So I changed the title. It was a little bit vague because it was a little bit hard. And so I started with observing that although it's a very wide spectrum of the subject covered by this meeting, it doesn't cover all the work by Tomahand. I think the most cited his paper is on symplectic geometry, which is actually in all textbooks now on symplectic geometry, the classification of toric or symplectic manifolds. It's just quite a nice theorem. I say, but we don't touch it here, right? And my point is exactly, indicate relation between two aspects of this missing negative curve between Kelly manifolds. And the problem, here it is a problem. So we give in a group and it's maybe not any group. You always can find count example. If you do it too broadly, but group is some niceness to that, or at least without apparent pathologist, and you want to construct geometric object. Or the group where essentially the group is fundamental group, but something like that, right? You know, it's a classical number theory. It was probably still a famous problem to realize given fine group is a Galois group of extension of the curve. This is not like that. So it's a realization of a group in a nice way. And nice here is what they indicated.  How it just moved? With the arrows? You want to do that? It divides, you see? It's supposed to divide, yeah? Can you see it like that? Okay. And so it might be kind of canonical construction, preferably in terms of the group, some extra structure in the group, still described group theoretically. And it might be universal at leastifying that if you take the object in a similar way related, all of them will be induced from that. Similar how classifying space of a group in general classifies all spaces with this fundamental group and maps it into there, right? Like K by one spaces. And so there are two examples which kind of somewhat inspiring. And one of the classical theorem of Abel, I don't know whom, is A and it says it works very well in the diabetes case, that the fundamental theorem, if you have an algebraic manifold or a K-manifold, compact K-manifold, and you have an isomorphism, is homology more torsion to the homology of the complex torus, the fourth module of the right dimension, then it comes from a holomorphic map, but this holomorphic map is very kind of rare animal. This homomorphic map is a multiple kind of easy thing, but having it covered from complex geometry is quite amazing, and it is kind of a theorem. And so, except that this complex structure on the torus depends on your manifold and it's essentially unique, it's a unique structure in the map essentially in Capra translations. So it's completely canonical, right? So you can out of the group, you make this family of K-manifolds, and this is just modular spaces of all this, you have to polarize them just, the technicalities of this complex, complex tori, and then they represent all manifolds with this fundamental group in a very kind of nice way, and so it's a kind of, I must say, okay, it's one of the most famous thermo-mathematics. Is it due to lunas? Well, it's called Abel Jacobi or Vanessa, I don't know, I don't know who actually proved it, as we usually don't know. It's classical of the 19th century, but it has one, if you kind of know this, but you know how to ask nice questions, say, are there any examples? That's an interesting point, because of course, there are curves in the algebraic curve, for every curve there is Jacobian, and this is the classical construction, there are many specific constructions, how you make Jacobian complex torus out of the curve, right? Analytically, pure algebraic or any field, there are those algebraic manifolds. For Kepler, it doesn't, but this is not a kind of Kepler stuff, pure algebraic. But then if you look at the higher dimensions and ask, what are the examples? Can you give me manifold? Kepler manifold is a given kind of non-trivial H1, which is not like product of curves, and I've been in a variety, so I can say, well, if you know a little bit, you can say, take this complex torus algebraic torus, and take hyperplane section or genetic section, but then to be there from the statutes, and the fellows don't solve this. Actual algebraic geometry is a kind of cheetah, so they solve algebraic manifold defined by equation throughout the time and complex projection space. You say these words, are they examples? No. It's extremely hard to compute how to produce, they don't come easily, right? So I would say this, maybe kind of overstatement, but nobody has any idea what algebraic manifolds are. What are they? Because there are this naive complex intersection, there are modular spaces, and there are some, as I mentioned, arithmetic varieties coming from these key groups, and then maybe one, two, and then you, very few sources of them. So we don't know. Actually, they are conjectures, classical conjectures.  And so, however, it's still a great term. And the core of this theorem is the case of the curves and my kind of quick skepticism about high dimensions not completely unjustified, because general case, trivially, more or less, follows from the case of curves, at least for algebraic varieties, but complex, projectile, algebraic manifolds. In the following way, because, so, given this homomorphism of groups and this typology, we know there is a continuous map implementing this homomorphism, but continuous in a defined up-to-homotopic. And then, on the other hand, your algebraic variety is built out of curves. They have a surface, they have pencil, right? They take some point and rotate plane around it, and have this family of curves, which meet at one point. For each of these curves, you know there's a complex structure on the torus and homomorphic map was there by this theorem. But at this point, they might disagree. Of course, it doesn't give you. However, if they don't disagree, it gives you map from this point, you have a rational map for rational curve to this modular space. But this modular space, you know, is simply connected. I mean, it's universal covering. But you don't have to think about complex structure. It's just simply connected. It cannot contain any rational curves. So that's... At this point, I want to elaborate later on. So the key of all that and all generalization is apparently what happens to curves. And this is very similar to how you can think about hyperbolicity in group theory, right? Maybe you may think in terms of surfaces or in terms of curves, in terms of parallel language. But this is on the homomorphic side. But what's remarkable, and this is less known, though it's more elementary and equally beautiful theorem, due in this form, John Frank's, actually proven quite a few other theorems. And this is for dynamical systems. Now, instead of a complex scalar manifold, you take a manifold, any reasonable space, compact and locally contractible space with an automorphism, self-homomorphism. So this self-homomorphism replaces a complex structure. So a complex structure was in the morphism of the tension bundle, multiplication by square root of one to one. And here, just manifold itself transforms to itself. And I think there is a kind of much closer relation. But on the surface of things, you see, it's completely identical statement, right? And then there is homomorphism from H1 of your manifold to H1 of the torus. And then on the torus, there we needed scalar. Here instead of scalar, we say this automorphism induces hyperbolic automorphism on H1. Which means it's got generic. There is no eigenvalue by absolute value equal one. So it either stretches some vector contracted. No vector kind of goes unchanged. Of course, there might be an important element, which we don't want to. And then the same theorem is true. On this torus, there is unique, also an automorphism, but it will be the automorphism of the torus. And again, essentially unique, you can unique our translation. Here, you might as well be careful. Yes, sometimes it might be more constrained. Continuous map which preserves the structure. Meaning commuting with this in the morphism. So this kind of simple theorem, but what I want to say about that. Historically, it has kind of history of how people arrived at this. John Franks who finally founded the, but the first precursor of this was Smale, who I think about 62 announced stability of hyperbolic automorphism of the two torus. And then he announced it, I think somewhere, it's a meeting in Moscow, and when he left, soon thereafter, Arnold and Sinai published the paper giving the proof. And then Smale was kind of referring to that at some point and said that there is proof here and there, but the proof by Arnold Sinai has an advantage of being published. And this is quoted in the paper by Anosov, who said it adds one disadvantage.  Not just wrong, it's nonsensical. The proof was... Absolutely, no proof. Yes, it was wrong. So, this theorem of Franks, it's proof implies that much recorded by all the magnitude of the powerful theorem, if you say it correctly, it takes five lines. And all these proofs are quite long. And then Anosov worked out some proof of stability. It was first correct published proof, but then it was realized it's not stability. It's much stronger theorem. It's not stability when you perturb the thermomorphism, whatever. You take any transformation in a different space, only remember about H1, and then reconstruct it. And it's a unique reconstruction. And when in dynamics, people apply it to the torus itself and use the word type semi-stability or something. Not because you see, but in certain quarters, still people think, oh, there are structures and there are isomorphisms. But from certain, but it was from here, and kind of...  It's kind of minor, isomorphism minor, kind of small potato game. There are morphisms in the whole of this category. And there are things happen. The morphisms are just little, little guys there. Important, but little. Still not leading. And this is where theorem is. It is really categorical theorem. And so, I say a couple of words about that. So, the point is how far this goes. How far the analogy goes. How closely things are related. At the very beginning, I said, look at the one that already is complex. Polarized. Complex story. They already give fantastic this manifold in vector bundle over it and group action, semi-direct product. And the same automorphism, which acts here on the torus, appears there in the definitional module space. Because on the module space, on the story, you have all these monodrome elements acting in some of them. Hyperbolic and some, of course. Non-hyperbolic majority are hyperbolic. So, this thing closely related. But on one hand. On the other hand, there is parallel story. So, the logic here is as follows. You look at something in one field.  And then you look what happens in the parallel one. And then you usually have conjectures. So, there is some way to generate conjectures, either about K-many faults in the fundamental groups or about dynamical systems. Or hyperbolic structure. You have a hyperbolic dynamical system where groups in the second will be in this box together. With hyperbolic and the automorphism of tori. So, what comes next? Excuse me. So, how do you do it in this Frank's theorem? So, what is the key concept? And this concept was coming from the work of Smale. Anyway, you see, what I failed to say. Why this picture? So, why this picture came from? So, who knows what it is? Niagara. No, why Niagara? No. What has to do with hyperbolic dynamics? It's HOS. HOS-SHU, absolutely. It's HOS-SHU shaped waterfall. That's where I have our list of dynamicals. First kind of pinpointed, I think, by Steve Smale. So, it's HOS-SHU. Because see just what I'm telling, so maybe I can go to the very end. Yeah, so there are references of how it didn't make them big.  