 Okay, good afternoon everybody. It's a great pleasure for me to welcome all of you to the ceremony dirac medal ceremony for the dirac medal of 2020. We were fortunate that we also had a very nice Nobel colloquium of Georgia Parisi just before this. And this year's dirac, the 19, sorry, 2020 dirac medal was awarded to professors Pierre Ramon, André Neveau and Professor Miguel Virazuro, who was a former director. Unfortunately, Miguel is not with us here today. But his wife is present here, and there will be a in memoriam in the in his to honor his memory, there will be a one hour session after the award ceremony. And this year's medal was given for the inception and formulation of string theory, which introduced new bosonic and fermionic symmetries into physics. And those of you who are familiar with their work know that the Virazuro Algebra played a major role in and also the Virazuro Shapiro amplitude in the formulation of string theory. And Ramon and Neveau Schwartz Neveau were responsible for the Ramon Neveau Schwartz super string, which later became as the super string. So it's a it's a very fundamental contribution to string theory. And I'm particularly I think it's in many ways, the work of these dirac medalist is closest in spirit to the style of physics of dirac himself, you know, sort of essentially by pure thought, and by the beauty and the elegance of the formalism, making progress in physics. I'm happy. Another reason I have a personal happiness is because Pierre is actually my academic grandfather. He's the advisor of my advisor, who is Jeff Harvey, and Jeff has kindly agreed. He's, as you know, he's a very distinguished string theories himself. And he is one of the people who formulated the heterotic heterotic string theory, which combined the Ramon Neveau Schwartz super string with the Bosonic string. So I think it's a very appropriate person to introduce today's dirac medalist, and he's joining us from the University of Chicago. Hi, Jeff. Hello, Ateesh. Hi. So, can you hear me and see me. Can we, can we show the Jeff Harvey on the screen. Okay. Hi Jeff. Okay. Hello. Okay, so I think the with this welcome words we can start. All right, well, thank, thank you very much, Ateesh. I'm very pleased and also honored to be able to introduce today's direct prize winners. As Ateesh has already mentioned, their work was absolutely fundamental, and it dates back, essentially 50 years now to 1969 and 1970. And is viewed very properly as really the beginning of super string theory and ideas of supersymmetry, which have grown into an incredible and rich set of ideas today for how to combine gravity with particle physics. And their work is very much in the spirit of Dirac, guided by the development of beautiful new symmetry principles. And any time that deep new ideas are introduced into physics, particularly of a mathematical nature, it often takes a long time to fully understand the implication of these ideas. A famous example is the introduction, introduction of Yang-Mills theory in the 1950s, which originally was developed to describe the strong interactions and 70 years later we're still trying to fully understand the implications but of course we found, you know, it's the basis for the standard model of particle physics. Similarly, the work of Nouvelle Ramon and Virisoro was also introduced to try to understand aspects of the strong interactions. The strong interactions seem to be a very fertile ground for new mathematical and physical ideas. And I think we're still struggling to fully understand the implications of the work that they did. Our first speaker today is Professor André Nouvelle from the University of Montpellier. And I first encountered his work, not through string theory, but rather as a postdoc, I was introduced to his work on non-perturbative methods in quantum field theory with Daschen and Hasslocker and the gross Nouvelle model of spontaneous breaking of chiral symmetry. And the 1970s were a very rich period when physicists were discovering that quantum field theory was not just a set of rules for particle scatter but also included extended objects, solitons, magnetic monopoles, non-perturbative effects. And Professor Nouvelle played a very central role in untangling all of this structure. His work has very deep connections to many parts of quantum field theory and string theory, really uncovering some of the basic structures that underlie quantum field theory and string theory. His work has been well recognized in the string community and has been awarded the Paul Langevin Prize and the Gentler-Castler Prize. His interest, certainly, I mean, his profound accomplishments in quantum field theory and string theory have not limited him only to those areas. He has very broad interests. And I think we're going to hear an example of that in his talk. So I hope that you'll please join me in welcoming him to talk about perturbatively conserved, higher non-local charges of free-surface deep water gravity waves. Professor Nouvelle. Thank you, Jeff. So now we will award the, this is the Dirac Medal Award, right? Thank you very much, Jeff. Okay, thank you. So before my scientific presentation with Pierre, we are going to re-enact for your entertainment. The first time when we met, which was a very, very strange coincidence. So this is where the play begins. I would like to watch it from the gallery. So I'm acting my own role and it's done for convenience in English. Although the original version is in French, of course. So this explains why I'm here. Okay. So then next slide, please. I thought I'd taken that paper by Foubini in Venezia back to my cabin. Let me go and check. There is a stretch. I must be going crazy. Who are you? Are you the one who's reading this paper? Yes, yes. I'm interested in the Pugnipoloziano factorization of dual amplitudes. You must be a physicist. Yes, yes. I'm Andre Neuve. Okay. Nice to meet you. Nice to meet you. I'm Andre Neuve. I'm an engineer. Absolutely. When I was in Morsé from John Witz, you collaborated. Indeed, I did. So this is quite an amazing coincidence. Well, we have to get together. We keep track of one another. I mean, this is quite amazing. And so, well, we have to celebrate. So let's go and have a talk. And a talk and a drink. And a drink. Yes. Okay. So there it is. Okay. Thank you. Ultimately, this is how the Neuve-Schwarz-Ramon model came into being through this coincidence because we kept in touch afterwards. And when with John Schwartz, we received Pierre's preprint on the fermionic side of the model and we started working on it and constructed the bosonic side. So all this is history. And now, well, we go to the present. My cat spread water on my computer. So I could make a proper presentation with a PowerPoint. So I go to the blackboard, which actually I prefer being more of a mathematician. So you see the title in the announcement. The idea is that living in Montpellier, we are close to the Mediterranean. And I like swimming. And by swimming and observing the waves, I thought that the waves, those waves are not really so chaotic as you would think. So I thought, well, perhaps in a simple model, there is more to do more mathematical structure. We could explain why it's not so chaotic. And so, so let's consider a simplified, but in some sense exact case of the Euler equations for the motion of the fluid. So XZ. So I have a fluid in the XZ plane. And this is the surface of the fluid. So the fluid is down there. And it's in the gravity field like this. And this is the surface, the surface, X eta of X and time. Now the Euler equations, I think we will know this. So a particle of the fluid has a certain velocity like this with horizontal component U, vertical component V, and which are all functions of X and T, of course, and Z, sorry. And the Euler equations suggest this, UT plus UUX plus VUX is equal to minus PX, where P is the pressure field and VT plus UVX plus VVX, sorry, PC, because minus T minus. Okay, so these are the Euler equations. This is an old thing known so the Euler discovered them. Now, if I take an irrotational motion, which is consistent with this, and of course concerned, sorry, incompressible motion, then U and V derive from a velocity potential, right? U is DX curly U. U is easy curly U of X and T, of course. And then there is the boundary condition, which says that the velocity of the fluid here is along the surface. And that's V of X eta T minus U of X eta T times eta sub X is eta sub T. Okay, so this comes from a Lagrangian, which is all this comes from a very simple Lagrangian, which is kinetic, which is one half UX squared plus one half UZ squared. Now, this is integrated over X and Z. So this is the kinetic energy of the fluid, square of the velocity, and then minus the potential energy, one half eta squared of X and T. So this is the potential energy. Okay, so this is very simple, and then there is a Lagrange multiplier, lambda to enforce the boundary condition, which is here. So this is the Lagrangian times eta T minus UZ of X and eta plus eta X, UX of X and eta. So this is the Lagrangian, and this is integrated DX, of course, and this also. Okay, so what can be more simple than this? Then, so from this you can derive the equations of motion by varying the Lagrangian, and then this is where things become interesting, that since the fluid is incompressible and irrotational, U is a harmonic function in X and Z. So we can use complex analysis to derive U of X and Z from the value, its value, at Z equals 0. Okay, and the formula is very simple. U of X and Z and T is minus Z over Pi, integral of, this is the, yes, ordinary integral with a quantity which I call U with a not query, X prime and T over X minus X prime squared plus Z squared, which is integrated DX prime from minus infinity to plus infinity. And this is for Z negative, strictly negative. So that U of X and 0 and T is precisely U, this uncurly U of X and T. So you want to take the limit Z going to 0, then the integral is concentrated at X, X prime equals X, and that's how I recover this. Okay, now, this doesn't mean that U, this curly U, is odd in Z as it would seem. This formula is only for Z negative. The other thing that you have is that there is also another function, V, which is the conjugate of U. So that you have DV, for example, DV, DV, DV, DV, DV, DX, DV, DX is minus D, U, DZ. So, and V, as a simple formula, minus 1 over pi integral U of X prime times X minus X prime over X minus X prime squared plus Z squared, DX prime. Again, for Z negative, okay? Now, from this, you can reconstruct U of X and positive Z by combining these two things. And this, when I call V, I have to introduce another non-second. Yes, V, or V of X, 0, T, I will call it capital V of X, which you obtain by, at zero, this becomes a principal value integral, right? Minus 1 over pi, principal value of U, over X minus X prime, DX prime. Okay, so from the knowledge of U of this, of this U here, you can reconstruct this V at the origin. So the derivatives are obtained this way. And so this, and what you find then the next thing is that you find that the large multiplier as a very simple expression, large multiplier. Well, let me, lambda of X and T is curly U of X, eta of X and T. Okay, so this means that you can construct by expanding in powers of eta. This is in my title. It was, I was doing perturbation. I'm going to do perturbation in powers of the small deviations away from the surface. Okay, so this is the setting. Well, this is classical mechanics after all. So you know what to do. You know that there is a momentum. Momentum is conserved, P of T, which is, which is obtained