OK. So this point we have yesterday, what I want to discuss today is the behavior of putting all things together and try to describe what happens to the workflow passing through singularities and the asymptotic behavior. Before starting anyway, I want to mention a couple of mistakes that I did in what I wrote at the Blackboard in the last lecture. If you want to correct on possibly your notes, since the part on the Blackboard is not available, only the slides are available. Well, one mistake that at some point when I did the estimates on the curvature and derivatives, at some point I wrote this, that the time derivative of the integral of the jS derivative square of the j derivative in arc length square of the curvature could be bounded after using Gallardo-Nyrenberg interpolation inequalities by this guy, 0t integral of s t k square 2j plus 3 s xc plus constant integral of k square 2j plus 1 plus a constant. So this was a mistake. Actually, this is not there, if you correct on your notes. And also, this is my first mistake. Second, where this is more precise, yesterday in the scheme that I showed you, at some point I say that when you take a blow-up, you get the generate that I never defined. What is this the generate? What does the generate mean, actually? And actually, the generate simply means that it's the limit of regular networks, and the generate encode the fact that, for instance, this guy here that we saw, it's a very important shrinker that we call the cross or standard cross. It's, in a way, a degenerate shrinker. It's not a regular shrinker. It's a degenerate regular shrinker, because actually you can see it as limit of these regular networks with angles of 120 degrees when you make this curve collapse. So the generate simply definition means limit of regular networks that yesterday I never used this word. But in the survey that I uploaded, it's quite a nice way because it suggests that you get it as a limit on regular stuff. OK, this is just to make things more precise. Now, what I want to discuss today is actually how to restart the flow after the singularity. Now, yesterday we finished our description of what can happen at a singularity time or a curve collapsing. And in that case, you have bounded curvature. And that was the case where no original collapsing. So then you can use this theorem by, very nice theorem, by Tom and Ma and Andre Knaps and Felicius. That actually you can find a bracket flow starting from your non-regular networks that actually, from the analysis that we did, only contains the only bad points are actually four points forming angles of 120 degrees between them. So actually, the point is how to restart this guy. And I'm going to give you a very rough idea on how they can do it. But it means to this theorem, let me say only one thing. I think up to now you know what is a bracket flow. It is a variational definition of a flow by mean curvature that actually is defined by means of the formula, the bracket formula, which is actually an inequality in general. And this bracket flow that this theorem produces is a very special bracket flow. In particular, because it's almost a smooth flow. For every time interval, which it doesn't get to zero, we have a completely smooth flow. It's infinity curves, all the compatibility conditions, it's a flow like all the ones we consider in this lecture. The only point is at time zero. Only here, you need the concept of bracket flow. Only in the interval containing the initial guy here, which is not regular, because immediately this guy opens and becomes something like this. And opens in the direction of the small angles, actually. Moreover, since, as I said, the bracket definition of mean curvature flow is actually given by an inequality. That inequality allows a sudden loss of mass. If your network vanishes immediately, you still have a bracket flow.  There is no sudden loss of mass in this bracket flow. And the inequality in bracket formula is actually inequality. Sometimes it's called a special bracket flow. So it's the bracket formula, given the variation of the finish of bracket flow is actually an inequality and not an inequality. So it's a very special bracket flow. And actually, we hope that you can even make the find out other special properties of this very peculiar bracket flow in this situation. OK, what is the idea that they use in order to produce this bracket flow? This is a very nice idea, technically quite complicated, but the idea is not so complex. The starting point is that let's do in this situation, which is easier and actually, for this case, the most interesting. If you have a very special network like this, exactly the cross, the flat straight cross. OK, there is an almost explicit solution, the most explicit bracket flow that let this guy evolve. The idea is to open. But it is known that from a corner like this, there is a unique expanding motion by curvature, getting out from the cone. It's something that does things like this. It's an expander for curvature flow. But actually, if you consider this guy, forget about this line here, while it disconnects the network, which actually, we don't want that. It's actually also a bracket flow. If I take the two curves, expanding curves of this and this, it's actually still a bracket flow, but it's not connected. So it's possible to perturb this expanding solution and creating an expanding network moving by curvature with angles of 120 degrees, which actually is still a solution of the curvature flow. And this guy is connected. This is OK for this special network, which is straight for a fork junction. So the idea that in the general case where the curves are no more two straight lines are curved lines, in a way you want to approximate the curved lines with the straight lines here. Because the blow up theorem tells you that the more you get close and close and look at things close to the origin, you actually find exactly the double cross that you have that. So the idea is that you get close enough here in order that the network is getting close to the standard cross, throw away what you have inside, substitute it with a standard cross, holding that ball, put inside this solution here, substitute it with this solution. There is a problem in connecting things. So you have to do it in a smaller ball, then you have to do some small curves connecting the outside, which is the original network, curved network with the inside, which is the small network given by this part here. You connect them, and then let it in the ball. Because after this replacement, that you replace the inside here with that guy there, the spanning guy there, then you let it evolve. This network is a regular network, so you can use the standard theorem for a regular network with smooth theorems. So you have an evolution for some time. And that's a delicate point. You want that this evolution doesn't develop singularities for some uniform amount of time. And then you do a sum r level with r, the radius of this ball, then you make it at the smaller levels, smaller levels, smaller levels, and you hope that all these flows, at every level you produce a flow, that all these flows sending r to 0 converge to some limit flow. If you are able to do that, then you hope that you find out at the end some curvature flow that actually is a good curvature flow for your original network.  This can be done. Absolutely not easy. A lot of estimates in this procedure must be developed. New ones, the estimates that are shown to you are not sufficient. You need estimates on the time of smooth flow, and so on. You have to do this gluing operation in a very careful way, actually, particularly in the connection between these standard guys here with the original guys outside of the ball. And in this situation, it is a little bit easier to do it, but the generalized case is quite complicated. Because if you have five points, for instance, you have several possibilities to find an expanding network for a guy like this, for instance, but actually it can be done. The paper is quite tough to read, but the conclusion is very nice, it's quite technical. But this can be done, and this is more or less the, I'm not cheating too much, the idea behind the proof of this theory. So approximation with almost explicit solution when the network has only straight lines. Good? In this case, you only need this special case of the theorem, which is a little bit easier. But actually, in general, as we said, if we have a collapse of a region, yesterday we concluded that under what we call uniqueness of the limit assumption or conjecture, we have a limit which actually gives you some C1 network only, with a non-regular multipoint like this, that about the curvature, you can only say that the curvature is going like 1 over d at the point where d is the arc length distance, intrinsic distance to the multi-junction, which actually doesn't get in this theorem. This theorem asks for bounded curvature on the curves getting to the multiple junction. But actually, the proof can be extended to cover also this case. It's actually unpublished, and we check with Feli Schulze. So I don't know if it will be published or in a notes or somewhere, or maybe in the future in an updated version of our survey. But at the moment, it's not available explicitly. But anyway, this case can be covered, so you can also understand the theorem and restart the flow also in the situation where you have a collapse of a region. As I said, possibly losing the uniqueness. You remember my very first example that for this guy here, by symmetry reasons, if you have an evolution, you also have the rotation of your evolution is still another evolution. And we hope that uniqueness could hold at least for the generic initial data without so many very special symmetries. Anyway, even if you can extend the theorem and cover this case, we can anyway conjecture, there are good evidences to conjecture that also in this case, the curvature of the limit guy is bounded. Not the curvature along the flow converging to the network S of t, but the curvature of what you find at the end. So all these curves are actually bounded curvature. This is only conjecture, but I'm trying to convince you why it's a good conjecture. This guy actually come from, for instance, the collapse of a fiber regions with this curve. And the region R is collapsing to this point. Instead, the curves here converge to this curve in the limit. And actually what is quite easy to conjecture is that the only problem with curvature are not coming from the five curves there. The only problem with curvature are coming from the region collapsing. That shrinking down, curvature must go to plus infinity. So you can expect that in all these situations, you can always separate the converging network in a collapsing part where the curvature is unbounded. Like I said, but then that vanish in the limit. And non-collapsing part, these five curves, where actually the curvature is bounded inside, up to this point. And then in the limit, since this curve, if you forget this and you know that the curvature on these five curves is bounded and take their limit, the bound on the curvature past the limit, so you expect that the five curves, which is all you see in the limit, has actually have bounded curvature. At the moment, we are not able to prove it, but well, it's quite a natural conjecture to expect that you can always make this separation between the vanishing part and non-vanishing part of your network. The vanishing part is the bad part where the curvature is exploding, but fortunately, at the end, it's gone. And the other part can be treated like we dealt with the case of bounded curvature. Today, I will state a lot of open problems and conjecture that actually we will be very happy if someone of you comes out with a good idea and let us know. So this is the standard, the easiest singularity case that I was discussing here, in my picture. So actually, this is perfectly coherent what the theorem of in my neighborhood, what it produced in this case, which the solution that is produced by that theorem can be analyzed a little bit better, so it's quite detailed. And actually, it's quite coherent with what we see in the simulation at the very beginning. So there is a collapse and an opening exactly with this central curve, exactly in the opposite direction of the collapse, of the collapsed one. There is also actually, in this case, hope that it should be possible to prove uniqueness that in general case is false. But in this case, there is hope to prove uniqueness of the evolution, at least in the framework of this theorem of a bracket flow. Which is at least, since when you deal with trees, these are the only singularities that you can encounter. So at least for trees, this would be very nice because at least for the motion of trees, you can conclude the uniqueness of your flow. So now after this analysis of singularities, what I want to discuss, OK, I have my singularities, I restart my flow, then I encounter another singularities.  