It's a great pleasure to have today Yevgeny Lyukovic from University of Toronto, and he's gonna talk about foliation of three manifolds of positive scalar curvature by surfaces of control size. So thank you very much Yevgeny for agreeing to give the talk and I remind that this is a shared seminar between the PD seminar and the Informal Geometric Analysis seminar. The floor is yours, Yevgeny, take it over. Thank you so much, Antonio. Thank you for the invitation. This is my first time at UNT, although digitally not quite in person. And I'm going to talk about a joint work with Davy Maximo. And the theme of the talk today will be how curvature, more specifically, positive scalar curvature, what kind of geometric features it determines about Riemannian manifolds. So let me very quickly give you an overview about curvature. So if we have a surface S in R3, we can pick a point and we can start intersecting the surface with various planes that go through that point and contain the normal vector to the surface at that point. And we can look at how these intersections, these various curves, how much they're curving and we can start recording these values. And if you look at the maximum and minimal curvature, which turn out to be perpendicular to each other, then the product of the maximum minimal curvature is here turns out to be a certain intrinsic invariant of the surface, something that only depends on the geometry of the surface itself and is known as a Gauss curvature. And so if our surface looks somewhat like this, then you can see that the curves are curving the same way. And so the Gauss curvature will be positive, but if our surface is, looks like a saddle and there will be a curve which is pointing one way like this and another curve that's just pointing the other way. And so the product of the two will be negative and then we'll say that it's a negative, negatively curved manifold. So this is the situation for surfaces. And you can see that curvature captures important information about geometry of the surface, but if you'd like to generalize it to and dimensional manifold, the situation is more complicated. The kind of full information about the curvature is contained in the Riemann curvature tensor, something that you feed it with three vectors in the tangent space of your point P and it outputs another vector. And Gromov has called this a little monster of multilinear algebra because even though it contains the description, all the description of curvature that we need it is very difficult to understand. So we may sacrifice some of the information that make this a little bit simpler by taking the trace. So if you have some vector x, we can consider a orthonormal basis of vectors perpendicular to x and we can sum over these scalar products to obtain something which is called the Ricci curvature of the point P. And so this already has a lot of important interesting things. It gives us a lot of interesting information if we know that this quantity is positive, as we will see in a moment. And then we can take another step and take another trace and then we will obtain a scalar valued quantity, something that just assigns a number to every point in our manifold. Here we have a function which takes in a vector in the tangent space and outputs a number. And here we have just the number which is just summing up the Ricci curvatures over an orthonormal basis of the point. So today we will be talking about this scalar curvature quantity and we'll try to understand the geometric consequences of this quantity being positive. There is one immediate interpretation that you can obtain by just Taylor expanding the volume of a small bowl in normal coordinates.  So if you're kind of in the positive curvature situation, then tiny bowls will have smaller volume than the Euclidean bowl. And if you are in a negatively curved situation, then tiny bowls will have slightly larger. So as far as supposed to be epsilon. That's right, thank you. But this holds at a small scale and it's not clear what's happening if we increase the sizes of the bowls and what it tells us about the geometry of the manifold. And somehow all of our success and understanding scalar curvature came from somewhat indirect methods, not from looking at this particular identity. Okay, so the theme will be that positive curvature implies that the manifold is small in a certain sense. And we have excellent results, classical results in this direction for Ricci curvature. We know that the Ricci curvature is positive, then we know in a very precise sense that the manifold is small. Particularly if you have a positive lower bound, which is the Ricci curvature bound away from zero, then we know the bound only the amateur of the manifold. And also if you look at our manifold M and we pick a point, here can we start considering geodesic spheres around that point, then their volumes and areas will be growing in a way that's not faster than the volumes and areas of geodesic goals on the standard round sphere of the corresponding curvature. And so we can sweep out this manifold by surfaces of controlled area. So today I will focus on the question of what kind of geometric smallness can we obtain if we impose positive scalar curvature condition. So one thing that one immediately sees is that we cannot hope to get these kinds of results. So if you have a n dimensional manifold, and let's say for now that n is to let greater or equal than four, if you have manifold M, then you can define a manifold and then dimensional manifold but taking a product of an n minus two dimensional manifold with a sphere of very small radius. And because you're averaging over curvatures in various directions, if you pick this R sufficiently small than your scalar curvature, you can make positive and arbitrarily large. In particular, for example, you can take the n minus two hyperbolic space and multiply it by a very tiny two dimensional sphere with standard metric. And then it will have large positive scalar curvature but it will have infinite diameter. And if you take a point and can see that geodesic spheres around that point, then the areas of the spheres and the volumes of the balls will grow exponentially. So you don't have smallness in the sense that you have it for positive Ritchie curvature. And if you have three dimensional manifolds, then you can do the following construction. If you have two manifolds M one and M two, and there's a construction due to Gromov Lawson and Cheng Yao, where you can take a, connect some of those in a way that preserves the positivity of the scalar curvature. It will be still positive. So if you take any sort of graph, one dimensional graph, with bounded degree, maybe three or maybe more complicated graph, then you can construct a Riemannian manifold with positive scalar curvature by just associating to each vertex, some manifold with positive scalar curvature with just the sphere S three. And then corresponding to each edge, you can perform the Gromov Lawson, connect some this way you will obtain manifold and you can make the diameter as large as you like. And also it will be large in a sort of isometric sense. You will not be able to cut this manifold into two pieces of approximately the same volume by some hypersurface of small area. For example, if you take an expander graph, then those are very connected. And so the hypersurfaces you want to cut will have to be very large. Or if you want to construct some sweep out, the areas will have to be very large. So this kind of example show in what sense manifolds with positive scalar curvature can be large. But they also suggest a certain notion of smallness because all of these manifolds, when you look from far away, look like they're two dimensions smaller than they are. They look like something n minus two dimensional times something else or maybe a tubular neighborhood of some n minus two dimensional polyhedral complex in some larger space. And that's precisely what Gromov conjectured that they admit a map into a polyhedral complex of dimension n minus two. And the fibers of that map will be small in a certain sense. So in the 80s, he conjectured that they will have small diameter.  And then he combined the two conjectures to make it as hard as possible to prove of both small diameter and small area. Okay, so I'm going to talk about some progress in this direction in dimension three. Let me maybe pause for any questions. Just a question. Here, when you say the bounds are on the wall fiber, so not so that in principle, they could be composing in component, in several connected components. So the conjecture is, so the diameter should be bounded on all the fiber. Right, right. But because we have freedom in how we choose this complex, we can modify it so that it's really just the connected components. Yeah, yeah, sure. It's a kind of a re-graph construction that you can do. Okay, thank you. So we proved that there's just a foliation of any closed remanifold with positive scalar curvature, which has nice bounds on its area diameter and also its genus. And in some more specific situations when the manifold is three-sphere or it's one-crossed two, then actually we have foliation by spheres. Okay, so here, the theorem is dated in terms of a Morse function and connected components. So it's kind of a choice for aesthetic reasons. So it's people are more used to Morse functions, but you can also formulate it as a statement about some maybe different map G from M into some one-dimensional graph, gamma, this is my gamma. And then we're looking at the bounds on the areas, the ameters and genus of just fibers, not the connected components of the fibers. Then you can replace the connected components with just fiber. And in fact, in this case, you can improve this to six. Bound to the genus. And right, so these bounds are not sharp. The way we prove things, it's tricky to produce sharp bounds while controlling all of these three things. But if we drop one of those, if you drop the diameter, then it's easier to get closer to the sharp bounds here. If you just think about the area, then in the case of S3, there's a Morse function whose fiber, whose connected components of fibers have areas of most 24 pi over lambda zero. That's the area of an equator in the standard S3. So that I expect to be sharp. And we get a similar bound for S2 cross S1 into, for fibers of a map. Let's do cross S1 into S1. And more generally, we get the slightly worse bound for the areas and we get bound of genus two, which I expect to be sharp because two is the Higor genus of some spherical space forms. And so when we do the fallations, we'll have to pass through those. So two has to have to be the sharp bound here. One can use this result to construct another kind of singular fallation, in this case, by closed curves. So we have a fallation, a singular fallation by surfaces. And then each surface, you can also fully it by curves. And this way you obtain the map from M into R2 and the bounds on the areas