by just the author theorem P of T, it's conserved. So it's, it doesn't depend on T. P is integral minus infinity to plus infinity, lambda of X, times eta X of X. So this is concern momentum. And there is a conserved energy. Compute from the Lagrangian, you compute the Hamiltonian turn the crank. And this is minus infinity to plus infinity, one half. And then this is slightly more involved, X and eta of X, QZ of X and eta of X. Maybe I won't read it in the global. Then plus one half, G, eta squared of X. So this is, this is the kinetic energy and this is the potential energy essentially from the DX. Okay, now this is very, this is nothing new up to now. So we have, so now we come to, to find, try to find more conserved quantities than just energy and momentum. You see, UZ, this is, this is, where is it? The derivative of Z, see I had it here. I have to read, no it's here. DUDZ, so that's UZ. So it's related to DVVX, so you can express it this way with a principal value integral. So you see the P is nothing special, but this contains the principal value integral. So I thought, well, since the simplest conserved quantity, energy is already a principal value integral, why not look for other conserved quantities simple enough, which would be also principal value, which would contain principal value integrals. Okay, so I tried the simplest possible thing, simplest possible thing. Yes, before that, you see, I have been working at Jeff, Jeff mentioned it on integrable models in one space, one time dimension, one system, one system, one system. And the Sengodon system also has an infinite set of conservation laws beyond momentum and energy. And these higher conservation laws involve higher derivatives here of the fundamental, of the dynamical variables. In the case of Sengodon, there's a Sengodon field. So you have the higher and higher derivative, derivatives as you move into the higher, higher conserved quantities. So, so the idea would be to try to find some conserved quantity which would begin like lambda x of x, eta xx with higher derivatives, plus perhaps other things. And similarly for a higher equivalent of energy where you put x derivatives a little bit everywhere. Okay, so the question is, does there exist higher conserved quantities which would mean that the original system, the other equations would be probably a new integrable model, an integrable system of a slightly different mathematical type than those that we know it to now. Well, indeed. So I tried, I tried the simplest, a simple expression, minus infinity to plus infinity, v, is that v over there? Okay, this v, v of x and t, v of x and t times eta of x and t, dx. So as I told you, it contains a principal value integral a little bit like the energy. Well, found that this, et, okay, indelinarized approximation of the Lagrangian which I erased, then you find that this is conserved, but that's rather trivial. But when you include the first power in the expansion around eta equals zero, you find that if you add one half eta squared of x times lambda of x, dx, then this is conserved. Up to higher order terms, eta cubed, square lambda, that would be eta fourth, sorry, eta cubed lambda and lambda squared, eta squared, eta squared, et cetera. So I was very surprised when I found this and I thought, well, this is encouraging because like in usual integrable models in one space, one time dimension, as soon as you find just one more conserved quantity, usually there are many, many more and the whole thing ultimately turns out to be integrable. So from there, I'm not going to write all the formulas because it gets very complicated. Just to give you the summary of what I found, oh, by the way, this is in archive, this was the, this is on the, this is the archive, the archive number. In general, three mechanics after that. Okay, so then, so from here, then I found the order, fourth order explicitly, then there are probably higher orders but the fourth order I worked out explicitly. It's in the archive and it becomes quite messy actually. I'm not sure I want to write it in the blackboard. Okay, so that's the first conserved, new conserved quantity that I found. Then just, I'm just going to make a list of the other ones and just only of their lower, lower order. So another one, which I found was conserved, sub x and sub x simply the same but with taking derivatives of both and this press to big. I worked out also the cubic, the cubic expression for this conserved in that approximation, the cubic approximation, of course, then I even worked out the vxx, and so on and so forth, plus cubic, also conserved. That one becomes quite messy. There are many, many terms in the cubic approximation to this. Then I found other ones. Lambda x is one half, lambda x, lambda squared, lambda x squared plus g over two pi, that's the set, the x, lambda x of the silver x. And this is minus infinity to plus infinity. This is minus infinity to plus infinity also. The x prime, eta of x, one, this is a principle value over x minus x prime, eta x prime of x prime plus cubic. Also worked out a cubic term conserved whereas in that approximation. Okay, so these are, okay. So then coming back to the generalization here of energy and momentum, okay. So then I came back to this one, the higher, presumably next conserved quantity with more derivatives analogous to the momentum. And I found that this was actually not too hard in next order, three over five, eta x times uxx, or this is function of x, of course, times one over x minus x prime, so this is eta of x prime, x prime, and this is integrated the x prime. This is a principle value again, minus three halves, x squared dxx. So this is the third order term, also conserved, and I have also found the generalization to next order of the energy, which I'm not going to write down. Okay, so discussion now. So this is where the calculated, I stopped calculating because the number of terms when you go to higher orders becomes extremely high and some deeper understanding of the whole mechanism behind this is necessary to really to really put it on firm footing and show that the system is presumably completely integrable. So a brief discussion by analogy with sign Gordon, the sign Gordon equation in the image I'm over. So the sign Gordon equation is this, so it's a field phi of x and t, a scalar field, one space on that dimension, and the sign Gordon equation is phi tt minus five sub x, xx plus sine phi equals zero. So this is sign Gordon. Now if you take the cubic approximation of this, so phi tt minus phi xx plus phi minus 16 phi cubed equals zero, then this one is integrable. This we know. This one is not integrable because when you try, so of course it has conserved energy and momentum, but nothing beyond except that you should try, if you try the analog of the higher value of the momentum, then what you find is that, oh, okay, this will be the last formulas. You find that the momentum, sign Gordon momentum, integral of phi x, phi t, zero. So this is the canonical momentum. So no surprise, which is conserved. But when you, so when you take, try the next one, phi xx, x, phi tx, x, phi xx, x, and then you take prime, when you take the derivative of this, respect to t, then you find that at fourth order, phi cubed, phi xt, minus phi t squared, phi t cubed, phi x, minus phi x cubed, you find that this is zero at that order, at fourth order. And if you try, so, so, so the phi fourth theory which is here looks like it would be integrable. Well, at least it has a higher conservation law, but only at fourth order. And if you keep churning out the time derivative, you find that at six order, which is the next order, then it does, the time derivative is not zero. And to make it zero, you need higher expansion of the sign. So maybe the case of the Euler equation is similar, perhaps that what I found, which was only the lowest order, say, conserved quantities with more derivatives, perhaps it's like this, I'm only dealing with the analog of this, not with a completely integrable system. I don't know, you would have to compute more or have a deeper understanding of all this. However, however, this equation, which is the lambda phi fourth theory in two dimensions, nevertheless, helps to explain in solid state physics the existence of permanent structures, breathers, overall breathers in solid state physics are not one dimension, are not exactly soluble, they are well approximated by a almost, well, at least something in which there are conserved quantities in higher orders, but only as an approximation. So it has to be a small phi, relatively small phi. You can have breathers in phi fourth theory, which are almost stable because you have these approximate conservation laws. So I was happy because I thought that maybe what I observed while swimming in the Mediterranean in Montpellier, what I observed with the waves, which don't seem so chaotic, is just the reflection of the existence of the higher conservation laws like this, but maybe not much beyond, who knows, we'll see. That's for the future. So this was the present, we had the past, we had this is the present, we feel sure we don't know for the moment. Thank you very much. Don't know whether any questions are allowed or what? Yes, of course. Are there any questions? I had a lot of fun anyway with this. Okay, so then we can move on to the... Can I ask a question? Yeah, please. Yeah, so since you have these things, we take the... I'm sorry, I'm sorry. Since you have these things which are almost conserved, at least up to a certain order, do you have any physical feeling for them? Well, my feeling was when suing... No, I know, I know, but I mean... You know what, these are very complicated. These are relatively... Well, if you are complicated until you understand that they may be simple. Yeah. So have you done... Have you talked to some of your colleagues to do simulations of these things in the lab? No, no, no, no. I'm happy with the ocean. They're fishing, too. Okay, there is another question there. There's a question here. No, just by analogy with the Saint Gordon model. So that's a model that can be quantized. And there's a quantity... Sorry, yeah. Just drawing an analogy with the Saint Gordon. Yes. So that's a model that can also be quantized. And there is a... Yes, of course, yes, quantized, yes. So my question is, this is a fluid field theory, even though it is stars as a classical field theory, is there also a quantum field theory? A quantized version of the... I have no idea yet. Okay, it just... I haven't had enough time to work things out, even at this level. And who knows, perhaps with liquid helium, it would be... There would be something to be said. I have no idea. But that becomes a... I have no idea. This is purely classical, of course. Okay, if there are no further questions, let's move on to the next part of the ceremony, which is the awarding of the Dirac Medal to the first... to Andrei. I have to say that I have not seen a play before with two Dirac medalists in it. So it was quite interesting. Also, those of you... I should add here that actually our students, New Year students are joining. Many of them were here, and some of them, most of them are joining from remotely. We have about 50 students from, I don't know, 40 different countries. And this is their first day, and they were treated to Nobel colloquium and the Dirac medal ceremonies. I think it's very nice. And for them, I should tell that, actually the Ramon and Nehru Schwartz are just the two sectors of the same theory. It turned out historically later on. And somehow, Nehru Schwartz is the Bosonic part and the Ramon