 Thanks a lot, Mike, for this introduction, and I'm very happy to be here and from the name of German professors of HES. I'm happy to be your next guide on this virtual tour of our institute, and I'd like to share with you some of the ideas which play a role in my research. And actually, in research of many physicists, because this concept of universality in my title, it is one of the central concepts in physics. So, in this talk, I will explain to you what the physicists mean by universality. Because we have some technical meaning for this term, which is maybe not exactly the same as in everyday life. I'll show you a few examples where this universality can be seen in concrete physical systems. And we will also see a few remaining puzzles that I'm trying to address in my research. So this is probably a very diverse audience, but I hope that there's going to be something for everyone's intellectual curiosity. So let me tell you what universality is. In physics, we often have to deal with complicated systems, which have many parts, and also many parameters, characterizing these parts and how they are connected to each other. So you might think that because the system is so complicated, any theory, any theoretical description of the system is going to be as complicated as the system itself. But actually, more often than not, it turns out to be the other way around. The system is complicated, but there's going to be emerging some equations, some general laws, which are first of all, relatively simple. And second, they have relatively few parameters compared to the total number of parameters characterizing the system. And moreover, this, this general laws, they're going to be often universal, meaning that they're going to be many different systems characterized by the same general equations. So universality in physics is basically all what I just said. So to summarize, by universality we mean emergence of simple and general laws in a priori complicated looking systems, which is accompanied by a reduction in the number of relevant parameters. So maybe as a caveat, I should add that of course not everything is going to be universal, that is always going to be some tiny little details, which will depend on the system, but the most important things, they are usually universal. So this, this is probably rather abstract. This is just a definition, but in now I'm going to show you some examples, some concrete examples of physics systems, where this universality as I described to you is realized. And, you know, a common feature of these examples is going to be that all the systems is that they will be made out of many particles, many parts in chaotic motion. So my first example is a liquid. So what is a liquid? A liquid is made of many molecules in chaotic motion, so they're bouncing off each other there, somewhat densely packed in this box. And in this movie, in this idealized movie, all molecules have a round idealized shape, but of course in real liquids the molecules are not round balls, they can have a complicated shape. But what's going to happen is that the shape of the molecules is not going to be important for how the liquid behaves. So this is going to be my example of universality. But to see how this happens in more detail, I would like to consider this universality in liquid flows. So I wish to take this liquid and I wish to put it in a pipe. So I apply a pressure. And so the liquid starts flowing. So it, it would have been very difficult to describe the flow of a liquid if I had to follow every molecule with its chaotic behavior. So in order to simplify, I'm going to introduce average velocity. So what this means is that I'm going to take a small volume surrounding a point. So this volume has to be rather small compared to the diameter of the pipe. But it has to be still rather large so that it contains sufficiently many molecules. And the average velocity is a mean velocity of all molecules in this, in this little volume. In terms of, if I have to follow every molecule individually, and then it's complicated, but in terms of this average velocity, the flow of the liquid in the pipe behaves much more regularly, much nicer. So I have a regular velocity field. I have the velocity is maximal in the center of the pipe, then it gradually decreases to the sides of the pipe because of the friction of the liquid against the walls. So it looks much nicer. So this, this is a very idealized, very regular flow. So if I consider a more realistic flow, then, like in this movie over here, the velocity is going to have some trivial dependence on, on space and coordinates and also on time. What is important is that in any liquid, the dependence of the velocity can be computed, can be calculated by using just one equation. It's called Navier-Stokes equation. So I wrote it here. I'm not going to explain all the terms in this equation. You see here some derivatives of the velocity, you see derivatives of the pressure. But what is important for my story is that in this equation, there are only two parameters. There is the density of the liquid, raw, and there is the viscosity of the liquid. You see, the liquid was very complicated, but for all liquids, I have exactly the same equation with just two parameters. That this, that this is possible is a manifestation of universality. Okay, bye. So now, okay, now you're probably starting to see the meaning of this concept in your side and why it is powerful. But perhaps some of you are not very surprised because after all, liquid flows are not so esoteric. And, you know, I imagine many people are familiar with them. You will find that my next example, more interesting, more unexpected. So in this example of liquid, we have an equation which contains two parameters. But now I would like to discuss something which one can call total universality. It means that there's going to be no three