What I am expecting is that since the flow is decreasing the area, the length, the total length of your network, and the boundary part now fixed, if passing singularity, your flow goes on for every time and doesn't vertically converge to a critical point of the length among the families of network with that fixed end point. And in doing this, we define this flow for every time. The only problem in defining this flow for every time, if the singularity times start to accumulate. So you have a singularity always faster and faster and faster. And this is a problem. It's, well, again, there are evidences that this cannot happen. We have a partial proof in the heuristic argument. We only miss some estimates in order to conclude that this cannot happen. What can actually happen, even if you are able to prove this conjecture, is that the number of singularities is not finite. So if they don't accumulate, you can always go on, go on, go on, and at some point, but still continue to find singularities, singularities. And then you don't have no clear idea if actually you can take a limit at infinity if your network doesn't stabilize. So actually the stronger conjecture is that actually the number of singular times is actually finite for every initial compact, at least for a three-like network. As you can guess, the collapsing singularity regions going away are surely finite. Because if initially there are finite number of regions, at some point if they start vanishing, at some point your network, if they all vanish, becomes a tree. And also because the Ilmane never shoots a theorem, it never produces regions. The expander here, that you glue in order to restart the flow, are always locally trees. There is no, in this case it's easy, but in general, no new regions can arise after the restarting theorem of Ilmane never shoots a theorem. So the number of regions during the flow is always decreasing. And starting from a finite number at the beginning, since your network is compact, at some point the number of collapsing of region singularities can be finite. Are the other singularities? The singularities where one curve is collapsing and then you have to open another equation. That a priori could be not finite. You can have an infinite number of such singularities. If instead such number is finite, well, at some point the flow becomes smooth, no more singularities. Become smooth and the evolving network converge up to some sequence, asymptotically, to something which is flat, connecting the fixed end point. Critical for the line function. Sometimes I would call it Steiner configuration. Why this happens, this is not so difficult to see. A version's part is the more delicate. Well, the fact that what we know, that the total area of your network, one of the very first computation, was given like standard curvature flow for curves by this guy here, by the square of the curve, the integral of the square of the curvature. So since if we integrate this, what you get, the area at the length at time t minus the length, well, length at time zero, minus the length at time t is equal to the integral between zero t of the integral of k square. And this is clearly positive. So if you send t to plus infinity, this is bounded clearly by L of zero. So we have a uniform bound of that integral. If you send t to plus infinity, supposing your flow is defined for every positive t, then what you get, again, an analogous argument that you have an integral for an infinite interval of some guy which is positive and this integral is bounded by some constant fix at the beginning. So which means that you can extract a subsequence of times going to plus infinity such that this guy inside is going to zero, which actually means that on this subsequence, your curvature is going to zero in L2, then you do some estimates and lower semi-continuous. If you are able to take a limit, the integral of the curvature squared is lower semi-continuous. So in the limit, it must be zero, which means that the limit is made of three segments without curvature. Moreover, if you are able to get as it is, because this guy controls the c1, if you have sequences where curvature is bound in L2, you have c1 convergence. It's one lock convergence. Then not only are made of a straight segment, but also they are made, the limit network keep the herring condition, the 120 degrees condition. So the limit guy, if you're able to take it, it's actually a regular network made only of straight segments, which is exactly what is called a Steiner configuration. This is up to a subsequence. Since here I struck the subsequence converging, so possibly change the subsequence, you change the limit that you get at the end. But actually again, what you can expect, actually, is that this limit is actually unique. So you have full convergence of your sequence to, again, another conjecture, but another expected one. If all this is what actually can be wrong, if this conjecture is not true. You could have a situation like this. These are quite easy networks, which is a tree. At some point, this curve here collapse, you get a full point, it opens in the other direction. Then after some time, it collapse again. And reopening, you get the same topological shape. So what you want to avoid is that this oscillation goes on infinite times. So oscillation of shapes. Again, here you have this guy that, a lamp type, collapse of this curve, opening, you get what I call an island. Then again, for some reason, this curve collapse, you get this guy again, it opens in another direction, and you got another lamp. And again, the oscillation is the one I like the most, oscillation between theta and eyeglasses. Again, notice that the corners here are 120 here, 60. And now here, instead, they are 120, 60, they switch. And then you get a theta again. We don't believe this can happen. And the only very speculative idea about how to avoid this is to find out some mixed combinatoric integral geometric quantity that decreases during the flow of the network. Because it's bounded below, decreasing, and decreasing on definite amount at every singularity, at every switching of shape like this. So hoping that in this way, if you find a quantity like that, you can, at some point, since you decrease at every singularity of definite amount, if it is bounded below, you cannot have a lot of infinite changing of shapes. But actually, we have, at the moment, very few ideas about the possible analytical shape of this quantity. OK, now I want to show you and collect also some problems that I mentioned during the course, and show you some other open questions and research direction. Well, the most important problem, actually, it's to be able to show the multiplicity of one conjecture that you saw enters in the whole analysis that I showed you. We really need this guy. We have a possible line very recently that we hope can be carried on in order to show it. Several, some years ago, we were able, actually, to prove it in a very special situation, a very easy one. It's a weak conclusion that if, for some reason, you know a priori that you don't have triple junction collision, well actually, the multiplicity one conjecture is anyway true. Or if your network has only one or two triple junctions, then you are able to prove it. And very possibly, again, it's quite technical, very possibly, it should be able, even locally, you only have two triple junctions. So the really bad situation that if you're able to exclude that, then you should be able to get the full conjecture in general. It's the best situation like this, where three triple junctions go to collide together at the same time. In a situation like this, that I'm going to make the curve straight, but actually think of this curve like you have some curvature. In a situation like this, the shape of your network, now I draw them straight, but think they are a little bit curved. And you have this three triple junction that for some reason are getting close each other. And after some time, they get close and close, you can imagine what you get in the limit, you get this guy. With multiplicity one and one, with multiplicity two. OK, if I draw them straight, they don't move. So it's not a counter-example. So if you want to look for a counter-example to multiplicity one conjecture, you actually have to put some curvature here around and hope that this makes your network shrinking down and getting in the limit is something like this. Well, we all believe it's not possible, but actually you're not able to exclude it. If you are able to exclude this case, well, actually this is the worst case. The case that possibly there is a possibility that multiplicity one conjecture is false. When three triple junctions locally go to collide, actually. If you're able to exclude this case, you are in good shape in order to prove the full conjecture. This is the most delicate situation that at the moment you are not able to deal with. Instead, when you have only two triple junctions, there is a geometric argument to prove multiplicity one conjecture, which is, in a way, pushing a little some geometric ideas of Hamilton and Wiesken because you are only two triple junctions. Well, let me do it in general for a network. Do this stuff. You take a couple of points, p and q here, the lines between p and q. Only if this line doesn't intersect other lines in the middle, consider the region that you get by the rest of the network and your line, call it apq. And then you consider this quotient, the distance pq. This is the distance in R2, exactly the length of this segment, divided by apq. The area of this region. OK, this is a kind of isopereometric ratio. We call it, this is also depending on t, because this is your network. Then minimize this guy among all the possible points pq on your network under this property that the segment doesn't intersect other parts of the network. And you call it q of t, it's a minimum of this guy. It can be shown that neither p, neither q, when you take the minimum, the minimum is realized by a couple of pq far from the triple junction. So you have this guy. This quantity, take the time derivative, q of t. If this quantity, this time derivative, is larger or equal to 0, well, if you take this minimum for a regular embedded network, for instance, for the initial network, this minimum is positive. Because if this minimum is 0, it's a minimum. It is realized. Means that p and q are the same point. If your initial network is embedded, this minimum is positive. If then you are able to show that this derivative is non-negative, then it's bounded below uniformly the real flow, always positive. And when this minimum is positive, your network cannot, at some point, go to touch itself. For instance, doing things like this. Why? Because otherwise, I take p from this side and q on the other side, and I get 0. So this kind of measure of embeddedness of your network. In particular, if this argument, q of 0, we know that it's larger than 0, and if this holds, so q of t is always larger than some epsilon to 0, it's another proof that embedded networks cannot lose embeddedness. Moreover, this quantity is scaling invariant. Look at this. If you rescale your network, you have quadratic factor here, quadratic factor here, the quantity scaling invariant. So if you rescale your network, your minimum is always the same. And if you take a limit again, your minimum is always the same. So that means that every limit of networks satisfying this must satisfy this. But then, suppose you can get the double line, the double line falsifying the multiplicity one conjecture. But this means that some part of your network is going to converge to something very, very close like this. And then here, there is some other part of your network. And also in this other side. But then I take p here, q here, and you see you can have an unlimited double, the double line means that these two guys get together, get close, and your minimum of these guys must be zero. Instead, since it's a limit of guy satisfying this, also the limit must satisfy this. And you have a contradiction. So all this stuff is to prove this inequality. It's a computation. Not immediate, but solid computation. Unfortunately, and we made a mistake in our very initial work on the subject. This guy here is larger or equal to zero