is the Fermionic part and there is a supersymmetry, space-time supersymmetry and there is modular invariance. So somehow, in the history of string theory, their names are kind of linked, not only on this boat that they met on, after they met on this boat, I think their names are really linked in some immortal way because you cannot really separate the Nehru Schwartz sector anymore from the Ramon sector if you want a consistent theory. So I think it's kind of nice to have them both here. So now we will proceed with the awarding of the medal and then we'll move to the next talk. Okay. Jeff, would you like to, this is your chance to say something about your advisor. Good or bad. Thank you, thank you, Atish. So it really gives me particularly great pleasure to be able to introduce the next prize recipient, Pierre Ramon, who's the distinguished professor at the University of Florida. So not only am I a great admirer of physics work that he's did, but as a PhD student, I benefited from his encouragement and support, his very good taste in physics and his sense of humor. For example, it used to be that if you would call him at home and he wasn't around, you'd get a message to say you've reached the Ramon sector. I really couldn't have asked for a better PhD advisor he made coming in to work as a graduate student, something that I really looked forward to. So in preparation for this, I went and reread the paper that he's being given this prize for. And it has this idea in it that I still find incredibly creative and beautiful. And the idea was just very roughly that you have some wiggling string. It's a complicated thing, but if you stand back from the string and average over the motion, it's just going to look like a point particle moving with some momentum. But that's all the information that you get out of it when you stand back and average. And the original Bosonic string only incorporated spin, integer spin particles, that is bosons, and the world has fermions. So Pierre had this brilliant idea that to describe spin a half, we know that we need the Dirac matrices, which appear in the Dirac equation, and that these should be some kind of an average over some kind of new degrees of freedom, not that specify the wiggling and position of the string, but some degrees of freedom that live on the string and which average to give us these gamma matrices. And this was incredibly a successful idea, led to incorporating fermion fields into string theory. And as the teacher said, when combined with the work of Nibbun Schwartz led to supersymmetry. But this is only one element of the many things that Pierre has done. So for example, there is the anti-symmetric tensor field, which occurs in all string theories, often called the Calbremont field. And today it's closely related to the axion field, axion physics, which is still a very active candidate for dark matter. He's worked in many areas, not only of string theory, but particle physics, grand unified theories, the seesaw mechanism to explain why neutrino masses are so small, ways of incorporating CP violation into the neutrino sector, constraints on the standard model, trying to understand the fermion masses and mixings that come out of the standard model. So he's worked very broadly and had a tremendous influence in many areas of particle physics. He's also the author of three textbooks, which have helped graduate students like I was to learn various aspects of particle physics in quantum field theory. His work has been recognized by the Oscar Klein Medal and by the Danny Heineman Prize in mathematical physics. And I know from my time as a graduate student that Dirac is one of his heroes. I would often be told stories about how I should read all of Dirac's works, that there were hidden gems there that Feynman had been motivated to develop the pathological formalism by trying to understand some formulas that were in works of Dirac. And I think his own work, as Atish said earlier, really exemplifies the search for mathematical beauty of Dirac. And so I'm really looking forward to hearing his talk following in Dirac's footsteps. Thank you so much, Pierre. Yeah, is this live? Well, thank you, Jeff, for giving my talk. Okay, I'll give you a bit for a few more details. It's very kind of you. And let me see. Oh, I'm sorry. Okay, I'm sorry, go ahead and try this. Yes, I think we tried it before. We tried it before. Yeah, okay, good. So my, I'm extremely pleased and awed by the fact that I'm awarded this Dirac medal because in a certain sense, this is going full circle. And this is just a unique experience, so stereo. And so that's the title. And now I guess I will start. So my background was an engineer. I wanted to go to physics. I went to Syracuse University. My first advisor was Sudarshan. Then I alumned Balashandran. And the Sudarshan taught me the importance of equations. It was very, and Balashandran told me to stay away from the Manussem triangle in the complex plane because you could get hurt trying to get out of this. And when I first came here, right after my PhD, I was awarded by the center two or three months stay here where I met Jean and Iroh Taka. And they completely changed my direction. I wasn't very happy with what I did in graduate school but my direction just changed into the Veneziano model, dual resonance model, the RSO, et cetera. And since we did not like to fly my wife and I, I went to Syracuse to the ICTP in June of 1969 on the France. Okay, so this is where I was. Okay, now when I came back, now you know the story, okay? I went from the ICTP where I met, I saw Girac from the first, the first time. I was very surprised that his head was so small. And I remember I was two rows behind him. I was thinking of this. And as I mentioned to Artish and Andre, suddenly I hear footsteps during a talk, boom, boom, boom. There's a woman coming towards Girac, just pokes him in the shoulder and says, come on, Paul, you can sleep at home. And that was horrified. One of my guards was being treated this way but he followed neatly. And I was so awed by him, I never talked to him. He was like, you know. So anyway, so you just heard this peculiar sketch that Andrea and I set up where basically are accidentally in the middle of the ocean. Okay, we both reading Fubini Venezianos on the level structure of dual resonance models. Fubini and Veneziano were at MIT at that time. And they had a very fruitful collaboration. And the attitude was that people were talking about S-matrix theory. I mean, this was basically matrix theory. And there was just an extra ingredients which was this duality, which was exemplified in first in the Veneziano model, then the Virasoro model, which came shortly afterwards. And I met Andre Nouveau who was going to, for instance, and I was going to do Fermilab. So there it was. Okay. Now, in 1939, Dirac gave a absolutely remarkable lecture which I urge everyone of you to read if you haven't read it. Yet on the relations between mathematics and physics, it is a relation that is oftentimes attributed to Wigner, but Dirac was actually the one to talk about this. And his arguments were basically as follows. He talked about the two modes of doing physics, experiment and observation, and mathematical reasoning. Of course, it worked for him. It doesn't work all the time. And he talked about simplicity in the sense of Newton. The equations were simple. By the way, he mentioned that the complexity in a classical world, actually, you know, the boundary conditions, of course, are subject to vacuum fluctuations, et cetera. He made that stuff in the 1930s, amazing, et cetera. And that explains why you can have simple equations, but you have lots of stuff coming up. And then of course, there's Einstein, which he talked about special relativity in terms of mathematical beauty. And that was this, okay? Now, he said something quite remarkable was simplicity in beauty clash, opt for beauty, which is something one doesn't hear very often from physicists, but in this case, it worked, okay? And it is, and I will come back with his sentence too beautiful to ignore, in particular, the Dirac equation, of course, okay? So I'm, okay. So Miguel, I went to a Fermilab, which was then called National Accelerator Laboratory, it was mostly all in the ground at the time. And I met Miguel in Madison, and where basically he had just invented a lot of, you see, in a dual resonance model, they were oscillators with the wrong metric, okay? And therefore they led to ghosts and the question is how could you get rid of them? And Miguel had just invented that you could get rid of all these guys, except there was a big problem, which kept him up at night, which was that for these decoupling equations to work. He never wrote an algebra, by the way. Was that fundamentally the intercept had to be at zero, and therefore there was a massless spin one particle in strong interaction. But he had the common sense too beautiful to ignore and he published it. And now of course, this is how it is. So therefore when you think you've got something by the tail, just go for it, okay? Even though there may be some problems. Now duality, the Veneziano model, before there was this group of four people in Israel who were just looking at such models, et cetera, and you know, Veneziano founded a tangible model to write this down. This is the notion of duality was an extra input to asymmetric theory. And then as people started working, they were in America, people worked very hard on it. But then they quickly found out that this did not make any sense for phenomenology. And it became a theoretical question and people, but the theory of course started taking off, okay? And that was, this was the way it was. And for example, Fubini and Veneziano were at MIT. And but then they left because there was not, I mean, people lost some interest in this stuff, even though it was obviously fertile ground. Now, so by looking at mostly Fubini, I learned in retrospect later on that Nambu had done this, this and that, but I did not, well, I learned it a little bit after the fact, but when I was coming back from Trieste, the paper that was interesting to me that I could read was a Fubini and Veneziano paper in the series. And in it, there was an oscillator. I mean, you look like oscillator vertex, oscillator vertex, oscillator vertex. And the oscillator looked like a point particle oscillator, except there were lots of oscillators, okay? So it was started with, I'm sorry, there is a pointer somewhere here. Well, it started with a P squared, okay? As a good thing should start. And then there was some decoupling, there were some P dot oscillators and an oscillator squared. And we also took care of that, okay? And then the vertex, interestingly enough, looks like a point particle vertex, okay? Except the X was complicated. Again, it was like X, small X mu plus oscillators, okay? So it looked like that was the pattern, but I think a lot of the people who were working on this at that point were not equation minded, they were S matrix minded. And the question is that I'm surprised to this day why people did not really lock on on this, okay? Because it was kind of obvious from the work of extracting this stuff from the S matrix, okay? All right. So therefore, when I was in the summer in Aspen, thanks to Bob Wilson who was mentioned this morning, and the good taste of sending me there, basically I started saying, well, let's pursue the analogy, okay? And of course the paper got rejected and then I basically, by physics letter and therefore I published it in Nuovo Cimento, okay? But anyway, so there it was. But nevertheless, then