parameters at all. And so this is something that I am quite interested in and it's something that I'm working on. And this total universality is going to be realized in magnets. I'm going to show you as my next example. And magnets, the inner workings of magnets are probably not as widely known as for liquids, so I'm going to spend a few slides so that we can develop some intuition. In a, to begin with, the very basic level, a magnet can be thought about as a bunch of arrows, which represent the magnetic field of each individual atom. And these arrows, they can point, so this magnetic field of individual atom, it can have two directions up or down. The attractive force of the magnet appears if all of these arrows point in one direction. So as here I showed most of the various point ups, so I painted my magnet. Now, if you take, if you look at these arrows and you look at two arrows which are right next to each other, then it turns out that if these arrows are misaligned, if they point in the opposite directions, then there is an aligning force which tries to align them in the same direction. So if you ever held little bar magnets in your hands, then you felt this force, you certainly felt this force. So, since every pair, every neighboring pair of arrows tries to be aligned, then you can imagine that basically all arrows in the magnet are going to point in the same direction. And then you would get a very strong magnet. So this, this is the kind of magnet that would attract other things and you can attach it to your fridge door. So this is a real magnet. But actually it turns out that this does not always happen. And the reason being is that here we are ignoring the effects of the temperature. So let me explain that the effects under the effects of the temperature, you can think of the temperature as causing some sort of random kicks to every little arrow under the effect of this kicks. The arrows vibrate. So here in this picture, the arrows vibrate, but they still point mostly in the same direction. But actually, from time to time, what's going to happen is that they're going to be two arrows which are aligned, but they will get a rather violent random thermal kick, which will disalign them. And so you see you have two effects, you have the effect of the lining force, which tries to take the misaligned arrows and deline them. And you also have this random thermal kicks, which can reverse this process and point the arrows in the opposite direction. And so, because of this random kicks. If you take a real magnet even at a normal temperature, you will see that most of the arrows are going to be pointing in one direction, but they're going to be some random flips from time to time. You can see so that arrow will flip down, then it will flip back up. So, so this is still a good magnet, this magnet still attracts things because most of the arrows are still pointing in one direction. But now, as we increase the temperature, this thermal kicks get more via more and more violent. Then, under the effects of this thermal kicks, the directions of the arrows is going to be completely randomized. So, when this happens, then this magnet is going to lose its ability to attract things because basically half of the arrows is pointing up and half of the arrows is pointing down. So this kind of magnet is going to fall off your fridge door. So basically at sufficiently high temperature, magnets stop working. And so, just to summarize what I just said, because of this random thermal kicks, the magnets, they gradually lose their strength. They become weaker and weaker, and then at some temperature, they lose all of its strength. So the strength just disappears and the magnet is no longer a magnet. So I call this temperature in this talk, of course in physics we call it differently, but in this talk I will call it fridge fall off temperature. And this temperature is important for my story because it is at this fridge fall off temperature that this total university that I mentioned is going to take place. But what's going to happen at this fridge fall off temperature, and it's kind of hard, it's kind of easy to understand that the magnet at this fridge fall off temperature is going to be very complicated. And if you took an electronic microscope, and if you looked at this magnet, and if you managed to make a movie, then you will see something like this. In this movie I see arrows up painted black and arrows down painted white. And you see that there are, you know, since they're at this fridge fall off temperature, the effect of the aligning force and the thermal kicks, they basically are almost essentially compensate each other. And if you see that there is this very complicated dance of islands of arrows up surrounded by arrows down then again arrows up. I actually personally find it quite beautiful and even mesmerizing. You can call it fractal you can call it many other words. But, but let me tell you where this total universality enters this picture. Actually, it, it enters it in in very many ways. But in this talk I'm going to just show you one way. So let's let's do this thought experiment. Let's look at two arrows separated by some distance. In this soup of fluctuating errors. So this this errors are, of course, constantly flipping up and down. Okay, here I painted them both red but they're constantly flipping up and down. So part of the time they are going to be aligned. Part of the time they're going to be disaligned. So let, let me ask, what is the probability. There are these two arrows, and I find them aligned. So probability, basically means fraction of time that these two arrows are going to be aligned. So this is going to be this probability to find these two errors aligned is going to be some function of the distance between the areas. What is this function. Think a little bit. You take to nearby arrows to neighboring