Okay, we can start. So it's a pleasure to have Irosha Guri from Caltech and the APMU, and he's going to talk about entanglement and geometry. So please. Thank you. Can you hear me? Okay, good. Thank you. Good to have a response. So it's very, I'm very happy to have this opportunity to give my set of lectures here. I have given many lectures at this spring school and topological string theory and supersymmetric queue theory. But this time the organizers asked me to talk about entanglement and geometry. And the study of ADS-CFT correspondence in the last several years revealed that the quantum state that described a gravitational system seems to have very interesting entanglement properties and exploiting that we have gained quite a bit of useful information about quantum gravity in general. And then I would like to review some of these development in the past few years. I think I have one hour for my first lecture which means until 1240 or something like that, right? One hour. Yes, thank you, great. So today I will basically talk about the very elementary thing about information theory, entropy, mutual information, et cetera, so that we know what we are talking about in the rest of the lecture. And then tomorrow I plan to talk about primer of ADS-CFT and then introduce notion of holographic entanglement entropy. And then we'll go on to talk about the entanglementary construction, symmetry in quantum theory of gravity, et cetera. So let me start with a concept of entropy which I believe you are all familiar with. In start mech, we learn that entropy S is given by log of the number of microstate in the micro canonical ensemble. I'm setting Boltzmann constant K to be equal to one. On the other hand, in information theory, in the information theory, so suppose for example there is an event A that happens with probability P. Can you read my handwriting on this side? Okay, good. So suppose that there is some event A that happens with probability P, okay? And then you don't know whether it happens or not but if you learn that it happens, like for example, at the presidential election last year, we didn't know which one is going to win and then on the day after, we learned, oh, this guy won. And then that's some information, right? So then you gain some information. So there is a way to quantify that information which is minus log P. So this is a notion of entropy in the information theory. So for example, if P is one, you're sure that it's gonna happen and it happens, you are not gaining any information. So then the amount of information is zero. So I hope that this lecture is going to be actually P less than one, but we'll find out. But on the other hand, if a very rare event happens and you are surprised by that event happening, I have had that such experience last year, then this is going to be very large, right? So if each microstate is equally probable and if the amount of information, so in that case, if all the event, suppose we have omega events and if all the event happens with equal probability, P is equal to one over omega, in this case, this minus log P is equal to log omega. So these two notions coincide. There are various good reasons why we are considering logarithm. One of the primary reason is the following. So suppose you have two events, A and B. And suppose these are independent and suppose these probabilities are given by P of A and P of B, these are the probabilities that these two events, A and B, happens. And if these two events happen independently, then the joint probability is the product. So if I take log of this, then it's a sum. But what this means is that information is additive, that if you learn that both A and B happen simultaneously and they are independent, the amount of information you gain is additive. And in fact, you can prove that the log is the only function which has this property. So this is why we use logarithm. Now, suppose you have n events that are mutually exclusive with probability P1, P2, Pn in such a way that they sum up to be one, okay? So then you can ask, well, we are going to do some experiment to find out which one of these n things happens. But we don't know yet. So what is the expected amount of information you gain by doing that? Well, the amount of information that you gain by seeing that event I happen is minus P, minus log P. So that means that the expectation value would be sum of all of these, right? So this is denoted with S and it's called Shannon entropy. So this is the expected amount of information you gain by doing this experiment and try to find out which one of n events happens. There are a couple of important property that this Shannon entropy has. So this is going to be exercise for you. Both are very simple and algebraic. The first is to show that S is, of course, non-negative and the question is when S is going to be zero. So that's the first question. The second question is that S is maximum. If all the events happens, and if and only if, in fact, all the events happens with equal probability, namely that P i is one over n for all i. Okay, so these are simple algebraic exercise that I ask you to try doing that. Now, one of the notions that come up very often in the rest of the lecture is a notion of mutual information. So I would like to discuss that. So first I'd like to introduce a notion of a conditional entropy. Okay, so suppose we have, here I considered one set of events, so you do one experiment and to find out whether one of n things happens. So suppose you have two sets of events. So you have a one to a n, b one to b m. Suppose you have two sets of events happening and then they are not necessarily independent, so they can be correlated, for example, and so there is a joint probability which I denote P of a i, b j. So that is a probability that event a i and b j happens simultaneously. So then we have this conditional probability that supposing that you know that a i happens. What is the probability that b j happens? Well, that would be given by, so this is something you probably learned in the high school that this should be given by this kind of ratio. And similarly, this is given by this type of ratio. Okay, so this leads to the definition of conditional entropy, which is the following. That suppose you know that event a i happened. Suppose you know that event a i happens. What is the amount of information you gain by knowing that b j happened? Well, that would be given by just substituting this into that formula there. So that means that the S of a i b j is given by sum of all j's, a i b j, log of P of a i b j, right? So namely that, so this is a probability of b j happening subject to, you already know that a i happened. So therefore this is the amount of information you gain by knowing that b j happened under that circumstance. But suppose you didn't know, you haven't done that measurement to measure a i either, but you know that you are going to do the measurement. And then you want to find out how much uncertainty you have about b j. That you can define by averaging this over all possible a i's. So that means that you sum over all a i's with this probability. And then it's a simple algebra to show that this is given by minus sum of i j P of a i b j, log of P of a i b j plus sum of i P a i log of P of a i, okay? So this is called conditional entropy. So this is conditional entropy. That is that entropy for doing the discovery, entropy about information for b j's subject to the condition that you have already done the experiment a i. Ah, excuse me. So I actually put the wrong. So this is the information, I apologize. So here I have already summed over j's. So this is the amount of information you gain about b when you already know that a i happened. This is the amount of information you gain about b after you did this experiment a i but you don't know the outcome of it yet. So that's why I average over a i's. Okay, so this leads me to define mutual information. Is there any questions so far? Is this clear? What I'm talking about? So this leads me to this notion of mutual information. So this is a following notion that suppose you want to know about b, what you want to know, what is this b? So for example, who is going to win the election or something like that? But then you are curious, well I don't know what, it's very hard to know what b was, what kind of b happens. But suppose I find out about a, how much can I learn about b? So the general uncertainty about b is just s of b. Yes, let me see. Ah okay, so you're saying that this can be b. Okay, I might have made a, it's very hard for me to double check in real time so can I collect it later? Okay, so this is an uncertainty I have about s of b. But now suppose you know you are going to measure a and then you ask how much uncertainty you have about b. So that would be s of a of b. So that means that this is the amount of uncertainty you can reduce by doing the experiment a, right? So namely, this is a measure of how useful it is to do the measurement a when you want to find out about b. So this is a mutual information. Interestingly, this mutual information is symmetric in a and b. That is that if I write this out, then I can express that in terms of Shannon entropy. So one of the important properties is symmetric and b. Namely, so this mutual information tells you that how much you learn about b by learning about a. But it's mutual, that is that this is the same amount of information you learn about a if you measure b. So the information is mutual. So this has been rather abstract. So let me give you some example to think about this concept.  Where is my key? Where is the key to the apartment? Okay. So you discover that there is a 50% probability that is in your pocket. Okay. But then there is another 15% probability that is in one of 16 drawers in your room. This happened to me very often. Actually, it happened more often than I would like. Okay. So what is the uncertainty of the location of the key? Okay. So key location uncertainty. Well, so there is a one half probability that is in my pocket. So that's this one. And then there are 16 possibilities. There are 16 possibilities that is one of the drawers. The probability that is in each of the drawers, I assume that they happen in the equal probability is 32, one over 32. So it's one over 32. And just make the calculation easy. Let's compute a log with base two. You know that different base just give you a different normalization of the entropy. So here I'm using base two. So then this is three. So when you wake up and then you are in this situation that you don't know where the key is, the uncertainty you have is three. Okay. So that's how you quantify your uncertainty.  