I started thinking about the road to fermions. What do you do with fermions? So let me remind you a little bit about it. So this is the Dirac equation, not exactly in Dirac's notation, but close, okay? And so the alphas, this guy's here, the alphas here, okay, for Dirac, they were always dynamical variables. There was, okay? Even though to a lot of people look like matrices, but for Dirac, no, there was content in it. And he says so. He offers a new dynamical variables, blah, blah, blah, blah, and he was an Englishman who wrote English very well. So this is a long sentence, but the fact is that it has to do with the internal motion of the electron. He didn't quite know, but it wasn't true. But nevertheless, that was his idea. There was a dynamical scheme behind. There was Dirac. So the question is that I went on and I followed Dirac. I mean, I say, well, let us look at the, what's in the Dirac equation. So in modern language, there is a gamma matrix, okay? And therefore, if we want to generalize, I got to put oscillators, I added oscillators. These are technical reasons, et cetera. Okay, and, but then you know that when you square the Dirac equation because of the anti-commuting of the Dirac matrices, you get something that looks like a Klein-Gordon thing together of other things, but never mind. But the interesting thing, and little did I know that there were oscillators, of course, I get the pointer, this is pointer work. Yeah, it does work, it doesn't point anywhere, but. Yeah, it's a pointer work statement. Oh, maybe it works, but, oh, maybe I got it the wrong way. The pointer is this over here, I know. Where does he point? There you go. Yeah, so yeah. There was, there was something there? Point, point there. Yeah. You can point here. You can point here and then it shows there. Okay, wait a minute. Okay, hold on a second, I have to go back. Where am I going? What's going on? Yeah, no, I know, I know, but in the process. So this is the pointer, okay? And I point here, oh, I'm sorry. Okay, I'm sorry I did not realize this. So the one thing that happened, of course being 20 some years old and not knowing anything, there were oscillators, they were, they had to anti-commute to satisfy what was going on and they had what looked like a vertex index. And every physicist knows that you cannot have a fermionic thing with a vector index. I mean, that's terrible, but I did not know. But I followed Dirac, by the way, the oscillators which some people now call D, but they were called these, that was the way, this is what I call them, et cetera. So there were two sets of oscillators, but I didn't pay any attention. I just followed Dirac, okay? And now I'm going to give you a little bit of mathematics, which is interesting, okay? Is that in retrospect, later on it was learned string only worked in 10 dimensions, okay? Okay, so that means there were eight transverse. And the one thing that is quite remarkable is that in eight transverse dimension, that's where the degrees of freedom are, the group S or eight is at work and the spinner and the vector representation have the same size, they're all eight dimensional, there are two spinners and one stuff. So there is no obstacle, no group theoretical obstacle to identifying one with the other. And this is where the string lies and et cetera, okay? So I thought that was quite remarkable that just by following Dirac, forget about something, but then you see that it can work in one case and not the others. Who knew, as they said. Okay, so I write this thing, dual theory for fermions, I write this, et cetera. And then again, there is all that stuff I square and then there is Virasoro and there is Supra-Vrasoro, okay? Why not, it's working, okay? And I'd say, now, then it leads to all kinds of stuff, the algebra, and this is what completely blew my mind. He said the algebra was purely anti-commuting algebra. And then I went to ask mathematicians and I was basically ignored completely. There was this man, Jacobson, very famous mathematician, et cetera, and you didn't see any use for these things, et cetera, but nevertheless, they were there. Now, in the process, then they're all these things, I knew there was a symmetry behind, I knew there was conformal symmetry because by then I knew about Nambu's work when basically I looked at that, not in a supersymmetric case, but the regular one. But so there it was and this is something that came for free, so to speak. So that was very lucky. Okay, now diagrams because people like diagrams. So the idea was that this is a fermion, this is a boson, okay? And then the dual pylons, not mostly because you can go across that way, okay? You get these guys here, and of course here you can by factorization, you can get rid of this and that, of course it's the dual pylons model. And this is, I think is how the thing was looked at and then it looked the same formally except the oscillators were a little bit different. I don't know how they got to this. Anyway, it was wonderful, it's wonderful. And then you have fermions and bosons. I don't know, it's magic, okay? So super string, boom, there it is, okay? And then one thing that was interesting, I tried to put interaction in the string model, but I followed Dirac, okay? In this case, when Dirac looked at the Dirac equation, he used the electromagnetic coupling. Well, that was the wrong thing to do because there are all kinds of gauge stuffs going on. And the right thing was just putting a gamma five in there, which is what this gentleman did. The gamma five is really the small gamma five times minus one to the number of fermion oscillators something like that, okay? There it is. So now I'm gonna, this is history just to give you an idea. So my lesson to this, number one, I was very lucky. Secondly, follow the gods. It may be bad if you read the Greek mythology, it can be very bad. It can also be rather good, okay? So you take chances, okay? And in every great man's paper, they are gems, okay? And just trying to reinterpret things one way or the other. I would urge you, you are young enough to not to know too much, which means that you can make progress. Okay, so one thing I want to tell you a little bit about is the work that I'm interested in right now. And we have a problem in particle physics, which is the standard model is as a problem that is beautiful, it works fine, except if it has anything to do with the vacuum, it's not quite easy to understand. So it reminds me, since I'm in Florida, like a beautiful beach side condominium on sand. Okay, because the vacuum that is being used is a flat space time, et cetera. We don't know, but nobody knows anything to say about it. So they are the value of the Higgs math, the cosmological concept. And I even said the axion problem because the better parameter is computed purely in flat space time, et cetera. There may be some correct, I don't know how it goes. I wish I did. But whatever it is, the vacuum, slapping on the vacuum onto the standard model works, it's pragmatically beautiful, but okay. Now, historically, because I like history, in Descartes' way, okay, the vacuum was full of vortices. In Newton's way, it was full of nothing because that's the vacuum. And Einstein's scale is full of quanta. So we don't, at the end of the day, we don't know what's going on. I would make a stupid comment. I think it's a stupid comment, but I'll make it anyway. That if you look at the Brownian motion calculation of Einstein and Smoluchowski, okay, when basically he looked at Pérez's experimental values of the Brownian motion, okay, and he got Avogadro's number out of it, that was a game changer, as they say, okay. Now, so I think when in the future, one of you calculates the value of the cosmological constant, okay, in terms of an underlying theory, okay. If you get the right value, everybody will have to believe with that underlying theory, no matter how crazy it is. So probably it's a blessing in disguise. Oh, and I should say one thing, how do I go? Oh, I go back this way. Mark Twain said, history does not repeat itself, but it sure rhymes, which is the saying I attributed to him. I don't know if he does. Now, so my interest at the moment really has been obsession, I would say. I'm not the only one. It's the neutrino sector. The most interesting thing that happened in phenomenological standard model. Physics, in fact, in the world, is that there are two large angles in the neutrino sector, whereas in the CKM sector, there's almost no mixing, okay. The greatest angle is the capybara angle, 12 degrees. And so, but the left-hand mixing matrix is a mixture between, excuse me, here. Delta i equals zero is what Gellman calls electro week. That means it breaks week as a spin by half a unit, okay. And then there's the unknown sector, which has to do with something we don't know. And therefore, it's an extremely interesting thing to study and to make models, okay. So, let me introduce you to the left-hand mixing matrix, which is now known as PMNS, Pentecova, Maki, Nakagawa, and Sakata. Basically, once they were more than one neutrino known, okay. So, there was something aspect, the first aspect is this matrix, which basically is used to diagonalize chart minus one. You cover couplings of the standard model, and it appears in there, and it provides what I call a capybara ace, because since it comes from the electro week sector, it probably has to do with a capybara angle, okay. And then there's the other thing here, which is unknown physics. And this is where it's worth to make models and see, okay, even though none of the models work. So, the experimentalist Perkins, an experimentalist, mind you, okay. Many years ago, proposed actually the two large solar angles, which are the atmospheric and the solar angles, okay. The atmospheric is almost 45 degrees, the solar angles about 35 degrees, okay. Not known with great think, but he found out that there was a beautiful matrix here, called your zero, which is basically 45 degree angles. That's another way he was marking up the two large angles, okay. And of course, what happens for this idea to be true, and I don't know where this is really coming from, but it does, there's a zero here, and he tells you if that's where the only mixing, there will not be any reactor angle, which of course we know has been observed and measured quite accurately, about about eight degrees. Okay, so for these models to make sense, the capybara guy must be basically able to produce that big an angle, okay. And that turns out to be a challenge. So let me give you a quick, oh, I still have some time, okay, I'm gonna bore you a bit more, good. All right, so the standard model Yukawa matrices, there are two of them, up quark, down charge to third quark, minus one third, charge to minus one. And one thing you should know, because most of you don't know, or maybe I forgot and or never knew, about SU5, one of the Grand Unified Groups, which has something to say about the pattern that relates basically leptons and quarks in terms of the Yukawa's, okay. And people for the last 30 years have been building textures of these things based on some symmetries, and those again, okay. And the idea that for example, you build a texture which satisfies the said the Wolfenstein parametrization of the Cichlian matrix, the Gatton relation, you know, the famous thing that it can be bored, the tension of the capable angle is the ratio of MD over MS. MD over MS is renormalization independent basically. So it's a good thing, et cetera, et cetera, okay. And but what happened is that if you played with it with textures where basically these matrices were flavor