and the genus of the surfaces translates into a bound for the length of curves in this fallations. So we have a family of nice curves, short curves sweeping out our manifold. It would be really nice from here to conclude the existence of a short closed geodesic in our three manifold. But unfortunately, when you do the mountain pass argument on these types of things, you don't quite get a closed geodesic. Instead you get something that's called the stationary geodesic network, which is eternalization of closed geodesic to graphs. So basically you get a graph, something like that, that has geodesic arcs and then the vectors at the vertices sum up to zero. So here, for example, they would have to form 120 degree angles. So it's a stationary point of mapping of a graph into the manual. Okay, so this was a quick overview of results and now I'll go into the proofs, but let me maybe quickly pause for any questions. Okay, so the main technique in the proof is to use minimal surfaces. So it was a very important observation about scale curvature that one of the ways to get at scale curvature is through minimal surfaces. So ambient positive scale curvature using stability operator gives us information about smallness of certain minimal surfaces in the manual. Mainly, there are the following diameter bounds from the arguments of Shane Yellen and also Gromov Lawson, that if you have a stable surface with boundary, so let's say you have some curve in your manifold with positive scale curvature and then you feel that curve by some minimal surface, let's say this and then you take any point on that disk, then the distance from that disk to the boundary will be at most to pi or square root of lambda zero. So it's going to be controlled. Actually, one can slightly improve on this. Well, this is not sharp, but it's good enough for us because some of the other arguments are not sharp in any case. And then from this argument, one can also conclude that if you have a closed stable minimal surface, closed stable minimal sphere, then it will have to have controlled diameter. And you also get the bound on an index one minimal surface because if you have some index one minimal surface, you can look at two points which are at the maximum distance and you can go halfway between them so that both parts are kind of borderline stable. So then you will have bounds on half on the length of half the distance between these two points. So you get bounds for the diameters of index one and stable surfaces. And you have bounds in the area. So this is a kind of a classical bound, but Marcus and Nevis proved also a bound on the area of the index one minimal sphere using some clever computation with stability operator and the harsh trick. So if you have index one and stable minimal surfaces then you can control their size in a nice way. Now we'd like to go from that, from nice control for minimal surfaces in our manifold to existence of these nice fluctuations. And generally speaking, why do we even expect to have some minimal surfaces in our manifold? Well, if our surfaces, if our three manifold is something like S one cross S two, then you can imagine that we have some non-trivial two spheres and so we can minimize those two spheres in the commodity class. And then we will obtain some minimal two sphere. So we know that it's small, okay, but it doesn't kind of tell us much about the rest of the manifold. And if we have something like S three, then well, we don't have any reason to believe that if we minimize something we will get any minimal surface. So instead we need to do a mountain pass construction where instead of minimizing surface in its commodity class we consider a whole one parameter family of surfaces. So a sweep out of S three by two spheres and then we somehow try to minimize them simultaneously and try to minimize the maximal area over surface in this family. And so there is a theory that deals with this problem and kind of using this intuition. It shows that this is possible. So it's a kind of, it's called the Simon Smith version of Albin-Pitts-Meanmax theory. And in this particular setting, sorry, my daughter just woke up. So in this particular setting we can obtain minimal surfaces that come from the Higert splitting. So if you have a three manifold then we can decompose this manifold into two handle bodies whose boundaries are, is a surface. And if they know that it's a spherical space form then we know the three manifold topologies tell us that if it's a land space then the handle body will be a torus. And for other ones we will have a genus two handle body. And so we can run, we can construct a sweep out using this Higert decomposition. And we can construct a minimal surface and it will be index one minimal surface which is kind of natural since it comes from a one parameter sweep out. And it will be isotopic to the Higert splitting of M. All right, in case if it's not RP three. So now if it's RP three for M, RP three we have a dichotomy. So either it will be index one torus either we will get an index one torus which of course we will not in, no, that's the truth we actually do. We might get an index one torus or we get an RP two stable minimal RP two with stable double cover. We'll have one of these two possibilities in case of RP three. Okay, so now we have these index one surfaces and possibly some stable minimal surfaces and we want to interpolate between them. And the idea will be to use mean curvature flow to flow the index ones until they hit the stable minimal surfaces. So let's try to understand what's happening topologically. So we know by Perlman's work by classification of manifolds or free manifolds in this case of positive scalar curvature that our free manifold can be decomposed into pieces one, two, three and so on where each MI here so these are minimal two spheres in fact, minimal stable two spheres we can cut it into pieces and each piece will be a spherical space form. Then we might get as one crosses two but if you get as one crosses two you simply cut it by another stable minimal sphere or we might get a RP two process one. That's another possibility. And then in each of those pieces we can do mean max and we can obtain stable figured splitting sorry, index one figured splitting. So maybe it's or it's original steward sphere of that manifold, any questions? So we can formulate this as follows. So the pieces into which to cut. I'm sorry to interrupt. I have a question. I'm probably asking at the wrong point though. Yes. I'm wondering about the whether there's any issues of regularity with the minimal surfaces, you know it's like automatically smoother. Right. So that's a very important question. And it's a very complicated question results of me, a lot of work of many people. So for the mean max construction only in the sixties formulated the very weak notion of minimal surfaces that can be obtained via these methods. And then with the work of Shane Simon, Shane Simon Yau and the kids, they were able to obtain regularity in some dimensions. So in co-dimension one, we have regularity or manifold of dimension less than eight. So in particular in the situation we have. Now starting with dimension eight and up we will have some singular set. It will not be smooth. That's a very good question. Luckily in dimension three, we have results that give us smoothness of this minimal services. We have curvature estimates that will guarantee smoothness. Yes, thank you for a great question. So in this particular situation, we decompose our manifold into pieces such that one boundary component it's going to be some index one surface. And then all the other boundary components are going to be minimal spheres. So this is going to be stable minimal as twos. And this is going to be index one minimal surface of genus less or equal than two. So it's index one minimal surface. So the fact that it has more index one means that there is one direction where you can push it and decrease its area. So if we push it in slightly, it's going to become mean convex. And then hopefully we start applying mean curvature flow to it and the surface will flow. Sometimes it may disconnect into pieces and eventually it will converge to the boundary minimal twos spheres. And because we already cut a maximum of this joint collection maximum joint collection of minimal twos spheres it will not encounter any other minimal surfaces in this process. And it will fully the whole manifold. Now mean curvature flow may have some singularities. And so if you want to have a sufficiently nice flowation, we will not be able to have a smooth flowation. We will have to have some singularities. But for example, we want only more style singularities. We won't only have finally many singularities which are of more style. Then we need to do some extra work, but luckily not that much because mean curvature flow is very well understood. So there are words of Brendel and Heisken and Hasselhofer Klein, Hasselhofer Beethoven and Buzan and Hasselhofer and Hirschkevitz which describe mean curvature flow with surgeries. And so they give a very detailed description of how singularities happen and how one can cut them away and how those regions where you cut them away look like. And basically the idea is that you will have some regions where your surface will become very close to cylinder and then potentially it will pinch off but right before it pinches off, you can zoom in onto this region and in the region where the singularities has to happen actually want to zoom in on this region. So right before the singularity has to happen, we can map it into R3 by some one plus epsilon by Lipschitz map and we will see something very close to the standard trial cylinder. And then we can basically by hand describe that if you have something very close to standard trial cylinder, then you can cut this away and you can construct a family of surfaces with exactly one singular point of voliation in here. In the process, we may lose the correct sign of the mean curvature here. We may slightly increase areas or diameters but because it's happening on a very small scale, whatever we lose will be really time. And so basically the description that they give about mean curvature flow with surgery lets us take any problematic region where the singularities has to happen, zoom in, see a nice Euclidean picture, cut it, decompose it and then restart the flow. And then we know from their estimates that the flow will have to run at least for some time before it happens again. So we only have to do it violently many times. So basically we end up with the proposition that there exists a more voliation of a geometrically prime region that starts to the index one minimal surface and that ends up with a bunch of stable minimal spheres. And the areas will be smaller than the area of the original index one minimal surface. That pretty much proves the result and we need just to put all of this together and then we'll have a voliation of the whole. So just a question. So