinos are different energy we're oscillating with different frequencies. Now the oscillations can be at the same frequency. So they get synchronized. And not only that, the nature of these oscillations can be very different. Whereas previously you had sinusoidal oscillations, now these oscillations can be much more intricate. And in particular, they are described not by sine and cosine functions but by more complicated elliptic. In particular, they look more like the motion of an inverted pendulum. An important energy scale or frequency scale in this problem relates to the background density of neutrinos, which I show here as n sub nu. And multiplying it by some overall factors, this symbol mu is the frequency that is given by the neutrino background. And this can be much, much larger than the natural oscillation frequency of neutrinos, which is this omega. And once mu is larger than omega, these collective phenomena start. The question then one asks is that this cloud of neutrinos, at what frequency does this oscillate now? Is it proportional to omega or something else? And just from dimensional analysis you could expect that it could be something like square root omega mu because that has the right dimensions. Or it could even be proportional to mu, which would also have the right dimensions. But now it does not depend on the neutrino energies at all. We will see that indeed both of these things are possible. And the second class of instabilities, which are proportional to linearly proportional to the neutrino density are called fast instabilities. And these are the very intricate phenomena that we will now try to understand in the rest of this talk. So just to recap what we are going to do. So we want to understand neutrino oscillations in medium. This is a very rich and complex problem. It's not completely solved yet, but it has observable consequences as you will see. And the key point that we are going to pay attention to is that the high evolution of any neutrino state, nu sub i, is given by a matrix which involves the density matrix of all the other neutrinos, nu j's in this way. And there's a pre-factor that depends on one minus the cosine of the angle between the velocities of the two neutrinos. So the neutrinos are relativistic. So these unit vectors along the momentum when you take the dot product, that's just the cosine of the angle between the velocity vectors of these two neutrinos. And this kind of a Hamiltonian exists in our theory because of the standard model. And the question is that if in a box, I allow this index j, the other neutrinos to go over one to n, under what conditions is the evolution of nu i proportional to n? Normally, you know, the lowest normal mode of a harmonic oscillator coupled to each other is some sort of an average of the frequencies. That does not scale with the number of agents in the system. But here, this evolution of the dynamics is at a rate that is linearly proportional to the number of agents. Why does this happen? When does this happen? And what are its consequences? Just to again set the perspective, these neutrinos, which are being emitted from the center of a star are initially trapped because the density is very high and they can't escape very easily. They diffuse out of some surface and just at the time that they're diffusing, this is called the decoupling region, all of this fast dynamics will happen. Then there are other kinds of neutron oscillations that will happen. Some of them are collective, some of them are not. And then these neutrinos will reach the earth and we will measure them. So this is the picture to keep in mind. And we are talking about neutron oscillations in this very deep region of the star. The neutron oscillations are described using a formalism that is a mixture of the Schrodinger equation and something like the Louisville equation. So on the left-hand side, you have the density matrix and this capital D is the Louisville derivative, i del t plus v dot grad. And on the right-hand side, we have these commutators of the density matrix rho sub p with each piece in the Hamiltonian. The first one comes from the masses of the neutrinos. The second comes from the background electron density. And the third complicated looking term, where this one minus cosine is the one minus p dot p that we talked about. And this rho minus rho bar with subscript q is all the other neutrinos. And then we sum over these neutrinos in the background given by d3q. So this is the setup. And again, without going into the calculation, what we must remember is that this equation has the dimensions of frequency. Every term in the equation has the dimensions of frequency. So there are three frequency scales in the problem, omega, which is the neutron oscillation frequency we talked about. Lambda, which is proportional to the electron density, we will not talk about this too much. And mu, which we said was proportional to the neutrino density. And an interplay of these different frequency scales will allow for various kinds of neutron oscillations to occur. In particular, when mu is much, much larger than omega, we will have collective neutron oscillations. This is a complicated problem because there's a partial differential equation, first of all, because there are derivatives with respect to time and space. And I have to do an integral over all of momentum. And on top of that, I have to deal with not the equation for a num or a function, but the equation is for this density matrix rho. That's a fairly complicated equation, which we can't solve analytically in general, but we will see how far we can go. So first of all, if we insist that mu is much, much larger than omega, one approximation we could make is just throw away the first one. Omega is much, much smaller than mu. And then we notice that this equation does not explicitly refer to energy anywhere. And so therefore, the solutions will become independent of energy that already goes in the direction of realizing why the motion is collective that all energies behave identically. The second interesting thing is that this only happens when a certain condition is fulfilled by the neutrino distribution. So what you see here by this colored arrows are three different kinds of neutrinos. So let's focus on the red and the blue. So the red neutrinos are the new electron antineutrinos. They have a slightly more forward peaked distribution. So that's why you see this ellipse is more extended in the z direction, whereas the electron neutrinos, which have slightly stronger interactions are more isotropic, which is why their distribution is shown as being spherical or circular. As a result, there is this point which I'm pointing at right now. If you look at emission directions which are more forward than this, you have an excess of antineutrinos, new e-bars, whereas in the direction that's behind opposite to it, you have an excess of electron neutrinos. And this sort of crossing of the distributions is the necessary and sufficient condition for getting fast flavor conversions, where the evolution, the rate of evolution scales linearly with the number of neutrinos. So this can be proved mathematically, some net has been done very recently in a very general way. But rather than give you the truth, I want to tell you about a very simple model where one can see this. So imagine four neutrinos, which are represented by these four arrows. So what we actually mean are four momentum modes, so four momentum modes, worth of neutrinos and antineutrinos, and they meet each other at this angle theta as you see. Each of these is represented by this polarization vector P that we have talked about, so which now I give the names PL because it's coming from the left PR that's coming from the right, and then the same things with a bar because these are the antineutrinos. You write down the corresponding block vector equation for these four polarization vectors, a little bit of algebra just rearrangement of you know linear positions of these fees can be given certain names, and it just becomes a very simple classical mechanics problem where this vector Q can be shown to have a very