Okay, good afternoon everybody. Okay. Good afternoon. So welcome to today's colloquium I'm very happy to have a professor on as a BC as the speaker today So I'm as a joined the high energy cosmology and astroparticle physics section of ICTP very recently just four months ago and She will be talking about It's a very interesting title the conformal bootstrap from boiling water to quantum gravity So an essay before coming to ICTP. She was an associate professor of theoretical physics at Uppsala University and She did her PhD from Niels Bohr Institute, and then she was a postdoc at Oxford and also at Harvard And now we are very happy that she has joined ICTP ICTP has been actively pursuing the policy to increase the number of women scientists on our faculty and We were happy very happy to get somebody with her accomplishments to join us. I know her She is close to she works in areas very close to my own research So I'm familiar with some of the things that she has done So as you know conformal field theory has been an extremely important tool For analyzing all kinds of physical phenomena, especially for example even in condensed matter physics The boiling water as she said at some way high pressure at some second order phase transition critical point is described by a conformal field theory but one of the really amazing surprises of the Maybe last 20 years is that conformal field theories of a very special kind are Have at exactly equivalent to a theory of gravity and this is really a big surprise because Conformal field is a normal field theory Things don't fall in a conformal field theory and it is equivalent to something where things fall and this connection Anise wrote an important paper one of one of our important contributions is to really extract properties of gravity at At the quantum level by analyzing the conformal field theory. So it's a very interesting way to learn about gravity By analyzing conformal field theory. So I hope it's probably one of the topics that she will come through towards Maybe end of her talk So, so I'm very happy and there's a floor is yours. Thank you very much. Thanks Thanks for So thanks for the nice introduction and for giving me the chance to talk about my work and what I'm Working on since the last 10 years almost So actually a tissue spoiled all my talk But I'm very happy that at least we are all on the same page. So I would like to start this talk by something that you might be all familiar about.  So Here you see the pressure here. You see the temperature. So in this part Here the water is like solid these two lines in between these two lines water is liquid and all in this part here the water is on his vapor face and Actually, you see that these lines they go up here But the face diagram here stops and this is not a type or a problem of my drawing here actually the Face diagram really stops and this red point is very important and it is called Critical point So let's try to understand why this point is important and essentially the next 10 or 15 minutes are devoted to understand why this point is important and what are the property of this point here so This is this critical point is the end of the face equilibrium curve and in the neighboring region of the critical point the physical property of the Liquid and vapor which are the two regions which are close by the critical point to change dramatically and The faces so the liquid and the vapor they become very very similar to each other so the idea is to understand again why this happens and why And how we can describe this critical point more in detail. So let's try to understand again a bit better that So in order to see that Oh, sorry, we would like to To study some fluctuation of the fluid density which I will denote by this DRO here. So you see that Here we are studying this fluctuation at different positions and we see that actually if we go to longer and longer distances which are Measured by this parameter psi, we see that these fluctuations behave in two very different ways So in particular, we see that there is some Exponentially suppressed behavior here where when the distance is much larger than this parameter While there is this power low behavior when the distances are much smaller than this parameter psi this parameter psi actually changes As this very interesting behavior when the temperature goes to the temperature of this critical point So this TC labels the temperature of the critical point here. So this is the Coordinate of this point TC here now when T goes to TC this Correlation length become infinite So what does that mean? It means that near the critical point and at fixed pressure They correlation length diverges. So it means that all the scales of our problem drop out now From this kind of Relation, it seems all a bit abstract. So in the next slide, I would like to show you a Simulation that so this is a real simulation that has been made by this person here I'm not sure if this slide will be available But you can click here and go to the person who made the simulation and here we can see that there are three Blocks, so this is again the critical temperature and we see how if we zoom in or zoom out from the system So this is exactly the same system that I had the critical Sorry the face diagram before and you see on the left. We are a bit below the critical temperature on the right We are a bit above the critical temperature. So let's see What happens? So here we are essentially you see this B is denoting how much we zoom out So we go we go we go and we are evolving to some situation in which We have this kind of equilibrium. So we go a bit above So you see we are not very far from the critical temperature and you see that now we go into another phase So we have to think about the white dot to some Vapor phase and to the black dot as the liquid phase so instead of the critical temperature You see that nothing happens if we go it seems that we are repeating are repeating the same pattern So this is very interesting Maybe I didn't put the video until then this is very interesting because we see that Exactly you have to be exactly at the critical temperature that something happens. So there's something that happened It's essentially that the if we zoom in or out nothing changes So we see maybe we can go back for a second. So we see that Here while here we go to a some very order phase at the end of this zooming in and out and on the other side here If you remember we had some like all black Configuration so here we go to a very disorder phase When we are exactly at the critical temperature, we keep seeing exactly the same object This goes again in the same description that I was saying before that essentially when we are exactly at the critical temperature Lord the scales drops So if we are very very close to the system and very very far to the system We exactly see the same patterns and this is what this simulation is showing now the Another important feature of this kind of point is that Critical exponent all the critical exponent that we see before we saw psi we saw new They describe the behavior of physical quantity near continuous phase transitions are all divergent So all the critical exponent s t goes to tc. They are all divergent And also there is something else that if we change the kind of substance that we look so in If we take different liquids for instance or superconductors While the phase diagram that I show you before is different We see that the critical exponents are the same so the PC and tc may be very different But this exponent psi that I show you before eta that I show you before they are all the same This goes under the name of Universality which makes this critical point even more important Because we can study this critical point only the critical point to kind of Discuss all this correlation length that I show you before for a lot of systems so What I would like to to discuss in the next few minutes is to understand why there is this Universality the specter fact that we are talking about very different systems So Okay, this is what I said So for instance if we consider water this this is what we show before This beat has been measured to be this number here but if we go to the spontaneous magnetization of uniaxial magnets while these TC is different from the one of water we see that the behavior of these Mt which is the magnetization is of the same type and in particular this beta is exactly the same number So as soon as we find a way to compute this beta We are able to describe this d row t But we are also able to describe the magnetization of uniaxial magnets So with a number we can describe a full range of systems So why this is the case? Why can we describe so different systems with the same class of numbers? so the reason for that is that those here I Put this drawing of boiling water here. I put the magnets they belong to the same universality class So this seems a triviality, but what does it was that what does it mean? It means that while the models are so in particular in this case Water and the magnets at finite scales are very different So you see it already from this picture that these two pictures are very different in the vicinity of the point they the In the vicinity story of the critical points the asymptotic phenomena which are described and modeled by the critical exponents are the same and In particular again in all models falling in the same universality class We have that the critical exponents are the same So when this happens actually this always signals some symmetry which is emergent and in this particular case The symmetry which is emerging is a scaling variance You could have thought already about that from this small video that I show you So you saw that when you were very very close to the system of very very far as before like when we were going We are zooming in on zooming out to the system before we had that in the middle Panel here where we were seeing the same object we had some scaling variance so because nothing will depend on the scale any longer and Actually, this the scaling variance in this invariance under rescaling which are dilation of all coordinates by a uniform factor So it's essentially scales all the coordinates by us the same factor, which is this lambda here Okay, so a class of transformation which are scaling variant Are called conformal transformations which are the transformation that I will be interested in and those kind of transformation are pretty interesting because while they do not preserve distances they do preserve angles and The way to think about this transformation I will see I will show you another way of thinking about that a bit later, but essentially at each point to locally they are Described by a rotation plus a dilation with a rescaling factor, which depends on the axis So is what we saw before but they rescaling this lambda depends on the points where we sit and in particular in 1970 Polyakov conjecture that the scaling variant theories that describe the critical points are actually conformal invariant which is something that we are going to discuss and Again now we see that the description of Fixed points so the fixed points that we show before which are scale invariant boil down to Classifying all the conformal field theories and what I'm going to do in the next part of the talk is to understand how exactly to compute these fixed points