The paradox is as follows. Suppose you actually check because you have to go out and then check your pocket first and then you discover that it's not in it. Okay. So what's your uncertainty now? So you check the pocket and then you discover that it's not in my pocket. And then what is the uncertainty about the key location? Okay. So we can use this conditional entropy to evaluate this. So A is not in my pocket and the key location, right? And so if you evaluate it, so it's 16. Now there are 16 possibilities. One over 16 log two of one over 16 is actually four. So it's greater than three. So why is it that you actually, so this means that you lost information. You did something and you lost information. So that doesn't seem to be fair. Uncertainty has been increased by knowing that key is not in my pocket. So what's going on? Actually, this is not the correct calculation to do. The correct calculation is the conditional entropy that you obtain by checking your pocket but you don't know your outcome. Okay, so check the pocket, check my pocket and then uncertainty of key location. So let's calculate that. Well, so we can use that formula. So that probability is one half for four. So let me just mention the calculation. So there is a probability one half that it's in my pocket. But if it is in my pocket, now you know where the key is. So uncertainty is zero. And then there is another probability that there is another half probability that it's not in my pocket, which is in that case, it's in one of these drawers. I have already calculated that to be four. So this is four. So that means that the conditional entropy for the key location is two or good. So it's less than three. So this is what's going to happen to you in the morning. As far as the key location uncertainty is concerned. So you wake up and you don't know where your key is. You figure that there is a 50% probability that it's in your pocket. There is a 50% probability that it's one of the 16 drawers. Your uncertainty is three. Now you are going to decide that, well let's first check my pocket because there is a 50% probability. You are going to do that because you know that the uncertainty will be reduced to two. So you do that. That's why you do it, right? But then you discover that it's not in my pocket and you really get upset because uncertainty is now increased to four. Okay, so it actually agrees with your intuition about what uncertainty should be. Okay, so far I considered classical information theory that I was dealing with information that are classical that have already always have fixed value. But of course I'm going to talk about, since I'm going to talk about quantum gravity. So I should talk about the quantum information. So that can be measured by von Neumann entropy. Okay, so suppose you have a Hilbert space and suppose you have an ensemble which is a set of states. And I say that each one of these states happens with probability P i. So then let's take this to be also normal. So you have ensemble of also normal states each happening with probability P. So this can be described in terms of density matrix like that. The von Neumann entropy is defined, the von Neumann entropy for this density of state is defined as log of a trace, so excuse me, what am I writing? I just came to Japan last midnight, arrived here so I have an excuse. It's trace of minus log of a log of a log of a log of a log of a actually I just learned this morning that Nima Al-Khan-Hamed gave a lecture last week discussing inequality property of this quantity. But I briefly saw the beginning part of the video and so what I'm going to do is actually give you explanation of why this is a good quantity to measure. Okay, so in particular if you know that the row already have this basis like that, then it's easy to show that this is actually equal to sum over i, pi, log of pi. So in this basis, so when you know that density matrix can be presented in this also normal basis, then it agrees with Shannon entropy. Now let me talk about, so here I talked about joint probability and conditional entropy, etc. So we can repeat the discussion quantumly. So we can consider a notion of joint entropy, which is to say that suppose we have a density matrix, rho of AB acting on the tensor product of two Hilbert spaces, HA and HP, then I can define the notion of joint entropy S of AB simply as minus trace of rho AB log of rho AB. So this will be a quantum analog of this type of quantity here. So this is a joint entropy of A and B, classically, and this is a quantum counterpart of this. And again, when rho can be also diagonalizing also normal basis, these two agrees, okay? Now this joint entropy has various important inequalities. Nima, I saw, gave a very nice surprisingly creative proof of various inequalities, so I'm just going to state those things. So the one important notion is sub-auditivity, which is to say that S A plus S B minus S AB is positive, but you see that this is actually nothing but the mutual information. So the mutual information being positive is one of the property of the von Neumann entropy. And so that's a good thing to know because that means that when you do something, you always gain some information. You never lose information by measuring other things, right? Because it's zero. When they are independent, two events are independent, the mutual information, of course, is zero. So that means that learning about B does not reduce the uncertainty for A, but when they are correlated, when you measure B, you always gain some information about A. That's what it means, that's what sub-auditivity means. Another useful inequality is the concavity of entropy. So the concavity is the following notion that if I consider entropy for some linear combination of density matrices, can you actually distinguish my P and rho? Should I write them more distinguishably? Is this okay? Then the concavity means that it's actually always greater than or equal to this thing. You can take PI out. And then there is another side of the inequality, which says this, where this guy here is a classical Shannon entropy, which is minus log PI log PI. So the concavity means that this entropy for the linear combination superposition of density matrices is bounded below this and bounded above by this. This also has some nice interpretation. It actually is useful in many ways, but one place where it appears is the notion called horrible information. So horrible information is defined in the following way. And this shows up in many circumstances in information theory. So for example, suppose somebody send you some mixed state of this kind of density matrices and you are supposed to do some measurement to figure out which one of these raw eyes was being sent. And horrible information gives you an upper bound of your ability to figure out which one that was sent to you. And it's actually have a very nice interpretation in many circumstances, including holographically. And I might, if I have time, I would like to discuss those. But anyway, so the concavity in this case means that this horrible information is bounded both from below and above. So those are two inequalities. And there is a third inequality that I would like to also mention, which is a strong subadjectivity. And I believe this is what Nima talked about in his lecture, which is S of A, B plus S of B, C is greater than S of B plus S of A, B, C. And this is slightly more difficult to prove. We'll discuss holographic proof of this inequality maybe tomorrow. But for now, let me mention that if I use the notion of mutual information that I erased, oh, no, I have not. So if we use this mutual information, then I can actually write this strong subadjectivity in an equivalent form as S of A and I of A, mutual information between A and B, C, is greater than I of A, B. And I leave this to your exercise to check this. This is a very simple algebraic. You just substitute the definition of this and then check it. But this gives you a very natural information. What it means is that the more you learn, the less uncertainty we are, which is encapsulated in this inequality. So this is the amount of information you know about A by knowing about B. This is the information you know about A by knowing B and C. So that means that more you learn about subjects that is not directly related to A, nevertheless you learn more about A also. So this sounds like a profound life lesson, but this is stated in the form of strong subadjectivity. So now let me come to the main sort of concept of this set of lecture, which is an entanglement. And one of the reasons that entropy is useful is that it gives you a way to quantify the amount of entanglement that a given state can have. So let me first start with a very simple example. So suppose you have two Hilbert spaces, both two-dimensional. So suppose you have HA, which consists of two states, zero and one. And another Hilbert space, which also consists of two states, zero and one. So then you consider tensor product of these two Hilbert spaces, and you consider various states. So for example, you can consider a direct product state. In such a state, we consider really regard as having no entanglement. On the other hand, you can have a state which is sort of deeply entangled, is of this form, for example. And this is actually a particular state that Einstein, Podovsky, and Rosen considered in their famous 1935 paper, where they exhibited the surprising property of entangled state. The term entanglement itself was coined by Schrodinger, I understand, after their paper. But for this reason, let me call this as EPR state. So this is entangled state, and this is a state which is not entangled. So I would like to use entropy to quantify the amount of entanglement. So let me define entanglement entropy. So suppose you have a state in a tensor product of a Hilbert space, and you want to find out how much entanglement between A and B, this particular state, is coding. So for that, we first evaluate what is called partial trace of this state, which is, you start with this pure state density matrix, and you take trace over Hilbert space of B. Then you obtain some state which is acting on the Hilbert space of A, and then you compute the entanglement, sorry, von Neumann entropy for this density matrix in the Hilbert space, of course, of A. So this is the definition of entanglement entropy. So as an exercise, let's evaluate this for these two states that I introduced. So again, to simplify our calculation, let's do that with base two. So if I do that, and if I substitute this and this into this definition and the work out, which I encourage you to do by yourself, sorry, yeah, I keep doing this. Maybe I should do the global replacement, but then this is going to be changed, too. So that will be a problem. Thank you for, please point out any errors. I appreciate Mukund and telling us, Mukund and Atish are collecting, and I encourage you to collect, and maybe I'll give prize for people who collect my mistake. Anyway, so suppose I evaluate this for this pure state which is just a tensor product, then you can actually check that this quantity is zero, whereas if this is EPR, then this is one. And in fact, this is a maximum amount that you can have for this particular entanglement entropy. So in that sense, EPR pair is actually maximally entangled. In fact, in some sense, entanglement entropy defined in this way is measuring how much EPR pair you have between these two Hilbert spaces. And it is because you can actually prove the following theorem. I'm not going to prove it, but you can actually find the proof in the literature, which is the following. So suppose you start with this state that I have. So suppose I pick any state in this tensor product. This can be any superposition of this state in this Hilbert space. But then I consider n tensor product of this. So I compute n or consider n copies of these Hilbert spaces, and then I consider n tensor product. And then what I'm going to do, what information cell is called, local operation and classical communication, which is the long word, sometimes called L O C C, which is an operation which you are permitted to do unitary transformation on A only or B only separately. But you don't do any quantum operation mixing A and B. So for example, if you can do arbitrary unitary transformation, certainly there is a unitary transformation on this total Hilbert space which maps this into here. You can find that unitary transformation because both are normalized to be one. So you can do that.  