arrows they try to influence each other. Now that neighboring arrow is going to influence its neighbor, and so on. So clearly, after many, many steps if you take two arrows far away from each other. And of course they feel each other but they, they don't feel each other very much so, which means that if you look at two distinct errors. The probability that you will find them aligned is going to be very small for this function that that we are trying to find is going to be a decreasing function of the distance. That much you can guess without doing any computation. But what is the shape of this function. Now, it turns out that if you take a magnet, and if you put it precisely at the fridge full of temperature. Then this function this probability takes a very simple form. It's one over the distance between these two arrows to some power, call it X. This power X, this number particular number. It's the same for all magnets. So, this number is totally universal. So this is what I mean this is the fact that this number X is the same for all magnets is a manifestation of this total university. I'm talking about. So, what do we know about this number X. Actually, we know it with good precision, but not yet exactly. So we know that this number X equals 1.03629. We would like to know more but that's as much as we know today. So you might say, if we don't know this number X exactly. How do we know that it's universal. Good question. We know that this number is universal because we know that this number is a solution over universal equation. So, recall that for liquids, we had the Navier-Stokes equation, which had two free parameters density and viscosity. So this equation which is called conformal bootstrap equation, it's totally universal it has no free parameters. And, okay, I put this equation here on the slide for purely aesthetic purposes. So I, there's no way I can explain this equation in this talk to take a separate seminar to do this. But you know, every important equation has some beauty to it so I just for this beauty I put it on the slide. So unfortunately we don't know yet how to solve this equation exactly. But, you know, in the last 10 years, thanks in particular to my work, we know that this equation exists. And we know, we know how to solve it approximately at least. And by doing so, we managed to compute this number X with some good accuracy. So hopefully, in the future, someone will be able to solve this equation exactly. But, you know, there may be something else that that's probably surprising you here, because magnets are known, of course, since time immemorial. So, how is it possible that this number X has only been computed in the last 10 years. Actually, there is some interesting history here. Actually, as a matter of fact, there's another famous method called renormalization group, which can also compute this number X. And for this method, an American physicist Ken Wilson got a Nobel Prize already back in 1982. So it's so this renormalization group method is an older method. It's older than this. New York and from a bootstrap method that I'm working on. This method is less precise. So it turns out that the conformal bootstrap method computes this number X with better accuracy. So I'm mostly working on the conformal bootstrap method, but I'm also quite curious about this renormalization group idea, and I'm also trying to understand how can it perhaps be improved to be made more precise. But in general, I think it's, it's quite exciting that there are these two different complementary points of view on on the same problem of total university, which are actually quite different if you look in the details very very orthogonal almost, which can compute the same number at which can always, and we can also explain university but from two different points of view, so it's quite, quite, I find it quite exciting. So, basically, I'm, I'm at the end of my talk. So if you have to remember just one thing from my talk, then please remember this, that magnets falling off the fridge are totally universal. But on a on a more serious note, perhaps this phenomenon of total university that I explained to you using the example of magnets. It is believed to play a role in many other unsolved problems in physics, actually, some of them quite famous. I give here just the problems there's a problem of turbulence. And there is a problem of high temperature superconductivity. I, I'm hoping that this methods and these ideas that I've been developing in the conformal bootstrap and total university in general, that they will one day also be used for solving not only magnets but also this other interesting physics systems. Thank you. Thanks lava. That was a great talk. We have opened the Florida questions there's the, both the Q&A slot and the chat slot. It's mentioned by a participant that ETER has an important use of man is of course man is have, you know, infinite number of uses of modern technology. This is for a slava floor for manual Jim, you know, any of us while we're waiting for question from the audience. Let me ask you a question slava, which is perhaps as starting in math and, you know, continuing in physics you particularly your point of view is interesting. Would you try or where would you try to draw a line between mathematics and physics and so if we refer to your talk. The, I counted three equations in your talk, and I think the Navier Stokes equation and the power law decay or physics. Now, if somebody asked you whether the conformal bootstrap was a physics equation or a math equation or both would you how would you answer them. But, you know, I, I don't think that the dividing line is so sharp, not definitely not for me. So in the equation is an equation it's, it belongs equally to physics and math. So physics may be interested in, in analyzing some aspects of the equation while physics may be interested in