and So here to Let give you a maybe a better idea of how this conformal transformation work I put this This map so this is a map that comes from the 16th century by this guy here, which actually I Discovered while preverting stock that this is not his name. I don't know why it has been Latinized so he's a Flemish Cartographer which was called the Kramer but now we know him as Gerardus Mercator and This guy was the first person who did the conformal transformation in order to find Maps and it was the first person who Gave the name of the Atlas to what we call Atlas now. So you see here that So the objective of this guy was to make maps which were very useful to sail So he wanted to have the maps useful to sail So what is very important if you want to sail is to understand the what are the angles that you need to to Maintain so he decided to have this 2d map in such a way that the angle were preserved But as you can see shapes are not really preserved because there is some distortion and the distortion is bigger and bigger As we go to the south and north pole. So you see that the south pole is much bigger than we expect to be so this is an example of a map which is conformal and There are also still now. It's not something that ends in the 60th century. We use this kind of map to sail So in particular Yeah, you can see how things are are changing from the equator north and south Okay, this was just to give an idea of what the why this conformal transformation can also be visualized a bit Again, so let's go to the second part of my talk, which is how can we find this critical exponents? So now that we understand why they are important. How can we find them? So the idea that I'm going to describe is an idea which is based Mostly on the symmetry. So the idea is to use the symmetry of our of our system in order to Understand how to fix this critical exponent. So in particular, I'm going to use strongly this Universality, which means that we I we don't think we don't need to think about the specific realization of the System that we talk. So in particular, I'm not going to discuss water or magnets. I'm going to discuss a specific I mean a general Theory that has the same symmetry So in particular, we are going to study conformal theories Using an approach which is based on symmetry and with little or no input at all about the Microscopical description of the theory. So studying conformal theories means that we need to classify all the possible conformal theories that we are going to discuss. So this is just a scheme. I'm going to Say later what that means and from here we can sorry we can find all Or at least some of the critical exponents and with the symmetry We are using the fact that our theory is conformal invariant and that exists a special Object, which is the operator product expansion that I'm going to discuss later So on one hand we would like to find the critical exponents which will Characterize all our system and on the other hand we are using the symmetry So on the right side of this slide you see the symmetry that we are going to use on the left hand side We see what we are going to get Okay, so let me start by Specifying a bit better. What are the observables? So what we are going to study in these conformal theories and in particular The conformal group, which is so d comma 2 where d is the number of dimension is generated by Translations so the usual translation that you know Lawrence transformation Which are essentially this Related to the spin or so to the rotation dilation which are the transformation that I discussed before so which are Where you go from a point and you dilate with a factor your position And then some special conformal transformations which are the one that I was trying to discuss later So those transformation are essentially an inversion of again the coordinates Combine with a translation and then inversion back So this is somehow the way to think about special conformal transformation. So This is the symmetry so those are the generators of my transformation, but now how can we describe Objects so the observables in these theories. So we have operators So the operators are labeled by two number these of these delta here and the li what are these objects? So delta is related to the dilation. So it tells us how How these operator changes under dilation and this li which are is that they're related to the Lawrence transformations in addition to that there are What we can say interactions and those are related to this Operator product expansion that I was telling before so we can take two operators and Understand how what happens if we bring the two operators close to each other. So in the case of our conformal theories so we can take these Two operators one is labeled by i and j that essentially encode both these two numbers here And we can expand these two objects in terms of another operator here This okay, and then here we have a number a set of number which depends on the two operator that we are bringing close to each other and of the third operator that we have on the right-hand side and This function here this f which depends on the position where these o seats and this o j seats and Okay sits and the dimension and the spin of all these three objects Sorry forgot to write that it depends also on the spin But the most important point you don't need to remember anything about that Just the fact that this function is completely fixed by the symmetry structure So this c is not fixed by the symmetry but this function f is fully fixed by the symmetry and Pictorially you can see that in this way. So you have this o i o j then you bring it close to each other This point is this c i j k and this ok is the other operator that you get so you can think about Having like writing this object As an infinite sum over all the possible operator that appear here and then instead of having two operator You essentially have an infinite number of other operator with this weighted by this number here c i j k and Again this object here is completely Fixed by the symmetry notice that you may know Feynman diagrams Maybe and these object is not a Feynman diagram. So it's just the same way of Writing it, but it doesn't have anything to do with Feynman diagrams. Okay, so this is the operator for that this function that He's acronym is OPE Okay, now we would like to construct again the correlators which are really the observables of this theory and actually the conformal symmetry is strongly constraining two and three point Correlators, so in particular you see that two point correlator is essentially fully fixed in meaning that is completely Kinematical so if we it depends essentially only on the on the coordinates and Of this delta o this delta o is the number that I was showing you before Which is called the conformal dimension which essentially is a property of the operator that we have in our correlator So two-point function is essentially fixed that three-point function are all also fixed up to this number here Which is called the three-point function coefficient now you can say okay, but we have already seen this number Why do you want to use the same? Same letter to denote two different sets of number, but actually that's not a typo those numbers are exactly that OPE coefficient Coefficient at the tenth are saying to this expansion here So the three-point function you can clearly see maybe from here So if you put another object another operator here We you get exactly the CIJK and this three-point function coefficient are exactly the same of this object here so again two and three-point function are completely fixed as soon as we specify the operator and the OPE Which is again completely dictated by the symmetry of the theory for instance. I wanted to show now how this Delta sensei are related to critical exponents because remember again that we said that we wanted to understand The critical exponents that we had before so in the case of the icing model Which is the one that I show you at the beginning like the one of water and the one that we saw there the small video the dimension of the of the first Operator that we have is one half plus it over two so eta which was Which we saw in the very first slide is exactly given given by a dimension of one operator that we appear So this is the way of from the dimension reading off The critical exponents so there is a map between the dimension of our operator So we can compute the two-point Functions which are again observables and then we can read off for the critical exponents and Again those critical exponents are the critical exponents of all the universality class of the systems that belong to That include the icing model Okay, now let's go to the next point. So what happens to four-point function So we saw here in this slide that again this space-time The space-time part of the two and three-point function is completely fixed what happens to four-point So conformal symmetry is not strong enough to fix completely the correlator of four points. So now here to avoid cluttering the formula I completely removed the Letter down I jk. We assume that all these objects are identical and the only conformal symmetry what it does it constrain this Correlator to be a function of some UMV and UMV are just this combination of distances over this Factor and again it depends on the conformal dimension of these objects here and UMV are at this form because again this is dictated by the conformal symmetry and The Four-point function is the first one which contains some dynamical information which is encoded in this function g of UMV now we can say okay, but why don't I use the Information that I said before meaning why can't I think about expanding using the operator product expansion of these two Operator into an infinite sum of one operator and the same thing On the other two operator and this we can do that. So let's try to do that together So we can take these two operator bring them again close to each other and expand it and then we get this This kind of diagram that we saw before We can take also this other two operator and do exactly the same thing. So we gain again two factor of C's and We gain also an infinite sum So now the way that I'm labeling this object is again through the dimension and the spin of this operator that Appears inside the operator product expansion. So we can rewrite a four-point function as an infinite sum of coefficients of this OP coefficients or three-point function square so we get one factor of C each time that we do an operator product expansion and Another function this function. So this we get it from the definition of this function G that I show you before But this function G delta L U and V It essentially encodes these two functions F that I had in the operator product expansion But again, you don't need to remember anything of that The only important point is that this function is completely fixed again by the symmetry So as soon as we specify the symmetry of our problem this G is completely fixed So the only information that we don't know is this C square and this delta L Which depends on the kind of operator that we have inside So this function of this object depends only on the theory that we considered and the number of the space-time dimension That we are in and on the kind of operator that is inside here So we manage essentially to rewrite the four-point correlator