simple second order differential equation that it obeys. And it derives out of some Lagrangian, so which must be familiar so this looks like the half MV square kind of a term. So this is the kinetic energy term, and then this is the potential energy. By doing this mapping of this neutrino problem to some classical mechanics problem we discover the effective potential that these neutrinos have to live in, and we can plot this potential. And if you plot this potential what you find is that for this angle, you know such that the cosine of the angle is positive, the potential looks like this bowl like potential. And then the particle which starts at one end of the potential rolls into the potential and you have also whereas then this angle theta is such that cosine of the angle is negative, where this angle theta is obtuse. Then the particle starts at the bottom of this here, and it won't execute our selections, and this is indeed what is seen, and this is related to having or not having a crossing. There are more involved and intricate phenomena that come out of the system. So you start with a box of neutrinos at high density, and they undergo these new oscillate flavor oscillations, and eventually the flavor gets completely mixed up. It's like you start with, let's say 100 electron neutrinos and 120 electron neutrinos, and what you find is that in the end you have 110 of each. There are certain conserved quantities that have to be made, but modulo that what you find is basically all the flavors become equally populated. So this is something again that we can compute in detail, which we did recently and numerically you can see that this colors red and blue correspond to neutrinos of two kinds. Everything starts out by being this blue colored neutrino and over time what you get is an equal mixture of the red. This is what is called depolarization, and one can then compute exactly how much of this depolarization happens. Now this is very important, because if the neutrinos change flavor, then what used to be a muon neutrino becomes an electron neutrino, and it changes the amount of heat it can deposit in some medium because electron neutrinos can interact more. So let's, before we get into that just one final thing, a tutorial way of thinking about this problem. So what we see here on the upper row are a bunch of neutrinos and how they're evolving with time that's running along the horizontal axis. And on the bottom, the same thing, if I think in a coarse grain sense that I don't pay attention to each neutrinos separately for each polarization vector separately, but I construct bunches of vectors and look at these bunches all at once. And what happens is that this bunch of neutrinos have a tendency to tip over. So because of the action of this potential, we discussed that this article starts at the top of the potential and rolls down, this corresponds to this polarization vectors tipping over, but once they reach the horizontal plane, then these polarization vectors spread fan out in the XY plane. This is related to a very well known phenomenon that occurs in NMR physics called T2 relaxation where the polarization vectors of a bunch of spins defaces relative to each other. Once they reach the transverse plane, the same thing happens here. And as a result, the length of the bunched spin, so the coarse grain spin becomes smaller. So the coarse grain polarization vector becomes smaller, and then it tips over. So, although one started out with this big vector pointing in the upward direction, by the time it tips over, its length decreases. This is what is then seen in the previous couple of slides as the idea of T polarization, which is that the length of the polarization vector decreases. And this is the reason that each polarization vector is thought of as a bunch of microscopic polarization vectors, and there is relative defacing between them, which leads to the effective length of the coarse grain polarization vector at a decrease. Now, why is all of this interesting? This is interesting because all of this flavor dynamics is happening very deep in the star, happening very deep in the star. And in the very deep region of the supernovae, nuclear reactions decide which elements are made. And the flavor ratios of the different neutrinos enter into, for example, the reaction rates for creating different elements, in particular, for let's say, our process nuclear synthesis. What you're seeing here on screen is the periodic table. And in green, all of these elements are the ones which are dominantly produced in these exploding stars in the supernovae. So the abundances of these vital chemicals like oxygen and iron and calcium, which are important for existence of human beings, these abundance of these chemicals is decided by the flavor composition of neutrinos very deep in the star. And because we can measure these chemical abundances, we can then find certain information about whether or not these collective neutrinosilations take place inside the star. Of course, the present day data isn't good enough for us to allow us to do that, but hopefully when we see a supernova in our galaxy, the data will be good enough for us to be able to make more precise statements about this. Similarly, very fact that the star explodes depends on neutrino heating as we discussed. So consider this cartoon of a star, consider some point inside the star at radius R. The heating of this star is the luminosity of neutrinos multiplied by the cross section at which this neutrinos interact with divided by 1 over R squared. And the same shell cools using Stefan Boltzmann like behavior as sigma t to the 4. This sigma is not the cross section, but the Stefan Boltzmann constant. And when these two heating and pooling rates are the same, we call it the gain radius below the gain radius, the star dominantly cools by emitting neutrinos above the gain radius. The star is dominantly heating up due to deposition of. Now this sigma is itself energy dependent. So the heating rate depends on the energy of the neutrino to the power to quadratically on the neutrino energy, but the neutros that interact most the electron neutrinos have the least average So the heating is not very efficient. However, if fast conversions are allowed, then new ease and new muse can get exchanged. And the new muse, which had higher energies transmute themselves to electron neutrinos and interact, therefore leading to a stronger heating effect in the star. So this is what is shown here in this view graph. The dashed lines here up top as a function of time from bombs close the enhancement of heating in some model in some simulation that we did many, many years ago, compared to what would happen if this additional heating was not there if this flavor conversion was not there. So if flavor conversions can occur below the gain radius, which can happen because of fast conversions, then the heating can be enhanced by a factor of almost two, which is very large and which may be sufficient to explain why these supernovae explode. These neutrinos can also be observed on earth. And depending on whether or not these fast flavor conversions happen, you get either the green curve or the red or blue curve. So the green curve is the case. And the red curve is the case where fast flavor conversions have happened leading to complete depolarization. And as you can see that this error bar on the green curve is small for some choice of detector, some choice of supernova in the neighborhood. And by measuring the number of events or the function of energy, you may be able to infer whether or not these fast conversions indeed take place inside the star. There's a lot more physics that one can do with supernovae across the entire explosion timeline of the star. I can't go into more detail here. But spices to say it spans a huge variety of physics from particle physics to nuclear physics astrophysics and even beyond the standard model physics related to things like axioms. This is an activity in which a lot of people are engaged. There are many many large scale experiments that are looking for these exploding stars. They're prepared to observe