I put huge parentheses too early. And exactly about the matters I'm talking now. And so, nobody read the article. Now, I just read it and tried to explain it. I found out it's very hard to read. I had difficulty reading it. But a little understood from this I'm telling you. Well, but definitely, just I pinpointed quite a few. Point is the interesting observation. And one of them was motivated by the book by Toledo whose contribution will come in a short while. So, coming back. So, orbits and quasi-orbits. So, when you have an action of a group somewhere and it doesn't have to be a group, just set of transformation. It will be generating set of transformation. An orbit meaning you have a map from your group, a semi-group to the space, such that it's compatible with action on these elements. So, I have finitely many elements which will be generating such finite. And you have a group itself, from one side, from the left or from the right. I cannot, when I say this word, I don't know what it means, yeah. You know, what mean left or right? No, no, it's not a joke. You better communicate with somebody along the way, say along what, left or right. So, what is, how you can explain it? You know, there's only one explanation. I know only one, when you know a second. You know what? Well, left, right, right, from right. It's a weak, in the weak interaction, yeah, this particular, you know, nuclear decay when left and right slightly different. And so, you have to know details of that, if you don't know that, don't say these words. And I don't quite know the details of the experiment, neither really young logic, so I don't say left and right, because you have to be responsible for what you say. Mathematicians are mostly responsible for scientists, because they don't refer to the real world. They speak about their intuition, right. Which is certainly least reliable of all kind of, of all measurable instruments we have. So, it acts somewhere, somewhere, right, from some side, whichever it is. On the other hand, it acts in the space, and these two actions must commute. But if they commute up to by an error, so if they commute here and here in the finite error, it's quite the orbit, if it's finite. If it's epsilon small, it's epsilon small, very small. And so, these are orbit, quite the orbit. And how do you construct your, in the case of a space, it acts by homomorphism, and you want to build up the stores with an action in an economical way. What you do, you go to universal covering, and then action of the finite generating set, in this case, there's one element, and it's universal if you want. Act on the space, they act on that, right. And so, there are orbits and co- and action time approximated by corresponding sequence in the group, this will be quite the orbit. And then the remarkable thing, every quite the orbit is followed by a unique orbit, right. The scheduling principle. Why so? And this is exactly as in geometry because for orbits, for actual orbits, distance between two orbits is concave function, yeah. In some way they're closed, and then they diverge in a very sharp way. So it is a stable concave or convex function, I don't know how it's called, convex. And just once it's being observed for this action, okay, you have this theorem, it's always consequences, and it's quite simple. However, there is another way to approach that. And this was in classical dynamical system of a north of Smael real, you know, who defined them in this final way, which can be done in a more formal method without appeal to a group, or to universal covering, but it has kind of only partial power of what I'm going to say. So instead of saying this universality for which you need have concept of a covering or something like covering, and so just bound that error without specifying by how much, it will be just epsilon bounded and epsilon will be small depending on the station. So how to describe in dynamical system in a kind of, what is simply dynamical systems on compact spaces. So we have, we're going to describe.  They are more the same as hyperbolic, but not quite. There is slightly more general, but the full extent I am not quite certain by how much. So number one, dynamical system for any group. It is a Bernoulli shift. You can see the function from your group to your final set. And this is a compact counter space. And then in a group, quite simple. And then you say, you can take subset there. So you take some, in the group, you take some finite region and say I only allow particular function there. When I restrict to this set on all the shift, I want to be in a certain subset of all functions. So I impose finite to many conditions. And then I have what is called Markov shift. In combinatorial terms, it means you have a directed graph and it is easily reduced to that. And the system consists of all maps of infinite graph and infinite path going along the line and then the transformation, the shift. Because you don't take the full graph, you don't allow all propositions. But this is Markov systems and they also counter. But now we have something like torus. And the torus you have is endomorphism. There is apparently no counter set. And then you can reduce to that. And this is reminiscent of what I'm saying now, unfortunately. Unfortunately, there is nobody who knows that. There was this recent wave of ideas called going under the name of condensed spaces. Implemented by Schultz and his collaborator, I've forgotten his name, but when they describe continuous objects in terms of category of essentially counter spaces over this object. And then, in particular, they were describing in a fairly, fairly algebraic way. Because counter states and their projective limits of finite sets. They're still not waved by using Markov partitions. No, no, no, no. Markov partition, I agree with you. Markov partition gives you slightly more. The point is, what I'm saying, listen, what I'm saying makes sense for any group where there is no Markov partitions. Indeed, traditionally, actually, before Markov partition it was used by North of using the discovering by smell. Then I'll come back. Markov partition is something else which is related to that. Absolutely. But what I'm saying is there is much more kind of high-brow thinking along possibly similar line that very many continuous objects describable as categories of particular categories of profiled sets. And here, from this point of view, you replace your dynamical system by a general dynamical system by all Markov system over it. So those provisions are quotient with all kind of diagrams which commute to this quotient map. And this is very much how it goes. And so this is now the definition. So what's the definition? So you want to represent your dynamical system as a quotient of a Markov system which is zero-dimensional. You know any topological space quotient, oh, compact. Because door space is quotient of a canter set. But you can do it together with dynamics. You can say that, but that's not a big deal. It's not so interesting. So what's interesting is that the relation which defines it. So you have a quotient space. So it says you have binary relation on your original space. So you have a Markov space. Forget about this Markov, that Bernoulli shift. And then you identify certain orbits. Now you do that. You identify them again by a Markov rule. You can see the system by itself, times itself. Now it's an X on a product or space by itself. And again, you identify pairs if this identification given on pairs or on final sets. So on each final set, you take this binary relation, generate corresponding relation on infinite sequences. And they say, I wanted to be equivalent relation. Extremely strong condition. And miraculous is the right example. So for some reasons, for one parameter dynamic system, when you have groups? It makes sense for any group. Any semi-group. For any semi-group. Now already for dynamical system, it gives you the following way of representing them. Very much in the spirit of small cancellation theory. On one hand you have a graph. This is directed graph. And then you identify finite pieces of the orbits. So there are this segment and this segment. And you attach square to this. And to this segment and to this segment you attach square. This will give you binary relation and say two sequences, two strings equivalent. If any time they pass here, they satisfy this relation. What you get, you'll be not in general equivalent solution. You can spend equivalent solution. But then you have non-house door space. You have very ugly space. But miraculously there are examples. Conjecture. There is nothing else but this miracle. All these conjectures kind of have a fancy fancy name of the genitive theorem. You have a miracle and then you say, ah, it doesn't repeat itself. And it's called the genitive theorem. First it was very exciting. Most of the genitive were good arithmetic. At some moment I think it's a ball. Of course we have miraculously kind of tight object. It's very unlikely it appears twice. But here, however, it's unknown. Conjecture, he is going in a way going back to Smale in a special form saying that if you have such a system and resizing space is a manifold then it will be one of the classical examples. It will be endomorphism when it's being manifold or something of the kind. On the other hand, I guess genetically a huge amount of such system where the phase space will be solenoid. It will be cantoset times line or something. And then there might be kind of parallel theory like small cancellation theory where in Smale cancellation theory we describe a whole group where boundary one dimensional and here it will be a similar thing. It will be a generic dynamical system. Generic such combinatorial scheme will give you such. This is none of this is known. And there are a lot of high score of problems which is unknown here and I mentioned only one of them. But this concerns that and this kind of more or less rethinking of the classical conjecture of 50 or 60 years ago development by Smale and also Boeing and other people on hyperbolic dynamics. But now what about other groups? So the example when the first definition appeared there was only one example and these were boundary of hyperbolic groups. Boundary of hyperbolic groups also like that. And they can be described exactly in a similar way. You can see on the hyperbolic group kind of the map to the space of self mapping of the balls or something. It is described in a way that is the mark of presentation of the boundary. By the way, I was referring to the question about mark of partition. So mark of partition in this context mean that this question map is finite to one. And the proof kind of extremely unpleasant because you artificially order some elements in the graph and using this to prove it and in exactly what is wrong you don't work in the right category. So this categorical thinking which I mentioned in the categorical description is just a dream. It was not implemented as a tool to prove theorems. Because eventually when I think if you develop it you get by audible profound theory of hyperbolicity. And now we are coming to the general case. So one example of that. But