in terms of an infinite sum of three-point function and two-point function Because remember that this dimension and L here can be written in terms of Can be rid of essentially from the two-point function So we reduced a four-point function into an infinite sum of three-point functions and two-point functions Okay, so now why am I doing a lot of fuss about that? Because we could have done also another thing. So the operator product expansion is associative So what can we do? This is not very hard to do But what can we do? We can take this OP here as I showed you earlier, but I can also so which essentially does Can be like pictorially depicted in this way So we are taking this X1 and X2 is denoting the fact that we are taking the OP between these two operator and X4 And X3 are these two other so we can we take this OP here But we can also take another OP Which means that we consider we take X2 and X3 and X1 and X4 So like this one here and these two expansion here That should be identical because again the operator product expansion is associative and on and on the other hand These two four-point correlators should give the exactly the same result So these two kind of expansion that should be completely identical So let's try to understand if this equality brings us some kind of Way again Our objective is to find this delta and L and the three-point function coefficients so Sorry another way to write this object is to to write it in this way So remember this left-hand side that is the way So the left-hand side is this object here if you remember this object We can be written as an infinite sum over delta and L of some coefficients this C delta and L times this function g uv and The right-hand side is exactly the same object where Here we have just the exchange of v with u because this is essentially a symmetry when we take When we take the different OPs, this is just a kinematics It's very simple to see but I didn't want to write it here to clutter again the relation But this is just a relation in formula of this picture that I have before and This u and v to the delta O comes let me go a bit back maybe So this comes because if you remember the four-point function is also this term here So now you and we are this object. So if we swap The label 1 with 3 we swap u with v and we also get this extra factor Which is essentially the u over v to the delta O that we have in that relation there But it's not it's not super important for what I'm going to tell Okay, so this is essentially a consistency condition on this Object here so on the c squared and L and on this delta and L here notice again that these functions G of u and v and v and ur are completely fixed by conformal symmetry So those are fixed that the only thing which is not fixed is the c and the deltas This fun this relation seems very simple So it can be it can seem that is completely useless that we don't Really know what to do with that. But actually that's not Very true. So in particular, let's look better at this equation So the first thing is that on the left-hand side and on the right-hand side there are infinitely many equations So you see that there is this sum here sum over delta and L and This sum runs Over delta and L which goes from some value to up to infinity So there are infinitely many equation and also they conformal dimension. So this number delta is a real number so This sum is infinite and over real numbers. So this is the first complication of this equation here The second complication is that okay, you can say I can truncate this sum here up to a certain point Let's say I cut it Until 10 and here I cut it until 10 and this should be satisfied. So I don't really I can simply Find some c squared and some deltas from this consistency condition But that's not actually true because one term on the left-hand side Is not mapped into one term on the left-hand left-hand right-hand side Sorry because remember that here this function is different on the left-hand on the right-hand side So you have U, V and V and you actually One term on the left-hand side is mapped to a infinite infinitely many terms on the right-hand side So this property is Is makes these relations much more complicated to solve but actually this is very interesting and we will see later why this is very interesting and The third thing that I want to mention at this at this point here is that This relation here does not depend on the microscopic description of the theory what that means It means that I don't need to specify again if we are talking about the water or the Magnets or any kind of system that I'm talking about. I just need to talk to say which is my Symmetry group and that's it essentially just to specify what is the number of space-time dimension that I'm working in and Then I don't need to add any extra input about the specific theory In particular in general conformal field theories can be strongly coupled So I don't even need to I don't need to be in some perturbative regime or anything like that so those are valid that any value of Of the coupling constant or in general for any particular microcovic description Okay, so now let's try to understand how to use this relation. So those relations are pretty old. So they are maybe I Don't know how much about 50 50 years old and So for 50 years We don't know really a way of completely solving them in our In general form So we don't know how to find c square of delta L and delta from this relation here So we don't know really how to solve them in full generality But we have two ways that is what I'm going to discuss in the next ten minutes to Find some solutions to this equation Okay, so again, I want to stress that the unknowns of this relation are the c-squares and the delta NL So there are some particular theories some particular case So which are where the when the theories are unitary for which this c-square delta NL Are positive which means that the c are real numbers and for this particular case we can think about This this problem in a slightly different way So I don't want to enter much into the details But I just would like to let you understand the procedure that one can use in order to find some Information about this delta NL here. The only thing that again I'm assuming in the next few slides. It's the fact that this c-square delta NL is a positive number Okay, so the machinery is called again conformal bootstrap I'm going to discuss a bit later what it means about the idea is that we would like to find some Solution to this equation here. So at the end of the day, we would like to understand What are the delta NL by assuming that the c-square delta NL are positive that fulfill this equation here Okay, so the idea is that you can hand Some a box where all these balls are dimension and Spin and Lawrence Quantum number of a particular theory that you like you just put them in a box Then you take one of these blue Ball which has associated to eat a delta one and an L one So those are the dimension and the spin of this object. Then you put your ball To you give it to some scientist and you ask is this Operator which is denoted by a delta one and L one part of a CFT or not. So is this Operator does this operator belong to a CFT or not then what the Scientist do they put it into some computer. So you run through another an optimization problem And the kind of answer that you can get is yes, sorry, maybe it does No, it doesn't so that's the kind of Procedure that you have in order to to use this consistency condition notice that this is not So here I didn't put maybe because I felt pessimistic, but just because this is what he can give so he can say that those kind of relations are Do not allow to say if For sure they come from a conformal field theory They can only say that maybe they can come from a conformal field theory But they can ensure you that they cannot be part of this. They cannot be consistent with this relation here So if you get from the computer Sorry a pink Ball Then you are sure that the ball that you were that was coming from the box here Cannot come from a CFT so that you can iterate here in this slide I just show you that for One of these balls, but you can keep running the computer until you want and you will get some maybe no maybe no and so on so the kind of Usage that you can do of this machinery is Into it can go into this Into these plots so these plots has been made by so that this numerical way This optimization procedure has been revived by this group here Eric may be seen the room, but surely see interest so it's Here is a local person and The kind of plot that you can get so is here you have some dimension delta sigma Which is related to this delta sigma that sorry this is delta epsilon This is delta sigma and the way to think about this diagram is to say that Sorry, let me not spoil so that this purple regions are filled my babies and The white regions is from no what I mean is that if you have if you want to describe Dimensions of operator that belong to a conformal field theory. They cannot have a dimension which is smaller than 1.2 in epsilon by fixing delta sigma to be 0.58 while if they are here Then they can come from a conformal field theory now the point is Do we know any theory by say by assuming some other information that are In this plot here and the answer is yes So the 3d icing which is essentially the three-dimensional counterpart of the model that I was showing before is exactly in this region here So we can use despite the fact that this is just a maybe no plot So we can use this information to zoom in into this cross here to read off the critical exponents of the 3d icing so Though those are this is the way of to think about that before so you can run this procedure you can get all this Green and pink blobs Okay, so this is very nice because again by just we didn't assume essentially anything and we were able to find At least the regions of possible critical exponents again Those are numerical ways of finding this this regions another way is to use analytic methods again The the problem in this particular case is that there are these infinite sums that I show you before and That one term on the left-hand side of the relation that I show you before is not mapped into another term on the right-hand side But the idea is that can we overcome somehow this problem? The answer is yes We need to focus on a specific kinematic regime by kinematic regime is a specific Regime of you and me where those sums simplify So this is a very technical topic. I don't want to go into this Technical topic, but I wanted just to show you one thing which I think is very important and very nice so By focusing on a specific regime you can focus on the contribution for instance on the left-hand side of this equation of The identity operator so inside this operator product expansion There is also the identity operator at actually in particular the identity operator and this counts as One term on the left-hand side and we see one can actually compute that by assuming the fact that you have the identity operator in one of these Operator product expansion we see that we need to have an infinite sum of operators on the right-hand side which have Large spin meaning a spin that cannot be finite so the presence of the identity operator which always appear in this kind of operator product expansion is Ensuring us the fact actually is