That would change the amount of entanglement. But suppose I do unitary transformation on A side only. Suppose for example, I just define this to be one and change this to be zero. The amount of entanglement is not changed. So if I do the unitary transformation on A side only, then it won't change the amount of information. So L O C C is sort of formalization of this kind of concept, the kind of operation you can do in this joint Hilbert space which won't change the entanglement property of this state. But then you can show that if you consider any tensor product of this, it's actually always you can always map that into tensor product of EPR pairs. And the amount of EPR pair you have is given by the entanglement entropy times n. Where this symbol, this mathematical symbol just means that it's an integer part. In general, entanglement entropy is some real number. So you multiply n and then you take the integer part of it. So this is true asymptotically, so for large n. So for large n asymptotically, this can be mapped into, so this roughly saying that the entanglement entropy with base two is, so this two means that I'm using logo base two is roughly the amount of EPR pair that this particular state can have. So this is sort of useful, sort of intuitive way to think about entanglement entropy. Now I should say that, so this was about pure state. And for mixed state, you can start, you can certainly start with a mixed state. So instead of this, you can also consider row A to be trace of HB of row AB for more general mixed state. And then one can define the entanglement entropy for this one. So this actually is not symmetric in A and B. Yes. So suppose I put minus here, so this is still one. So this one has the same entanglement entropy as the EPR pair. And so in fact you can relate all this by LOCC. So one would consider this as having the same amount of EPR pair as this or this. They all have the same amount, same number of EPR pair, modulo LOCC. Now coming back to the mixed state, so far I talked about pure state, but for mixed state you can still consider entanglement entropy, but that quantity is actually not symmetric in A and B. So may not be necessarily be a good measure for quantum correlation between A and B, because you hope that notion of quantum correlation would be symmetric in A and B. So in that case it's actually maybe more useful to consider mutual information. And this has added a benefit that if you consider quantum field theory, which I'm going to do next, then this quantity is actually ultraviolet finite. So it's more well defined than the entanglement entropy itself. So any questions so far? So I review the notion of shadow entropy, and then I discuss various inequalities. I introduce a notion of phononema entropy, which is a quantum counterpart of it, and discuss various inequalities. And they use the phononema entropy to introduce a notion of entanglement entropy as a measure of entanglement of state in the tensor product of Hilbert space, and explain that it's actually basically count number of EPR pair in it. Any question? So let me present to you one particular example of how entanglement entropy is calculated. So this is going to be an example that will be used in the next lecture. So this is the primer of information theory, and the next lecture I will discuss, I will cover some basic relevant aspects of ADS-CFT correspondence. So naturally we should consider entanglement entropy in the context of conformal field theory. The entanglement entropy in conformal field theory in two dimension has a very nice expression obtained by Karaburese and Cardi in the beautiful paper in FTH 0405152. So let me, in the remaining time, let me review their calculation. So it's a two-dimensional conformal field theory, so it's defined on the circle in the space-like section, and then you have a time in this direction. And then you consider some particular state. I'm going to actually consider a vacuum state, but I'm interested in entanglement between different spatial points of this conformal field theory. So what I'm going to do is to separate this space-like part into two parts. So you have this segment A, and it's complement A bar. So we have quantum field theory, so that means that we have some kind of local degrees of freedom on this space-like section distributed. So intuitively, you would think that the total Hilbert space is decomposed into tensor product of the Hilbert space associated to the degrees of freedom on the sub-region A, and it's complement. It's not quite precise because you have to actually specify how you regularize when you cut the Hilbert space into two parts. One way to think about it is that you first consider a lattice model where you discretize space and you put some degrees of freedom on each lattice. There it's quite clear how you separate things. Of course, even in the case of lattice, there is a subtlety if you have a gauge theory, the degrees of freedom are not on the lattice point but in the link. So then there is an issue of how to separate. So you have to specify the boundary condition here. But in fact, in all known examples, there is a way to separate the Hilbert space into two parts if you add some degrees of freedom in the ultraviolet. But the result is that the way that is separated depends on how you do this. So namely that there is some kind of ambiguity or some freedom to choose in introducing some ultraviolet degrees of freedom in order to do the separation. So that would change the amount of entanglement entropy by some amount which is additive. So for example, if you consider mutual information like this, then that subtlety is actually canceled. So that's another reason why mutual information is sort of more well-defined quantity than the entanglement entropy itself. And this has been discussed in various recent literature. For example, in a particular case of two-dimensional conformal field series, there is actually interesting paper by Tachikawa and Oomori, and this is the number. So if you are actually interested in this type of issues, then this might be one of the place to start. And then there are also some literature on how you do it in lattice gauge theory. They discussed that in the context of actually CFT2 that I'm going to talk about, and parameterized how much uncertainty you have when you try to separate the Hilbert space into two. So anyway, so let me assume that you can do this separation, and then start with the vacuum state of conformal field theory and define the density matrix by taking trace of a complement A bar of this space, and then calculate the entanglement entropy. The procedure that was employed by Karaburese and Cardi is first start with evaluating a quantity called the rainy entropy, which is defined as SN of A, which is 1 minus N log. So I'm going to from now on take the base to be E, and then trace of rho HA to the N. And you can easily see that if I take the limit of N goes to 1 of this rainy entropy, then this gives you the desired entanglement entropy that you wanted to evaluate. So density matrix is of course a positive definite operator. So you can take a logarithm of this, and this is sometimes called modular Hamiltonian. So knowing a rainy entropy is quite closely related to understanding the spectrum of this modular Hamiltonian. Now this quantity can be calculated in conformal field theory, because this is related to computation of a correlation function in fact of operators that generate branch cut on the worksheet. The reason is the following. So here, so pictorically what we are doing is that we have the space like section here, and we separate the space into A bar, A, and it's complement. And we are taking trace in order to define rho A, what we are doing is taking a trace of a complement of the vacuum state. So we have this vacuum state coming here, coming here. I'm taking trace over here, but I keep this thing open. We have in state on this side and out state over here. That is this. So we have in state here, out state here, which is in state here, out state here. Now this quantity is obtained by taking n trace, n product of this. So that means that this is now glued to here and then glued here, glued here, etc. You do this n times. That's a rainy entropy. So if you have a vacuum state here and here, this can be evaluated with a sphere function on the sphere with cut over A. And if I take n product of this thing, what you are doing is taking product of this n times. So that means that you are taking n spheres and then cutting, introducing, adding n slice over A and then gluing them together. So this is the same as doing introducing branch cuts here, where it's n for the branch cut. If you go over n times, you come back to the same sphere. Okay? So such quantity can be defined in conformal field theory and then basically this amounts to calculating the correlation function of this operator, where I call this point u and v. So the distance between them is u and v. And so I actually only have five more minutes, so I don't have time to discuss more detail. But this quantity can be evaluated very easily by knowing how energy momentum tensor of this conformal field theory transforms under coordinate transformation. Suppose I do the coordinate transformation in two dimensions from z to w, then it is known that the energy momentum tensor of conformal field theory transforms like this, where this is Schwarzian derivative. And using that, we can actually evaluate this quantity, this correlation function as u minus v to 1 over 6 times n minus 1 over n, where u and v are locations of these branch cuts. And then from this, you can actually calculate this rainy entropy. And then if you take the limit, so this amounts to, so I'm sorry, this is actually this part. And then if I take log and multiply 1 over 1 minus n, then the rainy entropy is obtained as c over 6, 1 plus 1 over n times log of distance. So let's call this length of this to be small l. So this is small l, then you have log l plus some constant. And this constant is related to the ambiguity that you have in separating the Hilbert space into two parts, the one associated A and the one associated A bar. You can see that there is actually such, there should be such ambiguity because l is actually dimensionful quantity. On the other hand, we are considering conformal field theory, so the quantity that you can actually evaluate should be dimensionless. And in particular, it's funny to have dimensionful quantity in log because if you change the scale, you would change the value of log by shifting some constant and that is absorbed into this constant part. So from this, you can also see that somehow this constant part has to be related to the way that you regularize and separate the Hilbert space into two. So at any rate, so from this, you can actually show by taking the limit of n equal 1 that this is given by one-third of log of l plus constant. So actually, this formula is true when the size of l is much smaller than circumference, the radius, the circumference of the entire sphere, the entire circle. The more precise formula when the circumference of S1 is l is given by l sine i small l over capital L plus constant. So I had to run a little bit quickly to do the calculation. If you want to know more detail, I encourage you to consult the original paper where this is actually explained very clearly and nicely. But I just wanted to give you an appetite for getting into this reference. And also, I'm going to use this formula in the next lecture, so I wanted to have something to refer to. Okay, so today