then when I was writing this article I just realized there is another nice class of examples. Namely if you take any semi-simple lig group which satisfies Marguerite's rigidity theorem. So you have to throw away throw away the real complex hyperbolic spaces as a factor. And this lig group semi-simple lig group divided by compact by co-compact lattice then the action of this lig group has this universality property. Why? You take semi-simple lig group divided by by Gamma and then Gamma acts there from another side. But this action has this universality property. Which means if you take this group this anywhere else. And this anywhere else you have a homomorphism from the universal fundamental group here. Then there is a unique continuous map implementing that. And the proof. Quite simple modular no known result by by client with consequence of quasi-asymmetrical rigidity of this corresponding spaces. And then there are other examples you can make. But still it's unknown. If you have just torus and there is a subgroup of homomorphism of the torus. We show them have this property. Some of them do, some of them don't. And this is one of the question which is unclear in general for this group and so in terms of the group this orbit and quasi-orbit what acts as the group? In terms of the group it's an in-automorphism. So the group of in-automorphism may have this property that quasi-orbit uniquely followed by orbits. But this orbit now represents elements in the really group enveloping the group. However this is not the final story because what you get topological structure how you can get geometric structure of the group. And this is not quite clear. I think I know what it is but I can indicate it is definitely so. It's canonically constructable. We know it's episterior. But there is the following way to think about it which you can see strangely enough most clearly in the case where there is no this rigidity, namely in the real hyperbolic case. Now in real hyperbolic space so you divide by co-compact lattice or even co-volume lattice. How we can reconstruct out of the group how we can reconstruct the space. This is geometry. Every way except of course for dimension 2. In dimension 2 there are modularity it's not that you have to throw it away but it requires more thinking. Starting with dimension 3. So what you do, you construct the boundary you know the boundary. Topologically. But then what you have extra. In your space if it's co-compact if it's not compact you have distinguished homology class. You have fundamental homology class of your manifold. So you have fundamental homology class. And this class is bounded in some way represented by measure in the space of simplices representing this class that is actually bounded. And this is an extremal one. An extremal one, some plotted on regular simplices at infinity. And once you have them you can reconstruct the full structure. So you have sphere at infinity you have topological sphere and you have distinguished configuration of points corresponding to regular simplices and this reconstructs all geometry. And the same nowadays we know that the same truth for all local symmetric spaces the fundamental class bounded there is a distinguished measure and this measure at infinity I think reconstructs all geometry but they never got out. It's hardly questionable. However, we still have very special examples. So the question is how we can go further. And so what will be the next steps over time? Not very much time. Because they wanted to say something to turn to complex geometry. What goes along? So I say it just works as an indication. An instance of a theorem. So there are two basic theorems there. One of the grower's theorem it says its solution on Levy on Levy problem and it's properly interpreted. It tells the subject about Kelley von Demenz group. Then there is theorem by Schuch. Together they imply as it gives a case corollary. I indicate some corollary. What does it say? Schuch's theorem? Schuch's theorem says in this special case we have a Kelley manifold. A compact Kelley manifold. A map to say compact a manifold is a complex geometry. The complex is divided by a compact lattice and you have a map which is rank at least real rank map more than two. Then the map is hematopic to halomorphic or anti-halomorphic map. A grower's theorem says that if you have a polyconvex, the manifold with a polyconvex boundary then all cycles above middle dimension are realizable by complex manifolds. This is a grower to the great theorem because a very soft condition makes the complexity of the boundary and it gives you cycles. Cycles as you know in the boundary area they function in origin. As I said to produce interesting you have to secretly solve some differential problem which may or may not be solvable. They shouldn't be there. But this gives you a soft mechanism in generating them. Not that they truly understand the implication I never thought to but this one corollary combining the two saying they're related. And then maybe say just one word all this construction which I know associates with some distinguished cycles. For example, manifold we have a group where there is top dimensional homology class and this class organizes the geometry of the class. And then there is an issue what are these high dimensional homologies? And this is very tricky because the fact that there are groups where there are ample kind of high dimensional rational homologies I forget about torsion of course there are lots of these final groups but in general it's very hard to produce specific examples of groups with interesting homologies. Again you start making examples pretty fast around other examples. And here is a conjecture because they were speaking about problems which related to that and it's one of the rather actively studied problems these days which is a version of the Novikov conjecture about high signatures. So Novikov conjecture itself is purely algebraic and says that homology of the group of any group which is conjected probably wrong it's too general to be true is expressible in terms of roughly speaking in terms of quadratic forms of a group ring of the group. Well I don't want to formulate more precisely but sensitively what it says. And geometric counterpart of that which is again there is no count example for the moment but probably it's not true says the following which I formulate in a very special case we have a spherical Riemannian manifold we have compact probably with a boundary a spherical Riemannian manifold so universal covering contractable so all I know. And then conjecture says in a rather tricky way which takes time to explain to what I'm saying before is as follows that if I take any complex vector bundle of this if I add it to itself sufficiently many times then it admits given an epsilon then I can take some of the bundle with itself so in K theory I multiply it by big integer then the resulting bundle admits unitary connection where curvature will be everywhere point-wise less than my epsilon so every element of rational K theory is a bundle this is a it's not as general as a Noigo conjecture but much stronger would relate to that but it takes some time to explain what it has to do with what I said before about structure of this structure of this cycle and again it's infinity of question comes from playing back and forth between these two domains I didn't say what was another essential part and this we can find in paper by Toleda in mine about Toleda hyperbolicity how you can reformulate and improve the few theorems in this kind of hyperbolic type of language very similar to how works in dynamics and in manifolds in geometry of manifolds of negative curvature but I have to stop at 45 minutes, right? I have 3 minutes I have 3 minutes you have more information I have 15 minutes I have 15 minutes great so let me say what is relation between this making of the structure this implicit volume and the Noigo conjecture so I want to give yet another question which is related to so when I speak about a simple volume of manifold or a homologous class but say fundamental class of manifold so what you do you look at all pseudo manifolds when I say pseudo pseudo manifolds meaning oriented pseudo manifold dimension equal to a manifold in map to my manifold and then I see how many simplices are there divided by D at the degree of the map right? so for any manifold you can see that all the pseudo manifolds map there and take a degree of the each map and divide the number of simplices by degree and then minimize this number and go to infinity when D goes to infinity so I have a number for most manifolds simply connect to get 0 but for interesting manifolds it's not 0 it's a number and it's an variant of your manifolds topological variant not obvious so there is a variant ever non-zero but apparently it's non-zero very very general class of cases on one hand but not covering just just say non-covering would be kind of p-p-carapinas exactly it's not covering any map but now let's do the following on one hand we say instead of pseudo manifold we say manifold this seems kind of little difference after all any pseudo manifold there is a manifold which goes there with about the degree by tom therm but this degree magnification is significant but now instead of number of simplices needed for triangulating it you take the minimal number of cell on a Morse function minimal number of critical points on Morse function there or the number of cells in the composition and also have an effect and now if you look at the first invariant then it's non-zero for all locally symmetric space of negative type compact space universal covering symmetric space with non-negative curvature without flat factors this invariant non-zero which was recently proven for generality I'm sorry I've forgotten the names they were proven after I wrote this paper I don't have it in my list of references but on that hand if you take a manifold on one hand you restrict class of object but now you relax it and say ah instead of number of simplices I just look at the number of cells in the cellular composition and then the picture will be different because again for all even dimensional manifold of constant negative curvature negative constant negative curvature all the formulas have symbolic spaces or generally for all those locally symmetric manifold with non-compact type which have non-zero early characteristics its invariant non-zero which is already non-trivial for product of two surfaces right and on the other hand if you take three dimensional manifold as we know of course it's false because this manifold sends you five over circle and the five over circle of cells doesn't grow and then that's all we know we don't know nothing more about this invariant and it's certainly related to the simplification volume and it's exactly a decor of this knowledge of conjecture it's just kind of quantification of the knowledge of conjecture because the proof of what I said goes through the index theorem applied to some twisted deregoperative there is no elementary proof of that even for product of surfaces the proof is elementary geometry is a simple system but there is the only proof is by index theorem it would be a very kind of amazing thing saying how much manifold differ from pseudo-manifolds and so the question of course about hyperbolic groups for example do all even dimensional manifold of negative curvature have this invariant non-zero or it may be zero yes even for very simple examples we