forcing us to have infinitely many operators which has to which need to have a Spin which has to be very very large. It cannot be finite Okay, this is This may seem like a very simple exercise to do, but it took again from this 73 to 2013 to be established completely The same The same machinery can be run for a lot of systems and in particular He can it is possible to reconstruct in some cases the full Correlator in some other cases part of the correlator and this works Sorry, this works much better in the presence of some perturbative parameter meaning that for instance you can take Some parameter in your theory, which can be whatever then this Perturbative parameter you can tune it and you can see that in If you have a perturbation expansion you can reconstruct the One loop to loop expansion and so on by looking at previous order to using again the same method This is a super technical issue that I didn't want to discuss in this place But if you are interested I recently with some collaborator wrote a review about that so this just to say that it is possible to do this kind of procedure and There is a lot of topics that have been approached by this method here But now I want to quickly go to gravity because now you can be very confused actually a tissue ready It's pulled a bit, but you can be confused why we are talking about water now You want to also talk about gravity? Let me just mention in a couple of slides Why gravity and why we really care about Quantum gravity in general also general activities are classical theory and in particular it describes How gravity work and in particular gravity is due to the shape of space and time So we can describe how Heavy objects move actually all objects, but in particular heavy objects move into Into space time and the the essence of gravity is related to the shape of the space time On the other hand we have quantum fish theories which are based on quantum mechanics And they describe how matter and strong weak electromagnetic interactions work So in particular here we focus on very big objects and massive objects and here we focus on very small object In particular, we go to very very small scales But there are particular case in which there are situations in which quantum fluctuation of the geometry Are important so for instance at the beginning of the Universe or in the vicinity of black holes where we would need to have the two description together So in particular we have very massive objects, but in a very tiny region of space so in particular the two Description need to merge but to do this merging dismerging is what has been dubbed by the name of quantum gravity because we would need to go into the Quantum regime of gravity is very hard to achieve in particular if you want to use some naive Method of taking into account the quantum correction to the Einstein gravity Which was the general relativity that I depicted here. You don't get any consistent result In particular all the object that you would like to compute are affected by infinities So if you it's impossible essentially to compute anything that you want to compute But actually there is a way that is what Tisha was mentioning before which is essentially a definition of what Quantum gravity is and the idea is that there is a story. There is an equivalence between a theory of quantum gravity which leaves on Curved space time which is under the sitter space to a conformal field theory Which lives on the boundary of this space here and those two theories are essentially the same theory and in particular which is the most important part of this slide here the observables that you can compute in the theory of gravity and the Observable that you can compute In the conformal field theory are exactly identical. So this provides us an operative definition of what Quantum gravity is. In particular since I already talked for 50 minutes about conformal field theory now we know how we can construct the Observables on the conformal field theory side. So by using this information we can read off the observable on the theory of quantum gravity. In particular, I mean I'm not talking about Very exotic things. These things have been computed for ages in some regimes. Now, there is one regime that where those these correspondences been very little explored and is This particular regime is very important in order to again use it as a Definition of quantum gravity. So let me just briefly sketch and then I will conclude how to do this kind of Computation and how can we think about this object? So we can again think about Space this is just an illustration So we have a gravity inside here and we have the conformal field theory at the boundary So what we can do we can use Again this analytic and numerical techniques that I was showing you before to the Conformal field theories that lives at the boundary of this object to infer information About the observables of the theory of quantum gravity here. So in particular we are able to compute This kind of a four-point amplitude. So I don't have a lot of time to discuss what they are But those amplitudes are observables in this theory of quantum gravity here so again These two theories are completely equivalent. So if we are able to compute the correlator At the boundary of this theory. We are able to infer information about quantum gravity again The techniques that one can use are Exactly identical to the one that I showed you before at least I sketched from the analytic side and I didn't write any References to this page because otherwise it would have been filled of name instead of this picture But this has already been carried out. There is still a lot of things to be done So computing this object. It was completely unattainable until a few years ago and Now with this technique by looking essentially at the symmetry of this theory So these theories in particular that sometimes You can study them also in the presence of another symmetry, which is called the super symmetry Which is even more constraining and this power Gives this extra symmetry gives us a lot of power and we can completely reconstruct This first box here. We can completely reconstruct the say Not completely we can reconstruct a part of this object and we have a way also of attacking all the other Objects. So this blob are essentially we can have a perturbation Theory along this line here. So this is the simple thing. This is the next to simple This is the next the next to simple and so on so and the idea is that we can completely reconstruct this object By knowing this one we can completely reconstruct this object if you would know this and this and so on and so forth And this is again something that is completely unattainable with any other technique that we know now Okay, so I don't have enough time and also I would need to have more technical ground in order to discuss how to do that in practice, but this Come let me to come to my conclusions. So what I hope I have Told you is how To essentially use this machinery of the conformal bootstrap despite the fact that I didn't really discuss how to do that In practice, but I hope I gave you an idea of the fact that there is a machinery that Allows you to find the critical exponents and to find at least in the numerical side Some constraints which are completely rigid and robust so they don't depend on any perturbative expansion And also one can find some analytic In analytic way these Critical exponents for a lot of class of theories so here I show you the magnets the boiling water This is supposed to be some superconductor. I just Google it. I don't know if this is correct And also for for instance black holes and those systems of quantum gravity. So thank you very much Thanks. Thanks and easy for this nice talk Okay, the floor is open for questions. So thank you Given I was wondering what if there is a Understood comparison between the applicability of the analytical versus the computational methods So given a theory and a symmetric content Is it clear a priori which route will be more successful in providing the more meaningful constraints or one has to try? You mean at the difference between numerical and analytic approach It depends on if there is so a priori I would say that The numerical ones are surely efficient to give you an idea of where there are Theories or not like you there can also be that I don't know There is only one theory into this realm for instance. There can be like a purple only a purple point in your in your Numerical side like in your numerical scan and then you can focus on that particular Articular theory by using the analytic approach. So you can use the numerical Techniques to scan to all the possible theories that can that you can have and then you just focus on a specific theory This is just more ideal way of behaving the other The more realistic ways that if you have some description for instance You have a theory which you have a large parameter which can be for instance You have an extra symmetry like an extra global symmetry There is the rank of the symmetry group But then you take this rank of the symmetry group and you do it very small rank or very large rank So you can take a perturbed of expansion around this parameter And then this is much more efficient to do it analytically because you have some parameter that you can control But if you don't have this parameter usually applying analytic results is very complicated. So I think that's a bit the the the way to think about Here Yeah, I mean I got missing this numerical part because you show this maybe So how you really know that you get the a conformal field theory because otherwise Then how you connect with the gravity side? Yeah, so I don't know. That's why I wrote maybe It's really a real maybe like nobody knows You need to have extra inputs to say if it's a yes or a no in the maybe Actually, no, if it's a yes or a maybe again So the way for instance for the quantum gravity how it works is that you can compute so in general there is this symmetry which is called a supersymmetry that fix some other Critical exponents or conformal dimension so you can take these numbers that has been already computed using other methods And this fix the point the region of this space where is Where they maybe becomes yes But you are not sure that in the region where it is maybe is yes or No in general. So there is not a priority. There is no way in which you can access this point Sorry, I didn't hear Yes, if there are other symmetry you can think about that But if there are no other symmetry, you don't know if there can be region So another way of thinking is that here I show you the consistency condition only using one correlator So the operators are all identical You can take correlators where the operator that you have are different So you can take a one or two or three or four and then you can study all these correlators together Usually what this study does so the consistency of all the possible correlators that you have in your theory is much more Constraining than one single correlator. So this region they just shrink Into smaller regions in general the problem is that this computational is much more Heavy so this requires Lots lot of time and other things but another way of shrinking the region is is that So and this you can see for instance if there are other symmetry you can even shrink the region more So that's another way You