basically I covered the concept of entropy in information theory and introduced various inequality for both classical Shannon entropy and quantum for Neuma entropy and explained that the entanglement entropy defined in this way count the amount of EPR pairs and then discuss how you can actually evaluate this quantity in the case of conformal history. Okay, any question here? Yes, please. You said that the LOCC doesn't change the entanglement entropy. And on the left-hand side, it's a product state, so the entanglement entropy should be there. And how could the right-hand side be there? There is also this state belongs to tensor product of this Hilbert space and this Hilbert space. It is true that it's a product state for this Hilbert space, but there is an entanglement between here and here. So it depends on what you mean by product state. So, namely, suppose, for example, suppose you have a product state of HA and HB, but HA itself may be a product, tensor product state, and there can be entanglement within it. So when you say it's entanglement, you have to tell me entanglement between what? So this is a tensor product, so that means that it doesn't have entanglement between different components of this product, namely, HA times HB, so there are n copies of this, right? There are no entanglement between different copies because it's a product state. But there is an entanglement inside of each copy. So the whole state, so there are two n components in it, right? There are two n Hilbert space in it. There is an entanglement in some part of that Hilbert space, okay? But of course, it's a product state for this, so there are no entanglement between the copies. Any other question? Down there? Just trying to understand your construction of taking the spheres, letting it along the interval A and joining n copies of that together. Is the resulting thing an n-fold cover of the sphere branched at the two points, UV? Yes. Okay. That's what it is. Yes. So if you think this through, so you know that if you consider the vacuum amplitude with some object, it's the same as the sphere with that operator you started. And what I'm doing here is taking, so there is a subset, sub-region A, and then I'm taking trace on the complement. But I'm not taking trace over A, so that means that I'm opening up this so that you can have state coming in and coming out. And then I'm gluing this together here. And I think on the covering, the log becomes a single- So this is U and V, by the way, yes? On the covering, the log becomes a single-valued function? Yes. So in n-fold cover, it's a single-valued thing. So what you're supposed to do is to consider functional integral of this conformal fuselage on the n-fold covering of the sphere. And compare that with the partial function of the n-product of the sphere. And that is this quantity. Thank you. And that is actually shown very carefully in this paper. So if you want to know the detail, this is a good reference to look at. Okay? Yes? Can you be a bit more explicit about the assumptions that go into being able to separate the Hilbert spaces on spatial slices? Beg your pardon? When you separate your space in A and A bar, what are the assumptions that go into being able to also separate the total Hilbert space? So let me try to understand you. So you're talking about this separation of the Hilbert space? Yes. What is your question? What are the assumptions that go into being able to separate the Hilbert space? A would be, sorry? There are assumptions going into being able to separate the Hilbert space in H A and H A bar, right? This is not true in general? You're asking under what assumption, so if you can have, actually depend on the kind of UV regularization, you can have, for example, if you can define conformal field theory as an infrared limit of some lattice model with degrees of freedom residing on each lattice point, then you can separate the Hilbert space. But for example, there can be a case where you have degrees of freedom on the link, then in that case, you have to actually have prescription of how to separate the link. What they did in this particular paper, for example, is use open string field theory to define separation of conformal field theory. Because if you have open string field theory, then you can have a vertex operator which turns closed string into open string, in a way that preserves conformal invariance. So you can have closed string coming in and then you can have open string coming out like that. So this will be separating the Hilbert space or entire Hilbert space into A and it's complement. So in fact, you need two open string vertex operators here and on the other side. But what happens if you do that, is that you have to specify the D-brain boundary conditions. You have open string, so you have a boundary condition here. So you have D-brain, you have to put D-brains on it. Now, you don't necessarily have a unique choice of D-brain. In many conformal field theory, you can have different D-brains. So you can have D-brain called denoted by alpha and you can have D-brain denoted by beta on the other side. That's one of these ambiguities. And what these people showed was actually this ambiguity can be traced back to the ambiguity in separating the lattice model into parts using this. So there's actually a nice match-up in that case that they studied of how the ambiguity in separating the Hilbert space in the UV definition of the theory in the lattice model is reflected on the ultraviolet description in terms of conformal field theory. Okay? If there are no other questions, we can probably thank Hiroshi, yes.


Opening session of the 159th ARL membership meeting, welcoming remarks by Carol Mandel and introductions of the new ARL member representatives. I'm Carol Mandel. I'm the Dean of Libraries at New York University and President of ARL for another few hours. And so I get the honor and pleasure of welcoming you to the, let's see, 159th membership meeting of the Association of Research Libraries. I get to declare it open with the scabble, I guess that's what I get to do. Yeah, here you are. So one of the first things, just to get oriented, so I have a few remarks before we launch into the really excellent program that we have for us all this afternoon, is just to make a few introductions and orientations, you know, it's a meeting, we need a little bit of logistics, et cetera. I think one of the things I want to do is recognize the members of the Board of Directors so that you know who they are, those of you who are guests or new, and realize that how important that board is to the Association. They do wonderful work and work very hard. And they're also ears open to you and that's why it's important that you know who they are and I really thank them. Please don't applaud. I know some of them would like to be applauded, but let's just do that, because, and we do and you can applaud them, you know, at the end or something, but let's just get on with this. So, but please do board members stand so folks know who you are. Deb Carver, University of Oregon. Colleen Cook. Miguel. Colleen. Carol Pitts-Dietrichs, Ohio State. I'm not, there she goes. Ernie Ingles, University of Alberta. Deborah Jacobs from Duke University. Anne Kenney from Cornell. Wendy Lujet, University of Minnesota. Jim Mullins, Purdue. Sandy Yee from Wayne State. Another person who could borrow my school when she wants to. Errol President-Elect and Vice President Winston-Tabs from Johns Hopkins. Is he here Winston? There you go. Past President, Brinley Franklin University of Connecticut. In addition, and I really, it's wonderful to work with you folks, in addition, board members include the ex-officio, the chairs of our strategic direction steering committees, and it's, I can't tell you how terrific it is to have them and to be on the board and be able to talk in an integrated way about programs. And that's Carton Rogers, who is the chair of the Transforming Research Library's steering committee from, Pat is Carton here, and I know he certainly will be interested in hearing from any of you that want to talk about board business or his committee's work. Jim Mullins from University of Colorado at Boulder, public policies. And Anne Wolpert, MIT. Reshaping scholarly communication. Thank you. And I hope you all know Charles Larry, ARL executive director, but in case you're not sure what he's wearing to the meeting areas. Okay, so together these really are the people that keep ARL policies and programs in place and looking ahead and aimed at you. So they're important for you to know. Please talk with them during the breaks. So this is a really, the next part is introducing people that many of you may not yet know, and I hope you will soon. And that is our new member representatives. We have four of them with us here today. And four of our old members, or older, or just established members who have agreed to introduce them. Actually, the first, the first introducer isn't old to us or that established, he was just introduced recently, so we get to see him again. So first, Simon Liu will be introducing Joyce Backus to us. Joyce is the new director at the National Library of Medicine. So you can use the podium or you can use them, Mike, if you both want to come on up. All right, good luck to you everyone. Can you hear me? To this particular organization, the Association for Research Libraries. Currently Joyce, she is the Deputy Associate Director for Library Operations at the National Library of Medicine. Prior to that, she was the Deputy Chief for the Public Service Division. In that capacity, Joyce developed and deployed the Menon Plus Connect. This particular services linked the patient's portal and their electronic health records to authoritative information from NIH, NLM, and other resources. In the past, Joyce also have served as the Section Head for the Reference and Web Services. She's also the Head of Web Management Team, a System Librarian, and also a Reference Librarian. So Joyce has joined, has been with National Library of Medicine since 1985. As start as a so-called Associate Fellow. In the past many years, Joyce has a distinguished career. She has received numerous and many, many professional recommendations. Let me just kind of list a few of them. First is we call Thomson Scientific, Frank B. Rogers. Some information and advancement of work from the Medical Library Association. And also Aida and George Price, Aida Price, from also the same thing, the Medical Library Association. She has also received the Merit and Directorate Award from the National Institute of Health. The Frank B. Rogers Award from the Board of Regents of the National Library of Medicine. And also most recently, the Innovative Innovation Award from the Secretary of the Department of Health and Human Services. So Joyce has a great distinguished and outstanding career. She has an AB degree in Sociology and also English from Duke University. And Master's Degree in Library Science from the Catholic University of America. So with that, let's give her a big welcome. Thank you, Simon, and welcome, Joyce. And Ann Kenny is going to introduce our new colleague from Harvard University Libraries, Helen Shit. So I'm one of those old directors who can't do what Simon does, which is to rattle it off the top of his head. It's been decades since I've been able to do it. But I'm very, very pleased to introduce Helen Shenton, the first Executive Director of the New Harvard University Library. Helen, we're really pleased to welcome you to our midst, not just for the opportunity to get to know you, but we're really