only when realizing your minimum. The other part of the network bound in your region here contains at most two triple junctions. Which is actually true if in general your network has at most two triple junctions. So if you are able to show that when you go and get this minimum, the minimizing couple that determine the region of APQ on the other part contains only two triple junctions, one and two. Suppose that this region was not like this, but was this. Then this derivative is larger or equal to zero. Unfortunately, we try a lot, but we weren't able to have an argument to say that every time you take the minimum, you only have two triple junctions in the pink part here. So the only strong requirement that we made that ensure this is that the initial network at all has only two triple junctions. In that case, this line works. The recent idea that we are going to employ in order to multiply and conjecture is completely different because we gave up following this line because we didn't find any reason why these must have only two triple junctions. They have the minimal regions, actually. But anyway, if you actually have networks with few triple junctions, the analysis is the multiplicity and conjecture is there. It's with the theorem. And then you have a real complete description of what happens at a singular time. This was done, actually, by me and in our second paper by, well, putting together first and second paper with the Matteo Novaga, Tortorelli, and Magni, Alessandra Pluda made the full analysis for the spoon, actually, the one that I showed you some lecture ago. The other guys are more or less scattered around. We use these guys several occasional examples for the local descriptions of singularities, what can happen. Because anyway, even if they are so easy, the easiest network can imagine, they already encode a lot of phenomena that happens during a net-of-flow. OK, now I want to mention some other questions. Small and more important. Well, uniqueness issues are there in several points of this work. There are two kind of issues. Four regular networks, I recall, I said the natural uniqueness would be geometric uniqueness in the class of C2 in space, C1 in time networks, actually. We all believe it, but actually it's still an open problem, and the difficulty in trying to get such result is the lack of maximum principle. For non-regular networks, uniqueness is the uniqueness in this space of bracket flows. And at least in the nice situation of the cross that I showed you before, should be possible to prove on uniqueness in the theorem of Ilman and Neves-Schultz. In general, it's not, but we hope at least for the generic initial network, which means if you have an initial network that doesn't give you uniqueness, perturbing a little, you can have a network that gives you uniqueness in the restarting theorem of Ilman and Neves-Schultz, the short-term existence theorem of Ilman and Neves-Schultz. The generic initial network should have uniqueness. But let me say that we are very far in having such a result. Genericity results are usually very delicate, not easy to be proved. Another problem that I mentioned, this is not absolutely super relevant, but actually it's a natural question that's also still open also for several cases of smooth hypersurface from minkological flow, the uniqueness of blow-up limits when you do the whisking or other blow-up procedures. Another natural question that I mentioned to you yesterday, if actually type 2 singularity actually exists. We believe, like for curves, like for embedded curves, that they cannot have type 2 singularities, that in the motion of an initial embedded network, you cannot have type 2 singularities. Just to remember, type 2 singularity is a singularity where type 1 is a singularity like such that your curvature is of order 1 over square root of t minus t, type 1, and type 2 otherwise, which means that at least on a subsequence, you don't have no constant such that k max is bounded by a constant divided by square root t minus t. Thus, it does not exist such that it works like this. For curves, this is a good dichotomy between singularities because for curves, one already knows that the curvature approaching a singularity is for curves, smooth curves, is always larger than 1 over square root of 2 t minus t. This is no type 2 for embedded curves, embedded closed curves. For networks, we conjecture that these guys are not there, again, there are no type 2 singularities. Moreover, for networks, we are not even able to prove this, that the curvature getting close to a singularity goes to plus infinity at least with this rate, that also we conjecture is true, again, conjecture also for natural. Because actually for networks, the only we are able to show at the moment is that k max is larger than 1 over t minus constant, t minus t to 1 fourth, which is actually quite weaker. And the reason is that here is obtained by being a maximum principle, so it's a point-wise estimate. Instead, all our estimates on the curvature are integral. And taking integral and passing to a point-wise estimate from integral to point-wise, you lose a square. So possibly one needs to find another way to get to this. We also believe to this, even if all the two main conjecture uniqueness of the limit network when t goes to big t and the multiplicity conjecture are true, even with that, with what we know at the moment, we could not, well, possibly we could be able to prove this, but still the conjecture about type 2 singularity will still be there, actually. So it's not the consequence of not knowing enough about singularities. And actually, it was exactly what I was saying. In the case of bound of, this is possibly after the multiplicity conjecture, the most important open conjecture, the uniqueness of the limit network at a singular time in the case when a region is collapsing down. This is possibly the second main open problem. Another very large bunch of conjecture comes from the analysis, which means proving existence or non-existence according to fixing the shape, the shapes that I showed you yesterday in that gallery of Tommy Mannen, of actually of shrinkers, studying possible properties and hoping to get to some full classification. Studying on properties, well, there are several conjectures, means, for instance, I can mention a couple of conjectures about the space of shrinkers. Well, one, what I found the nicest is the fact, a strong fact that the possible shape of shrinks are finite, which is due to Tommy Mannen that also has a partial argument, but not a full proof. But for instance, there are sub-conjectures of these. For instance, if you take an unbounded shrinker, we saw that the unbounded part must be half lines. And a natural conjecture is that you cannot have more than five half lines going to plus infinity in a shrinker. This is related to the fact that regions with less than six edges contract with six edges keep the area constant and the more than six edges they expand. So actually, in a way, this is reflected on the number of unbounded part of a possible shrinker. This is another open problem. We would like to have better estimate in the restarting theorem of Ilmar and Neves-Schultz related to that construction that I mentioned you before, because actually, the existence of that bracket flow is performed at the end, taking a lot of sub-sequences in all these constructs. Construct, replace, glue, then take a sub-sequence. At the end, you get something converging. And in several points, you take this sequence losing or making a rough estimate. So this means that you don't have so much control on the behavior of the curvature when you restart. The point is that you start with something which has bounded curvature, possibly the limit in the first case, standard 120 degrees. You have this guy. This guy has bounded curvature. And then you restart it, opening in some way, by means of ENS theorem. And if you look at the curvature function, this is for big t and this is for t larger than t. If you look at, for instance, the maximum of the curvature, a big t, we say that it's k max bounded by c. And immediately after, because of the construction, the maximum of the curvature goes like this, comes from plus infinity. Well, not going to 0 or something. But there is a coming from plus infinity doing. If you imagine what's happening here, I told you it's like, for instance, in the stress situation, that immediately there is a shrink and expander getting out from this. And if you imagine that looking at things back in time, this guy is contracting to become a standard cross. But the angle here is 120. Angle here is 120. And it must contract to an angle of 60. So the curvature, in order to do this, must go to plus infinity, back in time. Forward in time means that immediately for t larger than t, the curvature is coming down from plus infinity. And then going on till the next singularities. What we would like to have, that it's missing now in their work, to have some precise control in the way this curvature is coming down from plus, and more precise control, quantitative, the way it's coming down to plus infinity. This is in the framework of showing that singularities cannot accumulate. If you have information on the way that curvature is going down like that, well, you can hope to have better information. You can hope to have information on how long after t your flow must be again smooth. How long? You like to have a bound from below, depending on this behavior, on the time of existence of a smooth flow. In order to say that next singularity is too far to accumulate, actually. But to do this, you need really to push, to get really inside their proof, and get better estimates in some parts of the construction. Final problem that I want to present, what are generic stable singularities? Again, in very special situations like the one that I showed you at the beginning, we are super symmetric. It's a symmetric pentagon shrinking down and producing a five point. But you can ask yourself, OK, I modify a little bit one of this curve, breaking the symmetry. It's still true that you get a five point, or maybe my modification here makes this curve vanish before the shrinking. So you get the four region. That means that here in the liberty, you no more get the five guys like this, but the four line guy. So in a way, you're asking yourself, how much are stable these singularities I see in the flow? If I modify a little bit my network, I still see the same change of the problem, the same structure. And this is a very natural question, because if you reduce the number of stable singularities, that means for the general network, you have very few kinds of singularities, or less singularities, better understanding of your flow. Actually, it's easy to see that you can analyze this fact by looking at a blow up. And what can be seen that if you get a blow up, which is a line, or a cross, or a circle, which is a very special network, well, if you modify your network, as I said before, you get a gain, another singularity, and again the same type of blow up. Other conjectural stable blow up are the bracket spoon, the guy's called the lens, and this guy here, which are all shrinkers. No more with an higher number of edges. So this is a conjectural, again due to Thomas Mannen, that these guys are the only dynamically stable shrinkers. So if you have a singularities with a blow up doing like this, you perturbate your network, you still see the same kind of singularity, which also means if they are the only ones that you have a region of more than three edges collapsing down, in the blow up you see a full region in the shrinker. If you perturbate four or more, you perturbate a little what is going to happen that possibly one of the four edges collapsed before the collapse of the full region. And you get something like this guy. Again, there are possibilities because actually you have actually to compute the stability of these guys, which is actually dynamical, but you can do it with a computation, not so easy. The difficult part is the only part. It should be possible to prove that these guys are stable, that they are the only ones which are stable, could be more difficult, with the only doubt on these guys. This could be unstable. These two guys, we are almost sure that they are stable. There are some doubt, some that doesn't doubt, we doubt a little bit, computation not completely easy, that this guy may be unstable. Which means actually, as I say, the conclusion that generically, for the generic initial network, only a region with three edges can collapse. If a region wants to collapse generically, it must before reduce the number