Thank you very much for inviting me to speak here. It's a great pleasure. Well, we have collaborated with Arthur on one loan project, I think, for about three years. And this was, I think, the most fruitful time for me, mathematics. And in addition to that, I learned from Arthur what a log scheme is and what Betty had a homology of a log scheme. And in fact, the work I'm going to talk about is, well, grew up also from a question that we discussed a while ago with Arthur. And so the question is a full in. So I have four log schemes. And then I have various homology theories. Well, for example, I can look at a TAL homology, or Betty, or say, the RAM. OK. And so if my log scheme happens to be defined over a finite field, so then this TAL eteladic homology of x with QL coefficients, well, it's a vector space which is equipped with an action of the Frobenius. And one can check that for a reasonable scheme x, the eigenvalues are all real numbers. Of course, they are of different weight. But in particular, because they are real numbers, this gives me the weight filtration. And so the question is, so let's see whether I would use it. So can one define this filtration geometrically? So I want a definition which would make sense for all these three theories. And well, more precise, well, so you can ask for rational Betty homology, or you can ask even whether it's well defined integrally, as for usual singular homology of algebraic varieties. So one can ask whether one can associate a motive, or maybe even a finer question, material homotopy type. Well, I want to tell you a little bit about this question, so what kind of homotopy type you expect to have. So the answer lies in the construction due to Cart and Nakayama. So OK, so I will recall it here at Nakayama construction. So they defined Betty homology. So what's OK? So that's Betty homology of a log scheme x. So this is a coefficients, any coefficients. Well, to be by definition homology of a certain topological space. So this is just usual, well, so this is x log. So that's what Arthur explained to me. So this is just a topological space. Well, in many cases, it's a, yeah, yeah, sorry. My x is now over complex numbers, of course. Thank you. Thank you. So x is a log scheme over the complex numbers. And so this x, well, it's just in general, well, it's a topological space, but well, in many cases it's a manifold with boundary. It has some additional structure. So what is it? So this is a topological space, which is equipped with a map. It's a proper map to x. And so, well, so the construction is the following. So, well, I have my log scheme. So I will denote by x underline, then the line scheme. And m is the sheaf of manoids. So, well, so I have the sheaf of manoids. I have a star that sits inside it. And I have a map to o, OK? So, well, the only thing I care about, in fact, this, well, it's true for the whole, for the entire talk, is the group completion, m group. So this is a sheaf of a billion groups. It has a star sitting in it. And it has quotient, which, well, I will assume I will look at fine log scheme. So it's going to be a constructible sheaf for, well, for a tiled apology, or if you wish, you can consider a version of it for the risky apology. In fact, in my talk, it will be more convenient to consider all these sheaves for the risky apology because, at the end, the object that, well, yeah. So let's stick to this. So this is, you can think of this, well, a good example of such lambda is just the constant sheaf supported on the device, for example. So you have such an exact sequence. And, OK, so to a scheme and to such an extension, I want to associate a topological space. So how I want to do this, well, if I have a point, well, I can sort of restrict my, so that is here, evaluation map, point x. And so from this extension, I can derive an extension of the stock of this sheaf lambda at point x. And this will be by c star, OK? So this is just a finitely generated abelian group. And this is c star. So it's extension. OK, so now. And so x doesn't mean the stock. Yeah, it doesn't mean the stock. It means pull, push out. So and here I have map from c star to s1, which is called the argument. So, well, let's give a name to this map. Let's call it gamma. So I look at all possible sections like this. We'll call it sigma x. So satisfying the property that if I compose gamma with sigma, I get argument. And so x, look. Which is the same section, so this is splitting of this extension. Well, push out of this extension, right? And then this space, as I said, is just set of all pairs, x and c. And your lambda is torsion free because you assume fs, right? It need not be torsion free. I'm going to assume, in the second, I will assume that it's fs. But for the moment, I don't even need this. So, OK, so I consider all such splitings. Of course, there is a map to x. And I want to, so, and the fibers, fiber over point x is a torsion over from lambda x to s1. So in the case of nice log scheme, fs log scheme, this is just a real torsion, OK? And so then there is a topology on, so any section of m group defines a function on x log is values in s1. Namely, it takes point x sigma to sigma of x applied to m. And I want these functions to be continuous. So I consider the weakest apologies such that the pullback of any continuous functions on x is continuous, as well as these functions are continuous. OK, so that's a topological space. And I want to see whether, well, I want to, the ultimate goal could be to realize this homotopy type, well, to leave this homotopy type of this log space into a martyric homotopy category. So, well, the possibility of such construction was suggested to me by a long time ago by Maxim and also by Nori, somehow independent at the same time. So they explained to me one single example, which is kind of really the key example. So I want to tell you about this example. OK, so what is, so this log structure, the log space that comes from a special fiber of a semi-stable degeneration. So this will be x0, this will be xt. And so semi-stable degeneration, so it's sticked. And moreover, so I will assume that there are no triple intersections, very, very simple. So in my picture, there will be only two divisors. It can be generalized in the case of many. So I have these divisors. This is d1, 2. And so then I have two line bundles on x0. Namely, I have l, well, i, which is o of di, restricted at 0. So this is, so I have i is 1, 2. And so this li comes with trivialization.  