just cannot cannot say because those which map to manifold of constant curvature that's fine but you know there are very simple examples of a different kind even when the boundary is topological sphere of negative curvature they are not simply related to manifold of constant curvature there are quite a variety of examples and we don't know so what happened there because the proof at some moment you is very special representation of the kind of dual Lie group to the semi-corresponding semi-simple Lie group due to Lucic so that's kind of question so what are the questions that I was mentioning so what are you going to mention I don't understand I don't understand that no, tori of course is zero tori of course is zero so for tori of course is zero it's a semi-simple group yes of course I'm asking even dimensional manifold of negative curvature celeron and celeron celeron and celeron no, it's unknown I mean it's only known being non-zero if there is a locally symmetric space of non-compact type we discreet it's being serious, it's not zero early characteristic it's obvious for covering because early characteristic takes care of that but it's true for all maps and the first example, non-trivial example it's product of surfaces so the proof kind of you don't need your representation just a very simple representation just at your hand but still you need index theorem or actually computation of a signature in coefficient in some flat bundle so it is a categorological computation but it's very bizarre question that when we come to manifolds say of negative curvature and we look at basic invariance we don't know if there is zero or non-zero another question of course which I mentioned for dynamical system of course appears for manifold or hyperbolic manifold where the boundary is spherical so again they are very limited for all we know and they all may have rigid geometric structure behind them but we don't know if it is true or not so there are groups many groups seem to go along with some very rigid geometric structure however we know little about that and some structures of course related directly and directly to lead groups for example we may start with manifold of constant curvature and then they can be fight covering or fight in quotient and still have interesting group or make more complicated surgery out of them we can build very very many things but they all come eventually from these locally symmetric objects and the point is that we cannot produce directly interesting cycles of high dimensional group for high dimensional groups so many for the negative curvature is really very even it's not so easy to produce they are there but for them for example all these conjectures are known to be true the cohomology is kind of simple in a way they are presentable by most flat bundles so cohomology is kind of group fully control the cohomology which is in a way similar to what happens in algebraic geometry where you know if you think about homology of manifold in etal terms it actually come from group homology of open the risky open sets so if you know group homology of all the risky open sets and how one goes into another all these errors from that you build your etal homology or homology of the group according to Grothendijk and the same picture appears here so again I think that there is no way to show this problem without really rethinking basic concepts in making them more categorical which is of course goes we lag behind what happens when people doing algebraic geometry but for example another question is again I can formulate it very precisely one of the properties of this hyperbolic dynamical system Markov hyperbolic defined combinatorially is the data function is rational so the counting function the number of periodic points and because it defined combinatorially you think they might be combinatorial proof and moreover everything indicates there is not a function but some kind of much more general object function in the variant category of graph or something like that which have this rationality however the only proof which was found at some point by David Fried is actually repeating argument with Markov partitions so you reduce the system repeat the argument we should do partitions use topological argument and you cannot do it purely combinatorially however this purely combinatorial theorem and actually about this categorical combinatorics which we don't know how to do that there are infinite number of problems they just cannot of course go through all of them you can look in my paper where it's written but maybe I emphasize again one simple and elementary problem if I had some time I can say what I wanted to say about Talerda convexity so see your theorem based on Bohner type formula Bohner type formula for maps from many fault from Kali manifold to other manifolds and this Bohner type formula rules out certain maps this kind of local computation however there is another approach close to what they indicated for how you reduce the curves in the case of Albanian theorem how to use it to classical Jacobi you can look what happens to curves and you observe that under curvature conditions where SU theorem is true the following more general property is true if you can see the map from a curve it's remaining in manifold to another manifold and observe first energy of the map is conformal invariant It's invariant of a complex structure. So if you consider a demon's surface, we are dealing with the magnetic. You can see these maps to another manifold. And look at the Dirichlet energy of that. This energy depends on conformal structure. So harmonic maps and minimum of this energy is conformal invariant. Therefore, becomes a function on the modular space of curves. So every remaining manifold and homotopic class of maps from a given curve into there give you a number. It is a minimum of this energy on this modular space. This function is true for every complex structure, for any conformal structure. When you vary this, you have a function on the modular space of curves. So every remaining manifold as an invariant now, and given these curves and homotopic class of maps, give you a function on the modular space. And this function is what is called Plutius subharmonic. So it's kind of convex in a homotic sense. Its restriction to any curve is harmonic, subharmonic, kind of convex. And now we can forget about complex structure. And you think, this is the key property from which everything follows by rather simple arguments. And so in this very of the same spirit, as I said, what happens to orbits. So what characterizes orbit of this way under the stability is that function between orbits have this convexity, this weak convexity. And this is the convexity in the complex sense, which, unfortunately, serves only true for closed surfaces. There is no counterpart for surface with boundary. If it were with a boundary, it would give you much more power, much more control about what happens. But still this kind of interesting. And for particularly geometries, besides those described in where it was observed first, I wonder why it's true. For example, if you take natural geometry from two-dimensional polyhedra, small cancellation group, whatever, you may have this property. And this will tell you something more that you usually get by other arguments. But this is certainly quite, quite, I think, basic concept in this theorem of Toledo, emerging from this theorem of Toledo. And the final, because I mentioned in my reference, I have another paper by Toledo which I received. Yes, that's the final. The final paper by Toledo I received a week ago. They eventually produced examples of algebraic manifolds, compact algebraic manifolds with negative curvature, which are not coming from the complex ball. It was a long-standing question. And the obvious candidate, we are removed covering over totally the genetics of manifold. But to constructs removed covering, you need to find a group. You have to know the corresponding group as subgroup of finite index. And they proved that the group is easily finite. And therefore, you have lots and lots and lots of manifolds of negative curvature, which are not coming from the ball, and they are cally and moreover, they're complex algebraic. And this is pretty nice. It is expected, but still it's a usual problem when you construct hyperbolic groups. By various constructions, you're getting stuck because you don't know the group is easily finite. And you, constructions don't go. Like there will be five covering, three-rate constructions. And here they overcame this difference, which, of course, it shouldn't be there. I mean, in a way, the construction must go anyway, but in a more general category, which is not at the moment well-defined. So maybe it doesn't be time yet. OK, thank you very much. Are there questions? No questions. How come? Yes. Yes. So in general, in dynamic system, what is the analogous, the modular space? In dynamic spaces, you have your torus and you have different anamorphism. And so it's a group of the torus, so a group of automorphism acting on this modular space. How to get modular space? Modular space of the torus is kind of a symmetric space, mod gamma. And this gamma is a modular space for the dynamic system. So they're really coupled. They're kind of two parts of a general picture. And on the case of the SU, there is no modular spaces. The map is just in the, because it's strictly negative curvature, it's just only one structure. Space is rigid, right? And therefore, and this, by the way, has a lot of questions related to that, which of the spaces is rigid or not? Immediate question appears when you have other manifolds. How you can get other manifolds in the same fundamental group? You just take a generic surface there. You take the plane of the right dimension. So it's in high dimensional, that locally have a modular space, you have a surface. So generic is completely, and then it can move. It's very movable. When you move it, of course, it has modular spaces. Conjectually, the only modular it has. Again, there is no geometry there, maybe somebody knows it. But this again, according to this logic, there shouldn't be exterior, extra, extra deformation. This extra deformation is like external automorphisms of the group, right? Like this, a group of high symmetries, and like surface groups, have no outer automorphisms. And here it corresponds, there is no outer deformations. So everything here is strangely enough, counterpart there. It just says there was slightly different linguistically. And you arrive at questions. And again, this logic, it's not fully justified. Example would say you must be careful. However, that's a very interesting question, algebraic geometry. What are modular spaces of this hyperplane section of this complex algebraic variety? And most likely, the modular space is exactly only the one which we get inside of there. There is no other deformations. Of course, I guess that it may be easily done by people who know the ropes, how to do that. But then, once you have it, it has against them good rigidity implication. Of course, it depends how you respect the rigidity theorem. My respect for them can weigh more and more and more than the general overview. But the question is to construct new objects, yeah? Which is more interesting here. Thank you. Question, question from line. Seeing any question on line, I don't know. OK. Yeah. So you mentioned several times there's small consolation phenomenon for this model. The dynamical