that's for me to see in the if I understood. So you first decompose and you get these boundary curves. Then with the mean curvature flow you have a propagation of the area bound. So is the, but I'm a bit confused on the bound on the genus and on the... So they get propagated as well with the mean curvature flow or you need... So the bound on the genus does get propagated because the mean curvature flow if you have a surface with some genus, what can happen? You may get something pinched off, right? So you may lose some genus here but you will not gain... No genus will appear, no handles will appear during the mean curvature flow. So the genus can only go down but the diameter bound you lose you cannot say anything about the diameter. That's what I'm about to say next. Okay, you need to treat after the... Okay, okay, sorry. So this procedure gives us nice bounds for the area and the genus. Now, what about the diameter? So that's indeed an excellent question. How do we get the bound on the diameter? So let us now go back to an argument of Gromov Lawson in the 80s that gives the bound on the diameter for filiation for filiations of simply connected or homology zero, first or manifolds the zero first homology picture. So the argument is really nice but it is slightly technical but I still want to kind of give you the description of this argument. So let's pick a point P and let's consider geodesic spheres around that point. Some point that geodesic spheres may have more than one connected component. So Gromov claims that each connected component of the geodesic sphere will have diameter at most 12 pi or square root of lambda zero. So let's for simplicity take the scale of coverage equal to one. We want to claim that the connected component will have diameter at most 12 pi. And by diameter, I mean the extrinsic diameter. And this is also actually in our theorem, the diameter that we have is the diameter in the ambient metric, not in the intrinsic diameter of the surface. So let's use a different color. Let us pick two points X and Y. Let's assume that they're at the maximum distance from each other. So the distance between is equal to the diameter. And let's consider a minimizing geodesics connecting these two points. Now we may assume that the distance between P and X and Y is large because if it's say less, if it's less than six pi, then obviously the diameter is less than 12 pi. So let's say that the distance here, the distance here, let's say is some distance L, greater than six pi. And let's go back a little bit and consider a geodesic sphere. Oh, that's at the distance L minus two pi plus epsilon. So we can see the geodesic sphere a little bit closer to P. Now, okay, so that's, so now we do the following. So we can connect Y and X inside of the level set because they're in the same connected component. So we can connect it inside the geodesic sphere. And we obtain a closed curve, the triangle here, and we can feel that triangle with the minimal surface. If the manifold is simply connected, we can contract the curves, in particular, if there exists a disc, we can minimize among all discs with that boundary. And so we obtain a minimal surface. Now, this minimal surface will intersect this level set. Let me call that level set boundary of BL minus two pi minus epsilon.  Some of them may be circles, but there will be a curve which connects these two endpoints. And because it's a disc, there will have to be an intersection with this boundary point, with this boundary point, we cannot have anything like that because those are different distances. So there has to be a curve connecting these two points which is the intersection of this geodesic with this boundary sphere and that geodesic with that boundary sphere. Let's give these two points names y one and x one. And the claim is that these two points, y one and x one actually close to each other. So let's pick a point on the curve in between. That is halfway between this, so let me call this gamma x, call this gamma y. So we pick a point, let's call it q, which is halfway between gamma x and gamma y. Same distance between gamma x and gamma y. We know by the estimate for a minimal surfaces that this point q has to lie close to the boundary of this disc. So if we draw a minimizing geodesic to the boundary, a minimizing geodesic to the boundary, notice that this minimizing geodesic to the boundary has to go to either gamma y or gamma x. It cannot go to this curve because this curve is at the distance to pi plus epsilon and this point has to lie at the distance to pi. Because it's the same distance from gamma x and gamma y, there will be another geodesic of the same length that goes to the other curve. Okay, this way we obtain yet two more points, y2 and x2. So this is now getting confusing. So that one was x1, this is x2. Okay, so now let's look at some inequalities. So we have that from p to y2 plus the distance from y2 to q by triangle inequality is greater or equal than the distance from p to q. The distance from p to q is exactly l minus two pi minus epsilon. And we know that the distance from y2 to q is at most two pi. This is less or equal than two pi. So we get that p y2 is greater or equal than l minus two pi minus epsilon minus y to q. So that's greater or equal than l minus four pi minus epsilon. Okay, so the distance from here, from here to here is greater or equal than l minus two four pi minus epsilon which means that the distance from y2 to y1 supplies that the distance from y2 to y1 has to be less or equal than two pi. And because y1 lies exactly at the distance two pi plus epsilon from y. This gives us a bound on the sides of this arc. And well, that means that the distance from y to q which is bounded by the distance from y to y1 plus y1 to y2 plus y1 to y1 plus y2 to q can now bound that. So this one is two pi plus epsilon. This one is at most two pi and this one is at most two pi and we get six pi plus epsilon. The same we get for x, for the distance from x to q is at most six pi plus epsilon. So we conclude that the distance between y and x is less or equal than 12 pi plus two epsilon. But the epsilon goes arbitrary so we get that the distance between y and x is at most 12 pi. So this is a really nice argument that tells you that this in radius bound for this disk somehow gives you a bound between these two on the distance between these two points. Okay, so this was slightly technical but feel free to ask question. One can sort of remember the main idea of the argument by saying that if you have a disk and you know that every point is close to the boundary and then you somehow decompose it into the boundary into four parts and these two parts are sort of far from each other then these two parts have to be close to each other. That's essentially what's in that argument. So we want to imitate the same kind of argument and but in a somewhat more general setting now we measure distance not from a point but from a surface but this surface has control diameter. And we are looking not at level sets of the distance function, not just the geodesic spheres but surfaces which are constrained which are trapped between two geodesic spheres of comparable diameter. So if you have some surface here and it is trapped between two geodesic spheres and it's connected, actually it's a statement not even about the surfaces. It's a statement about the connected component of your manifold trapped between two geodesic spheres at the distance which is different by 10 pi or a square root of lambda zero then by pretty much the same argument we get the bound on the diameter of the surface. You can relax this argument to saying that if you are like this and this is your geometrically prime region and your boundary here has control diameter then if you're trapped between two geodesic spheres and you're connected, then you have to have small path. So the rest of the argument now works out like this. We start with the index one surface and then we start flowing it by mean curvature flow. In the process of flowing it, the diameter may get distorted and also it may become long. It's distance to our original surface sigma may become large. And then whenever this happens, whenever the distance, the difference between distances of the closest point to sigma and the furthest point from sigma become large whenever it kind of stretches in space and reaches that threshold of how much it is allowed to stretch in space, we cut it. We can see that a geodesic sphere which cuts it halfway between these two points which are furthest and furthest away. So this is now a surface as let's say two dimensional surface we intersect it with other two dimensional surface we obtain a bunch of curves, one dimensional curves and then we fill those curves in the isotope class of one of the two halves. I did it the wrong way. That's exactly what we are not doing because this region we already swept out. We are minimizing it that direction. So the part to the left is what we already swept out here and we are minimizing it to the inside to the part that we haven't swept out yet. And so we have good diameter bounds but for this feeling by the diameter bound estimate for minimal surfaces. And then we cut the surface into two parts. This color now to obtain here a surface to one side and another surface to the other side. So this is a minimal surface. This is the original surface is a mean convex surface and then we have a corner when we smooth out that corner we obtain a mean convex surface. And so we can restart the mean curvature flow and we can restart the mean curvature flow here. And this way we shortened the distance we shortened the difference between distances to sigma of different points and therefore we put the diameter under control until again it drifts off and then we cut again. So now when we do this procedure we have to keep control of both area and the genus. And this is where we have to start need to make some difficult choices because suppose this is our situation. Maybe we have the genus all on one side and most of the area is on the other side. And we now want to cut and decompose it into two surfaces. So when we cut we have two choices. Either we can either we minimize in the isotope class of this or we minimize in the isotope class of the other part. And then we whatever choice we make then if you make the first choice then we will end up with a surface here after we cut it into two pieces we will end up with a surface of genus four we'll double the genus. And if we end up if you make the show the and here we'll end up with nice surface of genus two. But if you do the other choice then we will end up with a surface of control the area on one side. But on the other side maybe when you minimize here the air doesn't go down at all or just by a little bit. And then you effectively double the area of the right side. So when you make this choice you either have to sacrifice the genus or have to sacrifice the other. But the observation is that there