the neutrinos from this exploding star. And when we observe these neutrinos, we will also be able to correlate them with other observations of this exploding star, perhaps from optical telescopes, and maybe also from gravitational And with this multi messenger approach, you might be able to learn a lot more about the star and about the behavior of these dancing neutrinos inside dying stars. So what we know so far are what are the conditions for fast conversion, which is this crossing that I told you about when and where they occur. So in dense regions where this crossing kind of occurs and what are the final clock is going to look like and there's a tendency to become flavor equilibrated. And we want to know how do these conversions affect supernova heating. We have some preliminary ideas, but much more work is needed here and our momentum changing collisions important. This is something that is being looked at. You know, these days, more work is required. And we want to know what are the signatures and signals and detectors for such kind of another that occur inside stars and what physics and astrophysics can be learned. So I want to stop here with just a very quick summary. What I've told you is that in dense astrophysical environments such as inside massive stars, Newton of flavor evolves in a collective manner, the rate that scales with the number of particles, which can be up to a million times faster than the usual dynamics. This affects teller heating, the formation of nuclear elements and the signals that you will see on our. Why does this happen? This happens because Newton was exert a potential on each other that creates an instability in their flavor composition. This instability was exemplified by the rolling down of this particle in this potential. What we've understood so far through linear stability analysis and solutions in some simple cases is that such flavor conversion occurs on a very fast time scale and has a tendency to lead to equilibration of the flavors that all flavors get populated equally. However, this is not the final story and we don't, first of all, we need much more detailed numerical and analytical solutions in more realistic settings to be able to make this claim more robustly. And secondly, we really need data. We really need a supernova to go off in our galaxy so that we can actually test some of these ideas. And if not, at least we would like to have more detailed observations of things like emerging neutron stars where the nuclear synthesis could also be affected by phenomena like this. And so these are the kind of things that we are hoping to study more over the next few decades and hopefully we will come up with a more detailed and insensitive picture of how neutrinos change their flavor inside dense stars and what effect it has for the star and the signal that we see from it. So with that, I would like to stop. Okay, so if there are any questions, we will go to the next one. Okay, we will go to the next one and we'll take questions for both together. So I thank you, Basu. Thank you. Nice talk and I'll give the floor to Surat. Should I share my screen? Am I audible? Yes, maybe a bit louder here. A bit louder? Okay. Is this better? Can you hear me enough? Yeah, it's good. Okay, so thank you very much. First of all, to Ateesh and to Ashok for the very kind introduction. Thank you very much to ICTP also for giving me this opportunity to speak here. It's really a great honor to be invited to give this talk. And so I'd like to thank ICTP, Ashok, Ateesh and everyone for organizing this and for inviting me and for giving me this opportunity. When I first heard that this ceremony would be held online, I was sad. And one reason I was sad, as I was telling Ateesh earlier, is that I have a very unusual distinction which perhaps very few people in the audience have. And my unusual distinction is that I have never had an opportunity to visit Trieste before. And so I was hoping that this would be an opportunity to do that and I hope that as soon as the pandemic ends, I will get an opportunity to do so physically. But on the other hand, I realized that the fact that the ceremony was online was also good because in that way, many of my very important collaborators who might otherwise not have been able to make it to the ceremony have been able to attend this event. So I'd like to in fact start by acknowledging them. So these are collaborators whose names don't appear on any of the papers with me, which really they've been very essential and very critical to all the work and all this work that has been done. And so I'd especially like to acknowledge my parents, my brother Ajishman, my partner Mansi, her family also who's here and my two small kids, some more than Sumer and they've really been, you know, my most important collaborators, and I would like to start by acknowledging them. I'm going to speak today about some ideas that I've been discussing in collaboration with a number of other people at ICTS and elsewhere and I would like to acknowledge them as well. So my students at ICTS, Pushkal, Chandramoli, Joydi, Tuneer, Preetashi, Ruchira, Victor and Siddharth for postdocs at ICTS, Olga, who is a postdoc at ICTP, my faculty colleagues, Alok, who's a faculty member at CMI and Kiryakos, who's been a close colleague and was still very recently at ICTP, as Ashok mentioned in the beginning. And so I'm going to discuss some ideas in which their contribution has been absolutely essential and I'm just going to describe what those ideas are. So since this is a general and broad talk, let me start by giving you just a rough summary of, you know, the slogan of the idea that I'm going to try and describe. So I'm going to try and describe in this talk the following idea. And the idea I'm going to try and describe is that in any theory of quantum gravity, the information that is present in the bulk of a Cauchy slice, you know, if you think of a space time, and there are some qubits that are present in the middle of that space time, that I'm going to try and explain to you that in any theory of quantum gravity, the same information is also available, perhaps in some very scrambled form on the boundaries of these patients' slice. So just to emphasize how unusual this idea is, I want to contrast this with, you know, the usual way we think about how information is localized in ordinary systems. You know, if you think of an ordinary quantum field theory, we often think of situations where there is an excitation somewhere in the middle here, some bump here, and then everywhere else, you know, the space looks exactly like the vacuum. And then we can think of another state of the theory where we have changed the excitation in the middle inside this bounded region, but we have kept the state of the universe unchanged everywhere outside the bounded region. And, you know, the fact, you know, whether it's this excitation or this excitation is impossible to tell just by making observations in this region that is unchanged outside, and that's the way we usually think about localization of information. What I want to try and explain today is that in quantum gravity, things are very different. And first of all, if one thinks of a state where there is some excitation somewhere here, it is not possible to make the rest of the space time look exactly like the vacuum. And in fact, one has to have gravitational tails that go all the way out to infinity. And what is more, if one changes the shape of this excitation in the middle here, then one is forced to also change the shape of these tails. And this correlation between the excitation and the tails is so strong that, in fact, by just looking or carefully measuring the details of these tails, it is possible to completely characterize the excitation in the middle. And so this is a very unusual feature of gravity, which is what I'm going to try and describe. There's an operational way to say this, which makes it seem even more dramatic. And it is the following. If one thinks of some excitation or some object that is placed here, and one has a configuration of detectors that surrounds the object, then in a