curious about what Harvard Library is doing. And I thought she brought some really terrific talents and traits to the table. First, is her ability to imagine a new way of doing things and then actually bringing that about at the British Library. For instance, Helen was charged with confronting many of the issues that Harvard Library, indeed all of us, face today. Digital preservation, library space, storage of print and digital materials, and oh yeah, evolving patron needs. Helen transformed the British Library's collection care department into a world-class operation, including the establishment and opening of the State of the Art Center for Conservation. She's a trained bookbinder, and is probably the only brother Helen in this room, a title she holds as an associate member of the Art Workers Guild founded by William Morris. Moving beyond physical objects care, she helped build digital preservation expertise and costing analysis into the very fiber of the British Library. In 2004, you may not remember this, Helen, we served on a panel together at the British Library, and she was the first person I heard speculate about the role of a digital conservator. Helen was also instrumental in massive digitization projects at the British Library, including the virtual reunification of the Codex Sinaticus, the earliest New Testament in the world. She has also to her claim to fame until July of 2009. She was one of only several people living who had actually seen all parts of the Codex in the four locations of London, St. Petersburg, Leipzig, and, oh yes, St. Catherine's Monastery in Sinai. But by the afternoon of July 6, 2009, after the British Library had released the online Codex, 20 million people had viewed it. Second, Helen has a way of promoting collaboration and encouraging others, but then knowing when to get out of the way and not get bogged down in the details. In the early 2000s, Cornell, the British Library, the University College London, and the Digital Preservation Coalition collaborated in a digital preservation training program. An email list was set up to promote the exchange of ideas, and folks were given the choice to opt out. While confirming her support for the program, Helen wrote, I'm very happy not to be on the list during the development stage, and she ended, good luck. Yeah, I still got that email. Third, Helen takes people at their word. Little did I know when I offered to help in any way I could with her transition at Harvard, but that would extend to my AUL for technical services moving to Cambridge. I can tell you, Helen, that he's very excited to be there and to be working with you in this brave new effort. But to all of you, I'm warning you that watch your rhetorical flourishes around Helen. And when all else fails, a final trait of Helen's will come in quite handy. Her British accent, which most Americans just find irresistible. That and throwing around a few temporizing but soothing terms such as whilst, she does use whilst, and quite should go a long way when dealing with recalcitrant faculty, immovable staff, and an administration that sees the library transition as a prototype for the rest of Harvard. So, Helen, welcome to our side of the pond and to our world. Thank you. Thank you, Anne, and welcome, Helen. Now Susan Nutter is going to be introducing Denise Stevens to us. Denise, who is now in charge of UC Santa Barbara. Thank you. And I need to tell Denise that I'm not also going to be able to do what Simon did. I have my notes with me. And I prefer established, Carol, established, because I really am old. I saw someone look, I saw someone looking over that lineage chart of ARL directors, and I think we've got to stop putting that out. I must begin by crediting my colleague, Karen Wittenberg, with discovering Denise Stevens and getting her on the right path at UVA. And I say, I must because we got into a bidding war as to who was going to introduce Denise. And in winning, I had to make that concession. So, you all know Karen. I was privileged to have the opportunity to be Denise's mentor in the ARL Leadership and Career Development Program. And that's a program that I value highly and really worked hard within ARL to establish that and I think to be able to. Now, I'm known as one who likes to fast track people and people with talent and leadership potential. And my mantra is that one should take a job for which one is not quite ready. Don't take a job that won't challenge you and that won't require you to learn about yourself. And I tend to push people out of the nest and I find that they fly. Well, Denise Stevens has put me and my philosophy to the test and has flown at supersonic speed. As I worked with her and became a colleague, I was awestruck at her intelligence and willingness to challenge herself to take risks and she has surpassed all of my expectations. Khan and I have really viewed this with a sense of wonder and I have edited this so much that I can hardly read it. Denise started her career in research libraries at the University of Oklahoma as a library assistant and received her MLS from that school in 1993. Now, I want you to start counting because that's 18 years ago. She joined the University of Virginia Library, Kudos to Khan, that year and served in various program leadership roles for seven years. After participating in the inaugural ARL leadership and career development program cohort in 97, 98, that's four years out and that's when she became my protege. And I have to say that I did go around bragging that I had the best fellow in the program and I hope I'm not insulting anyone. There may have been people tied with her as well. Following that, she served a short stint as department head at University of Kansas before moving on to work with Peter Graham at AUL, as AUL for public services at Syracuse University and she was really very helpful to Peter and stepping up and serving as acting university librarian. So there she is, that's number one research library. Now, Denise then went on to become vice provost for information services and CIO and strategic and organizational research librarian at the University of Kansas where the library reported to her. So now that's two. Now Denise Stevens has joined the University of California Santa Barbara and she joined them in July and I think her UC colleagues are going to be thrilled to have her as part of the team. I am very, very proud to introduce you to Denise Stevens, a smart, savvy, witty and fun colleague who makes things happen. Her chief interests are organizational development, assessment and information infrastructure development and I look forward to see what her next accomplishments are going to be. Welcome Denise. Thank you Susan Ann, welcome Denise. And now Carmen Wittenberg did get her term at introducing someone as well and because she's going to introduce us to Diane Paul Walker who's now at Notre Dame. So certainly all the good things she says about Denise but forget believing about the bidding war. She actually is blackmailing me because she knows way too much about my sordid past. So it is my pleasure to introduce Diane Walker who came to UVA as the music librarian and like so many great music librarians was recruited somewhat reluctantly into library administration. At UVA she has been responsible at one time or another for virtually every area of the library and her leadership has met every part of the library better. Most recently she was deputy university librarian and in that role she made the library ever more visible and initiated a number of powerful collaborations. In addition she was co-PI for our eight very successful annual series of the Mellon funded scholarly communications institute and they wrapped up this we wouldn't let her go until she finished the last one. Diane is rather reserved so undoubtedly undoubtedly I have already gone on far too long for her comfort but I would be remiss if I didn't mention. I know that I'm not supposed to speak but I did tell her two sentences. I'll be short characteristics. She is unfailingly gracious and calm no matter the situation. She treats everyone with respect. She has successfully met her colleagues both at UVA and within the profession at large. She does the right things and she does them well. She is quick to give credit to others even when she has done the lion's share of the work. In addition she is a wonderful dining companion who enjoys good food and drink a critical qualification in my view certainly for a colleague of mine but also for a university librarian. She makes the best martini I have ever had and she was kind enough to part with the recipe before she left. I promise not to share it. She gardens enjoys the outdoors, is an avid traveler and is supremely musical. She also has a quick wit and very rye sense of humor. Diane will lead the Notre Dame libraries into the future they so richly deserve and you will enjoy her as a colleague. Thank you both very much and welcome Diane. We now have a little special announcement on the program that a little I'm going to let Simon tell you what it is. Good afternoon again. Before I join any service and associate director at the National Library of Medicine for ten years today is really my great honor and distinct pleasure to present to ARL the resolution at resolution from the border regions of the National Library of Medicine. So here it goes. I need to make sure that everything's at right. Thank you. To thank the association of research libraries for its long standing effort is supporting of research libraries and the diverse community they serve and its long support for the National Library of Medicine on the occasion of the library's 175th anniversary. ARL has since 1932 foster cooperative actions to improve the capacity capability and the collections of North America research libraries and to promote equitable access and effective use of recorded knowledge in support of teaching, research, scholarship and community services. NARM has benefited from membership in ARL since 1948 and has relied upon its training, evaluations, presentation proving and public policy programs. ARL has collected and compiled statistics to monitor the evolution of the field and to inform decision making by decreeing describing the collections, expenditure, staffings and service activity of ARL member libraries. ARL held association of academic health science libraries and NARM to establish a successful leadership fellows program to prepare future directors of academic health science libraries. ARL has steadfastly defined a balance between the right of the producers and the user of the work under copyright and has been a proponent of creative copyright arrangements and open access publishing models. ARL has been a strong advocate and a defender of the role of government agencies in developing and disseminating innovative information services including NLM's main lines, government central and also POPCAM. And ARL's full advocacy education and strategic alliances has been a key supporter of public access to the result of federal fund research and the NIH public access policy. Now therefore, it is resolved that the Board of Regents of the National Library of Medicine thank the Association of Research Libraries for its long and steadfast support of the National Library of Medicine and for its tireless effort on behalf of research libraries and their mission to increase access to research information for the benefit of the people of the United States of America and the world. Virginia Tenji, the chairman of Board of Regents of the National Library of Medicine, thank you.