showed in the beginning an exponent that was zero point three two five something and it seemed come to come out of a measurement But from your talk, I assume that you are able to calculate this from some So did I miss this did you calculate this number using this theory or did you confirm this number? Yeah, so This is if you if you go it depends in the case of water Yes, you can do that the point is that the Number that I show you it has been Calculated using some Monte Carlo or lattice simulation that you can find and indeed that you can confirm that actually you can Find it even with more accuracy that the previous that the previous Computation using Monte Carlo a lot is because again you can use this multiple Correlators or not to really with the meter that I was showing but if you can use more Correlators but again using the same idea you can you can contrast it with the result that was known. Yes There's a question here So I don't work on this at all When you We're showing the consistency conditions. He said it comes from the associativity of the operators So if the operators commute does that give you more consistency conditions and a more rigid theory And then I guess on the opposite side if the operators aren't associative then what where do you where do you look? okay, so In all conformal field theories that they open the piece associative So the the only problem that I didn't discuss because it's a bit technical is the region of Where this expansion is defined? So this is not true for all the values of x you need again to be this expansion is true when the two The two points are close to each other So there is a regional convergence of this of this OPE. So this is an asymptotic expansion. So you need to be in a specific region so the Issue that I didn't discuss is the fact that those consistency conditions are true if both the OPE are convergent at the same time and What it has been proven is that there is a regional convergence of all the OPEs that are in place So there is a regime in which one can use the associativity of both these operator product sponge this I didn't discuss it's a very important issue and But it's pretty technical. So I didn't want to enter into this thing But there is a regional convergence of the two OPEs and the OPE is associative for this kind of theories here Can we we can take a last question the director is No Okay I have a very nice question like if you if I give you like Say theories A and B would you be able to tell me like whether or not they would lie in the same universality class? Like for example from some microscopic You need to see how they scale where the T goes to TC you need to go to the very first slide that I show you and You have to see how how the correlators behave essentially and then if you you can find that that they have the same The same coefficient then they belong to the same universality class This is one answer The other answer is that if now that we understood that you need to look at the symmetry of your theory So if the symmetry group is the same Then they are the same theory essentially they fall in the same universality class So you can look at the conformal symmetry that That Describes the critical point in order to say if they belong or not to the same universality class But you could also find that the correlators One last question No, I just wanted to ask you what is the current status of recovering Loop corrections to gravity. I mean, where is where is this program stand? So far in the picture, maybe I can go back here So far this has been I would say computed this is The last paper that appeared two months ago Essentially Tells a recipe on how to compute completely this but there are some coefficients that cannot so this requires an infinite set of stringy corrections and those are not all Computed but there is a recipe to fix them using integrability and localization So you need to use other symmetries, but you can essentially compute that these Only few bits of this are known Okay, and so it is a tradition of ICTP that after the I mean I tell for the students but also for an easy that so the others Leave but the diploma students stay around that you can ask more Private questions to But the food that will stay for you outside so and let's thank and yes for You


Electricity flows through our modern world, empowering us to do a million things that make life possible and a million others that make it worthwhile. It is the energy that has barred development across the world and today it is the vital force that is transforming India, a country of more than a billion aspirations into a global economic powerhouse. Energy security for India is really about seeing the bigger picture of power. With electricity demand expected to leapfrog in the near future, the need is to develop a holistic vision of energy, a vision that maximizes energy security while addressing climate change issues by integrating India's diverse energy options. Several part-breaking reforms have put India on the fast track, realizing the vision of an efficient market-driven power sector, opening a new horizon of opportunities. Generation companies are no longer dependent on power purchase by the state electricity boards. Private producers cancel directly to industrial buyers. Captive power generation is allowed. Open access to the transmission and distribution system for all generation companies and end users. The huge field of power generation has been entirely de-licensed, with the exception only of hydro and nuclear power. The new climate has seen many private sector power generation projects take off and major players have eagerly embraced the new opportunities in power generation. There's a huge amount of capacity going to come from the private sector. In fact, in my opinion from 12th plan onwards, the private sector would be adding more capacity than the public sector in this country. Now you see almost about 15 to 20 new players in the power sector coming into development of power projects in the form of IPP. Whatever number of players you bring in, the power is so large that we don't need to worry. There's enough business for everybody. I think this is the direction in which if India continues to move, it will attract greater and greater investment from firms like ours. We see a big change in investor attitudes towards India and its power sector in particular. 14 ultra-megaprojects of 4000 megawatt each have been announced that will go a long way towards bridging the energy gap. Special purpose vehicles or SPVs make these projects truly hassle-free for investors. The concept of ultra-megaproject is that the Government of India would do the development of the project. It brings to a particular shape, then hands it over to the private sector. Each power project consists of 4000 megawatt, about 4 billion dollars. Other opportunities include coal-based plants at pitheads or coastal locations, natural gas or CNG-based power plants at load centers, idle power projects to generate 150,000 megawatts, the renovation and modernization of existing thermal and hydropower plants and transmission network ventures for an additional 60,000 km2 by 2012. Supplementing all this is the development of infrastructure for coal washeries with clean coal now becoming a mandatory requirement for all producers. This environmental friendly measure is also going to be an important emerging investment opportunity. Private sector participation with 100% foreign equity is permitted in all these opportunities. The total value is 150 billion USD over a five-year horizon, one of the largest infrastructure investment opportunities in the world. One of the areas where the impact of the new power environment can be clearly seen is distribution privatization. An example is Delhi, where private distribution companies have transformed the infrastructure as well as the consumer interface. New equipment, a fully metered network and efficient courteous employees backed by the latest in electronic data management and monitoring are changing the entire profile of operations. We have spent almost a billion dollars in upgrading the network of Delhi. We jumped from the really old ages into the world-class network. A spate of recent IPOs of both public and private power sector companies have been major successes in the stock markets. Profitability of these projects has become very, very visible and that has impacted investors from across the globe. With the Electricity Act authorizing de-licensed stand-alone rural power generation and distribution by village councils, rural India is being empowered to achieve self-sufficiency in meeting its power needs. Nuclear energy is hardly a new area for India, but it is an area that is poised for major growth. With new agreements signed with the United States, France and Kazakhstan and new framework for agreements with Canada and the United Kingdom being evolved, this sector should play a larger role in India's power profile in the coming years. American nuclear companies are anxious to participate with their Indian counterparts in the expansion of India's nuclear power sector. Rounding of the picture of the new power in India is the all-important issue of energy conservation, alternate and renewable energy sources in an era when emission controls and climate change issues have become important. India has a strong wind energy program. Suzlan, an Indian company with a global presence, is one of the top-ranking companies in wind energy across the world. The country has also launched the National Solar Mission for Harnessing Solar Energy with an addition of 20,000 megawatt of solar power by 2022. Instead of having one power station centralized somewhere, we can have practically every house acting as a powerhouse. Moza Bear, another Indian company, is a significant global player in solar photovoltaics with state-of-the-art manufacturing facilities. This is to say nothing of the successes in areas like biomass, biofuels as well as micro-hydro-products. Alternative energy in India is set to go mainstream. As the message of energy conservation goes out to millions of Indians through these high-profile campaigns, consumer behavior is beginning to change. As we move towards the future, we are also looking at power transaction services that maximize market efficiency. India is one of the international pioneers to have made power a tradable commodity with its own dedicated power exchange adjusting prices early through competitive bidding in the open market. One can buy and sell power even as low as one megawatt even for one hour any time of the day. The market linkages are being matched by physical links in the actual infrastructure. Today, power in India can move freely to where it is needed, when it is needed. By developing a synchronous, unified national grid, India is building a unique flexibility to link suppliers to consumers across the entire length and breadth of the country. As India moves rapidly to its rightful position as a global economic power in Asia, the power sector is charged up with an energy quite unlike anything in its creditable but checkout past. The new economy has matured from its tentative start into a confident reality and in this vibrant market-driven economy, the transformation of the power sector is really a transformation of the entire country an empowerment unlike anything ever seen before.