non-gravitational theory, which is how we usually think of obtaining information, one would have to wait for signals to emerge from this object and reach these detectors in order to tell whether the object inside was an ellipsoid or a sphere or whether it was red or whether it was blue. But the claim I'm going to try and explain is that in gravity, this is not the case, but rather information about the nature of this excitation is always available in these detectors around and it can always be read off. These arguments can be made precise in many settings. One setting which I won't focus on, but which is perhaps the most familiar one is to consider a universe with a negative cosmological constant, which is anti-decider space. And in the setting, if one makes these arguments precise, one can argue that all the information about this bulk space time is available on a small time band of its conformal boundary. And this is of course what ADS-CFT would lead us to believe, and this is consistent with ADS-CFT, but the arguments I'm going to describe do not assume ADS-CFT and can be thought of as a derivation of this aspect of the correspondence without assuming it. So the idea of this talk is that I want to present some arguments for this principle of photography of information, and I tried to arrange these arguments starting with the simplest arguments, also not the most precise to more technical arguments which are slightly more precise and then more technical arguments. And so let me start by just giving you some very rough intuition for why you might expect that gravity has these very unusual properties that I just described to you. So let me go back to just basic quantum mechanics of free particles and something that we learn when we are first introduced to quantum mechanics is that quantum mechanics has an uncertainty principle. And the uncertainty principle tells us that if we consider an energy eigenstate of the free particle, usually we talk in terms of momentum and position, but it will be clear in a minute why I'm speaking in terms of energy. If you consider a wave function which is very tightly localized on some energy range, then that wave function in position space is completely delocalized, and that's just a basic fact of quantum mechanics. So of course, all the time, you know, we would like to speak of localized excitations, you know, we speak of localized particles. And when we speak of localized particles, what we need to do in quantum mechanics is we can't consider a wave function that has a fixed or a given energy, but rather we take a wave function which is picked at one energy. We take another wave function that is picked at a different energy or third one which is picked at the third energy and in fact one has to take an infinite number of such wave functions. And one has to add them up with the right kinds of phases. And if we arrange for this addition to be just right and we arrange these coefficients to be just right. Then we can arrange for a situation where the in position space the wave function is very sharply localized at one point, and it's you know there's destructive interference everywhere outside some of the region. So that is the way we usually localized in quantum mechanics and also in quantum field theory excitations. Now, what is different about gravity. So what is different about gravity is that there is, you know, a very humble property of gravity which we've learned for which we learned the early Indian introduced to gravity, which is that gravity obeys a Gauss law. And the Gauss law is simply the statement that if you have some object or some excitation, then one doesn't have to go and actually explore the excitation to determine its energy. But one can determine the energy of the excitation by just measuring the gravitational field far away. So that's how, for instance, we know the mass of the sun, even though none of us has been to the sun. And this is true not only in Newtonian gravity, it's also true in general relativity. And what I've written down here is the famous EDM expression for the Hamiltonian, which tells us that, you know, if you want to measure the energy of some some state, then the way one should do it is just by looking at the sub leading fall offs of the metric, and then by integrating them on the boundary sphere. So what is the relevance of the Gauss law to what I was saying, the relevance is that if we go back to this picture of a free particle that I was describing which was delocalized completely. This free particle in a theory of gravity doesn't exist in solitary isolation, but it must necessarily have a gravitational field that's associated with it. It must have a field because if this has some energy, then you should be able to measure the energy by going far away and taking a Gaussian sphere and measuring the metric as one goes far away. Now what this, you know, here I've drawn this gravitational tail or this gravitational field is just a single red ring, but in fact there are many details to this field. There is a magnitude of what this field is, which tells us how much this energy is it could be different for states of different energies. So going back therefore to this picture of localization. If one now tries to localize in a theory of quantum gravity, the, you know, a state and excitation as one did in the theory without gravity. Then we find that the wave function, every time it has you know it peaks on a given energy is correlated with a given gravitational tail. And so while one might have thought you know in the absence of everything on the right hand side here, that one could have taken these different wave functions and added them up in the right way. So as to ensure destructive interference outside some bounded region, because these gravitational fields extend all the way out to infinity, they prevent this possibility of destructive interference. And that's why it is not that's the simplest way to understand why it is not possible to have strictly localized excitations in gravity. It's because every excitation comes with its tail. And when one tries to ensure that these excitations interfere destructively these states that we have prevent this kind of destructive interference. Here's a slightly more precise statement which one can make and let me give you a little bit more evidence for the statement. So one place where the statement can be made precise is in four dimensional asymptotically flat space times, which is not exactly our world but a good approximation we think to our world. And in this flat space time, if one thinks about massless particles, then usually in a quantum field theory to obtain information about massless particles, one way to represent that information is in terms of the conformal boundary of the space time. And one will need to make measurements on all of this conformal boundary to obtain information about these massless particles. But the principle of holography of information tells us that in a gravitational theory, one doesn't need to make observations on all of null infinity, but one can get away by making observations only on its past boundary, which in this case functions like the boundary of what I said was a Cauchy slice. And that already has all information about massless particles. So I'm going to give you some arguments for this, but I'll give you arguments starting with a simpler arguments just in perturbation theory, and then some more detailed arguments for the experts in the audience. So let me just start with a very simple perturbative verification of what I said. So here is a two dimensional picture of a flat space time. And imagine that we have observers who are stationed near the boundary of the space time. And they have detectors that like Cinderella switch off after some time. So these detectors only work near this past boundary for this amount of time. And then they switch off after some time. And then in the bulk, we have some shock wave. The shock wave one can think of as, at least in this example I'm going to think of as a perturbative excited state on top of the vacuum, which is which has some profile which is given by some