system, right? Yeah. So what kind of applications do you? No, you can produce. The question is, using small consolation on random groups, you know the exact. You do produce groups with certain properties, right? There are groups obtained by small consolation. And these are groups in your hands about which you can prove something. There is no such effective description of this dynamical system, of this hyperbolic system, yeah? So, of course, it doesn't, it wouldn't describe all of them, only this low dimensional one. But you, but they look superficially, they organize exactly small consolation groups, right? They are not groups, they kind of collect semi-groups because their graph is directed. And this kind of your two cells are also directed. So it's a two dimensional complex with extra structure. It's much more rigid object, right? Because it can respond roughly not to hyperbolic group, but to solvable groups, so to speak, yeah? But the question is, well, I can say this was all definition, but I cannot work out specific examples, look at the group, compute the entropies, et cetera. And this is kind of obvious thing to do, compute the, effectively compute the entropies, the zeta function and it is a world of nobody looked into. There's definition and that's it. And this somehow was forgotten by people of dynamical system because they focused on smooth system. And they're definitely non-smooth, right? And the problem which I left behind, the topological dynamics beyond resources which exist at the moment, yeah? And in my view, we have to redo the field in this more categorical way and then have a new perspective on that. It's certainly very, very old fashioned, but the beauty of that, unlike kind of what is done in dynamical system in a classical, traditional way, is categorical theory. It's very functorial. You just do these and things come by themselves if you do it right. And this is exactly what happened with geometry. And this was, I think it's interesting. And it may illusion, of course, the similarity may be an illusion because we, in our mind, we make things similar. Maybe it is similar, I don't know. I made this formulation personally. Of course, that sounds very similar, right? Maybe it was my cheating, right? I don't know. They look very similar. I put it this way, right? Who knows, who knows, who knows. But again, anyway, regardless of what I say, these are two great theorem, and especially the theorem of Franks, I highly, highly advertise this remarkable theorem in his simplicity and universality and potential for generalization. I think it's a remarkable theorem. Okay. Yeah. Okay. Thank you very much. There are no more questions. So, thanks again. Thank you. Thank you. Thank you.


Ever wonder why normally heavy objects seem to weigh less underwater? It's due to the buoyancy. Even a heavy metal weight becomes lighter due to the buoyancy properties of water. When an object is submerged into a liquid, a buoyant force is simultaneously pushing it upward. When an object is buoyed up, its apparent weight is equal to its actual weight, minus the weight of the liquid that it has displaced. This relationship is known as the Archimedes Principle. Archimedes Principle was discovered by Archimedes of Syracuse in the 3rd century BC when he sat in the bathtub and noticed the water rising around him. The principle states that the upward buoyant force exerted on any object submerged in a liquid is equal to the weight of the fluid that it displaces. If we submerge a 25 kilogram weight and it displaces 20 kilograms of water, then its apparent weight underwater is 5 kilograms, the original weight minus the weight of the displaced water. So the next time your friend is hoping to impress you with his feets of strength lifting a large weight while underwater, explain to him the Archimedes Principle and the buoyant properties of water.


Good evening. How's the healing nights? Welcome to the service tonight youtubers How's that? I'm you get I'm getting an echo. Are you can you hear that? Is the sound clear? It's clear. Okay alright, welcome to the service tonight. I got a nice Bible study for you and I'm ready to go my next seminar is on the spirit of comfort If you thought the last seminar was crazy, this one's gonna This one is really out of there August 25th. Here's our YouTube teaching channel. You go to youtube.com slash house of healing AZ and you get all the teachings Whenever you're in the mood Plus all the other ones that we have they're on the list it on the right there. We got several different categories I've been doing this for several years My local radio shows are on a Home page there on hardcore christianity.com you hit the home page hit media and then go to the streaming radio All my shows are archived there if you'd like to help us Switch from Google the good search and just put in our charity name. 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I'm on twice a day Monday through Friday here locally in Arizona I'm in America County 730 in the morning and 715 at night and I Started my new radio ministry on 1100 KF and X Conservative talk radio. They started religious programming on Sundays So I thought well, I'll get on the ground floor on that I'm on it eight o'clock every Sunday morning 1100 a.m. I Don't do that for a while and see how that works if you're a YouTube listen to me.  You've got a Covey of humans all Looking to get healed and delivered I Did that years ago at the dream center in Scottsdale many years ago? See what was that? 2004 something I Did that started a little terror cell in my church. I Had people left and right coming on Tuesday nights to get all word of mouth Nobody ever announced it or anything. You don't need an announcement when the Holy Ghost around He announces himself Yes, he does and It just took off from there Went great and then and they decided to get rid of me and That was a big mistake on their part because this personality Yeah, be kidding There's my three books in the bookstore Laurie. We'll show you where they are healing Satan and healing from mental illness Don't forget about my Sunday morning podcast which I forgot about last week. I Was watching my daughter last week and I was so wrapped up with busy with her. I forgot about my podcast I apologize for that. I've never done that before. Hopefully. I'll never do it since but this Sunday. I will not forget I'll see you nine o'clock in the morning. Yeah, that's what happens when you get a little older you get too many things going and Stuff falls through the cracks And that's what an old person is like Nine o'clock in the morning Pacific time twitch.tv put in HCC ABC and I will be with you And then here's all our platforms. We're showing the teachings on Rick's also on these Here's the ones that they will be rebroadcast on I think God to bit shoot and so on we like to use rumble Put in HOH ACC and all the stuff comes up HCC ABC on the others bit shoot God to Vimeo.  You are to transition And to your heavenly father's family tree and You had parents In your original family tree you now have one parent your heavenly father You have a New family when you're a born-again Christian. You're not in the old family anymore.  What have you?  He said the day is coming when the parents will betray the children and The children will be Tray their parents To death he warned us then That is not your family anymore and your new identity if you adopt it will yield you enormous spiritual benefits Staying in your old family tree is a long-term permanent Suck Time for you to go You need to cancel Your old generation the eternal God came to Abram and he said to him what?  Basically? Yes. Did he screw up? Yeah.   He brought lot with him Hey, God told him to leave these people behind. He didn't do it And he felt sorry for a lot or whatever it was but anyway lot came with him And he had nothing but trouble with lot Threat the rest of his life they let him out Save in his life It was awful But anyway the point of the call of God is he doing the same to you hey This was your old family over there and now this is your new family here You are to transition out To your destiny. This is your old family tree. There's your parents. There's your grandparents That's where you came from Everything about you came from that family tree, right? DNA genes cells whatever All came from there Here's an expanded family tree. You've got uncles and aunts and cousins and so on right But here's your new family tree. This is where you are now if you're a born-again Christian and This is your family tree now the old family tree. That's not your family anymore What am I supposed to do hate my old friend? Of course not. You're supposed to love them But your identity and who you are as a person is No longer with the Smiths and the Jones and the Williamson's and the Cortez's and what have you the Bush and now skis You're out of there and you have translated into the kingdom of His dear son anybody with me.   Did you know that a lot of backsliders here tonight, don't we? This isn't gonna go well listen.  You're not a child of Bob Smith or Carlos Rodriguez Hello, Romans 8 says a holy ghost was given to you He's in your spirit man right now all of you have him and he's the one who witnesses and testifies to you that you Are no longer in that old family tree.   You're a Son of God by what by adoption Hey, Jehovah the great God of the universe had one birth child and he has millions of Adopted children that would be us. I Wasn't a birth child. I mean new birth child. And so I was adopted into the family of God. I'm an adopted Son of God under Jewish law The adopted children had the same rights as the birth children and They were able to like the firstborn son in the Jewish family a Bach that meant The firstborn and only the firstborn could address their dad as a Bach Because that was the closest intimacy you could have with your dad No, the first born only had that privilege the first born in the Jewish family only had That privilege the other children did not Approach the dad like that Right now Because you are an adopted in the father's family you can Aba you are like a firstborn son See that that's your new identity.   Would you I don't think so What I mean? I mean look at Prince Charles Have you ever seen that guy?   I'm the king of England and he acts like the king of England They shine shoes they they give him bath. They wipe the spanny they bringing anything he wants They give him anything he wants why because he adopted a new identity.  I think they had her on speed She wouldn't die. How was she honored something? Man, he was waiting for her to kick off Couldn't wait for her to bag it Why because he wanted a new identity He wanted to be the king He wanted all the privileges that went with being a king you are a child of God and you have Privileges such as ABBA such as let us therefore boldly come before the throne of grace So we may obtain mercy and find grace to help in time when he just walked right in Why ABBA I'm a firstborn I'm the firstborn I've been adopted. I have all the rights of the birthed Children I'm adopted You're adopted. I didn't do as I could on that one the Holy Ghost Toss himself Tells us that we are the children of God Now in the book of Exodus in chapter 15 you've all read it is spectacular beyond belief it is once incredible victory after the other unbelievable millions of Jews Being hauled out of Egypt absolutely unbelievable the ten the ten plagues of Egypt's right Now what was going on there? Well? That was a major project wasn't it hauling five six seven million people out of Egypt. Hmm.   