symmetric, you usually got at most four degrees for the reactor angle. And you could never get to the experimental value. So what we did a few years ago, I mean, I'm sorry, I'm talking about my work or my group's work. I said, well, let's try an asymmetric texture. Let's try some asymmetry and see if it works. So at that point, it's really disgusting phenomenology. Okay, I mean, really disgusting. But we decided to do the following thing that let's see if it works. Let's do it and if it works, we'll try to explain it later. Okay, so what we found out was that, let me go back here, was that the angle, the theta one three angle here, if we in the asymmetric texture. So the point is the following, if it is a symmetric texture, the charge minus one Yukawa and the charge minus one third Yukawa's have a very close relationship with one another. Because according to SU five, one is more or less the transpose of the other. That's a Clebsch-Gordon coefficient. Okay, so if you loosen that, you have a chance because what happens of course, once it's loosened to the charge minus one third, that goes into the CKM more or less. Okay, and the CKM you know has very small angles. So that's the thing. But if you have asymmetry, okay, what we found out is that we made, it was very hard to find such a thing. We found it, it was fine, it worked beautifully. Except theta one three was, can people like exactly? But in other words, we overshot it. But one of my smart graduate students, okay, said, aha, but what happens if I put a CP violation angle in this because after all there is. And therefore we fixed it the angle so as to get the right experimental value for the Chinese, I shouldn't say Chinese now because people think it's bad, but I mean it's a very accurate determination of theta one three and that gave a delta CP, which happens to be, we don't know the sign. This is the Yarskog invariance for the view. It's exactly in the bread basket of the fits and it fitted everything. So okay, so what do we do? Okay, all right. We try to make a model to understand that because it's rigged, okay. So, but the fact there are two large angles and there comes the direct view. Maybe those two large angles, whenever, when I learned chemistry, okay, I mean large angles had to do with angles between crystal faces, that is what it was. So maybe there is some sort of a, some geometric object in there, okay. And all right, and that leads to ideas such as discrete family symmetry, Majorana crystal and edirax. I mean, that is we're doing it. Keep looking, it'll get simpler as we go along. Maybe that's not true, okay. So what happened is that I leave, I'm gonna dance only with some group theory. So the discrete family group becomes important because discrete family groups means that you have a geometric structure and you can rotate by this, this and that, et cetera. So therefore there must be, or it looks like perhaps there's a discrete symmetry, okay, there. And we start looking. So this is technical, but what happens with the asymmetry was very hard to see. When you take a group, usually you distinguish symmetric and anti-symmetric, and that's it. Symmetric or anti-symmetric, you multiply to represent it. When you have a symmetry, if you're below the diagonal and above the diagonal, you have different magnitudes. So you have to go beyond that. And so how do you do it by group symmetry? Turns out you have to take a group that has two in equivalent triplets for the three family and the one is one of the so-called Frobenius groups. Nevermind. So now I'm almost the end. I will tell you about the patterns that we saw in this, okay. The first pattern is SU5, that is the Gran Unified Group with this T13. So we have a five bar, which transform as one representation of T13 and a 10 as, okay. Now, for those of you who don't know SU5, five bar and 10 basically is the content of one carol family, okay, in SU5. Now, if you go to the next level, which is SU10, Jeff will enjoy this because he was part of his thesis. You ask yourself, what kind of unification is this when you have the same things, but you have different representations? Well, what you can do is that you can always think of this as a 16, okay, of SU10. And this is a 10 of SU10, 10 vector, okay. So you hear you have a spinner representation, you have a vector representation, but here you have a five bar with five. They can get married with a vector like mass and the carol structure is the same as before, okay. And then of course that leads me to my favorite thing, which is E6 cross 13, because what exceptional groups do, they make spinner representation with vector with the vector representations, okay. There it is. So it goes this and that. And then you see here, you have to add a new one if you're in E6, okay. Because if you decompose E6 with respect to SU10, you have a 16, a 10 and a one, okay. That gives actually four neutrinos. This one gives you the fourth, okay. And then you have the funny structure that basically somewhere there's a matching principle, which I don't know it always coming from, between the three representations of T13 and the three break the breakups of that. And I don't know where that goes, whether they have the same weight under some symmetry and the match, something like that I've tried, but it's been a bad summer this way. Okay, this is where we are. So this is where I am now, okay. So the symmetric texture, I didn't talk about symmetric texture, but another Frobenius group comes up, which actually turns out to be a discrete subgroup of G2. This guy here goes into these so-called, these are modular groups, as you don't know. And then it goes, it's again, subgroup of G2. It's very interesting because in 11 dimensions, when you go from 11 to four, you have a seven dimensional manifold, or you have G2 autonomy, as if Bobby, I don't know if he's here, but I mean, he lives on these things, okay. And, but I should remind you that there's something interesting going on. Is that in a Plato cave analogy, this is not good news because the Plato cave analogy, everybody in a cave, right? For them, the world is a concept. There's a project on the cave. Until one guy escapes. The guy comes back and tells them, no, no, no, the world is completely different. Now, this is very uncomfortable for the people who are in a cave, so they're killing. Okay, that was the thing. So we have to be careful because a great deal of what's going on in string theory has to do with concepts, okay. And maybe it's true, maybe it's not true. So I think this is more or less, yeah, this is more or less what I have to say, okay. It takes you away from a very simple thing, right? This is getting complicated, but it's looking for structures in it, okay. And the fact is that we have three carol families. We have a lot of experimental evidence for these things, et cetera. There has to be some beautiful thing at the end of the bridge, okay. And those are patterns that go on. In here, I mean, in CISA, there are a lot of people who do, you know, I see Sergei Petkov and Romagnino and people like that, who basically look at different symmetries, et cetera. I mean, everybody's looking for that, but I must tell you that up to now. I mean, you wouldn't buy any of these things, but you should listen carefully because for one thing, you don't wanna do it yourself because maybe that is wrong, but at the same time, you should be aware of the problem. And the problem right now is in the standard model is that the neutrinos are weird in their masses and mixing. And therefore, even though it's very difficult, you should pay attention to it and try to make models. And I hope you will do because the future is you. Thank you. Are there questions? Could I ask a question? Yes. Pierre, does it matter whether you think of these finite group symmetries that you use to constrain the texture? Does it matter whether you think of those as global or discrete gauge symmetries? Discrete. Well, discrete because of the, well, I mean, I know discrete, but I guess the question is, are they, does it matter whether you think of them as global or gauge symmetries? Oh, oh, I see. At the moment, I do not know. I mean, there may be the remnant of a gauge symmetry for all I know, okay? But I do not know what they are. I mean, what I am very interested in is the following thing that, for example, these groups, for example, if I take T13 or else T7, okay? There is a beautiful construction in lattice things that are due to Vladimir Rittenberg who many years ago, that if you're on a lattice and you put a spin as a given, so for example, you could do ising if you want to, okay? But what happens is that not only do you have the symmetry of the spin, but also you translate along the lattice, and therefore that means that you have an affine transformation that, of course, generates a semi-direct product, okay? So therefore, you can start thinking about the lattices, okay? Now, where those lattices live and where they come from, I don't know, okay? But then when you follow them up, okay? You go to, basically, like, you know, these PSL to T7, those are modular symmetries of PSL to T7 and PSL to T13, and one of them for the symmetric, my favorite symmetric texture, it leads you to a seven-dimensional thing, which is, of course, could be G2. The other one leads to a 13-dimensional thing, which is a discrete form of G2. I mean, G2 breaks down into things like that, and of course, G2 probably is an important group in a decomposition of the 11 dimension, but I don't know. This is purely speculation, but the fact is the tangible part is that those angles are there, the determination, unfortunately, dunes is late. Now, they're not getting enough money to measure anything. We don't even know whether it's a normal hierarchy, or et cetera, we don't know the actual value of delta-CP, but nevertheless, maybe within the lifetime, my lifetime, even, it might be possible to have a measurement, okay? I'm not sure now the way it goes because it's getting to be difficult, but I think this is tangible stuff, and most people say, of course, that most string theories seem to think of the standard model, basically without just the gauge structure, and your question is apt to this because it could very well be that the gauge structure is enhanced in some ways, and this is a remnant of it. I don't know. I don't know. By the way, Jeff, those oscillators are called B. Okay, anyhow. Sorry, boss. That's all right, look at that. Yeah, I can see that I'm still afraid of you. The fear never goes away. No, but... There is a question by Bobby. Thanks, Pierre, for a very nice talk. I actually just wanted to ask about the T-13. So I understood that you chose, you're interested in that group because you're interested in... Can you take your mask off? Because you're interested in groups with, I mean, discrete groups that have two different three-dimensional representations. But why that one in particular? I mean, you gave some motivation. That is the smallest. Yeah, millions of them. That's the smallest group. With two inequivalent triplet representations. Is that true? Yeah. Wow. Okay, that's fine. I mean, you know... I didn't appreciate that answer. I believe that is true. And of course, the progenitors are these, you know, these modular groups and these PSL tools, et cetera. And at some point, I was very excited because the PSL27, which appears in symmetric things, appears in mathematics everywhere. Doesn't mean that it's good, but that means that the mathematicians have worked out lots of the proper keys. I just, but I don't ask for anything. Okay. If there are no further questions, we