of visages to three. Then it can collapse, to three or less than three. Final remark, what are the possible future? Very far, in my opinion, to try to extend all these kind of analysis to higher dimensions. So the most natural guy to study is the cluster of bubbles. And in particular, the easiest one to test the ideas, which is simply a double bubble, which is the two-dimensional analog of the data network, actually. And what is the difficulties here in generalizing this analysis to the two-dimensional situation? Well, even from closed curve to closed surfaces, in R3, there is a huge change in difficulties, a huge change in the results that you can hope. A smooth, embedded, smooth, closed curve stays smooth, becomes convex, gets round and round, and then shrinks down to a point. It's absolutely false for a surface, can develop singularities, and you want to continue the flow. Sometimes you can break into pieces, and so on. So you can imagine that also here, there is a huge gap between one-dimensional and two-dimensional situation. Moreover, here, there's also the point that in the network case, you have two levels of objects, curves, and triple junctions. If you deal with the two-dimensional interfaces, you have surfaces bound in your balls, lines where three surfaces can arrive, and points where four surfaces, where four regions can arrive at this point. You can imagine something like the angles with the carbon atom, actually. All inside the tetrahedron, if you connect the regular tetrahedron, if you connect the vertices to the body center, actually. So you have three levels and three levels of equation to study. Your system becomes much more complicated. And at the moment, well, there are several approaches, the one of phallics by means of, well, generalized approach by means of minimizing movement, the approach by bracket flow, by Tonegawa, that you possibly saw in the previous week. But in the world of the smooth approach that was the one that we tried to follow as close as possible for the networks, actually, I'm aware only a couple of papers, these papers by Deppner, Garke and Kosaka, that they prove short-time existence for very special interfaces, not for the general case. And uniqueness similar to the TRMS that I showed you for regular networks, satisfying compatibility condition, the TR are more complicated. And another paper containing also estimates, more quantitative, again, only for special initial interfaces by Felicius and Brian White. Special initial interfaces means that the initial bubble, cluster of bubble, must only contains not possible that four regions arrive at the point. You only have two levels. We have surfaces and a curve where three surfaces arrive. But not a point where four regions are concurring, which actually means that more or less you are studying the double bubble situation. But in the smooth approach, I'm only aware of these two cases in this special, there is no theory and reason for the general case that would be very interesting to have. OK, just to conclude, since I have just very few minutes, I want to ask you a question. I'll let you have an open problem, a very elementary to say open problem, that we are not able to do it. So possibly you are younger, more energy, you are able to find out a good argument. We will be very interested in having an elsewhere. It will be very interesting. It will simplify some parts of arguments in our work. And I want to state it absolutely independently of the network flow. It's a technical, I'm opinion, nice question that could be useful for us. Well, if you tell you what is known, if you take a closed curve, C2, in the plane, well, it can be proved. Well, if you assume that the curvature is smaller than 1 for your curve, it can be proved that the area of your curve is larger than pi. It seems innocuous, but let me tell you, it's absolutely non-elementary. If what is interesting can give you a reference to some proof, there are several proofs around. In the star-shaped case or convex case, it's easier, but in the general case, I'm not asking anything about the curve. Simple, C2 curve, closed curve. It's absolutely smart proof for the general case. But I suggest you to try to do it by yourself. More precisely, if you're in this situation, the interior contains a disk of radius 1, which actually implies this. So if you have this, you have d1 is contained in the collet, which implies this. OK? Notice that you have this. It can be useful. It's a hint for your proof. The integer, sorry, quite tight, is a hint for your proof. OK, what we are interested in, we are interested in networks, can imagine this is related to shrinking regions. So now I consider, instead of this, this is a theorem. Instead, I have a conjecture. I suppose we have a region, curved C2, with five curves or less. But if you can do it with five, you can do it also with less, with angles 120. Curved polygon with angles 120. Five edges. And I want to conclude the same. I want to conclude that if k is smaller than 1 on this curve, then there exists epsilon, such that positive is such that the area of omega is larger than epsilon. This is false if I have six corners. Take a regular hexagon. Curvature is 0, so it's bounded by 1. But you can make it smaller as you prefer. This is false if you have too many corners. Suggestion to connect the two things. In this case, integral of k is equal to pi, 6, pi. Yes, should be 6. For hexagon, integral of k is 0. If you have a curved hexagon with angles 120 degrees, the integral of k is 0 always. So this guy is positive. So I think this can suggest you how to generalize the result if you are able to prove this. Because, let me tell you, it's open. And it will be very interesting because it will simplify some arguments in our job. Actually, we don't need in our work because this question, we ask it for moving regions, so they have other special properties, so the conclusion is true for the special region, moving regions, that we use in the network flow. But the question can be put in general. Can we ask in general? And you can see this, which is my opinion, in particular, the first one is independent interest for people in geometric analysis. Because actually, it's a kind of isoparametric inequality, reverse isoparametric inequality, without the perimeter entering, only curvature and a contended area. I can also tell you that the niger dimension is false. There are counter examples. So try to find a counter example for surfaces, for instance. But actually, the consequence of this is that k squared max times the area for a closed curve is always larger than part. And the consequence of this, if we are able to show it, would be that k square max of a larger than epsilon for some epsilon, open for curvilinear polygonals with these properties here. OK, I think my course finished here. Let me, before closing, thank you, thanks to the organizer for the very nice week here in Trieste. Let me also thank Alessandro Pluda that left today morning. Since several of my slides were based on other slides that she made for another occasion, in particular, all the figures was done by Alessandro. And let me also thank you for your attention and for following the course till the end.


Hello and welcome to this helpful guide on using the WSR6 library app. First things first, how to open the app. It should appear as this black square with the WSR6 County Council logo. Press on this and it will open the app. If you have not signed in, this is the screen you will get. If you haven't yet joined a WSR6 library and have downloaded the app, you can start the process through pressing on Join the Library. This will take you through to the library website where if you scroll down, you will get the Choose Your Library option which is step 1 in joining. So back to the home screen. To login you will need your library card number and your PIN number. Both you should have received when signing up at your local library. Press on Login to take you through to this screen where you need to put in your details. If you have forgotten your PIN you can recover it in branch of some form of ID and your library card. Once you have entered your details you just need to click Login. The home screen will now look like this. For the rest of this guide we will go through each square or box in turn, starting with Search our catalogue. To access this you just need to press on the square like before. You will now be presented with a search box and the more exciting option of scanning a book's barcode. To search put in the title and or author and it should bring up the books, if we held them in with WSR6. The Scan Barcode feature can be accessed through pressing on this box. This allows you to scan the ISBN at the back of any book, for instance in your local bookstore, and then see if it is available from the library. For this example we are going to use the British National Formulary or BNF. Simply place the barcode so the line in the middle of the viewfinder lines up with the barcode. It will then scan and show you the results. To reserve you simply now press on Reserve. Next up find a library. Press on this and it will bring up a list of libraries. To look at details of a library simply press on this name, for instance Billingshurst.  To get the contact details press on Contact Us. This will give you the telephone number and email address. So next we are going to look at my account and that is the image with the two cards. And you can go ahead and press on this. So from this menu we can do lots of different things, but the first thing we are going to do is look at our reservations. So go ahead and press on Reservations. This will bring up a list of the books you have requested. The first Easy Fish is ready for pick up and tells you which branch you can collect it from. Secrets of Sir Richard is on its way or in transit. And finally Collected Folktales has the reserved status. This means it is not being returned or dispatched from its home library. So next we can check the books we are currently borrowing. To go back to the menu press on the top left hand back button. Now you can go ahead and press on Current Loans. Here we can see the books we have at home. You can see the second item, the Film American Beauty, can't be renewed. There is no reason as to why this is. In this case the item has already been renewed today. If an item were overdue it would have this bold overdue in the title. And it would be in red. To renew you would press on the green Renew button. You will know this works by the next screen that states Item Renewed Successfully. Now we will look at the final menu, Charges. So go ahead and press on Charges. This will show you the money you owe and the reasons for this. In this instance we had not paid the three reservation charges and they were all on here. The eLibrary is where you can borrow our eAudio eBooks and more. Or just find out more information about them. So to access these you press on eLibrary the box of a tablet for a symbol. This will bring up a quick list of our various eProducts. If you wanted to borrow eAudio books you would go ahead and press on the relevant option. This will bring up the web page that will give you further instructions on how to download. Our eInformation option is where you can access all our great products such as Oxford English Dictionary, TheoryTest Pro and Encyclopedia Botanica. Press on this will bring up a list similar to the one for the eLibrary. To access any of these simply press on the one you want and it will give you further instructions on how to access it. This will normally ask for your library card number so be sure to have that with you. So Social is a link to our social media currently our Facebook page where Sussex reads. Pressing on this will take you through to the Facebook page. If you're logged in you could even like or share the page to help you stay up to date with events and activities. What's On takes you through to our events page on the library website. This is normally split into regular or one-off events and between children and adults. Any major county-wide events such as Geek Week will also be featured here as shown on screen. Finally the Settings. If you press on here it will basically just show you the option to log out or turn the notifications on or off. If you stay logged in it will remember on your next use of the app making it quicker to renew or use any of the other options. The West Sussex Library app is available now on the App Store for Apple devices and the Play Store for Android devices. You can use it today and discover the easiest way to keep track of your books and what is happening at your local library.