They were slaves in their mind That's all they knew and then it all changed or did it change No, it didn't ten plagues of Egypt Pharaoh coughs him up. He changes his mind the Red Sea miracle Wow Not sense Noah And anybody seen a miracle like that the Red Sea miracle What was God doing there? Ah, I'll let you in on a secret. It's a secret How do you change the mindset of six five six seven million? Brainwashed human beings How do you change? How do you change their minds? How do you how do you get them to think differently?  That's all they know Multiplied that by five six seven million people and we got a major problem here. What was God doing there? They had all lived the life of total failure.  He had to teach them that he could be trusted He had to teach them that he could be trusted because for over 200 years The Jews didn't trust anybody Had no one they could trust they were slaves by people who hate them. How are they going to change their minds? Jehovah had to show them Supernaturally that he could be trusted Because they had never trusted anybody in Their lives neither had their parents neither had their grandparents for over 200 years everybody a hundred percent Trusted nobody because they were slaves.  Trying to reprogram their mind How was he doing that using supernatural miracles ten plagues of Egypt? the land of Goshen Look the plague affects Egypt, but look hey Jews It doesn't affect you See you can trust me You can trust me. I know you've never trusted anyone. I know your parents and your grandfathers never had anybody to trust But look hold on a minute. I'm here now. I'm gonna teach you I can be trusted You can trust me Hardest thing in the world counseling people who had abusive fathers Trying to get them to trust their heavenly father when they grew up in an environment where they couldn't trust their human father The transition can be difficult to not trusting a human father to trusting a heavenly father. It's tough What has to be done? God had to show them look You can trust me the first born dies everyone of cats dogs Kids doesn't matter not in the land of Goshen Look you can trust me you can trust me father was saying Look all your cattle fine.  I'm taking care of you. You can trust me 200 something years worth of Slavery and trusting no one ever Now had to be Ground out of their thinking pattern. We don't trust anybody a Kid raise an abusive environment grows up without trusting adults. They're leery of everybody. They've got paranoia They don't trust people. They think people are they have ulterior motives the Red Sea Big as a miracle on the books. What was he really saying there? Hey? Hey, listen to me You can trust me I'm gonna take care of you. I'm gonna watch out for you 200 something years. Let's let's bag it. Let's trash it. Look look It went through on dry ground four or five million people walking through on dry ground You can trust me And they're celebrating there it is verse 12 total celebration Miriam the prophetess. She's leading the way. She's out in front. She's dancing like crazy Remember that yeah, I think that's Somebody said that's when they invented hip-hop, but I don't think so, but She's out in front dancing before the Lord hallelujah. She's spinning all over the place It's a time of celebration. I don't blame them. I'd be celebrating too. Why did God wanted to celebrate? He was trying to get their minds renewed transferring Decades of distrust of people to being able to trust him you can trust me I'm gonna take care of you. Well, then verse 13 kicks in well The 10 plates you'd be a good Egypt. Well, what? Nothing more than God telling you listen. I'm gonna take care of you. You can trust me Here's 10 reasons you can trust me Here's the Red Sea You can trust me I'm gonna take care of you. You can trust me. Let's get that part What was God trying to do the same thing he's doing to you? you and I are no different than brainwashed Jews With 200 and something years of slavery when you become a born-again Christian your mind has to be renewed renewed for what being able to trust God Without relabilities and they didn't have this verse of course Solomon wrote it Way long after the Red Sea miracle But here's what God was doing right here with those miracles he was trying to get them Not to lean on their own understanding But in all their ways just trust him You can trust me You can trust me. You can't trust your family. You can't trust the Egyptians. You can't trust the devil But you can trust me I am trustworthy. I will take care of you No matter what You can trust me and I'll prove it to you.  Everybody dies into it. What was God doing? The exact same thing he does with us He wants you to believe this verse and Receive it as an adopted child of God He wants you to leave your family behind whom you can't trust Human beings are not trustworthy. They may try that you may trust them for a while But they always make mistakes. They always screw up.   He is a hundred percent trustworthy You can trust him These Jews don't know that They have no idea. So he's trying to prove to them He's proving it to them. Hey, you can trust me watch Why are there so many Christians who are weak and failures here? They lean on their own understanding during trial times of trials and tribulations They try to figure it out rationalize it out. Think about it Ask some other human about it get two or three different things and then check YouTube And before they're done, there's bigger failures they were before they started Because they're trying to figure stuff out using their own understanding and their own rationale that's going to get us into a lot of trouble and Father's trying to get you to do the opposite Then it says in Exodus everybody's read this Moses brings out all these millions of people out of Egypt. They go through the Red Sea They go to go to the wilderness of sure They're three days in the wilderness and oh, oh Oh What happened? Oh Something that God allowed He didn't cause it, but he allowed it to happen. What's the good news here? They ran out of water This is great news Why is that good news because your trials and your tribulations are being allowed by God to Teach you that you can trust him all the water They took out of Egypt after three days in the wilderness of Sierra gone now They're starving for water Erica now They had an option shall I continue to trust the God who? Gave me the Red Sea the God who? Performed the ten plagues of it shall I keep trusting or shall I panic? Well, let's see what they did Well, let's check it out. Let me take a big gas here. Oh They came to Mara Which means better waters and the waters were not worn any good. They were you couldn't drink it What's going on here?  Why because he's a mass of this masochist or he's a sadistic No, he wants you to learn to trust Him nobody learns to trust God when everything is going great When you're partying you're not under any stress. Well, that's not a trial on a party You got everything everything given to you all your needs are met. There's no need to trust them. Oh What's going to happen to you? Well, what's happening is some of you write this very second You're going through a very dry hard period Good for you Why are you going through that period? Oh You're disappointed they came to the they found some water and they couldn't drink it When you're starving for water and you find water and you can't drink it. Wow, that's a Downer That's a medical term and what happened then instead of continuing to trust What did you do last time you had a trouble instead of continuing to trust you started murmuring? murmuring It's an emotional cancer Wipe out all your prayers. Have you wasted in the desert? They start murmuring start complaining so whining Yeah, I'm not being treated right. They stay out. I know who they're talking to What happened there? They weren't trusting you So what happened? God's mercy stepped in Again What's he doing there? He's providing miracles trying to get them to change their slavery mindset Hey, I know you don't trust anybody. I know you've never trusted anybody. I know you're few raised in that family I know how your parents treated you. I know you're stepdad. I get it But you can trust me now.  I need you to renovate your Thinking process because your heavenly father can be trusted the other ones cannot be trusted He's a Moses get your get down there Go down to the waters Gases stuff in the waters What happened maybe a? Miracle another incredible miracle What was he doing there NASA? He was testing them. Why are you going through the stinking trial? It's not a stinking trial.  They dumped in your lap Sending my fault. What am I doing? What happened? Why am I going through this?   What do you want the Jews to do? Here's what he told him But he knew they couldn't do it, but this was his goal This was his goal You can't tell somebody what to do who has raised Over 200 years of slavery and have him go. Oh, really? That's what I should do. Okay. I'm fine That's not gonna happen You can't sell some kid raised an abusive family. Oh, you're like you're unconditionally loved by right now You're fine Your future is bright They're not good. It's not gonna happen It's not gonna they have your mind has to gradually be renewed and change Very few people just oh I got it No six me and Jews they just didn't get it If you do this the Lord said I will do that Translation if you will just follow my instructions, you can trust me. I'm trustworthy You can trust me a hundred percent of the time It looks bad. It feels bad. It sounds bad. It doesn't matter You can trust me a hundred percent of the time Yehovah Rafa is what I am The God who heals you it's me I Heal not in slavery everybody got it everybody got sick and died Not in Egypt. Oh, they had witchcraft sorcery all kinds of potions half the people died. No, this is different What's he trying to do it different to trust him? I'm your healer trust me as your healer I'm your healer Rafa There it is then they went to where he limb Yeah, there it is today. There were 40 palm trees there at that time There were 12 wells there seven of them are still good to this day the rest of them have been filled in but There's still wells there to this day Saudi Arabia. There it is. We have we have something similar to elim and in America Here it is 29 palms in California I threw that in as a geographical tidbit for you. I Knew you enjoy it. Then they went to the wilderness of scene Exeter 16 What happened? Oh, no What happened there Egypt came back Egypt?  Renovate their minds. Well, how's he gonna do that by waving something at him going over and talking to him? No the only way people change is By overcoming hardships Haven't everybody hand you everything and every good all good things happening to you. Oh, it's fantastic That doesn't cause people to change God allowed them To starve and be hungry and thirsty. Why was he doing that?  To seen before they got there. What's wrong with the good Lord? Can he plan ahead? What does he got planning problems? I don't think so What he's trying to do is get you to understand That he can be trusted and you need to stop complaining Here they are griping about that they're even alive Hey all the first born died and we should have stayed back there and died Would have been better than this Or are they really saying I still think like a slave in Egypt My mind is a slave. That's what slaves do.  