can move on. I would just like to add that this operator F0 that you wrote down, there is another connection that Pierre has with Dirac because it's now known as the Dirac Ramon operator. I think that's a great honor to be associated with Dirac's name in this manner. And also, I think this Carl Ramon field from the Ramon-Ramon sector, I think this is the only object where you have to use the name of the same physicist three times, Carl Ramon field from the Ramon-Ramon sector. I should tell you the way I got the idea was again, this time following finally, because I was very interested when I was in graduate school in something called Action at a Distance Theory, which were basically, it didn't really fit anything. The propagator was just conformal, okay? And there was no advance and retarded. I mean, the propagator is usually different from the two and this one is, so what happened is that, but the geometric picture was that if you have a point particle running around, you get, of course, a one form coupling to it, namely, okay? So what happens if your string is going around? Yes, that's natural generalization. So keep looking at these famous people's papers. It's very important. Okay, okay. Okay, so now the award, the award. Oh, I passed the test, thank you. Do we have to go? Now we can move to the third, the work of the third, the Ratman list. Jeff, maybe you can go ahead. Okay, thank you, thank you, Ateesh. So we've heard a lot about symmetry here and when you first study physics, when you first study quantum mechanics, for example, you run across the problem of trying to understand the hydrogen atom and a very important ingredient is understanding the implications of rotational symmetry. You can take an atom and rotate it about the X, Y or Z axes and these three transformations leave the physics invariant. So imagine the power that if instead of three independent symmetries, we had an infinite number of independent symmetries. This is essentially what happens in the kind of symmetry that comes out of the Virisoro algebra, which is tied to the special behavior of systems in two dimensions that are invariant under scale or conformal transformations. And it plays an incredibly powerful role in organizing the structure of string theory, getting rid of unphysical states and organizing the structure of two-dimensional conformal field theory, which plays a broad role not only in string theory but in condensed matter physics and pure mathematics and even to some degree in recent ideas like quantum information theory. Virisoro discovered not only these constraints that led to this algebra but also the Virisoro-Shapiro amplitude which describes how closed strings scatter. And today that's an aspect of understanding properties of quantum gravity because the graviton emerges as a closed string in closed string theory. He also did important work on spin glasses that I think you'll be hearing about later today in the memorial session. So we were all of course very saddened by his passing. His work was very much in the spirit of Dirac on uncovering beautiful new mathematical structures. And these structures that he discovered continue to have growing consequences and leading to more and more understanding of physical phenomenon and also many new beautiful mathematical discoveries. So I hope that you will join me in welcoming Alejandra Filola, who I understand will be accepting the prize on behalf of her husband. Okay, so I think Alejandra, would you like to say a few words? Well, good afternoon. Well, it's a great honor for me to receive the Dirac Medal 2020 to Miguel Virasoro for his contribution to theoretical physics, in particular to string theory. I hope that Miguel's memory illuminates young researchers who like him have chosen the very hard way to science in a world full of fake news, lies, and so on. Well, thank you very much. Principally, thank you to ECTP for the invitation, particularly in the person of its director. And thank you, Daniela Matif, to impulse me to be here. And thank you, special thank you to the staff, the ECTP staff who made possible to my participation in this ceremony. Thank you a lot. Thank you, Alejandra. So Miguel, of course, was made very major contributions to physics, but he was also the former director of ECTP and under his leadership, ECTP went in a number of important new directions. And in his memory, we will have a session after 4 o'clock. So thank you very much. We will now break for coffee. Please, you're all invited to coffee on the terrace and we'll reconvene at 4 o'clock. So once again, congratulations to the Dirac Middlees. Thank you, Jeff. I wish I could invite you for coffee, but I wish I could enjoy the good Italian coffee, but hopefully in the future, not too long from now. OK, thank you. See you. OK, bye. Physics from Virazzo Algebra and Virazzo Shapiro amplitude and string theory. To his work in spin glasses. And so two of his close collaborators in particular, Gabriele Veneziano, he's joining us remotely. He could not make it in person. Gabriele, can you connect? Yes, hi. Hi, Gabriele. Hi, I just connected. OK, great. And then Giorgio Parisi, who was his colleague at La Sapienza, he will tell us about other us in the second half of his physics career. And we are also joined by the former CISA director, Danieli Amati, who was a close personal friend. So this is the program and we will start with. Would you like to say something, Alejandra? Yes, OK. Well, good afternoon, everyone. It's a great honor for me to participate in this session in memoriam, Professor Virazzo. And also in the direct medal ceremony to Miguel, an award given 50 years after he published the Virazzo Algebras in a physical review day in May 1970. Miguel Angel was a brilliant scientist who made important contributions in different topics of science, string theory, spin glasses, neuroscience, and more. But in this talk, I would like to comment on some other aspect of his personality. Miguel was also a political man, committed and capable of fighting for his ideals. In the turbulence 1970s, he was dean of the Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires for a period of seven months between May and December 1973. As dean, he worked to revive the faculty and bring it to the level of excellence it had when he was studying. He suffered political violence. His life was in danger and the arrival of the military, the dictatorship, forced him to leave Argentina. As a political emigre in Paris, he contributed to helping the persecuted in Argentina. He always supported those who needed help. He returned to Argentina in 2011 and continued working at the Universidad de General Cermiento where he created the complex system group that brought together researchers, students, and other collaborators from different fields. In particular, he investigated the dynamics of Pampa plain river to prevent floods, floods that do a lot of damage of the economy to the people. Miguel always tried to solve the society's problems as a scientist. In short, I think that for Argentina and Italy, Miguel was an essential man for science as well as his active participation in defending his political ideas. He enlightened several generations of researchers. We all miss him so much intensely. Finally, I would like to share two personal short stories with you. The first was on the first day we had. Speaking of Virasaurus algebras, he told me with his usual humility, I made physics advance one day because if I couldn't find it out, the next day, another researcher would have done it. The second was in the last month of his life. Miguel couldn't speak. He communicated by writing with great difficulty. One of the last things he wrote to me was about his will to go back to Trieste and meet his old friends. It saddens me very much that Miguel cannot be here and also that he has not shared the joy of the Nobel Prize for social policy. Well, I thank ICTP for the invitation, in particular the person of the director, Atish Dabulhar and all the staff who made possible participation in this ceremony. Thank you very much, Tour. Thank you, Alejandra, for being with us, actually taking the trouble to come all the way from Argentina. We really appreciate this because Virasaurus, as I said, I'm happy to hear about his non-scientific aspects of his personality. He made very important contributions to the growth of ICTP when he was the director. Under his leadership, the climate section was founded and it grew what it is today. He also took an important interest in international cooperation. For example, the Cezami project, which was realized in Jordan, bringing together, you know, warring nations to do science together, started by a conference that was arranged in Dahad. Miguel was the director at the time, where countries like Jordan and Israel and Iran and Bahrain came together to think of cooperation rather than of conflict. So I think this aspect of his personality is also equally important. So now we move to the scientific, well, not necessarily scientific, I think both Giorgio and Gabriela and also Daniela are his close friends, so I give the floor to Gabriela first. Gabriela, can you hear me? And can you see my screen? Hello? Yes. You can? Yes. Okay. Let me try to close this. So let me start by thanking Atish for this invitation to give a modest contribution to the memory of a friend and colleague, Miguel. And also I have to give my apologies for not being able to be there in person and in particular for not being able to congratulate personally André and Pierre. I was glad to hear that a preprint of mine held them on a boat trip. Anyway, I decided to talk here about a short period of time and I called my intervention. Sorry, I shut the phone. I called this talk of my souvenirs of a strong interaction, strong interaction in two meanings of the word. We were working on the strong interaction, but here I mainly refer to the strong interaction I had with Miguel. Let's see, how do I scroll by clicking? Sorry, I have a problem with scrolling. It worked a moment ago. Sorry, sorry. Usually by the arrows. Oh, maybe I have just two. So I want to start with recalling how our two word lines crossed. And that happened in the beginning of 1967. So let me describe very briefly our word lines along that time. So my own word line is that I moved from Florence to the Weizmann Institute as a PhD student around September 1966. Now my official advisor was Harry Lipkin, but in practice it turned out to be Hector Rubinstein. Argentinian had moved to Paris before accepting a professorship at the Weizmann Institute maybe a year or two before I arrived. And with Hector we immediately started to work very nicely together and even wrote a couple of papers on current algebra summaries. How about Miguel? In June 1966 there was a coup d'etat in Argentina and the academic people became the target of the military junta and many professors decided to emigrate. Miguel was working on his PhD thesis. He managed to finish it by working at home and eventually graduated at the end of 1966. Then he decided to leave accepting an invitation by the same Hector Rubinstein to move from Buenos Aires to the Weizmann Institute. This is how as early as the beginning of 1967 the three of us Hector, Miguel and myself formed a very close and friendly team. This team was extended outside working hours also to our respective families or companions. Now in June 1967 we all witnessed the Six-Day War in Israel which was a political turning point for Israel and for the whole Middle East as you know. But another turning point this time on research physics took place a couple