is an asymmetry in terms of these two regions. There is one region on the left side which after we resume the mean curvature flow will remain trapped. You see this this region is squeezed between two minimal surfaces. And so as we flow it it will remain squeezed between two geodesic spheres of comparable distance. And so we will not need to perform this cutting procedure on it ever again. But this one will move to the right and potentially maybe it will become very long and we will need to cut it again and again and again and we don't know how we actually need to do it. So we always know how to make this choice so that the thing on the right has both area and genus controlled while the thing on the left may double its area or may double its genus but we won't need to do it one time. And so we don't need to worry about it. So that's why we have sort of an increase in area and genus bounds in our final result. So thank you very much. Thank you for that beautiful talk. Are there any questions? Yeah, there are also virtual applause. So are there any questions from the audience for the beginning? So meanwhile, I had a question and this is related to a comment that you made along the way. So you were mentioning that this is the extrinsic diameter, right? But in principle, when you are building, I don't know if I'm getting the right intuition about it but when you are building this, this falliation so the issue is that these fibers may oscillate a lot and this would give you a problem in controlling the intrinsic diameter, right? So there is no way to try to control the oscillation on the falliation. Let's say I'm mentioning really a sort of adding to the process also a sort of pull tight procedure where you try to straighten up. So if you try to run a pull tight procedure along the way, now I don't know exactly at which point and you try to straighten up these fibers. At the end, the two things, the extrinsic and intrinsic diameter may become comparable. So this is what I was wondering. So have you tried this or do you think it may hold or? I think that's a great question. I guess we can check sure that for the result should be called with intrinsic diameter. For the minimal surfaces, both index one and stable, we have bounds for intrinsic diameter. And but when we start doing mean curvature flow and this argument was comparison, Rome of Lothan argument, we lose that. And it would be nice. One of the, and it would have some interesting applications. I think it will be helpful for obtaining a short close geodesic, for example. So with this methods, we only update a stationary short stationary geodesic network. But if you have a bound on the intrinsic diameter, I think one would be able to obtain the short close geodesic. And pulling tight, I think it's a nice idea. It's not immediately clear to me how to make it work. But I think that it should be possible. I see. Thank you very much. Thank you. Are there any questions for Yevgeny? Okay, so if not, let's thank Yevgeny again for the video. Thank you. Yes, so Yevgeny, if you want, we can chat a bit more. Let me stop the recording just a second.


Hello friends and how are you all today? The question says, integrate the following rational functions. Now here the function which is given to us is 3x-1 upon x-2 the whole square. So we can write the given rational function as a upon x-2 plus b upon x-2 the whole square. On taking the LCM we have 3x-1 upon x-2 the whole square is equal to a into x-2 plus b upon x-2 the whole square. Now on comparing we get ax is equal to 3x so we have the value of a as 3 and then we have to compare the coefficients of the constants that is minus 2a plus b is equal to minus 1. So on substituting the values of a as 3 we have minus 2 into 3 plus b as minus 1 minus 6 plus b is equal to minus 1 b is equal to plus 5. So we can write the function as 3x-1 upon x-2 the whole square is equal to 3 upon x-2 plus 5 upon x-2 the whole square. On finding out the of integrating both the sides we have 3x-1 upon x-2 the whole square into dx is equal to 3 integral of dx upon x-2 plus 5 integral of dx upon x-2 the whole square. Now we can write it as 3 log mod of x-2 plus 5x-2 raise to the power minus 1 for minus 1 plus c. So the required answer to the session is 3 log mod of x-2 minus 5 upon x-2 plus c. So this completes the session. Hope you understood it and enjoy.


Hello everyone welcome back to another session in dentistry and more today's topic in pedontics is bone grafts. So bone grafts are nothing but materials which is used for replacement or augmentation of the bone. So it is a procedure used to replace or restore the missing bone or gum tissues. So this session is about the biologic mechanisms involved in grafting and various types of graft. So let's get into the details of bone grafts. So grafting is nothing but implanting a healthy tissue from the donor side to the recipient side. So here the defect is present so we keep a healthy tissue to the new recipient side so that it is restored repaired and regenerated. So what are the rationality of this process? Because this process will enhance the regenerative capacity of the bone and it will achieve new attachment apparatus. Okay so these are the rationality of this grafting and basically we have three biologic mechanism which is happening in grafting. The first one is osteoconduction then osteoinduction and osteogenesis. So this is the process how the new bone forms at the recipient side. So you can see all is having osteo that is a bone. So one bone formation via conduction, second via induction and this is a natural process genesis. Okay so what is exactly osteoconduction? So osteoconduction okay it is a formation of bone by osteoblasts from the margins of the defect on the bone graft material. Okay so this is a graft material okay so this is a graft material we are implanted this is a recipient side okay this is a recipient side and this is a graft material we just remove this. So this is from donor side we implanted a graft here. So osteoconduction means formation of bone by osteoblasts from the margins of the defects on the bone graft material. Okay so this is a margin okay this is a margin okay so there will be osteoblasts here. So it serves as scaffold for bone growth it does not inhibit nor induce bone formation okay no inhibition no induction. So what happens is it facilitates bone formation by bridging the gap okay so bridging the gap. So there is a gap here that is between defect and the new graft which is implanted. So there is no inhibition there is no induction just facilitating the scaffold just facilitating to close the gap between the newly kept graft and the defect margins. So it simply allows the normal formation of bone by osteoblasts into the graft defect along the surface of graft material. So this is a surface of graft material. So along the surface of graft material there will be bone formation and bridging the gap. So this is osteoconduction okay. So whereas osteo induction is it involves new bone formation via stimulation of osteoprogenators from the defect okay that is means from the vasculature then it differentiates into osteoblast and begin forming of new bone. So here the bone formation is induced okay it is induced with the help of some inactive material such as bone morphogenic proteins okay. So these induction of bone forming process by cells that would otherwise remain inactive. So these bone morphogenic proteins induce bone formation in osteoconduction there was no induction it was just facilitating here the induction that is the osteoprogenators are stimulated via the new defect that is from vasculature to differentiate into osteoblast with the help of bone morphogenic proteins. Whereas osteogenesis is the normal process of bone formation it occurs when leaving osteoblast a part of the bone graft. So there is already present osteoblast within the graft so when there is adequate blood supply and cellular viability these transplanted osteoblast from the new centers of ossification within the graft starts forming bone and it creates the new bone okay. So because this osteoblast already exist and added as a part of the bone graft from ossification centers which contributes to the total capacity for bone formation. So these are the basic difference in osteo induction it is induced by BMP it act as a scaffold and close the gap this is the cells are present within the that is osteoblast is present within the graft here the inert material like BMP induce bone formation that is a difference between these three mechanism okay. And now let's move on to the types of graft so we have the autographed that is intraoral and extraoral type another one is yellow graft which is taken from the same species xenograft from the different species alloplast or synthetic graft so autographed is nothing but taken from the same person okay could be an intraoral tissue or an extraoral tissue. So intraoral sites we can use healing of extraction site, edendulis ridge the bony growth such as exostosis, maxillary tuberosity, the chin and the bone which is removed during osteoplasty and ostectomy so all these can be used as a graft they are the intraoral intraoral sites from which we can take up the graft and also we have extraoral sites from which we can take this the graft for implantation so they are iliac crest ribs tbl metaphysis even cranium all those can be used as a extraoral sites for graft okay. Now we have the second category that is yellow graft or allergenic bone graft which is taken from the same species so four types of yellow grafts are available one is frozen cancerless iliac bone marrow and the second one is cryopreserved bone from the head of a femur then fdba fdba that is nothing but freeze dried bone allograft and the next one is dfdba which is demineralized freeze dried bone allograft so these are the four types of allograft so the only material with human histological evidence to substantiate the regenerative user autogenous bone graft and this dfdba okay so these are the two materials which can induce the regeneration of bone and also it is important to understand the screening protocol of tissue bank that is procuring and processing the graft in donor selection processing technique and particle size the third one is xenograft xenograft is different species okay such as calf bone keel bone and an organic bone so these materials have been discarded for various reasons that is xenograft the last one is alloplast or synthetic bone grafts so a number of synthetic or inorganic graft materials are available for use in the treatment so they act almost exclusively as biologic fillers with this bone fill and very limited connective tissue regeneration and the last one is alloplast or synthetic bone graft so a number of synthetic or inorganic graft materials are available for the use in the treatment so they act almost exclusively as biological fillers with very limited connective tissue regeneration they can be classified by their ability