Hey, wait a minute. Everything looks bad. It sounds bad. It smells bad But you can still trust me You can trust me here.  That's real What's he's trying to say to you? You can still trust me It looks bad sounds bad. It is bad. It doesn't matter You can trust me What does Moses do exactly what we're supposed to be doing right in the middle of a trial and tribulation? You run to the Lord. Why trust in the Lord with all your heart. Don't lean to your own Standing in all your ways acknowledge you Moses ran to the Lord and acknowledged him. Hey These Jews are on the rampage are gonna stone me They don't have anything to eat and I'm gonna drink they had all kinds of other personal problems He says well, I'm gonna test them again and grace came through again, right? I'm testing you. Why is that trial? Why are you going through this thing? Is anybody going through a really bad trial right now? Just raise your hand real quick only a couple people are oh No, there's some more. Yeah You're going through a bad trial right now. What's happening here? You're having a father's allowing it to happen. Why is he doing that?  Mon, what is mon weird? Well, here's what it was. I have no idea what it was but some kind of nutritious food that fell out of heaven It rained out of heaven Right, you know the story and there was restrictions on how you could collect it How you could store it eating it and so on remember my manna mon Guess what they did with that mon Yeah, 40 years on that stuff. Well, that's that's a tough one. Yeah, that's hard to do What was he doing with mon? What's the purpose of mana? Hey, you can trust me Can you imagine that that was a bigger miracle than the Red Sea every morning? It rained mana for five six million people Every morning they went out filled their baskets up with Whatever it was. I guess it was a bread or something, you know Posts this cherry pie something similar that They went out and picked them up off the ground They named it mon, which means what is this? No one knew what it was, but it was miraculous But what it really was was father saying to them. Hey, you're starving You can trust me. I'm gonna take care of you. I grew up in a family with alcoholics and We were a neighborhood white trash and We didn't have money for food half the time. I couldn't trust my Parents for basic necessities Word the necessities go They drank them up when they were in slavery in Egypt. They couldn't trust anybody and Fathers now trying to teach them look. I'm using this mana as a sign That when you're in trouble and everything's bad You can trust me. I will come through for you I will win for you That's what it really meant. That's what man. It really is You can trust me. You know the story of the 12 spies, right?  I just want you to go Give me a report of what you're seeing.  They came back but what happened 10 of the 12 spies Circled through Egypt before they came back 10 of the 12 spies Went back to Egypt in their minds and they came back like a slave afraid Paranoid scared Worried Fearful for their lives Wondering when they were going to get it next Wondering who else was going to die next And they gave Moses an Egyptian report We can't take this land We can't do it. There's too many of them There's too much Egypt two of them two of the Spies did not come back from Egypt. Who are they? Joshua and Caleb. That's right They're stronger than we are there now.  I'd believe no they won't No, they won't if you got a slavery mentality. It doesn't have it doesn't matter how many miracles you see I'm not joking. We have people here who have had some of the most spectacular deliverances you could ever imagine hundreds of them Many of them have gone back to sin And back to failure back to addiction back to drugs back to alcohol Back to mental illness. Hey, whoever gets your mind gets the rest of the person 10 of the 12 spies came back from Egypt instead of the promised land and gave moses an egyptian report Hey, we're screwed Or are they afraid of what was the report for the number one thing number one thing that scares christians people Spouses kids co-workers church people People It's a my god. We they're stronger than we are Now there's there's nephelin there Giants are there they had seen all the miracles of egypt They had seen the red sea split Man's of people went across on dry ground. They saw it with their own eyes And never left egypt here We saw nephil the nephilim the giants You know the goliath type guys Anak that entire race was giants We were like grasshoppers in our own say What it what is god trying to do here? Wow? Why are you going through this trial? He's trying to get you to understand that what you see isn't really reality When you mix it with faith As wigglesworth once said I am not moved by what I see or what I feel I am only moved by what I believe They looked with their egyptian eyes and they saw themselves as grasshoppers You were raised in a dysfunctional family Where you had low self-esteem and a low self-concept and now The devil's putting the pressure on you and you're going back to your earthly family and seeing yourself As a grasshopper You see everybody else's a killer What's god telling them? Hey, I can be trusted I'm not phased by giants. I'm not phased by other people See you don't wrestle against flesh and blood people are not your problem.  That's what you're interested in That's what you're going to lose lose If you see yourself as a grasshopper. This was a mental exercise Not a physical one king david mentions this incident in psalms 150 years later numbers psalm 78 They tempted god they turned them back on him because they didn't believe They went back to egypt. That's a strange verse, isn't it? It's weird How how can god be limited? That's weird. I thought he was all powerful all seeing all knowing He is until he restricts it To your free will only a couple people heard that one See god is sovereign And has the ability because he's sovereign to restrict his sovereignty to your free will What happens to you in this life? Isn't decided by god It's decided by you for all the promises of god in christ or yes and amen god already said I got everything for you Are you going to get it?  Why that whole group had to be Removed it was sad There they are collecting their mon there they are every morning going out in the buckets That was a new career if you were A jew back then yeah man of collectors You had to sign up for it Then they went to where? Mephiden And and what happened there? God whose omniscient Knew before they got there they were going to run out of water Correct Yeah, how come he didn't do anything about it? The good lord screwing up again. He's a poor planner. We need to get him one of them Microsoft daily planners that what we need. No, I don't think so He knew there wasn't gonna be any water there. Well, what was he doing there again? What was he doing there again trying to get them to trust him? Even when things look bad and sound bad and feel bad You can still trust me for I will never leave you nor forsake you They come after moses again. What were they doing murmuring? What were they really doing they had gone back to egypt Mentally They were gone again They started griping finding complaints Mining What was god trying to teach him? Hey, you don't need to do that. You got to learn to trust me You see trust in the lord with part of your heart and the I don't think it was part He was trying to get them to learn to trust human beings will not trust by nature They have to face hardships to learn to trust That's the only way it works Revelation 2 revelation 3 he that overcomes will reap these benefits Correct set it seven times two chapters, didn't he he that over cometh king james Well, you got to have something to overcome to be an overcomer Correct, how many we're having a smooth life and everything's going great. Well You know, I don't I'm not trying to offend you, but if that's a consistent pattern over the years My guest god doesn't have anything really great. He's calling you too.   Are you listening to me? Hey, you should have killed us here. There they go again. They're back in egypt here. See that? Oh my gosh the cattle everything dead. Oh gosh. What are you doing? Moses said they're ready to stone me why? They weren't stoning him. It was the egyptian mentality They were stoned in egypt They died in the mosh pits God allowed all these things to happen to the jews as they left egypt Why he was trying to get them to learn to trust him?  I sure do. I got that in a case in a museum. Okay.  What do we do? What do we do? What's going on?   I'm trying to teach these Jews I'm trying to teach them look You couldn't trust anybody in egypt, but you can trust me watch I'm doing these miracles for you Trying to get you to trust me And not lean on your own understanding trying to figure it out yourself Because if you do you'll end up back in slavery egypt Lost again What did he do? Well, you know the story boom He hits the rock What happens? Man unbelievable miracle It's in numbers chapter 20. There it is that rock is still there this day. Here's a picture of it This rock was the rock that all that water came out of a river came out millions of people multiple millions of livestock everything everybody drinking Came out of the rock remember that story What was it? What was what was going on there? God knew they were going to be starving again He knew they were going to be thirsty again. He did it deliberately. He knows He saw your trial coming. He saw your hardship coming He saw it before it got there Why do you allow it to happen because He's trying to get you to trust him He wants you to trust him You can't trust god when everything's going hunky dory That's latin There's the rocket still in Saudi Arabia to this day Then later on the amylex attack attacked them, right? There was a war broke out They hated they saw these jews invading their land. They hated them. They wanted them all dead They went out to fight What happened? Yeah went to the rod deal again. Moses held up his rod What happened? They won When he got tired and dropped it They lost When they propped him up They won what's all that about He's trying to get Egypt out of their minds Listen, if you do what I tell you You can trust me Don't take care of you Raise that rod And you win Just do what I tell you Why don't people obey god? Why don't they listen? They don't trust him They don't trust They're using their own understanding. Well, if I do that this will happen if I don't do this this will happen I'm rationalizing it. I'm thinking it out No, you're losing.  You're failing again After the war they had Yehovah Nessi. What is that the lord our banner? What was he doing there? He was he was showing them. Listen, you can trust me. I told you what to do Just do what I told you to do Okay, I'm not an egyptian. I'm not going to lie to you. I'm not going to manipulate you I'm not I'm not like your parents or your or how you were raised That's not how I am Your heavenly father is not that way. He's completely trustworthy. He wants you to trust him That's why people don't trust god. They They don't do what he says because they don't trust him. They don't think it's going to work out They're going to have to come over the better way Let's skip that one Peter said beloved don't think it's strange That this fiery trial is doing what? If you ask us It's a trial. It's a test You're not supposed to think it's some strange zenos a foreign thing No, you're supposed you're supposed to be rejoicing Yeah, I know this sounds nuts. You're going through a trial. It's difficult. It's hard And god's telling you to rejoice why because You can trust him. He's got your back. He's got you covered He's already figured it out for you He wants you to trust him How's he going to do that by sending in truckloads of blessings? No People can't learn to trust god Without overcoming hardships difficulties Challenges pressure. That's the only way people by nature learn Good thing is happen. Good things that happen to people.   