of months later when we heard, myself I heard it in Erice about the Dolan Horn Schmidt paper dealing with duality between rege poles and resonances and the possible bootstrap which would be based on that. In Florence in September 1967 before going back to Israel I remember I discussed this news with Marco de Molo who was one of my previous professors there and we decided to keep in touch about this. He was going to move soon to Harvard as a visitor for two years. Soon after when I was back at Weizmann Institute and Marco de Molo was at Harvard this enlarged collaboration of the four of us started to work quite enthusiastically on the duality bootstrap. I remember that in the winter of 1967-68 we took advantage of a very useful and encouraging visit by Sergio Fubini of which I have a very dear picture. So this the four of us are in the middle of the picture then there are a few other guys around listening or sleeping I'm not sure but as you can see the three of us Hector Rubinstein here, Miguel here, myself here you know we're listening very very attentively to what Sergio was telling us. Now in the following year we worked on this duality bootstrap we published a number of papers showing how some simple parameterization of the rege and resonance contributions could satisfy the duality bootstrap with amazing accuracy which could even be improved step by step. We were also helped here by two quote-unquote young guys I'll explain a bit later who are Moti Bishari and perhaps you know better Adam Schwimm. In June 1968 the group dispersed because the three of us we all left Israel for different destinations Miguel went to Madison, Wisconsin Hector went to NYU and myself I was going to MIT via Sur. Now a few days before boarding a boat to Venice I went by boat to bring back my car to Italy I had an inspiration and on which I kept working both on the boat and later at CERN till the end of July 1968 and I then submitted the results to Novo Cimento and I remember I mailed unfortunately not emailed at that time took a few weeks to get answers both Hector and Miguel and probably also Marco about this development and both of them but particularly Miguel reacted very enthusiastically to this news and Miguel would soon write one of his most famous paper The Viral Sorority. Well Jeff and also Jeff certainly has you know I listen to him now I was guessing that he would cover much of the other groundbreaking work of Miguel so I will only mention one extra episode which perhaps not everybody is well aware of so as soon as I arrived at MIT I started to work with Fubini trying to understand what was lying behind this dual resonance model and that's when for instance we wrote that paper which we heard about whose preprint was was carried on the on the boat by both André and Pierre. Now Sergio had a nightmare from the very beginning after he saw my amplitude that the model could be doomed by the presence of negative normed states which we called ghosts. We had found in that paper a mechanism to eliminate a small subset of such bad states of this ghost but getting rid of all of them looked really hopeless you know a dream so when Miguel 1969 published in 1970 paper the one that led to the Viral Sorority appeared showing that under a certain condition the dual resonance model could be made completely free of negative normed states Sergio and I by the way the surgeon in particular was so impressed that he asked and actually obtained from his MIT colleagues permission to offer Miguel a position at MIT I guess a junior staff position. Unfortunately for us Miguel opted for another offer from Berkeley and in fact he moved from Berkeley to Madison from Madison Sorority to Berkeley in 1971 so exactly 50 years ago. In fact I will now jump over 50 years with the idea that this would be covered in any case by Jeff, by Giorgio and Daniela and I'll come to actually August 2020 so after receiving the the award the medal so these are emails that I got from Miguel I got also others but I will concentrate on three of them and here is my free they are in Italian and here is my free translation so dear Gabriele and Eddie my wife when I think back in perspective I see that year and a half in Rehoboth the one I described is one of the happiest periods of my life thanks to you to Hector and Helen Hector Ruby Stanis' wife to Marco and the mollo and also to the young guys I Giovanni he says in Italian I think I'm pretty sure I referred to Morty Bischari and Adam Schwib and then he says greetings to both then 10 days later he came with a beautiful idea he said well when Adam Schwib sent his congratulations from Rehoboth I had the sudden inspiration to ask him whether you'd be a good idea to invite all of us to the Weizmann Institute to celebrate those two years he Adam was enthusiastic about it what do you think of this idea it should be when I will be in Europe for the medal they did not fix yet but presumably around May 2021 I would be extremely pleased if Eddie would come with you I will be going with Alejandra also for doing some sightseeing she does not know is what do the two of you think we get so at that time he was really very happy unfortunately in January 2020 this year he said my dearest Adam and Gabriele I'm dreaming about this trip but unfortunately I have to share with you a health problem the stress not the coronavirus I was like diagnosed with and then it gives a few details the expected evolution is pretty bad but the timescale is uncertain could be months or years at the moment I would say that with a subjectively estimated probability of 90 percent I will be going to Trieste and to Rehoboth I would then like to make a tour of his repeats with Alejandra who has never been there it will be such a nice occasion you see he uses the future tense not conditional Sarah on a better occasion he really believed that he could make it now my last encounter with Miguel just before I finish this was in October 2014 it was the 50th anniversary of ICTP and it's so coincidental coincided with my own direct medal and we had a very nice time with Miguel, with Daniele and I remember we were both staying or at least he had I was staying at the Adriatic Hotel and then we walked down from ICTP to the Adriatico and it was dark the road is full of steps and Miguel needed my hand to help him not because he couldn't walk but because he couldn't see the steps a problem I'm very familiar with because my wife happens to have exactly the same disease that is a retinal degeneration disease but Miguel was happy nonetheless he arriving downstairs at the Adriatico introduced me to Alejandra and he was very happy that they were going to have a three pound Italy assuring me that Alejandra would drive and not himself and you know it's just too sad that I mean it looked that he had finally found a very happy companion and family life which he struggled for throughout his life and it's just too sad that this didn't last long thank you thank you Gabriele I request Georgia to take the floor please I have to um to exit full stream oh why is it no don't worry I think you do it okay take care of it you can just mute okay okay yeah please go ahead well the first things that I would like to do is to read a text that was been sent to me by Diego Villasoro the son of me of Miguel which is should be this year I think in 1942 the text is a phone hello I am Miguel Villasoro son Diego unfortunately I could not be there in person to celebrate my father's achievement but if you wouldn't mind I like to say a few words about my father Herbert virtually before anything else I have my mother Silvia and I would like to thank the SITP director Dr. Atish Dapokar for this price and memorial I'm sure that would have liked and enjoyed it surrounded by some of his close people and in play in a place that meant so much to him and we would also like to congratulate congratulate his co-winners Andre Nevere and Pierre Ramon why I'm sad that he could not live long enough for the ceremony as his son I incredibly happy grateful that he could receive enjoy the news before his health deteriorated he told me the news about the divac medal last time on the phone but it was clear he was very proud and somewhat humbled by the achievement I think he loved physics it was not a job but was more like a vocation nothing could stop him working on his research mid-day vacation his retirement or his partial blindness even at the end when the symptoms were already evident he could not avoid working on some new hypotheses and let me tell you he could even avoid applying his neck for theories outside of science to everyday life often with the bereavement of his family and shall we say the better but that didn't matter to him there was only one thing that managed he managed to take him away from his research directing ICTP and I think that he would have continued the full 10 years if we if we could have done among other things he enjoyed developing new groups to study fields even outside the more traditional physics where physicists their views and techniques have a lot more to offer such as climate science which today is so vital to humanity but most all arts believe the strong it was important to help developing country to develop their science and that was vital to keep the best physicists access to the best tool no matter what their background and where they are from and despite living only seven years since yesterday it remained one of his favorite places together with Rome and Buenos Aires where he spent most of his life therefore will not be a better place to receive this prize and celebrate in his life thank you very much please continue yes okay well my friends have spoken no no wait I think uh sorry no John you would like to see now ah no no but better than here no no but don't you want to talk about okay no but I will talk about talk about me here okay yeah yes yes yes no I wasn't just a full of chronological order okay I was very I'm very happy to see to see here because Miguel was a very very good friend of of us and all the family I mean I met Miguel in the some few times in the 70s and I started to frequently him in a regular way one here that we both were in Paris and we overlapped one with the other one and after that period we had the long discussion about strings the relation between string theory and gaze theory and so on and I remember that Miguel was reading carefully what I was writing about the QCD and related stuff I remember that one day he came to me and he looked and he said to me look I read the paper I checked the last paper I checked the computation and it's very surprising I found that the the result were right now I said why are you surprised that the result are right he said well all the intimated formula were wrong only the final one was correct anyhow and now what happened that apart from these colloquium discussions and so on seen outside school that we started to work on on spin glasses in some some strange way because I was working home with spin glass and they sent some information on the work that I was doing to some friend in Paris in Nicolás last Gerard Toulouse and Marc Mazzar they Miguel knew discover these things he found the very interested and we wrote as we start to work together with on spin glass and the paper that were written by myself with Miguel where is extremely interesting and also will say that most of the work was not mine I think that I mean these people were not written would not written without without the help of the French the same because Miguel at that time was for short while in Paris and therefore the whole idea of the fact that the complex