to be biopsoped such as absorbable material or non absorbable material so absorbable materials are ceramics hydroxyapatite calcium sulfate and calcium carbonate or beta tri calcium phosphate and non absorbable or porous hydroxyapatite or bioactive glass so this bone graft materials help maintain space to facilitate the formation of bone within a confined space so they should facilitate the growth of neo vascularization and migration of osteoprogenators and the size of bone graft particles determine the resultant space available for issues formation okay so the typical size of bone graft particles ranges from hundred to thousand micrometer which is conductive to the in-growth of bone so what are the basic requirements for bone regeneration there should be blitz supply adequate blitz supply there should be proper stabilization and the presence of osteoblast and the space should be confined there should be space maintenance and the proper wound coverage so all grafting techniques require pre surgical scaling or crucial adjustment and the exposure of the defect correction of exposure of the defect using a full thickness flap and the flap technique best suited for grafting purpose is a papilla preservation flap because it provides complete coverage of the interdental area after suturing okay so the graft purpose is suited with papilla preservation flap whereas the occlusion adjustment and the exposure of the defect is done with a full thickness flap so the fate of bone graft is different once a material is placed in the bonnet effect it may act in a number of ways which may decide the fate of this material so it could be such as bone graft material may have no effect at all or the bone graft material may act as a scaffolding material for the whole side to lay the new bone or the bone graft material may itself deposit new bone because of its own viability so anything can happen so that's also now so we discussed in detail about the biologic mechanisms just osteoconduction induction and osteogenesis and various types of graft autographed allographed to xenograft and alloplastosynthetic graft so all are very very important for the exam so each one can be asked as a short not or this entire thing could be asked as a short essay so I'll come up with a new topic in dentistry and more thank you and lastly guys we have started channel membership in dentistry and more channel so you can explore various exclusives for the channel members so you can explore various options by clicking on the join button adjacent to subscribe button so we have options of personal whatsapp help so you can ask any doubts you will get answered through whatsapp text messages or voice messages and we have one more option that is the PDF notes will be available but as of now we have only the public health dentistry topic the more topics will be applauded soon and the last option is one-to-one interaction session you will get the personal interaction or personal classes on various subjects from the faculties of respective branches so explore the join button and let us know if you want any further help from us thank you


The best thing about studying in Australia is that you not only grow professionally but also culturally. Really good facilities and really professional and qualified teaching staff at the University. Opportunity to interact and learn from the lecturers who are professionals and experts within their own areas of discipline. Everything is on an equal playing ground where I'm easy to participate in the university community and not I don't feel like discriminated or marginalized but I'm part of the community. The knowledge that I'm gaining is also current and very valuable to my future work. The one-to-one relationship that I can have with my lecturers is the opportunity to work with industry leaders and also sharing ideas with them and seeing what their perspective is. The facilities, the education level here in Australia is a very high standard. It provides me access to resources that I would otherwise have not been able to access at home.


We are in for a treat. We have Dr. Guido Holsman is going to speak tonight and his talk, The Cultural Impact of the Dollar, is sponsored by Greg and Joy Moran. Thank you to our sponsors. And to all of the sponsors for the whole weekend and all of the talks. It's really just been a fabulous event. So we really appreciate all of those who have sponsored these talks. We're thrilled to have Guido here back with us. He hasn't been here to the Miesen Institute since 2019.  But now we're glad to finally get to have him have him back with us. You may not know this, but Professor Holsman is a very well-rounded guy. He has degrees in philosophy and mechanical engineering and economics. So also if you haven't read, if you haven't read The Last Side of Liberalism, the biographer he wrote of Mises Highly recommended it. He wrote that while he was here in Auburn, was it five years? Four years in the making. And it's a great, it's a fabulous book. Of course, he's a senior fellow of the Miesen Institute. He's a professor at University of Angers where he directs the master's in law and finance and co-directs the double bachelor program in law and economics. So he's the author. He's got a new book coming out, Abundance, Generosity and the State. Also he wrote The Ethics of Money Production. Of course, Mises The Last Night of Liberalism. So we're looking forward to hear him come speak to us tonight. So. Dear Lou, dear Joy, dear Greg, dear colleagues, including David Gordon. Dear ladies and gentlemen, dear Natalie. It's true, I've been working for many years at the Mises Institute on the Mises Biography. And it was all in all 10 years in the making, right? It was 10 years. I mentioned this only because I said it was kind enough to downplay this a bit. It was only five years and so on. But I remember the many painful meetings that it was Lou and Lou and I would have, Guido, we need to have lunch as we sit together and stand. We talk about all kinds of things and research and so on. Then we look a bit when it's the book coming. It is terrible. It is really, and I'm slow. I admit this. So I'm slow. And so the most recent book was also five years. It just takes me a time. And everybody has got to work with his own weaknesses. So it just takes time. And then eventually it's there or not. So far, it was always there at the end. A few days ago, on October 10th, we've been commemorating the 50th anniversary of the passing of Ludwig von Mises. The name pattern of this Institute always went its own way against the socialist and positivistic fashions and fats of his day. He drank the cup of life to the fullest and never complained. He once wrote that we are all the lucky hairs of our fathers and forefathers. We at the Mises Institute and all people of goodwill all over the world are and remain the lucky hairs to this intellectual kind. Praise to his glorious memory. May God have mercy on him and may he rest in peace. His example has guided the Mises Institute throughout all the years since its foundation. It has guided Lou Rockwell. It has guided Jeff Tucker. It has guided Doug French. It has guided Jeff Deist. Whatever their strengths and weaknesses may have been over the years, they have always been faithful to the mission. Thanks be to that. Now the Mises Institute is taking a new departure and a new leadership. And I think we all hope and we all pray that the board will make the right decision picking the right person to guide us through these difficult times. My topic this evening is the cultural impact of the dollar. That's not really an academic discipline. It's an intellectual oddity that has been my fad for the past 15 years or so. I've been publishing on this a bit because it occurred to me initially just speaking about monetary policy and monetary interventionism that we cannot just limit the discussion to the economic consequences that follow from it but the manifold cultural repercussions of these interventions. The typical justification of monetary interventionism, so the creation of the toleration of fractional reserve banking, the creation of central banking, the imposition of fiat money on the economy, goes in terms exclusively of its economic benefits or sensibly its positive impact on employment and of economic growth. Now even as far as these benefits are concerned we have to say that there's an extreme discretion and even on the part of the advocates about the studies and the evidence that support this claim. Is it really true that central banks and monetary interventionism facilitate employment? Is it true that they promote economic growth? Standard empirical work that is conducted by well standard economists shows that monetary policy has an impact.  Well who'd have guessed so? So there are some guys who run a printing press. They can create as much of this as they want and they do have an impact on the economy. Well yes that's probably true and the impact tends to be positive typically in the short run. So short run meaning anything between 8 and 16 quarter years after the increase of the money stock. But then so the question is of course what happens in the longer run? That longer run so for many economists the long run is 16 quarter years or four years. That's the long run. Now we're talking about very different things. I understand the long run for me is something like 10 years, 20 years, 30 years but then I'm an economic dinosaur probably. Now as far as this really long run is concerned we have in the textbooks in macroeconomics we have what I like to call the great macroeconomic puzzle. Because all the textbook writers whether it's Blanchard, Mankiew, they all agree that monetary policy has a positive impact on the short run and no impact on the long run. That's the fact. Okay now that's a puzzle. I mean not for an Austrian economist but for a mainstream economist that is a puzzle.  