Hi, welcome to Seymour's World Commentary. The title of our show today is Can You Do the Impossible? What does impossible really mean? Is anything truly impossible? Humans can't fly, but the Wright brothers proved an airplane could get us close enough. When I think about the impossible, I don't really worry much about the undoable. I know I can't jump off a cliff and start flying. I know I can't close my eyes and teleport myself to China. Picture for a second your own life and your own dreams. What are those things that you've always wanted to do that seem completely impossible? Now hold that thought for a second. Is it actually impossible? Or does it just feel impractical because you don't think you can't do it? Possible for someone else perhaps, but not for you? There's the problem. And the solution, believe it or not, isn't all that complicated. It's commitment. The number one thing you must have in order to do the impossible is commitment. It comes before planning and action and everything else. It's the hardest thing to come by. But without it, all else is wasted. So what is commitment? Miriam Webster defines it as the state of being obligated or emotionally compelled. Commitment in my mind is the resolution to succeed. It's the burning desire that absolutely has to be present in order to do your impossible. It's the drive that keeps you moving forward when defeat looks certain. It's your obligation to risk everything for success because living without it seems pointless. When you commit, you have to commitment to do. You can't commit to try. Committing to try doesn't work. Committing to try means you'll give it your best, and if it doesn't work out, it wasn't meant to be. When you're doing the impossible, things don't work out because you tried. They work out because you kept trying and never give up. What does it take to commit? Clearly, the main reason people are afraid to commit to something is because they don't know what it will require. It's never completely obvious what you're signing up for. You might think that if you really want something, then it shouldn't matter because I don't think that's true. The cost does matter. So what is the actual cost? Sure, in any commitment, whether it's business or personal, there's a leap into the uncertain. But the idea that there's no way to know what's required is more of an excuse than a real barrier. Those are the questions you have to ask yourself. When you come to a conclusion, it's a lot easier to look at your impossible dream and say, yes, that's worth it, or no, I'm not willing to pay that price. Either answer is fine. But making that decision based on real analysis instead of fear is important. So my friends, can you do the impossible? Let me know. Thank you for watching Seymour's World Commentary on Think Tech Hawaii. I would love to read your comments. Aloha.


Okay, thank you for joining the average golfer. It's a bit wet. It's not the best day to be out there playing golf in the UK right now. So we may have just a few more of these kind of videos coming your way over the next few weeks through the winter months at least. And yeah, stay tuned and stick with me. But yeah, interesting debate this one. I hear a few whispers about what might be coming out early part next year for a major manufacturers. Not exactly what, but when some release dates might be coming. And straight away I got to thinking, what is going to happen during 2019? What are we perhaps going to see? Been changes in the last year, minor changes. Some of them you may just call kind of a bit of markers in blurb, repackage renamed. We're going to talk about some of them in a minute to see whether or not they're still going to be around in 2019. That's one of the interesting things we'll see. But I want to talk about the possibilities of what we've seen this year, how it will perhaps follow on into 2019. Will there be some major change on what, if anything, it's going to make you reconsider changing your set of clubs again when the 2019 new release has come out. So we're going to start with the irons. And the one thing that's gone on over the last two years is the strengthening of lofts. It upsets a lot of people. So we've got seven irons now that I've got number seven on the bottom of them. But what is the strongest I've seen? Maybe 28 degrees is it? I know that some of the pink stuff was a power spec option. I think we're going to write down some of the M2 irons. Versing everybody's range, there was a 28 degree or there or there about seven iron. Are we going to see lofts strengthened even further? Will there be a seven iron on the market next year that is even stronger lofted than 28 degrees? That's an interesting one. And like I said, it will cause a massive debate out there if they do. One thing that's possibly already happened in a release that I reviewed in the last week or two, it's not actually hitting the market until, I think it's March next year, which is the Callaway Big Berther irons. And that is producing a smaller, more compact, excuse me, supergrain improvements iron. And I think that's something that we might see happen quite a bit of in the new releases that come during 2019 from all the major manufacturers because it just seems to be that they've got this capability at the moment to be able to make everything just a little bit smaller but still packed with all the forgiveness that you would expect in a performance from a super game improvement iron as they're called. And like I said, already in that first test that we did of the Callaway Big Berther irons, that was visible. So they'd improve things like sound and feel. They improved the actual thinned out that top line. Overall profile of the club had gotten smaller, but Callaway themselves still turned it a super game improvement iron. And I think that's something that will happen from all the major manufacturers into 2019. No matter which iron set you're looking at, whether it be from blades through to super game improvement irons, will again, I can see this, the whole focus being increased MOI, looking at a greater focus on dispersion, which again, manufacturers seem to switch off the whole debate about length, although arguably 28 degrees seven irons is slightly contradicting that. But there was a lot of contradiction in the drivers in particular on concentrating on dispersion numbers. And I think an increased MOI, best performing driver in terms of MOI, measured MOI was from the Pingji 400 Max last year. And again, will that number be pushed even higher and will it be able to increase that? Is that something that particularly in the drivers maybe that is going to be focused on? I think another big thing that could happen next year again is shaft technology. Again, lots of changes. I know that even the offering from the traditional brand, the tight list then for mainstream offerings of the shaft type that they offered at least in the TS range has changed significantly to what other manufacturers are offering. But I think there should could be, we could see some changes in. There's a lot of things going on in shaft technology right now. And again, I think there could be some major changes and improvements in terms of shaft technology next year. That'll be interesting to see what happens. And talking of shafts, I mean, I personally think, again, this is something that I've looked at only in recent weeks, is a more visible, more, a greater offering and a standard offering with no upcharges, I don't think as well. I think this is going to