spins are complex in some technical sense the idea of the ultrametricity for example involves the fact that this tassonomy and that the tassonomy is something that is related to to natural tassonomy and therefore the connection between the spin glass evolution and so on this was really a part of the work that was done by by these people so this was and this was extremely interesting to work for because it was shed a very important light on the physics of spin glass and on the meaning on the solution there are the things there are the bigger collaboration that we did we did with with Miguel was two papers that we wrote together with Marc Mazzar in the time that Marc Mazzar came to Rome for two years and in that time I was completely busy in another project it was a construction of the Apple supercomputer so which was a full-time job because it also was an experimental one therefore there is some experimental schedule and that should go on I was spending a lot of time in the lab looking on the oscilloscope trying to understand to change the pictures that were on the oscilloscope and I had the chance that Miguel and Marc Mazzar were working together together with me Miguel Miguel and Marc were in the same office in the same room as Appianza I remember and I think that Marc started to speak in Italian with a little bit of an Argentinian accent because of the interaction with Miguel and they with myself which was acting like a market consultant that we did a very interesting paper took an interesting paper on cavity on the on the way to rederive all the things of replicas with a new different format of statistical mechanics that is the one basis of cavity field this was a great achievement because the previous formulation on replicas is something very abstract and the mathematics doesn't know is nonsense and the formulation that we found they found essentially we was was very important because it was at the basis all rigors development in this field and therefore with Miguel with Marc also very that without me there is a very nice paper the microstructure ultrametricity that it takes me a few years to fully understand the very relevance of that paper so at this stage Miguel did a wonderful contribution an essential contribution to the theory of spin glasses without this kind of contribution spin glass would be more really considered the curiosity will not have the culture in general speaking in physics impact that they had moreover Miguel at that moment ever having understood the spin glasses and I also we stopped to work more or less on spin glass so we started to work on some related the problem with Marc Mezzar on optimization and what happened Miguel is also because he was interested from for some let's say Miguel was interested from some cultural idea to psychology to the function in a human brain this is something that always interested started to try to understand if some of the things that were discovered in spin glasses could be this useful also in a completely different context so he was very interested in the the development of of neural neural network and there is an idea that maybe the fact the fact that he was mostly buzzing to him was the fact that we can do categorization that the human brain is doing categorize and categorize in a simple relative simple way I mean without effort without any special hardware for categorization he had at that time locked up on books on a psychology psychologist and so on because he was very interested to really understand how things were going and and also wrote some paper on how to have categorization in neural network and also was interested to a phenomenon I never heard before which is prosopagnosia and they also wrote a very interesting paper on prosopagnosia maybe and now in this period we were frequenting us very strongly also because with all the family because we had rented a house outside the room which we were going there with other friends for during weekend or during summer time and so on so we were seeing each other very frequently and when he became a director ICTP I guess in 92 he had to move out from from Rome and we frequented much less and also during his internship here we could not work together we started to work again when he came back to Rome but with much less intensity and before also because at that moment I was interested in something that was completely different from spin glasses and so on so I think that he's one he's had this wonderful friendship with him and the papers that are written from him are some of the best papers that are written so and they have been crucial in our understanding of spin glasses and understanding that they've been crucial also for the as you can see from the Nobel Prize so I also the books that were written together with on spin glass theory and beyond is a book that is put in the in the citation for in the long citation for the Nobel Prize so I am very grateful for Miguel because I learned many things not only about physics but also knife and also politics for Miguel was really deeply interested in politics he was deeply interested in Italian politics but as an outsider I would say because probably he suffered too much for entering to do politics again and we had a lot a lot infinitely a lot in a long discussion on politics that were with sometimes we did not agree but they were crucial for get for my understanding of politics that was very important because coming from a different not planet but country he could see the Italian things with a different view with the different subject so I am very grateful to him thank you well it's my turn my friends covered a lot about the what Miguel has done surely a lot about his scientific work but also his personal attitudes what I have my task was very limited and say something about his action here in GSD where of course we met we we were friends from from much before but nevertheless we found ourselves here we collaborated a lot we discussed a lot and also we we started things together a lot we I was directing CISA which was nearby and he was here so we had the possibility to do things together let me say that not as comes out from what my colleagues have said Miguel was not only a very intelligent scientist very very wide but his interests were very wide very wide he was interested in a natural characteristics mainly for instance in the in the neuroscience development of human beings about the social problems and the ways of tackling them and in his work here he always tried to enlarge the horizon of the scientific interest of of of ACDP he followed the abdu salam attitude and feelings that science is a is a crucial way to help developing countries not only in helping the education and the formation of people but also all of helping the rationality structure of groups of people who had to then deal with the reality of the countries so that his his his interest in the task of of ACDP was really very very frank and very important even if the probably the reasons were not exactly the same as abdu salam reasons but however it was in the line here he did a lot of things and mainly in in he of course helped a lot the scientists which are more mainly physicists and mathematicians and in physics really condensed matter and in particle physics but he also developed no things for instance within the condensed matter group he built up a group of people interested in in physics applications to to biology and neuroscience by putting a few young people together one of them is still here and is Matteo Marcelli I don't know if he's here but anyhow but then he has the quina coming here sirio france and who else have it here and also maniasco who was an argentinian in working in the united states unfortunately and so ACDP began also already to be a center in this development of physics that had to do with life science unfortunately this feeling about this particular field was not really followed by his successor and therefore for instance this group disgregated and as I said fortunately brazil is still here but all the others left the field but this was not the only one the only thing also he had important social motivated problems and he for instance made ACDP joined a group of of other institutions mainly the Bayer Institute in Stockholm and any foundation in venezia in which a lot of sociologists and economists collaborated among this group I remember das gupta arrow and mother all people of first class that that contributed to that unfortunately also there the the roots in cisa were not from the men they were not very important and were not really followed by his successor another thing that he gave a lot of importance is the weather and climate in which fortunately he built up a group that is still here and which is one of the interesting very interesting things in which ICTP has followed so this gives a feeling of the vast interest of him also because as I told you it was not only to form say technical traditions here but people that had a correct reasoning and reality attitudes in science I would say not much more of his activity here I guess that he had to he had also to follow what what all vectors is have to and which is to fight with with the the aggressivity of of bureaucratic structures mainly coming from the agencies in which for which I in which ICTP works and also on the stabilization of the batch for instance he was able working with cabibos at that time was if I'm not wrong the the chairman of the scientific council or perhaps council I don't remember in making changing the in accepting that the the budget of ICTP was part of the international agreements and not only part of the interest of the interest of helping third world and this made the the contribution of Italy stable and blocked independently of the of the flag on which the government was coming let me say that we did as I told we did several things together and I have the feeling that that they followed also other aspects of his life one very important thing for instance that that and as was said before by Giorgio was a his encounter with Alejandra that established a real very serious couple encounter and which helped him to live the the last the last years of his life in a novel way that not many people would have had the force and enthusiasm to to to take thank you okay thank you Giorgio and thank you Daniele is there somebody from the audience who would like to add something may add one word perhaps and this is one thing that that Miguel and me share was a close friendship with Giorgio and I remember the importance that that that he he gave with me many aspects of the fact that he could get the recognition that he deserves he considered and I also consider Giorgio as a extraordinary person one of the few geniuses I know sorry for this clarification but so and this was one of the one of the reasons why I'm sure that he that that say he's who could say a virtual member of this group that is very near for Giorgio his family in this moment right I believe that he would have been here he would have really pleased a lot as I was by the standing ovation that the young people of ICTP and CISA gave to Giorgio the moment he entered the big auditorium so let me also thank you to share with me the friendship that we have together with you and something else okay so I would like to now end today's session thanking of course Giorgio and Daniela and Alejandra to be part of it and for Diego for sending his message and also Gabriele thank you very much if you're still connected I hope and so and all of you for participating in this in the memoriam of Miguel thank you very much thank you thank you very much