It works for eight quarter years or for 16 but why don't we do it for another 16? So why shouldn't it turn out to be after 32 quarter years or 64 quarter years to be positive but it doesn't. So that's on the side of the benefits. So the benefits are essentially short run and there are no demonstrable benefits in the long run. On the other hand the costs of these policies are never considered, virtually never considered. The monetary and financial costs of monetary interventionism are supposed to be negligible. Nobody is really examining this except for Carl Friedrich Israel, he's a young professor who has been a Mises fellow many years and he's now teaching also in Angers but not at my university, he's teaching at the Catholic University, he's also teaching at the German University and he has examined in his work his research the monetary costs of central banking. So central banks usually escape from the scrutiny, usually the supposition is in their favor. As we imagine oh yeah there's a printing press, yeah there's a little machine and it costs whatever, $10,000, it's a one-time expenditure. Then you buy all the paper and you buy all the ink and there's one guy at the printing press and then you have whatever the press secretary and the president who tells the guy at the printing press how much he should turn right. So it should be very inexpensive. That in a case was the argument brought up by the classical economists by Adam Smith and David Ricardo and they said wow I mean we can save a lot of money, a lot of resource costs if we just substitute paper money at the place of gold and silver which are expensive, which are costly and so on. Well that argument was debatable at the time where we didn't have any experience of central banks. So at the beginning of the 19th century it's completely unacceptable in our day in which we have empirical evidence of the functioning of a fiat money system to give you just one idea. Just the number of people employed by the Federal Reserve system is in excess of 20,000 people. The Federal Reserve system has one central banking system. The German Bundesbank employs in the excess of 12,000 people. The French, Bonk de France, more than 12,000 people. And you go on, the central bank of Italy, central bank of Spain, everybody has these thousands of people. Now I can tell you one thing, they're not working at the cost of a gold miners, tariff okay. And so what Professor Israel has pointed out that is that actually the actual resource costs of our current system just in money terms are way in excess of what we had in previous times for gold and silver mining. And the great irony is that of course we haven't got rid of gold and silver mining, it's still there. So we have added an additional layer of costs on top of gold and silver mining, which we still have and which still serves people who are not completely confident in the competence of our central banks. And so therefore own gold and silver to protect themselves against the adversity of times. Now these are just the monetary financial costs. Any other cost items are supposed to be inexistent or irrelevant. On my talk today I'm dealing with some of these other cost items which are of a cultural sort. I will first highlight, so among these cost items are the role, the exaggerated role in place of the state and the wedge that monetary interventionism drives between the inhabitants of any country. It destroys a free society, creates a caste of underlings and a caste of supreme rulers. Then I'll talk about one of the most visible repercussions of permanent monetary interventionism, which is constant price inflation. And constant price inflation brings about redistribution effects between the haves and the have-nots. It leads the reorganization of the market economy and it entails a culture of debt, which has many negative repercussions on the economy, as I will spell out in some more detail. So let's start with one immediate effect of monetary intervention that should be familiar to all people in this room, which are the so-called cantillon effects. Cantillon effects are the redistribution effects of increases of the money stock, which these increases have an unequal impact on individual prices. Some prices rise earlier than others and some prices rise stronger than other prices. And the consequence is that there are always winners and losers. The winners are those, the selling prices of which, of whom, increase stronger or earlier than their buying prices and for the losers is the other way around. Now, this brings us immediately to the impact on the political organization of a country and the role of a state. Of course, cantillon effects are the prime motivations for government intervention in the monetary system in the first place. That's exactly the reason for governments to get into the production of money. Governments, by controlling the production of money, can position themselves as institutionalized winners themselves and their allies. And as a consequence, we have, thanks to government intervention, not just winners and losers, which you would have if the money supply would be artificially extended just occasionally, for example, by fraudsters, right? So, false money and so on. But governments position themselves as permanent winners and all other citizens become permanent losers. So, we not just have winners and losers, we suddenly have an impact on the structure of society. Now, suddenly, it's a permanent upper class and a permanent lower class. And we are seeing this today. Monetary interventionism is therefore irreconcilable, silable with the idea of a free society. This point is not stressed enough today, even by critics of the Federal Reserve. But two of the greatest monetary thinkers of all times, Nicolas Oresme in the 14th century and Ludwig von Mises in the 20th century, they have underlined, underscored exactly this problem. And Mises has said that a free society, and he was not an anarchist, and so a free society, so we have a government, and the government is under the control of the population by virtue of the control of the budget of the government. So, it's the representatives of the population that decide how much money the government can spend. If the government can decide unilaterally how much it spends, then there are no limits to the extension of government activity and to the reduction of purchasing power of the population. You cannot confine the government by specifying a specific, only a mission. For example, you might say, well, the government should just be a night watchman state. But of course, even if the mission is only to protect the population, so you forget about the welfare state, you forget about the protection of the environment, the fight against global warming, I don't know, just protect the population. Well, you can protect the population with one policeman for 1,000 persons, one policeman for 100, one policeman for 10, one personal bodyguard for everybody. It's a very different budget, and the policemen themselves, they can be armed just with a knife or with a gun, with a machine gun, with a tank, and so on. So, the simple specification of the mission is not sufficient to limit the amount of resources that are absorbed by the authorities. So, it is necessary to specify how much they can use. And the control of the printing press allows the government exactly to sidestep that limitation.  And then they're haggling over each million or two days or each billion, they don't care. The Federal Reserve can create any hundred billion that they need with a snap of their fingers. So, the whole democratic process becomes pointless, becomes ridiculous, because the truer decisions are made elsewhere. Now, that's a recipe for tyranny. The taste of tyranny, well, we fed it a few times in these past 20 years, and we're not at the end of it. Now, let's get to one of the most visible signs of monetary interventionism, which is permanent price inflation. Permanent price inflation, as I tell my students every semester, is not something that falls out of the skies and that is the law of nature, but it's something that historically has existed in peace times, only since World War II. Before World War II, we always had a tendency for the price level either to remain stable or for the price level to drop. I can show you the statistics for the United States. If you look for the United States data for the 19th century, previously, we don't have any reliable data. For the 19th century, it shows very clearly that the price level had the tendency to drop more or less vigorously. And this tendency was interrupted only by the regular wars that were carried on American soil, the War of 1812 and 1814, the Civil War, and then World War I. But each time, after the hostilities ended, the government reverted back to the peacetime monetary order, and that order is no artificial extension of the money supply or not much of it in any case, and as a consequence, the price level starts to drop again under the impact of economic growth. Since World War II, we are pursuing, for the first time in economic history, wartime monetary policies during peace times. And the consequence is that we have a permanently rising price level. That, ladies and gentlemen, has never existed before. Now, I have never experienced anything else. Some people in this room might be old enough to have witnessed something else in their youth days. Okay. And certainly, our students, they have never seen anything else. We've grown into this. So it seems to be something that is just part of the landscape, just part of nature. It cannot be different. But the study of history tells us, well, that's not. We are living in very exceptional times. We are living in an age of inflation, in an age of price inflation. And the economists and historians of the 1950s and 1960s were very aware of this fact there. So they've cried out and said, well, suddenly we're in this age of inflation. Today, we no longer care. Now, permanent price inflation comes with a heavy cost, heavy social cost, most notably in the form of the redistribution of wealth in favor of the haves and to the detriment of the have-nots. In an environment of permanent price inflation, perishable goods are traded at a discount and durable goods, which help us to protect our wealth against the loss of purchasing power of the money units, trade as at a premium. Now, what are the most durable goods? Real estate and financial titles. What are the most perishable goods? What's the most perishable good? Human labor. Human labor cannot be stored any second. You can store eggs, you can store other perishable items for a few days or a few hours, but labor cannot be stored even one second. Okay. So as a consequence, the labor trades in an inflationary environment at a discount as compared to durable goods such as real estate and financial titles. And this manifests itself in the increasing difficulties of the rising generation to accumulate wealth. It just takes many more years of work and increasing savings rate to catch up with the level of wealth that has been accumulated by previous generations in a shorter time and with lower savings rates. Now, the data are very clear in that respect. So we have a lot of whining sometimes with the younger generation and of course we need to slap them on their cheeks from time to time, but it's not without reason. They definitely have a harder time today than they had before. It is harder for younger people, harder for younger families just to catch up. One of my associates, Jeffrey Degner, who is sitting over there, he will defend his doctoral dissertation next month on the family in the inflation economy and which he studies the impact of permanent price inflation on families and especially young families. Now, the consequence is, of course, that some sort of growing despair, growing revulsion of younger people against the economic order that exposes them to such injustice. And that right now drives them into the hands of communists and various other people who tell them that their life situation is delivered. That's a consequence of capitalism rather than of monetary interventionism. So it's a false flag operation. We see something very similar as far as the world of business is concerned. So here too, permanent price inflation entails a redistribution between the haves and the have-nots, established companies who have already assets of various sorts, durable goods, can offer collateral on credits and therefore are better positioned in the competition for additional credits than startup firms and so on. Now, the consequence is that the optimal firm size in an interventionist economy is larger than in a non-interventionist economy. So we get artificial size, which works out to the detriment of family business and so on. Another consequence is that permanent price inflation creates an irresistible incentive for debt finance. Everybody in the room knows this out of his own experience.  