function f. And it's a shock wave that's made out of some massless excitation and always the team that corresponds to this massless excitation. And one can think of an excited state of this kind, which in the diagram corresponds to some shock wave that starts at some point in the bulk and comes in hits null infinity, at a later time. Now in an ordinary non gravitational theory, these observers would have to wait till the shock wave came and hit them in order to be able to determine the profile of the shock wave. But as I said, you know, they have this Cinderella problem, which is that their detectors switch off immediately and can't go on all the way. And they can't use their detectors at a later time. And so a very basic challenge that one could pose to the claim I made is if one uses perturbative quantum correlators near the past boundary of null infinity can when determine the profile of the shock wave before it actually emerges and comes and hits us and hits these observers. So, here is the answer, the answer is quite simple. In perturbation theory, remember the intuition I gave you earlier suggested that the information is unusual localization of information quantum gravity occurred due to correlations between the energy and between other matter fields. And so indeed, all one has to do in the state of these observers have to do is measure this following two point function, which is a two point function of the energy which they can measure by looking at the metric so that's M and the field itself. And this two point function is a measure is made for you in the range minus infinity to minus one over epsilon in this in this red region, even though the field itself the excitation itself seems to have support only in x equal to zero to one which seems to be very far away from minus infinity to minus one over epsilon. But you see that if you compute this two point function it's a simple calculation, you find that this two point function continues to have support even for you in this range, even though this function this profile of the shock wave f has support and not only does this two point function have support for you from minus infinity to minus one over epsilon, you can prove that this knowledge of this two point function in this range of you is enough to completely reconstruct this function f. Here is a more direct way to see that, you know, if one knows this two point function for large you, one just has a series expansion, and every term in the series expansion tells us one of the moments of f. And if we know all the moments of f, then of course we know as completely. Here you see two functions which look very close but if you know the first 50 moments you can easily distinguish them. The general one can do that so any function when determining enough moments. And so we see the gravitational effects allow us to determine this the shape of this excitation, even if one is very far away to start with, which is very unusual. Now this very simple put a bit of example the example I gave was technically very simple already contains a lot of physics. And one way, you know, it tells us it allows us to do a few sanity checks. You know, sometimes people ask that in non gravitational gauge series there's also a Gauss law there's also Gauss law for electromagnetism. And why isn't it that electromagnetism localizes information unusually like this. And of course the reason is that in electromagnetism that are both positive and negative charges. And you can use that to and there are also operators which it is neutral you can use that to construct operators which are just neutral. And therefore, in non gravitational gauge series, there are exactly local gauge invariant operators like the trace of f square or a small Wilson loop. And if you had a theory without gravity, then you could construct the shockwave out of a local gauge invariant excitation. And these observers, whatever they did, whatever correlator they measured, would be completely unable to distinguish the vacuum from the vacuum excited with this unitary operator, because just by micro causality, this unitary operator would commute with every observation these observers could do. So it's very important that this whole idea cannot work with gravity and even this very simple put a bit of example tells us why gravity is special. One can also see why quantum gravity is important. If one goes back to this two point function and just restores factors of H bar and C, you find that the two point function has a factor of H bar G by C cubed in front of it. And so in particular in the non gravitational limit which is when G goes to zero or in the classical limit which is when H bar goes to zero, the usual notions of information localization are recovered. In particular, in the classical limit, if the shockwave for instance was vertically symmetric, all we would know by Burkhouse theorem would be the total mass of the shockwave and not its profile, which, as I've just shown you, one can get in a theory of quantum gravity. So let me now, for the experts in the audience, give a few more technical details and try and give you a more technical argument for why quantum gravity has this property. So one place one setting in which all these ideas can be made precise. And in the beginning is four dimensional asymptotically flat space time. And what one needs to do to make these ideas precise is just impose the standard boundary conditions and four dimensional asymptotically flat space times, where one demands that the space time is asymptotically flat but then there are some sub leading terms in the metric and another fields at the conformal boundary of the space time. And then as is done usually one can associate an operator algebra with this conformal boundary. And this operator algebra has components of the metric some of which are called the bondy news and the bondy mass and also has other dynamical fields. In general, think of an operator algebra which is comprised of all possible products and linear combinations of these operators. And this operator algebra naively looks like it has support over all of null infinity, because it looks like we inserted these which have this you coordinate that goes over all of null infinity. But what this result tells us and I'll sketch the proof in a minute is that in fact, any operator in this algebra can be approximated arbitrarily well by what seems to be at first a smaller algebra this algebra between minus infinity to minus one over epsilon, but in fact is good enough to approximate any operator in this entire. So that's the statement that any operator all of null infinity can be written in terms of an operator can be squeezed down to an operator in this region. And since information in quantum mechanics always has to do with just measurements of operators. It tells us that all measurements in this little red region have all information about what's happening all over null infinity, which would be very surprising with theory of gravity. So let me just try and sketch very briefly how the argument goes. But it has been a lot of work and understanding the Hilbert space of gravity and potential asymptotically flat space fans, going back to much older work by Ashtekar and much more recent work by Strominger and collaborators and Alok and Miguel. And what one finds is that in, you know, a destructure of the Hilbert space is that one has an infinite number of back here, which are labeled by what are called super translation charges. And then on top of each vacuum one can build a Fox space, as one usually builds a Fox space and then the full Hilbert space of massless particles is just the direct sum of all of these four spaces. Now, to prove the results that we need to prove. There are three essential steps that go into it. The first step, we just use the positivity of show that any state in this Fox space, even though it looks like, you know, will require operators from all over infinity. In fact, can be approximated arbitrarily well, that's what this dot equal to tells us, can be approximated arbitrarily well by the action of an operator from the smaller algebra on one of these back