Good morning, everybody. I am just delighted to welcome everybody this morning to the US Institute of Peace. As you heard, my name is Nancy Lindborg. I'm the president here. And I am honored to be able to welcome such a distinguished group of foreign policy, national security, development experts, so many distinguished foreign dignitaries. So a special welcome to the many ambassadors who are joining us this morning. And I want to begin by thanking our sponsors and our thought partners who really helped make today possible. We had generous support, wonderful partnership, many thanks to LMI, the Boeing Corporation, Chevron, as well as Robin and Eileen Shields West, and Nancy and Harold Zirkin for their generous support, both of this event and continued support for USIP. We're very grateful for the partnership of many think tanks who have been both good counsel and really key to helping us bring together such a diverse crowd of perspectives and ideas and backgrounds, thanks to our friends at the American Enterprise Institute, the Atlantic Council, the Carnegie Endowment for International Peace, the Center for American Progress, and the Heritage Foundation. I'd also like to thank our media partners, Politico and Sirius XM Radio. They are bringing this event to a broader public audience. And also, I want to note that the event is being broadcast on C-SPAN. For those of you who are following us online or on social media, we invite you to follow along by using our mobile app, USIP Passing the Baton, you can download that on your phone, or on Twitter using the hashtag Passing the Baton. This is the third time that USIP has hosted Passing the Baton since 2001, when Sandy Berger first passed the baton to Condi Rice. And the goal of this event is to generate ideas, to share views, to bring together the kind of perspectives that we need to discuss together to contribute to a seamless passing of the baton from one administration to the next. And at a time that we have so many pressing global challenges around the world, we are pleased especially to host the event this year in our own building. This building is the newest addition, one of the newest additions to our National Mall. And as part of our congressional charter, USIP is founded to represent the American people's commitment to peace. And this building is really a physical expression of peace as the soaring hope of humankind. So it's appropriate that we're having this conversation here today under our Ansary Dove in the George P. Schultz Great Hall, next to the Madeleine Albright Wing. And looking out over the National Mall, which reminds us every day of the foundational resilience of our nation. So we're pleased everybody is here today to be a part of that. The US Institute of Peace was founded in 1984 by Congress as an independent national institute dedicated to the proposition that peace is possible, peace is practical, and it is essential for our national and our international security. So we research and apply the most effective ways to manage conflict before it can become violent and to resolve it when it does. We work in conflict affected areas around the world with local partners helping to build peace both from the top down and from the bottom up. And for us, peace is not an abstract concept. It's what happens on the ground. It's what saves lives. It enables families to be safe and dreams to be realized. And you'll hear later today from my colleague, Sarhang Hamasayid, who will talk about our peace dialogues into Crete, Iraq, which have saved lives and enabled hundreds of thousands of people to return home after the terrible conflict there. Just like we were able to do 10 years ago when the US Army asked USIP to mediate a peace accord among the rival tribes around the city of Makumidea in Iraq known as the Triangle of Death. So there, working with a team of Iraqi mediators who we trained and supported, USIP conducted a successful mediation that ultimately allowed the US Army to withdraw 80% of its troops to save $2 billion over the year and most importantly to save countless Iraqi and American lives. In Makumidea, peace was possible and today at the 10th year of that effort, peace still holds. And now I have the great pleasure to introduce a wonderful friend, colleague and wise counsel, Steve Hadley, a distinguished public servant, former national security advisor and our wonderful dedicated chair of the US Institute of Peace Board. Steve. Thank you so much, Nancy. This is an amazing group of people we have gathered here today and we are very grateful that you took the time and came. Before beginning the program, I wanted to share a few thoughts about why today is such an important day. I speak from some personal experience. I've been through a number of presidential transitions from both ends of the process, sometimes transitioning in happily and sometimes less happily transitioning out. But either way, the process could not be more important. Each administration assumes office with both the problems and the tools left by its predecessor. And a well-managed presidential transition can help the new administration get a jump on the problems and get a better appreciation of how to handle the tools for addressing those problems. And it gives the new administration a sense of what it has to build on as it fashions its own approach to the problems that face the country. The goal of a presidential transition should be for the outgoing administration to do everything it can to help the incoming administration assume the awesome responsibilities that it is about to inherit. That's what we tried to do in 2008. President Bush made it very clear to all of us that he wanted to do everything he could to ensure as smooth a transition as possible. And President Obama has been equally clear that he expects in his word a seamless passing of the Patan to the new Trump administration. And that transition can and should extend past January 20. The officials of the new administration should feel free to continue to call on their predecessors for advice and counsel. And the outgoing officials should be clear that they are willing to provide it. And we in this room should pledge together for the good of the country to focus on the substantive challenges and opportunities facing the new administration and offering it our help and support. And I would hope that the cooperation among the five Washington-based institutions that has produced this passing of the Patan event can be expanded to include others and replicated in various forms of ongoing collaboration and discussion. And I would hope we would do this on a bipartisan basis for the nation's security and foreign policy are strongest and most effective when they are underpinned by bipartisan support. And at the end of the day, it's not about the side of the aisle we sit on because we must all stand together to safeguard the national security of this great country of ours. As some of you know, the USIP hosted a number of private policy dinner conversations last night. The idea was to bring together senior government officials, members of Congress, representatives of the media, and leaders from across the business think tank and civil society communities to discuss the challenges facing our country. The conversations took place under Chatham House rules of non-attribution, but we wanted to share some highlights to set the stage for today's discussions. And for that purpose, I would like to introduce Damon Wilson, the executive vice president of the Atlantic Council, to give us a summary of the collective wisdom that emerged last night from our dinners. Damon. Thank you very much, Steve. Thank you, Nancy. I want to thank the US Institute for Peace, all of our partners that have helped make today's event possible, and as well as the rapporteurs, the moderators, that really helped collect the key takeaways from our conversations last night. As Steve said, my task is to offer some insights, some conclusions, and to try to summarize briefly the several hours of conversations that took place among 80 plus foreign policy leaders. Mr. Hadley, Steve, set the tone. Let's see, is that a little bit better? A little bit better. So Mr. Hadley set the tone. He set the tone for last night's conversations very much as he did now by underscoring the importance of how... Thank you. Underscoring the importance of one team helping to prepare the next for success. I had a chance to work for Steve during one of those transitions and see how he set that inside government. And it very much informed the conversations last night. As one of the participants put it, at the end to sum up the conclusions, count me in and helping to support the next team. The premise of many of the conversations while we were there to help share experiences, insights, and to help the team succeed, there was an acknowledgement, almost a premise to the conversation that the biggest challenge that folks are often likely to face are the ones that we're not prepared for, whether at 9-11, the Arab Spring. Among the first conclusions that I think really permeated the conversations last night was that U.S. success abroad is anchored in who we are at home and our strength at home, beginning with a growing economy that creates options for us internationally and a sense of a greater integration on security, economics, trade, and energy. The second part of that is our democracy and can our politics help solve problems, deliver results, and do their values, our democratic values, stand strong in differentiating us from some of our adversaries. And on the military front, are we able to come together to support the investments, bending sequestration, sustaining investment, and nuclear modernization? There was a back to basics theme in some sense on what makes the U.S. attractive at home and what makes us influential and effective abroad. The second main conclusion, I think from many of the conversations last night was the centrality of the U.S. role and the world and almost a call across to a word, to a tee, of more leadership, not less on the issues that are on our agenda today. Sure, a recognition of the complexity that we face, questions about the tools, whether we have the tools and imagination to deal some of these challenges, but that we agreed that it was in the U.S. interest to do so and acknowledge that we need to use the full range of tools, influence, power to advance U.S. interests. Our friends and allies want it. And in fact, in the absence of the U.S. acting on key issues, the situation often gets worse. And this therefore means we have to make a more intentional case with our own electorate. The third key conclusion, I would argue, take away from the conversations last night was that long-term strategies matter. There's an observation that some of our adversaries are very effective at having long-term strategies that span from one leader to the next. And an acknowledgement that a long-term strategy and a democracy like the United States, as Steve said in opening, requires bipartisan support is more effective and hence engaging our publics, the Congress, politicians in this effort, is important to ensuring a sustainable, consistent approach. The fourth set of issues last night were the common analysis of challenges that are high on the American foreign policy agenda. Beginning in the broadest sense with the fraying or the breakdown of the U.S.-led rules-based international order. Discussion from fragile states to hostile challengers to the rise of technology and how that impacts our effectiveness. A sense that the global system itself is in play. And therefore, there may just be an opportunity, if not a responsibility, to reshape that system in our interests consistent with our values. Related to that, there was quite a bit of conversation about a battle of ideas, a battle of ideals, if you will. Sure, information wars, but more than that. Is the world increasingly safe for free market democracies or for authoritarians? And how do we shape those outcomes? There is a sense as well in terms of our challenges of the return of the nation state, China, Russia, Iran, North Korea, a China that can be a challenger, but also a partner, increasingly a stakeholder in this order. A Russia that's also seen as a challenger, but where there are strategic areas of cooperation and how do you have dialogue that doesn't mean a blank check. An Iran where there is much focus more so on the future rather than the past on strict enforcement of a nuclear deal and checking nefarious interests. And a sensitive out of all the nation state challenges we face that North Korea may be the most likely to test. And of course, the non-state challenge, particularly from terrorism, ISIS, but it's broader than that with a sense of high impact, low cost challenges to American interests. As part of that conversation, there was an interesting exchange on black swans or blind spots, if you will, from space to genetics, genome editing, to global pandemics or the GPS system being attacked. And there was a special conversation about what it takes for us to rise to address those challenges and a conversation, therefore, about our alliances and our allies. A broad recognition of the unique asset the United States has with our alliances about how this is overwhelmingly in American interests that it helps us deal with these challenges and that the US is a catalytic power and galving as other nations to solve the challenges. But also a healthy recognition that we have to reconsider some of those assumptions and ensure that our alliances and the structures are adapted for today, are fit for purpose, if you will, and that we've set sufficiently high expectations whether it's on reform or defense investment or global engagement of our allies. To conclude, I think last night's dinner conversations really underscored a tone across folks that were both supporters of President-elect Trump as well as opponents in the political process. That first, there are some principles that are longstanding and therefore there will be some continuity. There also will be change, of course, but there's something to build on. Second, I think the part that reinforced all of the conversations was our strategies, our policies, our foreign policy is most effective when it does enjoy bipartisan support. Third, a real sense that there will be a need after the noise of our election and the divisiveness of our campaigns that there be some clarifying messages sent to the world, to our allies, so that our friends can count on us and our adversaries don't underestimate us. And finally, I'd close with a sense of optimism that pervaded some of the conversation. A complete recognition of the complexities that face the United States, the challenges of the task, but also a sense that the United States, perhaps more so than any other nation, is best prepared to help navigate this complexity to navigate these challenges, not simply to defend the past and defend the status quo, but to play a leading role in helping to shape that future and adapt the system for interest consistent with our values. Thank you. Turn it back. Thank you, Damon, and you can get a sense from that really excellent summation and thank you for doing that overnight with such articulateness of the breadth of the set of challenges. It's hard to just narrow it down and we do have the imperative to grapple with this so that we can play the role that the world expects us to play. Throughout the day, this event has been designed to ensure that there's truly interactive engagement. We have an extraordinary collection of opinions, of experiences, and views here in the room. So we have, coming up next, the first of our speakers, we will be delighted to welcome in a few moments Secretary of State John Kerry. And for the next few moments, I'd like to ask everybody to turn to your part, your neighbors, and have a conversation about what you just heard. How to...