And I bet there's not one of you here in this room who has financed the acquisition of his family home out of equity capital. All of you, like myself, have funded the acquisition of the home with the credit, with the loan. Now, why is this so? Simply because in an inflationary environment, our revenues are likely to increase. And if we take out a loan at a fixed interest rate, the weight of the debt service in our annual budget diminishes as time goes on. So it's the rational decision making in an inflationary environment. And that's very different as compared to our ancestors living in the 19th century and at the beginning of the 20th century who could not expect that their revenue, their monetary revenue would increase year by year and who therefore had an incentive to accumulate savings and eventually when they had enough savings to purchase their house out of equity capital. Now, what are the consequences of increasing debt finance? That brings us to the culture of debt. And here I have one, two, three, four main points. Either the list could be extended very easily, but my time not. First of all, modern man, man living in a price inflationary economy, in a debt economy, tends to be short-sighted and reductionist in his vision. He tends to be short-sighted because he needs to bring money on the table every single month. Month, he needs to service his debt. So he cannot just lay back as our ancestors would have done in the 19th century. They'd know that if there's no money forthcoming in any month or maybe there's a bad year and so on, well, we get over this. We have some savings and so on, we get over the time. Today, we need to make sure that every first of the month we have what it takes to service our contractual obligations. And it also makes us therefore reductionist because all other considerations are relegated, really quality of our business to other objectives that we pursue in life. So this becomes the number one objective. Second, modern man, the man living in a debt economy tends to be servile in order to benefit from this process, in order to be one of those who are first among the users of the new units of money. The only way for him to do this is to take out new loans. In order to qualify for loans, he needs collateral, he needs revenue, he needs to demonstrate that he's a servile and good contractual partner who will do whatever it's necessary and never disturbs anything. So we get here the whole history of credit scores which easily tend to be transformed and we've seen this in the case of China and even some western economies into social credit scores. So you frequent the wrong people, you support the wrong political party, you eat meat rather than fish or meat rather than vegetables, you don't do enough for the environment, you smoke cigars, I know more smoking at all, your social credit score diminishes and as a consequence you're relegated to lower places in the competition for additional credits. Third, in a debt economy, values tend to be turned upside down. The long run becomes less important as compared to the short run. Now, of course, the important word is less. It's not the case that the long run no longer counts but it becomes relatively less important than the short run. Even in a normal economy that is based on private property rights, there's no monetary interventionism, there's always a balance between the short run and the long run. Nobody lives just for the long run and so on. You always have short run goals that need to be balanced, equilibrated relative to short run goals. But in a debt economy, the short run primes because you need the short run, service the debt in order to survive the long run. Independence becomes less important as compared to the dependence that comes with relying on additional credits. And that leads to the sort of servility that I mentioned before, a highly indebted citizen is a compliant servile citizen. Just think of the experience that we had during the COVID years. Why did COVID doctors so readily given to pressure coming from the government? Because the answer is very briefly that they could not have survived three months without the money coming from the system because they were all indebted to the Hilt. And so they needed the money to be forthcoming, so they gave in. Debt makes compliance.  It's really the debt economy that turns us into, well, slaves of the state. Another aspect of this is that equity capital, of course, and I've mentioned this, diminishes in importance relative to debt finance. Another aspect of this is that ownership takes a secondary rank as compared to usership. Probably you have noticed over the past 15 years or so, we've been talking a lot about users of various services and so on, and nobody's talking anymore about owners. And the reason is that in a debt-based economy, well, you take out a loan and all that you're interested in is that you can sell at a higher price than at the price at which you've bought. Doesn't matter whether you keep the property in good shape. You don't necessarily need to be responsible. You just need to find another idea to pay a higher price than you did previously. All right, so ownership is relegated to a secondary place increasingly. And the consequence is, of course, that the cultivation of existing assets of land, of capital, of social relations takes an increasingly secondary place relative to the exploitation of assets of various sorts. Another aspect is that comes with the debt economy is the revised relationship between responsibility and licentiousness, which is related to this equity capital and ownership issue. So the respect for others diminishes, whereas brazen selfishness is encouraged. The attitude that was once characteristic of the American entrepreneur and of Western citizens in general, namely the attitude to do what is the right thing to do in any situation, takes a second place relative to the attitude that boils down to, well, I'll do whatever I can get away with. Genuineness takes a second place relative to impersonation. Relative to impersonation, a genuineness of virtue, of friendship, of leadership. Today we have in all Western nations, we have political leaders that are no genuine leaders, but they're impersonate leaders. Probably the first famous case with Ronald Reagan, at the time nobody paid much attention to this, and to the fact that he had this prehistory as an actor. Well, today we have Mr. Zelensky in Ukraine, it's another glaring case, so we have increasingly people who are impersonating something that they are not. And that's also a consequence of the debt economy, because you get away with this. We no longer have journalists, we have less and less journalists, and we have more and more influencers, again who are irresponsible because they do not care about their reputation, because what primes is the short run, the short run impact, rather than the long run development of their career. To sum up, inflation culture man tends to become increasingly cunning, materialist, short-sighted, reductionist, shallow and servile. He's bound to be morally low in every sense of the world. And the last item that I should mention here is, and I've mentioned this in my talk this afternoon, I was talking about my forthcoming book, is the death of generosity. The interventional state, and monetary interventionists in particular, attacks generosity at its root. It reduces the opportunity cost of for-profit activities, of selfish activities. And again, I'm not morally condemning selfish activities, right? So they are absolutely central for the economy. I fully agree with Adam Smith that we've seen not much non-selfish action that genuinely improves the situation of men. That's a different issue. But the point is that the opportunity cost of dedicating our time and our resources to the service of others is systematically increased by monetary interventionism. Monetary interventionism makes it possible to leverage investments and that makes it possible for, especially for rich people, creates irresistible, very strong incentives to stay invested, have every cent of their wealth in the market, in the service of earning additional revenue, rather than donating money to worthy causes to deserving or needy persons. And we see this tendency in the declining membership in associations. We see this in the increasing superficiality of friendship and the manifestation of dedication to sciences and arts in all walks of life. This, ladies and gentlemen, are the cultural costs of monetary interventionism. So to sum up, the benefits of monetary interventionism, in particular of dollar interventionism, are questionable or, as put it politely, are yet to be demonstrated. We're waiting for this. In any case, they are likely to be tiny. The costs of financial and cultural are massive and patent. I thank you for your attention. Thank you very much. Thank you very much. I think we have time for a few questions. Do we have time? Yeah, okay.  