but the fisheye lens is the GoPro, I understand, but that's the Atlantic Ocean. On approximately one week, we have gone from looking at the Pacific Ocean to looking at the Atlantic Ocean. We longed this road for 61 kilometers. It's squeaking, was it? Did you guys hear that? That's my radio. So coast to coast in Canada, I've never actually done that in one shot. I stopped at home along the way and went down to Toronto and stuff, but it's expecting some freight. And he saw in my videos that I was coming to Nova Scotia. He put two and two together, he was expecting me. So you know, we're supposed to be friendly Manitoba. It's on our license plates. I still think we got nothing on the maritime. I think that they're way nicer out here. We're gonna meander our way out of this beautiful neighborhood. We're gonna go to Port Williams, Nova Scotia. I thought it was, for some reason, I thought it was called Hollow Point, Nova Scotia. And then we go up to Lenox Passage to deliver weeks here in a good pay period, including Georgia and home, including down to Georgia. Really good miles this check. At least it feels that way. If it's not true, they do a very good job of making me feel good. As long as I feel good, right? Because everybody feels good. Trucker cop, that's a inspection vehicle. Don't you follow me, you stay there. Move out East. I think I might move to Nova Scotia, I think. New Brunswick's really nice too. I would probably have to live in Southern New Brunswick because I don't speak French and it's all mostly French up in Northern New Brunswick. Not that I don't like it up there. It's a really nice, it would just be very hard for me to communicate probably a little on an amazing place on this planet. Person, Southeast Manitoba. That's like my little corner of the country. That's where I feel most comfortable. Welcome to Port Williams, Nova Scotia. Somewhere in here, I got to bring them some stuff. Roads here are not designed for a 75 foot unit. No, I don't belong here. Local delivery. Workway drive and then approaching destination on the right side, into 120 meters.  I was gonna say they're definitely built before we had these big trucks rolling through here, that's for sure. All right, looks like I'll be unloading on the side of the road here again. That's okay. I got four big crates for them. And it looks like these crates would normally be on a flatbed trailer, but they're in a van and they don't have a dock here. So this should be interesting. I'll have to talk to you once we're done here. I won't be able to film this. I'll have to help them get them off the truck. We'll make it work. We'll get her done. We're right back where we started. Enfield Irving. The scale is still open over there. Slide right and then approaching destination on the left side, into 160 meters. Yeah, Karen. Warning, truck weight violation. That's not true, Karen. Approaching destination in 200 meters on the left side. That's why you were trying to take me around. You tried to take me around the long way again. Ah, it's smarter. I would smarter her this time. I'm smarter. Smarter than you, Karen. So Enfield, this is where- You'll have to get to your destination on the left side. I see it. It's right there. Circle came number 2079. Thank you. This is the gas station, I believe, where that RCMP officer caught up with that shooter that everyone associates with Nova Scotia now. And you know what? Nova Scotia may have one or two nut cases like that. I think that was the only one though, because like I was saying, this whole place is filled with amazing people. And nobody told me to tell you that. Nobody's paying me to say that, all right? They're just really nice people here.  It's really sad. But this is where it all ended. This is where the cops got him. I like to be different. Everyone's facing that way, so I'm gonna face this way. Does this make you uncomfortable? Sorry, hit him with my hand. Sorry, buddy. Need to go outside? Yeah, I thought so. I need to go outside too. You know, these Irvings are nicer than anything we got back home. I've said it before, they're even nicer than Flying Jay. And that's a lot coming from me. Diesel wet. Right? Oh, there was another dog here. He can tell.  Did he leave a little mark there for you? Come on Diesel, some long grass over here. You're gonna love this. Come on. Been trying to get him to go number two all day, but he won't go unless he can find some long grass. That's how I trained him too. That's how he was supposed to do it. But sometimes when you can't find long grass, the problem. There you go, look at all this good stuff over here. Diesel, hey. Oh, he's too busy searching for other dogs. Come on, man, get in there. Come on. He saw another dog when we were walking over here, so he's just freaking out. He wants to know everything there is to know about him. I think he's over here, man. He definitely was here. I can smell him. Smell him. I can almost tell what his name is, man. Okay, I brought you to the long grass diesel. Forget about the other dog for a bit. Come here. You got some business to do, remember? That's why we stopped again so you could do your business. Come here, come on. Time to do your business. No? I tell you, this guy. Come on. Come on, there you go. Came all the way here just for you, bud. So I'm gonna grab a coffee from inside here, as soon as he's finished, if he ever does finish. And we have two and a half hours, or two and three-quarter hours to drive up to Lenox Passage or Louisdale. Louis, is it Louisdale or is it Louisdale? Nova Scotia. I'm gonna stay right at the customer overnight. I called them today already and got to hold them. I can sleep right in their yard there. And I'll be there for them first thing in the morning. They get there at eight, so we should be unloaded by nine, I'm guessing. And by that time, I'll probably have my reload. And I can head out to Northern New Brunswick to pick that up. He's still not getting anything done. Shout out to Todd, who I just met here. They're over there in one of those trucks over there. I was walking diesel over there. He came over and said hi. Said he's watched all the videos. That's awesome, thanks for coming to say hi, man. I always love coming to the Maritimes here. Have I told you this already? Everyone is so nice. I think I've already told you that, I don't know. Just in case I didn't. Now you know. Great place. Okay, so diesel has been walked. I've got some food. I got a coffee. We have 260 kilometers left to go. And I was telling you before, right? We can sleep right at the customer. Don't have to worry about finding parking or anything. That'd be great. It would be the first thing in the morning. And then we got to wait. Wait for orders from headquarters. Because I know I've got to pick up a load in Northern New Brunswick. I just don't know where yet. The scale on the other side of the highway was open again. It was open this morning too. I'd very much like to say hello after they're done work. How about that? Very nice people. I'm definitely not overweight. See what they say. Read all my numbers, read my plates. Here before I change this mind. In five kilometers, take exit six. Airport, Halifax, Robert L. Stadfield International Airport. Coffee when there was a Tim Hortons right next door and I didn't even go get Tim's. I didn't realize there was a Tim Hortons next door till I was driving away.  Just Irving here. Also had the Tim Hortons and we're gonna get some real coffee. It's the last coffee did absolutely nothing for me. It's for very strong coffee and it's hard to find strong coffee on the road. I like my coffee to taste like coffee. I think this is a new Glasgow. The car coming there. Figure out where you're going on these missions. Here we go. There's my name on it. You see it, it's right there. It's very small, but it's right there. Trucker Josh's spot. No parking. Except for Trucker Josh. Says that too. It's very small. Right, so there's a Timmy's in that building right there. The world is all right again. There's almost the apocalypse. Good thing there's a Timmy's on every single corner. Who knows what would happen. Didn't get our Timmy's. This was another Timmy's where the espresso machine was broken. Now I go to Timmy's at least once a day, usually. And I think for the past week I've only found one Tim Hortons. So one out of seven. That's actually had their espresso machine working properly. All the rest of them are broken. What's going on? It's a darkro, so it's a little stronger. But just can't get a good cup of coffee. Man, I like my coffee strong.  I like to be able to know I'm drinking coffee. No doubt, you know? All right, let's get going. Another hour and another big stop. So we're just before that scale on the way up into Northern Nova Scotia. We're 30 kilometers from our customer.  I'll wake and grab a coffee first thing in the morning and I can have a coffee while I'm unloading there. Should work out a little better that way. But thanks for joining me today. It's been a Nova Scotia day. It was a lot of fun, met a lot of great people. Excited for tomorrow. We're gonna head over to New Brunswick and then we're gonna head on down to our amazing Southern neighbors. All the way down to Georgia. So I'm gonna go all the way down to the Eastern seaboard there. All the way through New York and all that again. We're gonna see if we can ride ourselves around the city. But it is what it is. If we gotta go through the city, we gotta go through the city. I heard everyone's left New York, so it's probably a lot less congested than it was last time I was there. There's only one way to find out. All right, Diesel? Who you got here? Who's this? Who's this right here? Who's this? It's my friend, man. Leave him alone. Leave him alone. Mine. He don't bugger me. He's my friend. He doesn't have a name, okay? So tune in tomorrow, everybody. Don't forget to subscribe. Hit that like button if you liked the video. Tell your friends about the channel and get them to subscribe as well so we can keep growing. We'll make more videos. See you later.