understanding other aspects of the equation. Mathematicians are usually so physicists and mathematicians typically analyze the same equation. And just when they see an equation, the first thought is to try to compute something to get the numbers out of this equation. While mathematicians, when they look at the equation, they maybe try to understand if, if this equation has a solution if it's equation is well defined. For example, the Navier Stokes equation is a famous mathematics problem, which is to understand whether the solutions of the Navier Stokes equation are globally mathematically well defined and smooth functions. So this is considered to be a major problem in mathematics and it is, but for practicing physicists, it, it does not necessarily strike as a particularly urgent, as a particularly urgent problem because the, whether they are or they are not well defined is does not seem to translate into immediate practical consequences, meaning that physically observable consequences. So the booster equation it is, it does have observable consequences so in this sense it belongs to the physics trial. And it also has very similar features to many equations studied in mathematics so I hope it will appeal also to mathematicians by its beauty and some structure so yeah. Okay, don't claim. Okay, good. So, so the difference is less the equation than the questions that prompts us to ask and they are interested in the questions. There are a couple of comments slash question a question about whether universality has to do really primarily with normalization perhaps quantum and statistical aspects or is it more general. So the problem points out that there's university and universality in the population dynamics and studied by Feigenbaum who even worked at IHS. Can you perhaps name other scientific context where a similar universality would appear. Oh, these are both great questions. So, in fact, one of my examples of university, they were statistical physics in in origin they were thermal fluctuations at play, but quantum mechanics is also a source of fluctuations and this quantum fluctuations they are in many aspects similar to the thermal fluctuations. Universality plays a role in in quantum systems as well. For example in particle physics, which is a quantum system par excellence it's in the vacuum of quantum field theories this university is very much at play so it's important there as well. So the second question from from Dennis Sullivan it's it's a great question indeed this Feigenbaum universality in in dynamical systems, which has been studied by IHS professor Oscar Lanford third in the 80s who did some work on it. And for me it's very, it's very inspiring because this university in Feigenbaum universality has been understood by organization group methods, an organization group ideas of Ken Wilson. But in that particular case, the mathematicians, they managed to obtain very precise excellent results, which we do not yet have as physicists applying the ideas of Ken Wilson, say to magnets. So I'm personally trying to understand why is it that in that field of mathematics organization group works much better than in physics where it was born. And I'm hoping that some improvements can be made. Very good. Let me continue a bit on the previous question. So this was about magnets and I turn I understand the sensitive question perhaps as I turn in many applications, one has superconducting magnets which are have to be kept at very low temperature just just a sort of theoretical work that you and others are thinking about help us to understand whether magnets might become superconducting a higher temperature help us in solving these practical problems. Would you like me to comment. Yes. So, so there is this nagging problem with high to see magnets that nobody basically understands the mechanism behind high to see superconductivity. And because of this, we don't actually know what is, what is the limit to high to see superconductive so people stumbled on high to see superconductivity by chance, but unlike for more conventional superconductive where we know how it works. Hence we know that limits we don't know. So perhaps there exists some much better materials high to see superconductors, which could have enormous practical application but until we know the mechanism so you can either like guess what is what is materials but trying to guess and didn't manage but you could try to understand what the mechanism is. And so people believe that that behind the the properties of high to see superconductors there exists some critical point which is what I call total uncertainty in my talk and but this is very mysterious and nobody knows yet what is like there's no good theory for this critical point quantum critical point. So, well, I don't know. I'm not an expert on this. I don't know if my methods can help but I also there's no reason why they might not help so I hope I will. That's that's right. It's a hard question out question from Leon Peshkin to you. Do you feel that biology has a different laws either they escape universality, or perhaps there's a different concept of your universality and biology. Thanks, Leon, for this question. So it's, I'm, I'm not. Yeah, I'm quite ignorant actually about biology but I know that but it is some situations, if not in biology but in population dynamics. Universality does play a role. There's a bit of exotic situation so if you look at some plague epidemics for rats in in Kazakhstan. Then it turns out that the population of rats in Kazakhstan it's governed by some universal laws of percolation dynamics, which are very similar to the laws of for magnets that they describe. As to, you know, by all biologists nowadays they, they think about very exciting problems of life and aging and consciousness for those things I'm, I don't know. I don't know if university plays a role there. Thanks.