He was cold next summer real quick Trust me. So put the work in man. Trust the process. Don't rush the process


Yeah, the leader of the airing brotherhood you've got power you've got control you've got money you've got people who would kill for you How hard was the decision then to leave it and then put your own life in jeopardy? Well, it wasn't difficult to leave it. I mean it was people asked me about that all the time How difficult was the choice? It wasn't a difficult choice, you know You do once I knew what I was looking at And I knew that that was contrary to who I was as a human being and the way that I was raised It was a very easy choice what followed I Never could have anticipated by way of more violence and corruption and Just an entirely different, you know by way of example The scenarios are so extreme by way of being opposite But similar nonetheless Then my time with the airing brotherhood is the first ten chapters of my book My growing up time in the airing brotherhood and that's that's ten chapters. That's part one part two Is once I stepped away working with law enforcement testifying in court threats on my life, you know snipers on a roof bombs on the Transportation car. I mean it's just corrupt administration That's an entirely different scenario So, you know, I'm really at odds here right now I may just go ahead and publish the first ten chapters and let that be out there because that says one thing and Then continue working on the second ten chapters and put that out there because it says something entirely different We'll see what was the reason for leaving Michael Well, it's those two truths You know, there was individuals that were going to be executed and had and were executed as a matter of fact Of course, there was a visit by the elders. That was huge so far telling me you can't serve two fires and Then there was the idea of There was a case up in Oregon and It was a Hell's Angel case And it wasn't something that was condoned by Sunny Barger. I want to make that clear Because he was the leader there the Hell's Angels. He just recently passed over Again, I'll say it rest in peace, you know, Sonny was a friend and But Margo Compton and her two six-year-old twin daughters and her boyfriend were executed by two shooters Now Margo was a witness against Buck Garrett who was the Second in command of the Hell's Angels time She testified for the Feds against him for pimping and pandering. He got four years But when he found out where she was at and he did He sent two shooters up there They went into the side door They shot Gary who was on the couch They went into the bedroom. They took Margo's two six-year-old twin daughters They laid him on the bed wrapped their arms around their teddy bears They held Margo and then they shot the little girls in the head while they made her watch and then they shot her in the head. I Cannot Ever under any circumstances seeing myself condoning that being a part of that being associated with anybody Who would be a part of that? So that was one of the factors and I went up and I testified against the Hell's Angels in that case And the courtroom was filled with Hell's Angels There was threats on my life and everything else and I would do it again Without hesitation There was a situation where an individual was testifying against members of the Aryan Brotherhood And so the subject was broached in so far as to kill this individual's wife and daughter and then his parents And it took everything I had in me to move them away from the wife and daughter and the mother and it left the father And I still bear the responsibility for that father having been assassinated Because I didn't stop it. I stepped away from the brand, but I didn't stop it You see I had an opportunity to stop two guards from being killed In the federal prison by AB members And so I went to law enforcement with that and told them that Guards are going to be killed and they laughed at me Because the Aryan Brotherhood had never taken a violent position against guards before but now that It shifted it had changed just like perpetrating violence against innocent people had changed And so with these changes Staring me directly in the face I had another choice to make was I going to be a part of this and I was not could not Would not and so I made the decision to step away but with that came a responsibility. I Had helped build this group this group would that was now going to Perpetrate violence against innocent people so I had a responsibility to bring that group down So I've done training films for law enforcement. I Went on a lecture circuit speaking strictly to law enforcement to put them up on that game same It and it continues to this day You know, I'll still work with law enforcement toward their understanding of what they're dealing with Whether it's drive-by shootings people that shoot into a house where children are killed.  That's a warrior. I don't think so How hard does that to live without pen make all that obviously you can see you getting quite emotional whiff Well, you can't get killed like how do you? It's it's it's you know, you cope you cope you deal with that, you know, yeah You know the old promo faction over there in Ireland There was a time when I supported that by way of running guns and otherwise well when they hooked up with the PLO and they started bombing civilians Then I removed myself from it See man to man. I don't have a problem with that If as men we're going out on a battlefield and we're going to do battle because we believe in some principle Whatever it may be even if that's just controlling your resources To this day, I don't have a problem with that What I do have a problem with is when you victimize innocent people And people call that collateral damage. I don't think so It doesn't work like that.  That's not a warrior That's not a human being Now I know it happens all over the world But in this context I'm talking about gangs and there needs to be a lot more discussion about it You know, I hear too much talk about all you know, he's a snitch. She's a rat That's what that's the language the gangs develop so that it won't come back on them They want to shame you So that you won't give up their game. I mean my goodness, you can go back years where you know, maybe your parents told you Don't be a tattletale Well, I understand that in that context, but that's not what we're talking about here We're talking about victims. We're talking about innocent people and that's important very very important And there needs to be a dialogue about it. What is it they say? See something say something You see in this gay and age that becomes critical If you see something and it doesn't look right say something


What's the word y'all, we gotta one take this one. I ain't got time to edit. We gotta, this feels like back in 2019 where brother one take everything. I'm a little bit lost from those times. Cary Irvin requested a trade. Right when we thought that O.J. Anubi was gonna be the biggest name on the market. Rival executives were talking about the 2023 Deadline so I do one of the worst in recent history. Cary Irvin said, nah, I'd rather be traded right now. Trade me before this deadline. Or I'm just gonna walk a free AT anyway, Joe Sasso.  Chris Hayes reported about a week ago that Cary Irvin wants to stay in Brooklyn. He wants an extension. He wants a certain amount of money. He wants a certain amount of years attached to that. And apparently Joe Sy and whoever's in charge over there don't believe that Cary Irvin's worth what he wants and boom, this is how we get to this point. And this is so crazy and so crazily timed because the Brooklyn Nets, when they've had Cary Irvin, Kevin Arant, Nicholas Klax and their top three players playing, they went from a team that were towards like the plan to at one point there was a number two seed in all the basketball right before the Kevin Arant injury. And now this man, Cary Irvin said, I want to be on a new team. It's crazy. Now I'm not a guy that's gonna get here and talk about priorities amongst NBA players and their own personal lives. It's not really important to me, at least in this moment. But I mean, this is a good opportunity if the idea is to win a championship. Brooklyn has a core that is good enough and they were trying to be buyers' deadline. Now they gonna have to finagle and retool and there's Kevin one out now that Cary is gone. Like I don't know what's about to happen in Brooklyn. But Cary Irvin said the bag is more important, which I can't be mad at him about. He wants this stability, I guess. And it's crazy all of this unfolds since this morning. So the first report, these are all from NBA Centrum. The Lakers believe that they're one move away from being a legit title contenders, okay? The second one says that the Lakers no longer are trying to preserve cap space for the 2023 free agency. Okay. And they just like that Cary Irvin requested a trade. That tweet had been out 22 minutes. They aren't looking to preserve the 2023 cap. And if you didn't know, the 23 cap space would have probably been used on Cary Irvin anyway. So they probably thinking like, hey, this is our time. And I saw my boy Isaac from the D3 podcast make a funny tweet saying that this is Rob Polinka's legacy game. Like this is what we've been waiting for. I made a video about a month or so ago when the Lakers won the streak and Anthony Davis playing in the Calibre level and LeBron was doing this thing saying that the Lakers have to do something.  