Box 13, with the Star of Paramount Pictures, Alan Ladd has Dan Holliday. Box 13, care of the star times. I should like very much to see you and offer a proposition which could be of mutual profit to us. Of course, there is some danger involved. But then your advertisement asks for adventure. So if you are interested, perhaps we could have lunch tomorrow afternoon. Say it one o'clock. Say it one o'clock, the golden arrow. Ask for Mr. Waring's table. There is some danger involved, he said. Yes, that's what the man said. And brother, that's exactly what he meant. And now back to Box 13 and Dan Holliday's newest adventure, Daytime Nightmare. This letter had brought you to lunch, Mr. Holliday. Uh-huh. Lunch and then what? Danger, it says. That sounds exciting. It always does.  Then follow up one of these other letters. There's one that asks for a babysitter. The woman says her children are an adventure. Oh, no thanks. I'll take Mr. Waring's letter and his proposition. Then you'd better hurry. It's almost 12.30 now. Oh, don't push, Susie. Don't push. What time will you be back? Probably this evening. But don't wait for me. Just lock up the ops and take off. So long, Susie. Arrow is one of those ulcer dining and luncheon spots where you can get a swell dollar lunch for five. I asked for Mr. Waring's table and the waiter showed me to an ice secluded corner. A small orchestra was playing. A couple were dancing. And Mr. Waring was just sitting there. I took a good look at him before I sat down. He was big and handsome. Maybe about 50. And the diamond he flashed on the little finger of his right hand was spelled with 1500 capital dollars. He looked up, saw me standing there. How do you do?  Yes, that's right. Your arm is to Waring. And you're right. Please sit down. I've ordered lunch. I hope you approve. Oh, thanks. I'm sure I will. You're younger than I expected. Oh, disappointed? No, no, please. Tell me, is a box 13 the way you make your living? Ah, not quite. Yeah, I read your advertisement several times. Adventure wanted, go anyplace, do anything, write box 13. Is that said with disapproval? No, not at all, Mr.... That holiday? No, not disapproval. The hand just regret. Regret that I hadn't the nerve to do such a thing when I was your age. Well, sometimes the regrets are mine. Huh? Oh, oh, I see. You mean once in a while you get something that's hard to handle? That's it. But you've always come out on top. Well, I've had a lot of luck. Is there, uh, any of it left? Do I need some? If you do what I ask, you will. All right. What's on your mind, Mr. Warrick? First we'll have lunch, then we'll talk. Will that be all right with you? You say so. Yes. Good. Charles, you may bring our lunch now. Now let's enjoy ourselves. There's lots of time to get serious after lunch. Well, Waring was a very good conversationist. I learned he was an attorney, an attorney for one of the biggest estates in the country. He kept leading the conversation around to that every time we got on something else. Then when lunch was over. Yeah. Enjoy it, Dan. Very much. It's a girl. Oh, no, thank you. No, if you'll come with me. Come with you? But I thought we were going to talk. Oh, I'd rather have more privacy. You'll understand why when I tell you what I have in mind. Oh, it's that important. Would you say $10 million was important? Oh, it commands attention, yes. Then please come with me. We left the golden arrow. The dormant saluted Waring and signaled a big limousine that sneaked up along the curb and purred to a stop. Please, get in, Dan. Well, no, pardon me. Where are we going? Oh, for rides through the park. Well, wait a minute. I, uh... I want to know what this is all about before I go into it. You're not very trusting, are you, Dan? Yeah, it's not very. Uh, something wrong, Dan? Yeah. Get in the car, Dan. Little air will make you feel better. All right. Go on. Get in. All right, Bert. You know where to go. I'd been drugged before, so I knew what it felt like. It felt exactly like this. I came crawling out of the long, dark tunnel with a buzzing in my ears, my mouth dry as cotton. I was lying down, and I at least held my arms. I was on a cot.  I sat on the edge of the bed, looked around. There was a window, but there were bars over it. I went to the door. Hey. Hey, open up. Open this door. Open this door, somebody, come on, open the door. Get away from it. Open it up, whoever you are. Move back away from it, and I will. Go on. I moved back in the way. There was a pause, and then... Well, Mr. Stokes, you've awakened at last. Stokes? What are you talking about? Come on, get me out of this gag or I'll break my way out. Samuel, Hugo. Mr. Stokes, you don't want Samuel and Hugo to take care of you, do you? What is this? Sit down, Mr. Stokes, please. Sit down. I won't sit down. Where's Waring? He'll be here in a moment. If you want to see Mr. Waring, I'm sure that can be arranged. Well, that's better. Call off those mastives and white coats. Wait outside, Samuel, Hugo, and close the door. Go ahead, I'll be all right.  Look, if this is a gag, let's run it off the boards and put a tag to it. Gag? Why, Mr. Stokes, you sound almost rational. Rational? What are you talking about? Just that. I have no doubt that in a year, perhaps a little more, we can discharge you. You mean... you mean this is no gag? No, it's not a gag. You're Edward Stokes. Remember that. You're Edward Stokes. Where's Waring? He'll be here to see you with your wife. My wife? Of course. I wonder if you'll remember her. I don't know what you're trying to get away with, but if I have to play rough, I can play it. Samuel, Hugo! I think Mr. Stokes needs to be quieted. Take care of it, Samuel. Get them away from me. When you've decided to leave, get them away from me. When you've decided to be more calm, Mr. Stokes, we can have a talk in my office. Until then, I shall take precautions against your homicidal tendencies. Well, it was no gag. Samuel and Hugo were too big for games, and they played rough. Samuel left, and Hugo sat beside the bed to watch me. I knew now where I was. A sanitarium. A why? I called Edward Stokes. I had to find out, so I turned to Hugo. What? Oh, Hugo, these straps are hurting me. No thanks, Mr. Stokes. I can't loosen them for you. Look, get my clothes. Take out my wallet. Take the money that's in it, and just let me get to a telephone. I'm sorry, Mr. Stokes. You know that's against the rules. Who was the man who spoke to me before? That's Mr. Cordon. Mr. Not a doctor? Well, yes and no. This here is kind of a rest home. Does everyone get as much rest as I do? You're all right, Mr. Stokes. That's pretty funny. Yeah, I'm dying. Where are my clothes? No, no, no. We'll get them for you later. Look, I'm not Edward Stokes. I'm Dan Holliday, get it? My name's Dan Holliday. I'm a writer. Well, I'll bring you a pencil and paper later. You go. Go to a phone. Call the number I'll give you and ask for Susie. Hey, she got a sister for me?  I'm not Edward Stokes. I don't know who he is. I never even heard of him. I'm Dan Holliday, a writer. Yeah, okay, okay, I believe you. Once I took care of a man who was Shakespeare, I believed him. I also took care of Michelangelo, Dante, Spinoza, why I... Look, I want to see Cordell. What for? I want to talk to him. What about? Does that make any difference? Yeah, because if it's not important, he'll get mad at me. All right. Tell him... Tell him I remember now that I'm Edward Stokes. It all comes back to me. Now, will you go to him? Okay, but please, Mr. Stokes, don't try what you did before. I... I hate to get rough. Right, I promise. It's a good boy, and keep on being a good boy, and you'll be allowed visitors this afternoon. I'll be very happy to see them. Very happy. All right, Mr. Stokes. I brought you to see Mr. Cordell, I guess. Now, promise you'll take it easy. Oh, sure. Thanks, Hugo. Yeah, it's nothing. And here he is, Mr. Cordell. Good. Close the door and wait outside, Hugo. Are you sure you'll be all right, Mr. Cordell? I think Mr. Stokes has learned his lesson. Are you sure? Please be a good boy now. Yeah, I will, Hugo. So, you've become reconciled, Mr. Stokes. I know I can talk myself blue in the face to Hugo or anyone else around here and not get anywhere. But I want you to tell me what this is all about. I'll be glad to. You're Edward Stokes. You're here for a rest. You were formerly at the Millhaven Sanitarium, but your wife thought this would be a better place. Don't you remember? Remember? Of course I do. You've made it all so clear. Good, good. Oh, by the way, you're looking so much better than when I saw your last, Mr. Stokes. Would you like to see how much better? What do you mean? There's a mirror on the door of that closet to your right. Open it and see how you've improved. I looked in the mirror. I didn't see Dan Holliday. I saw a stranger. Cordell's voice came to me from a million miles away. There's some gray in your hair, of course, but that's to be expected. As a whole, it's still a nice, deep, rich black. My hair's been dyed. I'll bet you think it was once blonde. I imagine you think your name was once Dan Holliday. Take a good look at yourself, Mr. Stokes. Get acquainted with your new personality. You'll be with it for quite a while. Cordell smiled at me. Then I knew for certain this was no joke. I was Edward Stokes. My hair dyed, clever touches of makeup here and there. Even Susie wouldn't have known me. Do you know why you've become Edward Stokes? Why, Mr. Cordell? Because Mr. Edward Stokes is dead. Now back to Daytime Nightmare, another Box 13 adventure with Alan Lan as Dan Holliday. Well, there was a twist. I was a dead man. Yet I was alive and being kept alive. But for what? Later in my room, I thought of making a break for it. But there was always Samuel and Hugo. Then later I was taken again to Cordell's office. This time Hugo went in with me. Cordell wasn't alone. With him were a wearing and a woman. The woman looked at me as I entered. Edward. Edward, darling. Would you mind just calling me Dan? Please, Edward. You remember me? Of course you remember your wife, don't you, Edward? Oh, hello, Waring. I must buy you lunch sometime. Lunch? Oh, of course, of course. I told your wife and Mr. Waring that you were so much better, Mr. Stokes. But now you've disappointed me. Oh, I'm so sorry, Mr. Cordell. Hugo, please wait outside. I'll call you if I need you. Sure, Mr. Cordell. He does look like Edward. Must you say it so loud, Phillip? Oh, sorry. How long does this go on? Not much longer.  