Thank you very much. It seems that there would be possibly one additional detriment to modern man in the debt culture, and that would be the spiritual detriment that comes. And you described it, the moral side and the ethical side, but it also seems that it compels people towards a materialistic approach to life and thereby distracts from the spiritual realities that might be greater. Could you comment on that? Yeah, absolutely. You're absolutely right. I mentioned among the durable goods financial titles in real estate, but that, of course, is relatively non-durable as compared to eternal life. So clearly then in a debt economy, these considerations also are discounted relative to the immediate concerns of daily life, and we see this also. In order to lead a spiritual life, you need to have a spare time. We need to have the attitude of Abraham who received God, and he was just available. God, three persons show up, God shows up at his house, and Abraham did not say, oh, wait, wait, wait, I need to take care of my car and then I need to run the children to the school and do various other things, right? May the paychecks and so on said, yeah, I'm here and I'm available. You're not available in a debt economy in which you tend to rush. There's permanent haste because you have the time of your activity. It's discounted relative to all these durable goods, so the only way for you to benefit from your youth and from your strength is to transform your activity as soon as possible into something durable. Whereas in a free market economy, the tendency would be exactly the inverse. In a free market economy, as in the U.S. in the 19th century, the price level would tend to diminish in the course of time, so the purchasing power of money would increase. The value of your labor would increase relative to all durable goods, so you have time and you have resources to consecrate, to dedicate to other people, to wealthy cause and so on. Yeah, we do have that problem. There was a question over there. Hi, so a lot of people have noticed that a lot of people are having less kids nowadays, and a lot of people will argue, of course, that's maybe because they don't need to for whatever reasons, you know, we're more productive by ourselves, but do you think that rogue monetary policy, if you can even call it policy, do you think that might have an impact on whether people are or are not having more kids and, you know, repopulating the earth, right? Yeah, I mean, of course, there are several factors that come here to play, but monetary policy, especially insofar as it funds the welfare state, plays a major role. The whole point of the welfare state is to replace the traditional role of the family in providing goods, right, gratuitous goods to the family members and so on. So why should you incur the costs of family life? Arrange yourself with a difficult wife. My wife is not difficult. With any human being, right? I mean, there's the old joke, right? Well, there are two, there's treason. So it's, and so I say this to all my students who always wax enthusiastic about communal life, oh yeah, we'll have, we transform all of France into one huge kibbutz or something like this. And so, well, look at divorce rates, okay? Apparently, it's difficult to get along just with two, right? And you want to apply this on a national scale? Well, good luck with that, right? And in a free economy, of course, all these difficulties that you have getting along with a different human being, whereas, well, not from the outset, but you're growing to become one in the course of time if everything goes right, right? So it comes eventually, but not at the beginning. And so how do you survive this? Well, because there are huge benefits in a free economy. You depend on one another as a division of labor. Now, if there's the guy running the welfare state and the welfare state checks and so on, if there's a slight difficulty, here's the officer will take your divorce, who will file a divorce, and here's the other guy who will pay you money and so on. Yeah, of course, you ruin the family. Absolutely. Thank you, Dr. Halsman. This is a very, very important topic. Just to show an example of what the young man just said, we have many, many students in the United States that have student debts. And that's affecting the marriage rate. The other thing that we've seen in the United States is in the 30s and 40s, this country had a wide variety of mutual aid societies, which were individuals who contributed capital to help others in their community. That entire system has been completely destroyed by government intervention and debt. So I thank you for this very, very important topic. Thank you, sir, very much. Yeah, on your first comment, I again refer to Mr. Jeffrey Degner, who has written a wonderful dissertation and discusses exactly this problem, the impact of the debt service on the formation of new families. And so he provides also evidence of statistical and econometric sort. As far as the second issue is concerned, yeah, that's actually very important. Maybe I should seize the opportunity to point out something that is of very interesting historical fact. The British in the 19th century up until the 1830s, they had a well public welfare system that relied on the Elizabethan poor laws, right from 1601. According to the poor laws, each municipality was responsible for the poor people living in his abut and it involved various mandatory services such as cash payments and so on. Now, of course, the consequence were all kinds of abuses that we can imagine, right, so people signed up in multiple municipalities in order to have more cash payments. There was no incentive to get a new job and various young women benefited from cash payments to mothers, unmarried mothers and so on and let life just based on welfare and so on, as we have it today. Now, the British then decided based on a report by one parliamentarian published in the 1830s to completely abolish this system. And the best description of this process is in a book by a British journalist with the name of James Bartholomew. Bartholomew was published in 2014 in the book of the title, the welfare state we're in. So not the welfare state of the morals and so on of the fairy tales told by welfare state employees but the real welfare state, right. And so he relates the prehistory of the modern British welfare states. Well, actually the prehistory was firstly Elizabethan welfare for more than two centuries and then suddenly the complete abolition. What happened after the complete abolition? Well, a lot of misery on the one hand because of course you have people who cannot lead a life unless they are supported by somebody. And so a lot of immediate misery. On the other hand, a lot of spontaneous readiness on the side of citizens to help out. So within relative short time, within 10 years, 15 years, thousands of private welfare agencies sprang up. And in particular, a system that is not much known in the US, which the British call the friendly societies. So the friendly societies are associations of co-workers or neighbors and so on, the purpose of which is to help out people in need. And these associations have worked, well today we would say miracles, well they've worked like free market organizations, they were very efficient. Because somebody who is obviously an abuser, well he doesn't get funded. People who are obviously in bad strays without any fault and so on, well they get supported. And so the consequences within a generation or so, you get all the bumps of the streets and everybody seeks for employment, the mentality of the population changes and various other things. So the Brits, they had tens of thousands of friendly societies until the beginning of the 20th century. And then under the impact of the developing modern welfare state, it gets steamrolled, of course, SS in the case of the US, with these consequences. So whenever we get confronted with this sort of objection, we should say, well there's historical precedent, it's not just theory or it's something that we know from experience. And whenever free citizens are challenged and to help their neighbors and other poor people and so on, they will do it. They would not just throw money at people, which is what the welfare state does. Hey, Dr. Walson, kind of building on that topic and the issues that young people have with student loan debt and like, I know we've talked a lot about the dollar side of things, this culture of debt, Murray Rothbard wrote about repudiate the national debt. I'm curious your thoughts about the rule of debt jubilee and a variety of standpoints on more trying to figure out ways to empower younger generations to try to better navigate this world they've inherited. Well, as far as the younger generation is concerned, I mean, we see two things, right? I mean, the only ones still living the life of their parents or my generation are those who are in the lucky position who have sufficiently higher revenues. Among the others, well, some who are very virtuous, they continue to struggle on even though it's somewhat hopeless and many others get disbared, frustrated, joined the revolutionary ranks and so on. That's the current situation in which we are. And it's a time bomb. If we go on like this for another 10, 20, 30 years, well, we get a generation of lininists. And that attitude is not irrational on the bottom. I mean, they might not understand anything about economics and might not understand where the problem comes from, but they see that they will never be able to build up a life, an economical life, a material life as their ancestors had done. And so they will tend to overthrow the system that crashes them. So do we want this, right?  That's the how many trillion dollar question, right? So it's 120 trillion or 150 trillion dollar question because that's the side of the American debt market. Well, we cannot get around. I mean, here I agree, of course, fully with what David Stockman said yesterday, we need to abolish the system. The problem is that the system has lasted now 80 years, almost. And it has created two generations of people who have never known anything else who are dependent on the system, also incapable intellectually of imagining anything else. So if you just push the button and you destroy it, take out the Federal Reserve and say something, well, they will be confronted with a new reality with which they cannot immediately cope. That is unfamiliar to them, which drives them mad. And the first thing they will try to do is to get back the old system. And we need to have, again, price inflation and so on. That's the problem which we are. And that is why it's so important that institutions such as the Mises Institute exist. Well, first of all, it illuminated the population about the issues that here at stake. It's not because we might get price deflation that this would be detrimental to the average working class person or average wage earner in the US would not. Of course, the money wages would not evaluate as they have evolved so far. But in real terms, of course, revenues would be likely to increase. Now, that's an uphill battle because the argument is theoretical, right? It's not empirical. It's the difficult sell. That's our task. And if we don't succeed, I mean, we are in dire straits. The lady had a question. Sounds like your position is that policy is sort of driving the culture. I'm just curious, to what extent do you think policy is driving the culture? Culture is driving the policy and does it even matter? Yeah, I fully agree. So the culture is also driving the policy at some point. So we are in the chicken and egg problem. But again, we need to convince a sufficient number of our fellow citizens here in the US and in Europe that what are the causes, right, of our present problems? And that's the only way to change the attitudes and therefore the culture. If we just change policy without the culture, the policy change cannot be permanent. People will long to bring it back. And, right, so I mean, this button push idea is irrelevant unless you really convince the people what needs to be done.