to us. This only uses the positivity of the Hamiltonian and doesn't use anything that's special to gravity. But what is special to gravity is that the projectors in the vacuum of the theory are also present in this algebra from minus infinity to minus one over epsilon this algebra a minus infinity. And this utilizes the fact that I mentioned in the beginning, which is that the graph, which is the gravity obeys a Gauss law which in quantum mechanics becomes the fact that the Hamiltonian and these other conserved charges are just boundary terms, and therefore boundary operators contain also these projectors on to back to us. And then one can do a calculation to show the transition operators between these back to us are also elements of a minus infinity which is just an explicit and simple calculation that one can do. If one these three steps, even though I haven't given you details are enough to prove the result. And that is because, you know, any operator in this Hilbert space, you can just expand out in a complete basis of states like this. And when one expands it out every state here I told you can be written as the action of an element of this algebra a minus infinity on one of these back here. But now in a theory of gravity, this operator that appears in the middle here which my mouse is circling. This operator which is ket s bra s prime is also an element of this algebra a minus infinity. And therefore you can write this entire expression as a linear combination of a product of three elements of a minus infinity, which is manifestly in the algebra because the algebra is closed under products and linear combinations. And that tells you that any operator from the hit in this Hilbert space can be approximated arbitrarily well by an operator near the past boundary of future null infinity. Let the same arguments can be also carried to an ADS. In fact, it's simpler to carry these arguments to an ADS because in ADS one has a unique vacuum and one does not have the super translation charges. And they tell us as I mentioned in the beginning that all information about the bulk is present in a small time band on the conformal boundary in a non gravitational theory you would need to make measurements on this entire boundary of the cylinder. And as I said this is consistent with ADS CFT, but the argument does not assume it, and one gets in fact a slightly stronger result than one had in flat space, because one does not even need to restrict to massless excitations and the results holds even for massive excitations. So let me now spend the last few minutes of this talk exploring saying a little bit about the implications of this physics for black holes. So the simplest version, the most popular version one might have was explaining the significance of these results for black hole physics is that if one has a black hole, one thinks of black holes as being sinks of information, one throws in information and then one can't determine, one doesn't know what's inside the horizon. These arguments that I presented tell you that in the theory of quantum gravity, if you had an army of observers who were to surround the black hole, and were to make complicated enough measurements were to make precise enough measurements. Then information about this black hole microstate would always be available outside with the right kinds of measurements. So that's a surprising result, but it follows quite directly if one accepts the fact that information in the bulk of a Cauchy slice is available also outside, because just applying that result to the space time tells you that information about the black hole interior is available outside. There's a more formal way of stating this result. The more formal way of stating this result is that if one looks at an evaporating black hole space time, one can use these results to analyze the for Neumann entropy of a segment that goes from minus infinity to an upper limit u of sky plus. And one can show that this for Neumann entropy is independent of the upper limit u. And so it's just a constant. And you know the fact that the for Neumann entropy is a constant is what is telling us that information is not emerging, but the information that you had here is the same as the information you have in this larger segment, which is a surprising result but it follows directly from this principle of polygraphy of information. Now, this result this flat curve for the for Neumann entropy that I'm showing you is obviously different from a curve which would which rises monotonically. And so in particular, it's different from the suggestion that Hawking made, which is that if one looks at a black hole, which forms and evaporates. And then one measures the for Neumann entropy of a segment from minus infinity to u on sky plus that for Neumann entropy would just rise monotonically, because the process of black hole evaporation would lose information. And one sees that the result I told you is not equal to Hawking's result. And so, not only is it not equal one can also, from these arguments, see the precise error in Hawking's argument. And the error in Hawking's argument for this curve on the right hand side was that it does not account for the unusual localization of quantum information in quantum gravity. In fact, to derive this result Hawking explicitly posited what he called a principle of ignorance, which was, which in more technical language was the statement that the Hilbert space factorizes into the Hilbert space outside and the Hilbert space inside. And in most in simpler language was the statement that observers outside would have no information about what went inside. And that is indeed how information is localized in ordinary quantum field theories, but it is not how information is localized in gravity. And when one corrects this incorrect assumption, then one finds that one can resolve this paradox which suggested that black hole formation and evaporation was not unitary, and one gets a curve for this for Neumann entropy, which is flat and consistent with unitary. And notice that this curve is also not equal to the page curve on which there has been a lot of recent attention, where, you know, the curve of an evaporating black hole has been in the for Neumann entropy of an evaporating black hole has been computed to go up and go down. In fact, although these results are different, they don't directly contradict each other. Because the models that have been used to derive this page curve are models where one switches off gravity at some point beyond some point, and therefore one gets a result that is consistent with unitary, but not a result that's applicable to gravitational theory but a result that's applicable essentially to a non gravitational theory. So these results are not in contradiction, but the result I presented in the left does imply that the models that have been used to compute the page curve are inapplicable to realistic black holes where gravity is dynamical everywhere. And this was also the focus of some recent work that we did with other collaborators with how gang and we are scotch Carlos Ferris, Lisa Randall, Marcus Riojas, and Sanjit Shashi last year. So let me end since I'm out of my 30 minutes, let me just end with some some speculations and some broader ideas. So one of the weaknesses of first of research on quantum gravity is that it's very hard to find experimental or observational tests of quantum gravity. So we hope that you know we might be able to realize quantum gravity systems in via some other systems or maybe we find observational tests of quantum gravity by looking at cosmological observations. And indeed, you know, one might find a way to test elements of quantum gravity in this way. But it may still be the case that the physics of black holes and the physics of quantum information associated with black holes, maybe hard to test in such settings. But this notion of the holography of information which I described, which is the idea that there is a very sharp difference between non gravitational and gravitational systems in how they store information is something that holds already at low energies. And so one might