Yes, how? We'll leave that until later. Clarice. What? You've got to sign those transfer papers. They're all right. Of course. Oh, Edward, it might be interesting for you to watch yourself being committed. I'm warning all of you, I'm going to get out of here. And when I do, I... Cordell, Edward Stokes. How does he know about Edward? Cordell, did you open your mouth? What's the difference? He can babble his head off and no one will pay any attention. Suppose something goes wrong. How can it? It's all too perfect. Of course it is. Sign the papers, Clarice. Get it over with. Good. Now let's go. Nothing can go wrong. Not unless you double cross me. You've got your money and you're in as deeply as anyone. You better see that everything goes all right. Good luck. Well, Mr. Stokes, you're now officially in my care. That should make everything just ducky. Oh, it will. If it's not asking too much, what happens now? My dear Mr. Stokes, if you knew, you wouldn't like it. What's to prevent me from reaching across this desk and knocking your head off just for the fun of it? This gun will prevent it. You wouldn't dare use it. No, not directly. But suppose you did try something. Suppose we struggled and the gun went off accidentally.  Who would be your witness? Not you. You would be dead. Not Hugo. Because he saw you attack me this morning.  Then he played the gun on the desk. It was so close to me. So close. He knew what I was thinking because his grin widened. But I had to take the chance. I jumped. Stay right there, Cordell. All right. Now that you've got the gun, what will you do? Hand me that phone. Certainly. Here you are. Keep your hands on top of the desk. With pleasure. Uh, whom are you going to call? The police. All right, go ahead. Hugo! Hugo! Mr. Stokes. Be careful, Hugo. He's raving. You've got to believe me. I'm not Edward Stokes. I'm Dan Holiday. Give me two minutes to put through a phone call. No, no, no, Mr. Stokes. You don't want to do anything with that gun. Better give it to me like a good boy. Hugo, please. Please stay back. Careful, Hugo. He may shoot. Stay back, Mr. Cordell. I can handle him. Hugo, listen to me. Listen to me. Give me two minutes on that phone. Just one minute. Mr. Stokes, give me that gun. Come on. Give it to me. Wait, Hugo. Wait. I don't want to shoot. Do it if you come any closer. Hugo, I'm in a spot. The real Edward Stokes is dead, Hugo. He's been killed by his wife and his attorney. Listen to me. Stand still and listen to me. Easy. Easy. Easy, Mr. Stokes. Easy. The real Stokes has been killed. He was taken from the first sanitarium and killed. I was brought here, Hugo. Brought here to impersonate Stokes.  Stokes! Hugo! I know all that, Mr. Stokes, but... But if you... Hugo. Hugo. I'm afraid you killed him, Stokes. Cordell... You shot the poor devil. Of course I did, Mr. Stokes.  That's perfectly true, Mr. Stokes. Ballistics can prove which gun killed Hugo. That's true too, Mr. Stokes. But who would think of ballistics in connection with a maniac? Ballistics can prove which gun killed Hugo. That's true too, Mr. Stokes. But who would think of ballistics in connection with a maniac? Ballistics in connection with a maniac. Cordell stood there, smoking gun in his hand. Cordell stood there, smoking gun in his hand. Oh, it was a beautiful frame. In a second, the rest of the people in the place would crowd into that office. What chance would I have? None. I'd talk myself into a lather. Cordell put the gun back onto his desk. Well, Mr. Stokes, what now? I... I can prove I didn't shoot this gun. Think you'll get the chance? I'll be back. Get out of the way. Be careful, all of you! Chase after him. He's got a gun. He killed Hugo. Stay back! I ran up into the night out into the rest of my nightmare. I cleared the grounds of the rest home and took to the woods. There was only one thing in my favor, the darkness. I stayed in the woods. But I had to get to a phone. I don't know how long I walked. Maybe an hour, maybe two. Then I saw a house. There were lights in it. I hesitated, but I had to get to that phone. Yeah, yeah, that's me. Don't. Don't scream, please. Get back. Please, please, don't.  I want to get to a phone. Have you got one? No. There's no phone here. Where's the nearest one? The villain's station down the road. Have you got any men's clothes here? In the closet. Would you mind getting them out? Go away, please. I won't tell anybody you've been here. But don't hurt me, please. You know who I am? The radio. They said. How long ago? Half an hour, maybe. Get those clothes for me, please. All right. They won't fit you. They're too small. I don't care about that. Throw them on the table there. Just trousers and coat. All right. I pulled the trousers and coat on over the pajamas I was wearing. The woman watched me and she watched the door. She was expecting someone. Wally, probably her husband. Then... Please, please go now. How far is that filling station? About two miles. There's no phone closer than that? No. All right. You stay in here. You're not going to get hurt. Just stay in here until you're sure I'm far enough away. You get that? Yes, sir. I won't move. Good. I'll return the clothes later. She screamed. I could hear her screams fading into the night as I ran. I had two miles to go. Two miles to the brush and woods I couldn't risk getting to the road. Then I heard something. I ran. I ran until my legs were torn by the brush. I ran until my breath choked in my throat. Then I saw the station, but I couldn't get to it. Crept closer and lay down in the mud-filled ditch. I knew then what a fox must feel like with the hounds tearing at his heels. I listened. I heard Cordell's voice. He's dark-haired wearing pajamas, but he may have picked up some clothes somewhere. I haven't seen any. Better be careful of him, Clay. He's got a gun. Already killed a man back at the home. I will, Sheriff. Thanks for warning me. Okay, Clay. Oh, uh, got a gun? Sure. Always keep one in the station. Good. Keep your radio turned on, too. We're running bulletins on the air. That way you can tell if he's headed this way. Sure. See you later, Sheriff. Remember, he's dangerous. A homicidal maniac. Take no chances. Okay, Mr. Cordell, thanks. Go on. I watched the attendant, Clay, go back into the filling station. I watched him take a gun from a drawer and shove it into his pocket. I cut across the road. My stomach hurt from pressing it close against the concrete. Clay came out of the station, looked up and down the road. Then he turned off the lights and locked the door. Don't take another step. Don't look around. Don't reach for that gun in your pocket. What are you gonna do? Nothing. You won't get hurt. I want to use the phone in the station. It's out of order. You're lying. I'm not lying. Why don't you try it? Where are the keys to the door?  You want the keys, don't you? Keep your back turned. I know that gun is in your coat pocket. The keys there, too? No, in my trousers. Reach in. Get them out. But be careful. Now, unlock the station door and go in ahead of me. Never mind the lights.  You haven't got a chance, fellow. The roads are crawling with prowl cars. They were here just a minute ago. Reach in and take out that gun. All right. Hold it by two fingers and drop it on the floor. Go on. Stand over there while I use the phone. It's out of order, I told you. Stay where you are. Hello? Hello? I told you. Where's another phone? The nearest one is about five miles down the road. You're lying. Like I was about this phone?  Give me that gun. We'll go into town.  I've got to take that chance. No, you don't. I want to give you a break, fellow. I want to give you a break because... Because? Once I saw a dog shot. A dog they all said was mad. It wasn't mad. All I wanted was water. But they shot it without giving it a chance. Please, give me your gun. Look, if I tell you a story, you won't believe it. I know you won't. Maybe I will. Go ahead. I'm not Edward Stokes. I'm not the man they're hunting for. He's dead. Killed by his wife and his attorney. What? I think because they wanted his state. If I'm killed as Stokes, they'll identify me as him. Please, give me the gun. You. You don't believe me, do you?  You're hurt. Never mind. Get me to a phone. I can't. All right, here. Take the gun. Take it. What's the way for? Now you've got the gun. I want you to do one thing. Get me to a phone. Let me call the police. Let me identify myself, will you? Come on. I've got a car. They've got me to a phone. I call Lieutenant Kling and tell him the story. And less than an hour later, the sheriff, his men, Clayton and I walked into Cordell's office. Ah, you've got him. Good work, Sheriff. Yeah, we've got him. I'm surprised you took him alive. Yeah, so are we. Mind stepping over here a minute, Mr. Cordell? What, what for? Get over. What is this? You'll find the gun that killed Hugo in that drawer, Sheriff. What? This man's mad, Sheriff. I heard different from the city. Look out. Get the gun, Sheriff. That's the gun that killed Hugo, not the one I gave Clayton. You were right, Mr. Cordell. No one would have thought of ballistics to see which gun had killed Hugo. I think I need a bath. And a nice, long rest. Stokes were arrested on suspicion of murder. Police are searching for the body of Edward Stokes. Gee, Mr. Holiday. Well, it wasn't nice, Susie. But let's forget it. Sure, I know what you mean. Oh, say, I have to remind you. Of what? You've got a luncheon appointment today at... Luncheon? Oh, no, Susie. Next week, same time, through the courtesy of Paramount Pictures, Alan Lad stars as Dan Holiday in... Box 13. Box 13 is directed by Richard Sanville, with this week's original story by Russell Hughes. Original music is composed and conducted by Rudy Schrager. Part of Susie is played by Sylvia Picker, and production is supervised by Byrne Carstensen. Box 13 is a Mayfair production from Hollywood. Watch for Alan Lad in his latest Paramount Picture.