change. Have graphite shafts available in irons as I think you'll see more of that. The success of that, in particular, the UST recoil shaft which was made available in quite a number of sets last year. I think the fact that they've got it good in the fact that there's still a stigma attached with the graphite iron. And I think the fact that it's effectively a chrome finish on it looks like effectively a steel shaft, but is obviously, is graphite. I think the success of that shaft, well, there's like the 10 size shaft which I tested recently in some iron testing. I've got a feeling that you may see a lot more people switching towards graphite shafts in 2019. That's another one that I think may happen. I think we're going to see all kinds of, we've seen new materials in the last year, maybe 18 months bore on chrome alloy, graphene, all these things were introduced. I mean, graphite even into the Callaway Chrome soft golf ball. So I think, again, you might see some new materials introduced into the clubs next year. Also, I think it could be the year of the one length iron. Bryson Dechambeau has obviously shown their worth. He's performed admirably with them. And I do think that on the back of this is where players' success then translates back into influencing purchase. Even at four golf where I do the testing, four golf chester, there's definitely been an increase in inquiries. I don't know their sales rate, but I know there's been interest straight away increased in the King Cobra one length irons. And I think it'd be interesting if just the new driver, which I've not tried and irons of the people I have seen who've tried and give absolute rave reviews. And I think that that coupled with, if that is as good as they're saying it is, and coupled with this option of one length irons, I've got a feeling we might see, it might be the year of the one length and Cobra could do some damage there in terms of sales. I mean, in terms of all the products, I mean, are we going to see the big one from TaylorMade last year was TwistFace? Mixed reception in terms of the, how people perceived the technology. I think they did very well in terms of selling the product, but there was a mixed reaction in terms of TwistFace itself. So again, is that something to be interesting to see if TaylorMade carry that on into the drives of 2019? And I almost feel like they've got to in a way because obviously having so much sort of emphasis behind the new technology, the way in which the face would operate, then for them to go backwards on that and not include it in the 2019 range would be, yeah, they'd have to explain that one a little bit. So I'm expecting to see that still in the TaylorMade 2019 range. I think then you've got things like jailbreak technology, which has appeared in, jailbreak obviously is the Callaway's explanation as to what they've got packed into their, without going into the detail of that, but we all know what jailbreak is by now, is that going to carry on into the evolution of the irons and whatever else from Woods and whatever else from Callaway next year, that will be an interesting one. And then finally, because I'm more interested in your opinion on this one, I'm not going to go on too long because it's a very straightforward debate. I want your opinions on what you think might happen. And at the end of it really is anything going to persuade you what it takes to persuade you to make a change, but the final thing is, and an interesting one this year, maybe towards the latter part of the year even, was the price of clubs. The price of clubs, everybody picked up on it. They seem to have really pushed forward in terms of standard pricing. I mean, the big birther irons that I referred to that come out in 2019, I think they're 1300 pounds, UK sterling 1300, steel 1400 graphite. And that's pretty much, I mean, as the P760s came out, that's kind of money. Everybody who released clubs would seem to be around the thousand pound mark for a set of irons. So that really raised the bar. And I just wonder how that's going to pan out into 2019. That's another big one for me. Drivers all went above the major brands all went above 400 pound mark in terms of first release. And again, now is that the standard? Is that what it's going to be for irons? I can't see them going backwards. It very rarely does. Will they bring out a sort of a more, I mean, I think Callaway tried to do it with the XR driver, didn't they? And try and just give that something into a little bit of a different price bracket. We shall see. But that's it. That's the thoughts on 2019 from my perspective. If I've missed anything then please do make sure you mention it in the comments as ever. It's your opinion that I really want. So what do you think's going to happen in terms of technology for next year? What are they going to spin on us? What are we going to be looking at in terms of these major brands? What are they going to tell us? Will it improve your game? Will it make you change? That's what I want to know. So yeah, comments down below. I'll speak to you soon. And like I said, it might be very soon because we might be having a few more of these debates in the coming weeks unless it stops raining out here in the UK.


I have these two beakers with me one with 20 ml of water that is on the top and one with 40 ml of water the one at the bottom And I want to increase the temperature of the water in these two beakers by five degrees Celsius Now the question is which beaker will take longer time to show a temperature change of five degrees Celsius? Will beaker one take longer to show a change of five degrees Celsius? Or will beaker two with 40 ml of water take greater time to show a temperature change of five degrees Celsius? Think about it. All right, let's see So here I have the 20 ml beaker and to begin with I will measure the temperature first I want to make sure that both the beakers 20 ml and 40 ml both start with the same temperature And then we increase the temperature by five degrees Celsius Note down the time and all but now let's measure the initial temperature So right now we have 20 ml water in this beaker and the temperature is coming out to be around 30.6 30.5 All right, good enough Now we will light up the candle And place it below the beaker and note down the time that it takes for the temperature of the water to change By five degrees Celsius So let's do that Okay, we have placed the candle below. We should start the timer right now And also start measuring the temperature. All right, so about to reach 35 and there you go. All right Okay, so we did not change the temperature by five. We changed it by 4.5 degrees Celsius We make sure that we do the same for the second beaker as well So it took one minute it took one minute for 20 ml of water to change its temperature from 30.5 to 35 Change it by 4.5 degrees Celsius All right, now let's see how much time does it take for the for the second beaker with 40 ml of water So to begin with we will make sure that the initial temperature is the same So even for 40 ml of water if we have temperature around 30.5 we are good to go All right. Yes, we are good to go So we light up the candle place it below the beaker and start the timer And then wait for the temperature to reach to 35 degrees Celsius Okay, so I started the timer and then I recorded the temperature So it did reach 35 and it took around one minute 50 seconds to do this Why was there a time difference? Can you think of an explanation using the words heat energy volume or mass?