think of it as, you know, a smoking gun for the presence of quantum gravity. And it may be the case that if we were to find observational tests of quantum gravity, you know, testing this principle may be an easier thing to test at low energies, and testing the physics of black holes. And that's one of the reasons why I think this is very interesting, because not only does it have implications for black holes and for non perturbative states. It also has implications at low energies, and gives us a very striking feature of quantum gravity, which is different from other quantum field areas. So let me stop here since I'm out of time and we can take questions. Thank you once again. Thank you. Thank you. So now we'll go to the questions. Giovanni will take questions. Alright, so now we open the Q&A session. If anybody has questions please write on the Q&A break the ice maybe I can start with a question to the first talk by Basu, Basu Deb. I'm curious to know a little bit more about the relation possible relation and sensitivity of the production of heavy elements that you mentioned that are important for life and the physics on neutrinos and weak interactions and whether maybe you can one can argue about their existence based on the existence of life. Thanks Giovanni. Good to see you for a long time. Yeah, so the question is, can I make a more clear statement about the connection between neutrino flavor oscillation and the abundance of nuclear elements produced in stars. And, okay, so most of these heavy elements are produced in these stellar mantles, just behind the shockwave. And one of dominant mechanism is our process nucleosynthesis and the neutron to proton ratio makes a big difference to which of these elements are produced and how much of each. And changing the amount of electron neutrinos or electron anti neutrinos will shift the beta equilibrium in one or the other direction, therefore changing the neutron to proton ratio. I don't remember the exact quantitative detail of exactly how much effect you could have. But let me just only say that these oscillation effects are order one effects as in, if you start with 100 electron neutrinos and 80 muon neutrinos and the difference is this 20. And this 20 is what you are allowed to play with in oscillations, because the sum is conserved by oscillations. This 20 can be completely flipped so you can have 100 muon neutrinos and 20 electron neutrinos. So it's an order one effect in this sense. And so therefore, among all the other ingredients that could change beta equilibrium, this is actually one of the larger ones. So whether this actually happens or not and whether the physical conditions are right for nuclear nucleosynthesis to take advantage of this neutrino oscillation instability, this I'm not so sure about there are a couple of papers but I'm not an expert. So I shouldn't comment. Thank you. I have a good. I have a question. Okay, I have a question for Surat. Okay, and also for Basu later but for Surat. So you said that somehow in gravity there is a, because of gravity there is a recording of the information non locally. But how does it get around the issue of hair I mean if gravity can only see the mass of the object. So, how would it distinguish between say different barion number or something like that. Yeah, thank you that that that that that question I think brings us to the point so indeed it's true that there is a no hair theorem, but the no hair theorem is a classical result. It's not the case that if one looks at wave functions of the black hole that the wave functions of the black hole are classified only by mass so that is no analog of the no head theorem just quantum mechanics. So even in this very simple perturbative example that I gave you know one could have just taken I was giving an example of a shock wave which had some profile and then trying to detect what the profile of the shock wave was from far away. As you said, even classically, all one would determine would be the mass of the shock base, if I had spherical symmetry, you know there is a no head theorem even in that case it's just the workhorse theorem which tells us that far away all I can get is the mass of the shock. But if one looks at correlators of the mass of quantum correlators of the mass and other fields that gives us more expect more information than just the expectation value of the Hamilton. So the no head theorem is a statement about the expectation value of the Hamilton. You see that in quantum mechanics you must have additional information for instance you have information about the moments of the Hamilton. You have information about it squared net cube and so on and there are black holes with different moments. And you also have information about correlators of the Hamiltonian with other dynamical observations. And it is correlators that contain information and that preserve information. And there is no no head theorem that tells you that these correlators all approach a universal value for black holes. Is it clear that, for example, a purely baryonic black hole can be distinguished just from gravity from a purely anti baryonic black hole. So if I look at black hole Mike. So one would have to look at correlators of the Hamiltonian with the fields that made up the black hole. You know a version of this question once again with one can ask you know in a black hole it's a proof one can give but one can ask this question again at the level of the shock wave. Let's say I had you know let's say I really had a global symmetry and I had a shock wave made of two different fields which were related by a global symmetry. You know, can you distinguish one from the other. And the answer is yes, because you measure correlators of the Hamiltonian with the field that makes up the shock wave. So you have to measure correlators of the Hamiltonian with other baryonic fields, and those would break the symmetry between the black hole so it's once again it's correlators quantum correlators of the Hamiltonian with other dynamical fields that break this symmetry. So we have one question now, it's from Paulo Caminendi. He asks, what is the possible interplay with gravitational wave observations. Yeah. Hi Paulo. So the question is, what is the interplay of supernova neutrinos with gravitational wave observations. So what is possible that supernova exploding in our galaxy will be coincidentally observed by neutrino detectors and gravitational wave detectors. And the time at which you get the signal, the precise details of what the signals are, they teach you a little bit about when did the shock bounce from the dense inner part of the star. At which time this shock wave took it, you know, to reach, let's say some larger radius details of how the shock travel this is something that you can in principle learn from neutrinos. The gravitational wave observations teach you a little bit about the equation of state of this matter. And together, you know, if you put all of this information in. There is some synergy. For example, you could you could rule out exotic phases of work matter that may exist or has been speculated to exist inside course of stars. So that's the kind of things that you could do using a multi messenger approach. But I think this has not been explored more but I think this is a speculation but that you can look at binary neutron stars. This has been one of those using LIGO and there have been optical for x-ray follow ups of those observations and we have been able to measure the nuclear synthetic years from such such events. I think if we have more data of the kind which gets a bit more precise. So you can learn about neutrino physics from such. So now this is not directly gravitational waves, because what you're learning from is x-ray emission from the source, but you point at this object because you saw a gravitational wave. And you, you know, do follow up measurements with x-ray telescopes, and then you infer something about neutrino physics at the end of it all. So that's another way I can think where there can be an interplay. Okay, thank you. Okay, maybe it's another question from somebody from outside the field, but