Hello everyone and welcome to my youtube channel my name is Kaye Felix and I welcome you to Kaye Felix Inspire the channel that gives you great inspiration of videos great music videos and of course trending stories well if you are new to this channel and you'd like to be part of Kaye Felix Inspire and follow what we do here I kindly ask you to subscribe to this channel turn on the bell icon so that you get all notifications whenever we post new videos all right in this video today we take a look at the very trending story here in Zambia about the death of a fish where the students from the copper belt university are mourning this fish this is a pet fish popularly known as ma fish which has sent shock waves across the country with reports of a planned funeral procession to be held in honor of this pet fish which has been considered a good luck you know as you may be aware this is the story that is going around um we have seen so many media reports and without wasting much of your time let us get into this video so that we get the details and the full story about this fish called ma fish this is an old fish that has been uh at the copper belt university for more than 20 years this fish was a symbol of good luck was a symbol of hope and strength towards the students it was a fish that was peculiar in nature every year towards the end of exams this is when this fish would only appear on the surface of the ponds and usually what students believed in and what would happen is when a student is approaching their exams and they go towards this fish pond if this fish surfaces itself and swims in excitement when that student is near the pond it means the student is going to really have a good luck in their exams and then when a different student goes there and this fish decides to stay underwater what would happen is it would send a bad message to this student that maybe something bad academically is about to happen to this student so it was a fish that a lot of people really put at heart i think even if you are stressed it would be like a stress reliever to you that is why when um the highest year of study at the copper belt university the nickname is called ma fish because of this fish this is also a fish that's on the copper belt university logo and so much so that people are now even talking about giving this fish a a state burial although i see others are saying okay how will the burial be will it be broiled or brazed or put on the you know some people who don't respect the fish and the custom so much making a joke out of it but seriously speaking is it going to be buried in any special way are there any kind of things you're doing on the campus to mark ma fishis passing yeah starting yesterday and the day for yesterday students had the kendo lighting for it where others even gave their experiences with the fish they had bought something that i can call maybe something like a bonfire but it sat around the fire and shared their experiences with this fish and as of today they also sang the national anthem alongside the fish pond where this fish used to stay and they threw flowers actually actual flowers on the fish pond where it used to stay so our students here demanding that this fish should not be buried eaten or burnt but it should be embalmed and it should be preserved so it's almost like a protected institution it almost makes me think you've now got guards making sure that nobody has taken the carcass of this fish away is that what's happened always the fish right now that's what's actually happening and the students themselves that are protecting the body of this fish it will be rotting though unless you put it in the freezer yes in the freezer are waiting uh embalment what kind of fish was it can you describe it for us it was a very beautiful fish in appearance and it's a brim fish that was a white brim fish it was ranging from 70 to 100 centimeters and will you now find a new mascot this fish is irreplaceable so it's really going to be hard but we'll try to find at least one was hi swa Walo pre Tuwana Tuna Wabunanda Na Turufiya Orako Esu Imi Paishi Esu Stref Jesu Nani ikaramukon jumuriwa Aka rimbusha karanda tii Tama isa pa ziti Mifuta ora ingramu krasi, umunama fishi, shoroka puesku, kata umunama fishi, wama miroku yao krasi. Mifuta ora inisi, umma fishi. Eri kweta, maambayakuru. Inisi kwa mwa swambu. Ero mwa fishi, umma fishi, umma fishi, umma fishi, umma fishi. nishile landashani, yumuana nipalu, yukuare kutanganika, 1984, Aishwen Sanfi, amafi Aishwen Swenyosa ni koma, afta baya kutanganika, baire morama fishi, kareto loka, ekumusenda, kurea kusibi, asaba iroch paziti, mafisha arejaja, mafisha 100% bisi, arefora kamoeshi, arefora na evritem, manu arejaja, vangoma isa punda, uyuma fishi, isa intumubike, baire loka asibi, mafisha musenda, kurea kutanganika futi, afta graja, na distinkshe, nomba vangoma isaka, waara mafisha ta, asama kashibatati, bari Jenny Tomso, feli Fapiri,


On this episode of Impulse, Zack goes over Call of Duty Advanced Warfare complete with a robotic arm and jet packs. Plus, we get to see Grandma in her Trash Talking 101. Then we find out who the three winners are today in the $100,000 sponsorship powered by Freedom. I'm your host Tiffany, and you're watching Impulse. Hey Freedom Family, I'm Zack Dalton, and today we're going to be reviewing a game that doesn't really need another review of it online, and that game is Call of Duty Advanced Warfare. Look guys, I get it. This game came out last month in its old news, but I have to get something off my chest. I only buy Call of Duty games to play multiplayer online, and Advanced Warfare was no different. Even with Kevin Spacey, this storyline couldn't hold my attention long enough to keep playing. Call of Duty always delivers on his promise to be mildly different than its previous version, but like everybody else, I keep getting sucked into buying them. Multiplayer Online is a huge part of this game, and that's what we will be rating once we go to Tiffany to find out who the runners-up are in today's $100,000 sponsorship powered by Freedom. Robotic gear and jet packs paint me red and call me Iron Man. And now in no particular order, let's announce the two runners-up in the $100,000 sponsorship picked by Heartbeat Chrome. And you get to choose from these select prizes brought to you by our partners with Freedom. If you want to learn more about the $100,000 sponsorship, click the video on the sidebar for more information. And now today's runners-up are Our first runner-up is Nebulcy Graphics. He proclaims that creating your own graphics instead of asking from others will result in more exposure compared to your fellow YouTube peers. Our next runner-up is The Gamer Sight. The Gamer Sight advises that by being original, instead of swearing like everyone else, will result in a bigger audience, thusly getting you one step closer to achieving your successful channel. Dude, I don't want to play Call of Duty with you again.  Congratulations Freedom partners, and remember, you're still eligible to win first prize in a future episode of Impulse. And now, back to Zach and Graham. Thanks Tiffany, now let's rate this game. For gameplay fun, I give this game a 7 out of 10. The jet packs are a surprisingly fun feature, and the controls are what you'd expect from any Call of Duty game. For multiplayer, I give this game a 10 out of 10. Call of Duty has really defined the multiplayer aspect for the modern gamer. It's fun, super easy to get started, and fun to play with your friends at your house or online. For price and value, I give this game a 4 out of 10. $60 seems like a bit much for a game that struggles through a storyline, and isn't really much different than its previous versions. For casual play, I give this game an 8 out of 10.  Overall, I give this game a 7 out of 10. Now for your viewing enjoyment, here's some footage of me helping my grandma talk trash online. Let's not call it trash talk. Let's just call it motivational support. Why do you torment me? So every time I kill somebody, you have to say something to them.   What are you gonna say then? You gotta say something. I'd say Zach, he shouldn't have done that. That's not really trash talk. Real quick, we're not playing the storyline, but if we did, Jetpacks, Robot Arm, Kevin Spacey. But today we're playing Team Deathmatch online and all you do is kill, so... Oh my gosh. Say something to them. What do you think about this game? Oh my. Can you hear me with those headphones on? Oh I didn't... I knew it. What bloodthirsty. That's when I kill, like, five people in a row. Oh, my. I'm bloodthirsty. Kingslayer... ...that... I got killed. That looks real. Can you hear anything I'm saying? Or are you just ignoring me?  Oh, talk trash. I know when you were little, your mother wouldn't have let you have this. Okay, well, I live on my own now because I'm an adult. Yeah, I know that. See what happened? All right, you need some help talking trash. So I decide to write some things down for you so you can say them. Oh! I'm not gonna say all that. You don't even know what it is. But don't flip the card over until I kill somebody and then say what it says, okay? Don't look and then say it. I will give you $100. I don't want your money. I swear I will give you $5 million. I don't know. Oh, killed him. Say it. No. Say the whole thing. No, I'm not failed. Say, don't look at the next one. Say that.  Now isn't that awful? Aw, she's such a sweetheart. Now, if you want to see more videos of me playing video games with my grandma, visit the link in the description. And now it's time to take you back to Tiffany for the moment you've all been waiting for, the grand prize winner of today's $100,000 sponsorship powered by freedom. And now for the moment you've all been waiting for, let's see who's going to take home $250 in grand prizes. And as always, you get to choose from all these lovely products brought to you by our partners with freedom. Okay, Rick, do that thing you do. And today's winner is... Bullets Gaming! Bullets Gaming states that being active on social media sites is a great way to bring traffic to your channel. This allows the audience to participate in your videos and will always keep them coming back for more. He was incredibly active in the comments and wishes he was able to attend VidCon 2015 to meet all of his favorite YouTubers. Congratulations, Bullets Gaming! You are the raspberry seed that's impossible to floss. No, Grandma, you just make the other gamers cry, okay? Congratulations, Freedom Partner, on a job well done. Remember, guys, to share your knowledge, discuss today's topics, and interact with other Freedom Partners in the comments below. You too could be rewarded for bringing the community together as a family. Hope you guys enjoyed this episode of Impulse, and tomorrow Alex will be informing us on all the latest YouTube videos. Until next time, I'm your host, Tiffany, and yes, I love Jetpacks. Hope you guys enjoyed this episode of Impulse, and tomorrow... I don't know what's happening. They don't keep that. Jetpacks, woo!


Opening new doors by choosing professional development It has been the most extraordinary experience in developing my skills as a teacher. My own personal philosophy is that life has no finish line, it's just a struggle uphill where you are continually overcoming adversity and constantly improving. This philosophy applies to many facets of life but few things better than the art of teaching. Role Models I think of the great teachers that I have had. I think of their various breadth of experience. To be sure some are born with a natural talent, a knack as it were, to teach and connect with pupils, but some of the truly great teachers who have presided over my own development acquired their skills over years of teaching. You could sometimes tell this at the time when despite your age you picked up on bits of wisdom your teachers espoused, but some of the truly brilliant moments from these people who touched my life in their capacity as educators only became revealed to me in hindsight and in my own experience teaching. Professional Development Taking the TEFL course and seeing the point by point breakdown of some things I previously an inkling but no fully formulated idea of was revealing. I had many oh and I ha moments as I studied teaching structures and how these had manifested in my own classrooms growing up. I would say I gained a lot more respect and appreciation for my past teachers as I came to realize that there is by all accounts a fine science behind it. You can be a good teacher who has a natural ability to connect with students and you can have a basic understanding of the concepts outlined in the TEFL units, but true mastery of these concepts can only come with experience. I have been thrilled to find that I am graced with at least one of the foremost attributes, I have found I have a natural ability to connect with my students. Now I look forward to internalizing the concepts I have learned and applying them. I believe this experience will give me some of the true mastery hindsight has allowed me to realize was at play in my own classrooms growing up. New Ideas It is also nice to put a name to the vague idea I had in my head prior to TEFL. In the case of the boomerang structure, for example, I had the notion already in mind in that I would take my classes full circle with what they learn. Now I find this arbitrary idea has already been broken down in thoughtful teaching structures. I look forward to applying the basic concepts I already had in their entirety with supporting information. At this time I feel very equipped to expand my teaching skills but as I said, this requires the practical application of the concepts I have learned by getting real world experience. I can't wait to test out some of these things in an actual classroom setting. I know exactly how to put the lesson plan together, where to source the relevant materials, and the concepts I only had a vague back of the mind awareness of I can now refer to. Do you want to acquire new teaching skills? Take a TEFL course. Learning teaching skills is a process. When this process is supplemented with the proper tools and knowledge you can certainly cut short the learning curve. In this way, I plan to expedite the process and long journey to becoming one of the great teachers to which I refer. That said I maintain that one never stops learning so it would be far too presumptuous for me to assume I can be on this level overnight, even with the necessary tools and knowledge. Speak with an ITTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll free at 1-800-490-0531 to speak with an ITTT advisor today.