You're in the family of god now Your parents are gone now your heavenly father is your parent He's trustworthy Is he not So you can rejoice when things are bad. I know that sounds crazy Rejoicing when things are bad.  This is a good thing because you can trust Peter chapter 4 first Peter chapter if you are unedito if you are verbally abused For the name of Jesus happy are you you're happy if someone Says bad things about you Well, that's the opposite of being a human being isn't it?   Anybody here parents dying had zero inheritance I'll start out. I had zero my parents left me nothing Anybody nobody else everybody got hit the lottery.  They'll come off as nothing It's nothing A thousand years from tonight what you're going through now We probably won't even remember I know I won't I'm talking to some of you you're looking at me like I'm from mars But a thousand years from now.  Okay, that's that's an oddity but that's The persecution is a blessing for you to grow People don't grow unless they face adversity If you put the heat on somebody they'll either quit and collapse And god can't use them Or they'll overcome it And move on to greater blessings and greater miracles. That's how it works Christians have to be weeded out Oh brother mike down.  You've been using your word of faith. Have you? Yeah, why don't you send me an email and tell me all these two things?  Where you everybody thinks you're great all the time.  What is that a divine? Appointment by god who allowed that to happen to you so you could learn to forgive Brother mike, would you pray for me so I could stop taking offenses? No, because what's going to happen is if I do that people are going to start offending you lizabeth lizabeth stop it You can't learn to not take offenses if people don't offend you You Is this really rocket science Am I visiting from nasa?    You have to learn Not to take an offense by being offended. You have to learn how to forgive People who treat you like garbage I thought christianity was all happiness peace love and prosperity and abundant life brother mike I thought that was what it was. Okay. Listen. You've been listening to too many people on youtube You need a reality-based faith system Okay, where do you find that? I'm not sure but when you come here, that's what you're going to get It's a reality-based faith system The only way for you to grow Is for you to get booted out of the nest Because the the the the eagle The the the eagles are not going to leave the nest if the mother keeps coming to feed them Okay, sooner or later that I got to get the boot.  I felt so sad for that third one And then later on they came back and it was dead But the other two were Soaring like eagles Okay Hello I was wrong To feel sorry for the dead one Fathers set the system up like that So that only the strong survive Because you have to be strong to survive Okay, american christians are our gutless losers because they want everything handed to them They want Blessings falling from heaven like manna That's not how you grow That's not how you become a warrior.  He's got your back. There's no Paris must there it is again same greek word The trial that's overcoming you the trial is coming at you. It's a normal trial.  You can trust me. I'm not gonna allow you to be tempted Beyond what you're able to bear. I'm not gonna allow it I'll make a way for you to get out of it You can trust me You don't need to go back to Egypt I got you covered. I'm with you Whatever you're going through now. It's Well worth it in eternity Did you know did you know that every time you overcome? Something god lays up reward for you in heaven Did you know that even the littlest things jesus said give him somebody a cup of water or something You do that in jesus name. There's a reward Put somewhere. How does that work? I don't know. I don't really think about it I just know what happens Okay, I don't have any insight on any of that I'll be honest with you. I don't even think about it. I just keep moving forward, but the reality is This crap you're going through here is temporary It leads to incredible glory there it looks like junk here But it has great spiritual value there says it right here. What are you doing there? Listen Egyptians There they there they come. There's the Egyptian soldiers There's the desert.  It's different You're not stuck anymore Somebody's got your back Somebody's provided a way of escape somebody's helping you That you can trust And he wants you to trust him Without having to see it in advance Right the things that you see are what? Los caros temporary they're seasonal They just come here and there. This is what we're facing What you can't see is eternal ioneus age after age after age What you're overcoming now will be of your benefit Thousands and millions of years from now in eternity Once it goes up in the book It can't be removed You've got it if we suffer here We're being trained to do what be kings and priests Your hardships are your training for your royalty in eternity You're being trained Not to be like king charles Where they put some complete more on and put a thing on their head and that's a king No, that's a joke This is eternal kingdom And this little stuff that is temporary It's occasional God's trying to change your mindset Right like he did wigglesworth All he knew was losing his temper and doing plumbing work It's all he knew plumbing And getting pissed the two peas But god over the period of years renovated Wigglesworth mind He no longer thought like a plumber He no longer had a temper How did you do that by overcoming hardships? Two weeks ago. There was a big fight on pay-per-view Some guy named crawford another guy named What's the other guy's name? Prince Spence Spence and crawford This was a big fight real big both these guys were like unbeatable In fact, they were unbeatable. They all had both had unbeaten records, right? Clash of the Titans Listen five years ago. Those those guys Couldn't have whipped your kindergarten teacher. Okay They had numerous fights They won This one they won that one they won this one they won that one then they won this one then and then two weeks ago They're in the super fight The exact same thing is true in the spirit world You don't just pop out and oh my god. I'm a super warrior Now that's it. Everybody gets healed. Everybody gets delivered. Let's plow through phoenix. Boom No, it doesn't work that way fight this fight that fight this fight this Overcome overcome overcome overcome overcome grow grow grow grow learn learn learn learn learn boom That's how it works in the spirit world You have to overcome your This little one then then then that one and then this one and then that one When I was a kid I was a comic book collector and in the back of the comic books they had ads and This was back in the early 60s and in one of the ads it had this Guy named Charles Atlas in the ad Little block ad in the comic book Black and white little ad like that This Charles Atlas guy it had a picture of him there Full of muscles and then in the picture next to him It showed him almost like a stick figure Of what he looked like when he started lifting weights And then you were supposed to send in some money or something to buy something from him I think it was a training kit or something. I can't remember but anyway the point is Charles Atlas started out looking like a victim of anorexia but Somebody waved a magic wand over him. He's bulging with muscles. No day month after month year after year Grinding it out in the gym He became a multi-main air selling little packets of how you too Could look like that That was a crock of crap, but anyways making all kinds of money off of it doesn't matter It's all marketing. Everything's marketing. It's all lies The point simply is you don't walk in and two days later.   Why are people talking down to you? Why are they criticizing it? Why is that happening? Well, they're rotten people brother mike. They're just terrible. They're that no God's allowing it to happen for what reason you're in training See you have to learn to not let things bother you By listening to people saying things that would normally bother you You know just wake up one day go I'm good No, you got to learn That what people say about you means nothing You got to learn Not to take an offense You know what my biggest challenge is with marriage counseling. I get crazy people coming to see me I really do I could write a book on it The first call I get is usually the victim's spouse The one that is being abused usually calls And they have finally convinced the other spouse to go get help But they don't they're not going to call This file spouses You know my biggest challenges with married couples 99 percent of them You know junkyard dog crazy Because they've been living with the other person for years They're gone Is to get them to see who's really talking to them That's the toughest thing because A marriage that's falling apart is spiritual spiritual And this person says that nasty thing and this one says that but actually behind the curtain there Like the Wizard of Oz behind the curtain is not there's an old man back there There are spirits in that each spouse Triggering the other spouse By saying something or doing something the demons know will trigger them And hurt them make them angry get them frustrated on and on it goes If I can get The both spouses to see that there's a spirit World behind their behavior their attitudes That marriage vast majority of They're going to get saved If I can't And the person still thinks it's them Well, she said this and he did that no wait a minute time out Okay, there's a spirit Behind that person saying that And they're being motivated and encouraged and pushed To say those asinine imbecilic idiotic hurtful dreadful things It's not just them It's spiritual If I get that in Here And get egypt out of there That marriage can be saved Most of the marriages i've counseled with are saved very few of them got divorced The ones that got divorced Not it's that person It's her it's him It's not Why is god allowing that?  All right, let's wrap it up here You're supposed to be exceedingly glad because your reward is great in heaven Yes, it is Let's close then Here's wigglesworth famous quote by him He worked a lot of years and took a lot of beatings to come to this conclusion Literally years Before he arrived here What does it say? Okay, what are you saying is What I see in my emotions do not determine anything What determines Is what I believe right Here's another one from him And let's close there Your trials if you're going through nothing and haven't gone through anything in a long time You know good for you and the probability is you're going nowhere I'm not talking to you right now. I'm talking to the people that are going through it right now That is a good sign. That's a That's a positive sign that God's got plans for you because that only happens When you learn to overcome You learn to overcome All right, let's Let's go ahead and pray then