And he made the Roo Hatch more trading than it's been what a week and a half since where he's been on the roster. He's been a plus. And now you have an opportunity. Maybe, again, maybe it depends on what Brooklyn wants to do to potentially bring in Cary Irvin who has won a championship with LeBron James. Whoa. Now, how do we get to this point? I made a tweet trying to figure, okay, we know that Cary Irvin wants out. How do we get him to his next team? What teams would be interested? And these are the teams I came up with. And I was thinking along the lines of these are the teams that might want him slash want to extend him. Cause a lot of teams could trade for Cary Irvin but his priority is getting his bag and getting his extension. So these are the teams I came up with. Obviously, the comment section is open. You let me know. Number one on my list was the LA Lakers. We're going to talk about what that potential package could look like. Number two was the Miami Heat. They feel like they need a big time move and Cary Irvin is really good. Save what you want about Cary Irvin. Save what you want about Cary Irvin. He's a really good basketball player. Number three, the Washington Wizards. And I saw some people like Washington. It's the goddamn wizards, man. They're on a six game win streak. They want to keep their top three court together. I'm pretty sure they have not all of their draft capital but tradeable draft pieces. Now, Brooklyn is probably looking to get people that can help them right now considering they, I don't, we don't know what Kevin is going to do. If Kevin wants to stay in Brooklyn, they're not about to trade Cary Irvin for a bunch of draft picks. They're going to probably want some stability but Washington would be a team. That's 100s of picking up the phone. That's what Washington does. The next team is the Dallas Maverick. Put a question mark because I think the Dallas would maybe draw a line in the San O'Carrie Irvin mostly because of the off course stuff. Again, we're not here to talk about all of that right now. We're talking basketball but we've seen some situations in Dallas's history where they don't really play games with some of the off course stuff. And then lastly was the LA Clippers who in desperate need of like elite level point guard play. Now, do these teams have the assets to potentially get Cary Irvin is the real question. You know what I'm saying? If you're the Brooklyn Nets fan, you say, okay, the Lakers want Cary Irvin.  Okay, we got 27 and 29 but we have Kevin around on the roster right now. And in 2029, we don't know if we're going to have Kevin Arana so why do we care about that pick when we see that this team can be good enough, right? So how do we, how do we give them Cary Irvin just for those draft picks of Russell Westbrook? That's not fun to us. Russell's been decent off the bench but he's not coming to Brooklyn and we're still one of the best teams in Easter Conference. He doesn't feel the shoes of what Cary Irvin have done this season. We're gonna have Nicholas Claxton, Russell Westbrook and Ben Simmons on the court together. I don't like the recipe for that. I don't know about that shooting.  But this is my proposal for something like this. If the Lakers are the number one destination, let's be real, it seems like they are. You know what I'm saying? Again, I'm being unbiased. I feel like the Lakers are the number one destination. So how can the Lakers make this happen? Of course, the Russell Westbrook concert has to be a part of it. They have 2027 and 2029. And if they're talking about completely unprotected picks that are tradeable, those are two of the most valuable picks in the entirety of the NBA.  It's gonna be a three. Damn, it might even be a four-teamer. And one of the teams I think holds the pieces. And a lot of this is that man Danny H. That man Danny H. can facilitate a big-ass trade again. Because one thing that the Utah Jazz have are competent and good players that you can put alongside Kevin. Does it lower the ceiling of the team? Absolutely, you're losing Kyrie Irvin. But it raised the floor a little bit. So in this hypothetical, again, I don't know exactly who the players are because I know they love Jordan Clark, she's been stellar for them. But if it is Malik Beasley, if it is Mike Hanley, if it is J.R. Vanderbilt, those three ended up in Brooklyn. And then the draft picks ended up in Utah. And then Russell Westbrook ends up in Utah. Considered to be bought out maybe. And then Kyrie Irvin ends up with the Lakers. Like I think the framework, again, that's not the official trade. I ain't even putting in the trade. I don't know if it works. But like the framework of a three-team trade dealing with those three organizations makes a lot of sense. But in this case, again, just like every other trade in the history, this man Danny A's been a part of, he has the ultimate leverage if he is going to be the third team. Whoever ends up being that third team has the ultimate leverage. And that's only in the Lakers' Brooklyn deal. Some of these other teams can maybe get it done without a third team, but it is a little bit harder. Like the mind of he would be interested, but what? Tyler Hero's money doesn't even kick in until next season. So now we gotta figure out a team that wants to take injured Duncan Robison. And it's like, it's going to be if... Honestly, the more I think about it, I feel like majority of these destinations for Cary Irvin will require a facilitator team that might take on bad contracts and draft capital to make Cary Irvin get to whatever team he needs to go to. Again, thinking about these other rosters, the Dallas Mavericks said that they are willing, they are willing to trade Dorn Finney Smith for a superstar. We laughed at him. We absolutely laughed at him. But maybe Dorn Finney Smith, maybe Spencer Dinwiddie. And again, I'm just talking. These are other facilitating players that could potentially be in a deal that you can put alongside Kevin to make you feel like, okay, we still got a chance because now we got more depth. Again, if we Brooklyn, are we happy about this? Absolutely not. Cary Irvin's an all-star star in the season. He's been phenomenal. They lost the first couple of games after Kevin Aram went out with his injury and cystin. They've been really good.  But the last time somebody on my organization, a star player requested to trade, we smoothed it out. It worked out perfectly. So this could be another situation where a player in the Brooklyn Nets organization requests to trade and nothing happens of it. But for us, this is fun. Now we do have to talk about whether or not this means, what happens with Kevin now? This Kevin go back and say, all right, Kai's gone and we not even, there's no star player that you get him back in the Cary Irvin trade, right? There's no star player. So now you telling me I gotta go get more role players, which is cool. But again, Kevin Aram made the interview where he's talking about, they throw me out there where Edmund Sumner. Remember that happened at the beginning of the season? It all looked like he really cared about the role players. He want another guy alongside him. So does it open up the worms of him requesting to trade again and of Kevin is back on the market? Oh my God, I don't even know what happens there. If Kevin is back on the market, I'm looking around, I'm looking around. I just don't know. The Nix, Nix fans, you missed out on Donovan. Maybe you can hit on Kevin this time. Like what teams, of course, a lot of teams would be interested in Kevin, but what teams will have the package? Cause if I'm trading Cary Irvin, okay. And I'm trading Kevin, this is where we're starting to think about draft capital and stuff. We're not caring about Dwarf and Smiths. We're not caring about the Mike Collies in the world. If I have to trade both of these guys, cause they both won out, this is the moment where I'm thinking about the future because we don't even own the right strong picks. We got some swaps and some other deals. So let's go ahead and get a lot of those Nix picks. They got a Dallas pick. They got this pick over there. Maybe we get RJ back because he got benched in the game a couple of days ago, but he followed it up with a 30 point win, a 30 point game and a win on national TV. So he backed it up. But the NBA is back in chaos.  Nobody, two trades have happened all of the season. The first one was for Noah Vanley. And I don't even know if I've seen Noah Vanley in a jersey since that trade. So the only move we've seen is Rihachi Moore ended up with the Lakers so far again has been looking really good for the Lake show. Kari Irving just changed the whole deadline because now a lot of teams are interested. I'm assuming I can't say for sure because again, trading for Kari Irving is deep and it's just trading for the basketball player. Again, they are one of the better teams in basketball with completely healthy. They have an opportunity to win a championship. They were a legit title contender. And he said, I don't really care about that right now. You know, so he is a guy that has become unpredictable. I guess he's always kind of been unpredictable in his career. And I can't maybe every team want to be interested, but a lot of teams will be interested in what Kari Irving and his worth and the things that he could do on the basketball court. So you let me know in the comment section. This is just my firsthand reactions. It's been 17 minutes, 22 minutes since the trade has been announced or not the trade. The rumor has been announced that he wants out. So I'm very curious to see what y'all think. And of course, like always, I'll be in the comment section. I was literally about to hit publish on my all-star reserve video. Y'all got to see that tomorrow. You got to see it tomorrow. I'm sorry, I'm sorry. It probably won't be as topical, whatever. We recorded that video. It's a banger of an 18 minute video. Y'all gonna see it tomorrow. Instead, y'all getting this one today. So let me know. Kari Irving wants out. Ridiculous.