Good day, fellow investors. I've been now researching full-time for six months the stock market and the more I research, the more, let's say, my perspective on what's going on in the investing world clears and I know what are my possibilities, what are my limitations. In that light, I really want to discuss my investing strategy to show what can be done, what do I think can be done, what are the risks and rewards when it comes to investing. We talked a lot about macro yesterday, we discussed inflation in the stock market news. But if you focus on great businesses, minimizing risk, assets, margin of safety, value investing, that a lot of those other things become noise and aren't really that relevant. So value investing, that is the key and I really have found really something that really explains what I do and therefore I want to explain the history of my investments to really clearly explain okay this is who I am, this is what brought me here, this is what I'm looking for and then we'll discuss okay what are the criteria when it comes to selecting an investment for the long term and then we'll discuss also my two portfolios. I have one portfolio and I add some money each month and now I'm launching a lump sum 100,000 portfolio that I'll develop over the next few years, you'll see about that in the strategy. So let's start with my history that will give you a good perspective and also it will be a great educational perspective on what can happen when investing for the long term. So let's start with my investing history. I'll describe three stocks that I'm, three investments, two stocks and one real estate investment that were the best investments over my history and that I invested a lot of my capital in them because I found them low risk, high reward so investments that you can put your money in and forget about them and that is also what I'm looking for but you cannot find that at will. You have to look, look, look, look, be patient and when those come to you then you invest and this is a key concept when it comes to investing. I'll talk a lot about something and then someone wants to change their portfolio immediately. You build your portfolio over time. This is a message that I will never get tired of repeating. Portfolios are built over the long term. They are not created in one day. Let's start with my history and I'll explain what's going on much better. Now this is a company that I put about 70% of my net worth into between 2009, 10, 11, 12 up to 2013. So it is a hospitality business in Croatia and I think I did put about 70% of my net worth into at the beginning of the 2010s. The dividend was about 8% to 10%. The revenue growth was between 10% and 15% and the company was investing half of the yearly cash proceeds and half was paid out as a dividend. The book value was very high, outbid hidden as it was at historical cost and the management was fair as they owned and still own the company. The top manager owns 8% and the other managers own between 8% and 5% of the company. Now there was one issue here and it was liquidity. The stock was very thinly traded in the downturn and my buying was done at 50% above the 2009-08 lows. So I was buying the lows were around 500, I was buying between 700 and 1000, 1100. So I was paying 50% to 100% more than the lows and this is also something to keep in mind. What was the issue there? Well investors were fearing another decline, more sales oversupply. It's always about supply and demand on the stock market but the business was still doing great. The business had a mode, there was a highway being built to it and everything looked so great in the business but the market was looking at supply and demand and that's an amazing opportunity you want to jump in. Today the stock is much higher I sold in 2014-15 as we turned into real estate which we'll discuss later but how to find such a company, how to find such an investment. I recently did a video about the Dando investor by Monish Pabrai and he shared seven great questions that helped finding stocks such as the one we mentioned and these are the questions and these are also the questions that I will be really focused on in the future because are great questions to finding great businesses at a fair price. Is it a business I understand well within my circle of competence? Hospitality in Croatia is something I know really well. I did a PhD on the Croatian stock market. Do I know the intrinsic value of the business today with a high degree of confidence how it's likely to change over the next few years? The business had a P-Ratio of 7, growth of 15%, high cash flows, price to cash flow of 5, dividend of 10%. Let's say the intrinsic value was a dividend of 5% for such a good business so there was a margin of safety which leads to question number 3. Is the business priced at a large discount to intrinsic value over 50%? I was somewhere there at 15%. Would I be willing to invest a large part of my net worth into the business? I said 70% I invested. If it would go down I would invest more which would increase my compounding returns, dividends, reinvest the dividends so it would be really great long-term investment. Is the downside minimal? The downside was 50% but here we have to differentiate between permanent capital loss. I don't think there was an opportunity for long-term permanent capital loss and this is also the difference between me and Pabrai. He's focused on the market to give him the returns and focused on the business so that's the difference. Does the business have a mode? Of course it was the only hospitality there and they were building a highway. Is it run by able and honest managers? I already said that there was no issues with it. So that was one stock. Now let's go to one of my first investments. The first investment that I really went big into and here the lesson gets a little bit trickier. The company actually went bust now 15 years later so it wasn't a great long-term investment but I fortunately made a lot of money on it. Let me show you. So this is a bottling company in Croatia. One of the first stocks that I was buying when I was 19-20, the P ratio was around 7, it was growing at 15% a year. All of the people I called all over the country had its products, had its water in their fridge so it was a really strong brand but the problem there was a 77% majority holding company and when you have such an owner you never know what will happen. The results for me were very positive but the story is much riskier. So I was buying at 10,000, I sold most of it around 50,000, two three years later. The company later went to 140,000 in 2007 in the bubble. It fell to 20,000 again but then I didn't buy because the company was guaranteeing all the loans of the parent company and that was a big red flag for me. Look at what happened. The stock went up as it is a great business, great brand, good profits, good margins but then the contingent liabilities, the guarantees materialized as the parent company went bust and now you see all the equity gone as the company was guaranteeing much bigger loans to the parent. So this is an example of how the market doesn't focus on the risks until those materialize. If something didn't materialize in the past it doesn't mean it will not materialize in the future so focus on risk is key. So let's say that between 2003 there haven't been such guarantees which is important but let's say this was a little bit more risky than the previous one so you learn with time. Now this is okay I was young the next great investment was real estate and I'm discussing real estate because it's extremely important to put things into perspective. Real estate is grounded much different than stocks prices don't go up that much all the time and I was living in the Netherlands I was renting and I was seeing that rent prices are 50 percent above mortgage prices not just the more the cost the interest plus repayment of the mortgage over a fixed rate for 30 years were much lower than the rent. Rent was 50 percent higher than the mortgage so I said okay let's buy it will lower our risks and probably the mortgage costs or the price of the houses will come in line with the rents because I have never heard that rents go down. So we did that we bought a house 103 percent mortgage no down payment we have extra money too because we went to buy a house that we had to completely refurbish and I'm still finishing on that and over the last two three years we did very well because we bought at a good moment in time. Why were housing prices in the Netherlands so lower than rent prices because nobody wanted to buy in a market that was going down because of fear. Since then everybody's rushing into buying and the market has exploded and now we are looking to sell to get the equity out because I don't want to hold so much equity in a house. So this will allow me to release some liquidity some will go in the long term 100 000 portfolio that I'll do for stocks and the other part will probably go for another piece of real estate if it will still be selling when I sell this house because I found an amazing piece of real estate that I want to invest. Now when it comes to real estate the usual comment is on YouTube do you think investing in real estate is good now? Investing in real estate is like stocks even more important than stocks you have to look at 1 000 10 000 properties narrow it down to five on the five make five extremely low ball offers and one of those files will be a buy. When you can do that then investing real estate is good just buying something at market price is crazy to invest in real estate so please refrain from asking me whether now buying a house is good or not.  So the moral of these three stories except for one where I was young the other two had practically no downside so the risk of permanent capital loss over the very long term was really minimum the most I could lose with the house was I could return the house the keys or rent it out so that the rent pays the mortgage and after 30 years I would have the house highly unlikely that I would go to permanent capital losses there so and that is something I really want to do on my stock market research with everything that I do limit permanent capital loss be it through buying at a margin of safety being too true taking advantage of a volatility if I know it's a good business I know I can buy more if it goes down so having some cash and managing that volatility if something goes down and I'm happy about owning it I buy more when it goes up I sell part of it to balance portfolio exposure and so I increase my return over the long term but I take advantage of volatility because volatility is the best friend of the value investor so when it comes to investment strategy I will start with the seven questions from pubry and then I'll add something more on it which is something different than what pubry does I think that pubry focuses on getting his part of his return investing written from the stock market he wants to buy undervalued stocks and then hoping that the market values them fairly which he says usually happens in three years and get the return from there that worked very well in the first 15 years not in the last five years I think his annual return is now 6% but that's still okay however I want to focus on businesses I hope to never sell my businesses and that's where I want to get my return and that's a big difference a big difference when it comes to investing I don't aim to make 26% like pubry let's say I aim for 15% but with limited permanent capital loss and if it is higher than 15% that depends on the market that's something I cannot know whether it will happen or not if we have a lot of volatility up and down then we might go to 20-25% over the long term if we don't have volatility we might be between 10-15% that's not up to me that's up to the market up to me is to find great businesses limited permanent capital loss happy to buy more if it goes down and from this situation in the current market it takes a lot of work to find such businesses and it takes a lot of time additional portfolio keys 10 year investing horizon when analyzing a business nobody knows what will the world look like in 10 years but let's go for high upside and limited downside or unlikely downside and this is something key as I said investing is done through time and this is something 20 investment punch card for the next 20 years if you're patient if you are willing to accept the market is irrational you can do this and you can really invest in a few businesses over time just buying five or six of them over time give yourself the time to find them and that is what I'm doing I'm giving myself the time to find that over the long time apart from that when you look for such businesses the focus has also to be on return on invested capital from the business reinvest and hold for the long term if the business is likely to continue to deliver returns treat the portfolio as a fund okay think of hedges when opportune to do so so to conclude this is the SAP 500 and you can see either it goes up or it goes down there is no in between with stocks with the market with people which is completely irrational there is a line that can be drawn that balances all out you have to see how to behave when the market is overvalued and when the market will go into panic mode as it always goes sooner or later so I also have another portfolio this is the lump sum a smaller dollar cost averaging portfolio but that will be the story for probably somewhere next week when we do a portfolio update on the smaller portfolio before I finish if you want to see all that I do please check my stock market research platform there is my portfolio my strategy everything written down and really I show my skin in the game and how it works see you in the next video