so some of these effects that you're studying in the coming upcoming detectors, I don't know, in super case, suppose actually a supernova did go off. Yes. So there's some very distinct signatures that you will expect to see like instead of, I don't know, 11 neutrinos, you will see 12 neutrinos or is there something that you can actually detect. Do you have the sensitivity and the possibility of detecting this difference. That's that's a good question and I should say the situation is far better than what I think you might hope. So we saw about 20 events, 20 neutrinos from Supernova 87A, and this was a supernova not in our galaxy because just, you know, this particular process about five times far away than a typical supernova in the galaxy. Our detectors have become much larger after 30 or so larger if I'm not mistaken. So today if a supernova goes, well, if a supernova, you know, is detected today in Super K, a supernova that exploded in our galaxy, we would see something like 10,000 events. Okay, so that's firstly huge statistics. Ice Cube will see about a billion events, 10 to the nine events, but not on an event by event basis just in some statistical sense. But let's focus on 10,000 in Super K. This is across 10 seconds. The key thing I think that we would see if these fast conversions happen is that the different flavors will have similar energy spectrum. This requires not just Super K, but other detectors that are sensitive to not electron flavor neutrinos, the new muse, new Taos, this is a bit harder to do, although there are detectors that are capable of doing it. So indeed, there are many, many detectors I gave you a list I'm sorry I could not go into more detail. And indeed we will see lots of events. And indeed, there are signatures that have been proposed. That could teach us about neutrinos flavor oscillations in these systems. Okay, thank you. And now we have a question from Ashok, please. Yeah, I have a question for Subrat. So, earlier, I mean, we are trying to resolve the black hole information puzzle, you are trying to see how to make it look like a piece of coal, right. What you are saying now is that you have been thinking about a piece of coal in the wrong way. Right, that in a, in a theory of gravity, there's no information ever going into the piece of coal. Now, is it something that is observable? Thank you. So, thank you, that's a good question. So indeed, the answer is that within effective field theory for two point functions that one measures in the black hole in the vicinity of the horizon, or elsewhere. It should look exactly like it does for a piece of coal. So, you know, in the, and that's, and that's important and as, as, you know, as you also described in the beginning, there were seeming no go theorems that suggested even for leading two point functions in the absence of gravitational effects, you know, black hole could not look like a thermal object. And indeed, it's important that it does do that. On the other hand, you know, when one talks about a piece of coal, the point I was making about information was that that information is available when one starts taking non trivial gravitational effects into account. So, of course, you know, if one wants to read what is in the, in the hard disk of this computer, you know, one, there's no sense in one in which one should use those effects because those effects are suppressed by M plank over the, over, over the energy scale. In the case of the black hole, those effects would again be suppressed by the, the typical energy scale, which is the Hawking temperature divided by the blank scale so that's one over the entropy of the black hole. So these effects that I'm describing now are not inconsistent with what we were saying before there, the statement that if one measures the one over S and the one over S squared and the one over S cubed and all terms in one over S including the minus S terms. Then one can determine the microstate of the black hole at all times, but it's still true that at order one the microstate or the black hole looks like a thermal object like the classical solution. And so both things are important. It is true that you know if you measure all orders in one over S you have the information at all times. And it's also true that you know, if you don't, if you measure the leading order term it looks like a thermal spectrum. To say something about the observable thing. I think that the perturbative example I gave in the beginning, which was an example where one has a shockwave or one has a very simple excitation one has a prior so that's not a black hole microstate it's just a simple shockwave with some profile. And one is trying to determine the profile of the shockwave before it reaches even that effect is suppressed by you know the energy scale of the shockwave divided by blank scale so it's out of reach of any, any observer any observation we can conceive of immediately. But in principle it's an observation that doesn't require non perturbative accuracy. It's an observation that requires us to be able to measure perturbative quantum gravity effects. And if you could do that we can already start seeing how gravity localizes information. In the case of a black hole of course to determine the microstate fully would require non perturbative effects as well. But there are simpler settings in which I think this might be something which is already an interesting effect about information which is visible. I mean, it's still very different from the usual questions we asked but still put but perturbative quantum gravity not non perturbative quantum gravity. So is there any sense in which the black hole will actually display page card in some approximation. So that's a good question. Yeah, thank you that's a that's a that's a very good question so we don't have. So it's something we've thought of and that up. It's possible that you know if one if one keeps the page curve as as an answer one tries to ask what is the right question one should ask that there is some sense in which one to see the page curve. But it's not so easy to find such an approximate answer. And that is because the for Norman entropy is a very fine grain quantity. So you know there's a sense in which if you measure two point functions those two point functions look like the conventional back home. So for Norman entropy is a very fine grain entropy and the fact that the page curve emerges is eventually due to either the minus aspect, even if one can you know compute it in some settings without keeping track of those effects. So that is the reason you know if the true curve is something different and one wants to ask about one one some approximation in which one gets the page curve the radiation. That's not so easy to get one natural guess is you know there is a natural guess for this which is that one can try and throw away some of these constrained degrees of freedom so one can throw away the body mass. From the set of observables and only try and measure the body news. And one guess is that perhaps that will obey the page curve so that's like saying we keep track of some components of the metric but not other components of the metric. In order to you know throw away the gravitational effects, but even that is not so clear because you know that depends on the entanglement between the hard and soft mode but perhaps that is an approximation in which the black hole will obey the page curve, but we don't know the answer to that in some precise sense. All right. Thank you very much. I think we are running out of time so we stop here with the Q&A and the floor to a dish for the last month. Okay, well, thank you very much for all of you who participated. It would have been nice to meet you in person, but thank you for connecting remotely. Congratulations once again to Professors Raju and Das Gupta for the ICTP prize. I would like to thank also Professor Sen and Professor Villadoru who are present but also Professor Eriyath Tosati is in the audience. He was the chair of the selection panel. So, I take this opportunity to thank you all and look forward to the opportunity to see you in the near future.