So and the y is, when I restrict it to ui, it's canonically trivial, right? So these two structures, these two line bundles together with such trivialization can be organized. This is given such two line bundles. This is the same thing as given extension of z, d1 plus z, d2 by o star. This is everything over x0. So I have on x0, I consider x0 as a log scheme. Well, the log structure is just the pullback of the log structure and everything given by this divisor. But while the same curve has this very simple description, so these are the constant shifts on d0, on di, extended trivially to everything. And I want to, in this case, I want to look at x look and realize it as a element of the a1 homotopic category. So well, what you do is the following. So well, I need another piece of notation. So let's call li-circ. This will be gm-torsor associated to li. So li is a line bundle. I take the total space, I remove the 0 section. And then so what I want to do, I want to consider the following complex of. So I want to construct, well, Wojewódzkii motif. And well, in fact, it will be even an element of stable homotopic category, and even unstable after a certain modification. So OK, so what is this? So let's first define it as a motif. So well, I want to do something very, very simple. I will take l-circ. So again, this is regarded as a scheme, leaving over x0. And I want to restrict it to u1. So sorry, I think I want to restrict it to u2, of course, because it's trivial on u1. And then the second thing that I want to do, I want to take l-circ2 and restrict it to u1. So when I write square brackets, it means that I consider this as a motif. Just that it's a plain scheme, so it makes it well. And what I will have here is l-circ1 times l-circ2 over x0 restricted to d1, 2. OK, so and this d1, 2 is intersection, OK? So well, so my motif is going to be sort of the cone of this map, this complex. Now, I need to tell you what this is, this arrow. So and here is a reminder. So well, this construction is possible because, well, in the category of Wojewódzky motifs, you have identification between punctured tubular near-bordhot of a smooth manifold with punctured normal bundle. And namely, if you have so smooth y and z, this is closet, smooth closet, then there is a canonical map in from the motif of the punctured normal bundle to y minus z. This exists in differential geometry. This can be lived in the motif of the category. And well, the map that I have here is exactly what comes from, is precisely that map. So here is the picture. So if I have, let's see how we get it. So OK, so here is my d1, for example. And here I have this line bundle, which is l. So and here I have this is d1, 2. So I apply this construction. So I have this line bundle, this GM torsor. It leaves over the whole d1, 2. And inside this, the total space of l1, l1 minus, I have this fiber over d1, 2. And I apply this construction to y being this GM torsor over d1 and z being its fiber over d1, 2. Then you get precisely this first map and the second map is constructed similarly. So you do this. And do you put a sign or it is not important? I don't think that there is any sign here. It must be symmetric at this moment. But if you have several things that intersect each other and then say, go in a loop. No, no, in here. Well, so I don't think that there is any sign in this picture. So maybe it seems to me that at least here you don't need sign. But maybe it's possible. So OK, so in fact, this map that I used here exists even in just in a one-homotopic category, but only after suspension. So you can kind of do the same gluing except that what you'll get, you cannot get homotopic type of X log itself, but you can get homotopic type of the suspension of X log. So at least you'll get something in the stable homotopic category. So the fact that that map exists after suspension is proven by Morell and Weyholz. So OK, so and well, one more remark about this whole picture. So in fact, this ELI have additional structure if they come from the semi-stable degeneration. Namely, EL1, TENSORL2 is trivial. Well, strictly speaking, this trivialization depends on the choice of a parameter here. You choose it T, coordinate, because this is OD1 plus OD2. So it's of special fiber, it's lifted from the base. And therefore, well, if I have a map from everything in this picture to this is 0 to complex numbers. So there is always there is a map from these guys to complex numbers, from invertible complex numbers, right? And therefore, so let's give a name to this. Let's call it motif of X0M. So it's motif of this log scheme, just definition. And in fact, in this case, this motif is not is a motivic shift, motivic shift over C star. And it's fibers, for example. Well, you can take fibers over. So every scheme here is a scheme over C star. So you can take fibers, you have still this map, to get what's called the limit motif, right? And the picture here is, I cannot really draw a picture of this gluing of this X log. But this X log here, it actually maps to log space associated to the log point. So it maps to the circle. And I can draw a picture of a fiber of this over a point of the circle. So imagine that, for example, you have the generation of elliptic curve. So OK, so here is my, so it generates an interrational curve with two double points, right? So this is non-singular elliptic curve. And this, now, it degenerates. So what you do, you sort of remove these two points, and then you glue along punctured tubular neurons. And then you get something back. Well, I'm going to pick it all into the original space. OK, so I want to kind of extend this construction to all of the schemes. And that, even if you have, in this semi-stable case, if you have many components and multiple intersections, it becomes really, well, direct the generalization. It's really unpleasant, because, well, you can kind of write down a similar complex. But you have to do it, lift it in somehow on digital level. And then the square of the differential will not be 0. It will be the homotopy equivalent to 0. And these homotopes are given by some double normal cone constructions. And so it's going to be completely useless, though possible. You can't really do anything with that. So instead, one should look at the dual thing. One should look at the motivic homology of this motif. And this has a very simple geometric description. I will show it to you at the end, in the case of this semi-stable degeneration. But first, I want to formulate the main theorem in a kind of in-abstruct form. So the main theorem is the following. So I need a bit, first introduce a bit of a certain category. I will call it the category of log motives. But, well, then you will be able to forget about this. I mean, so first I introduce a category that I will call the category of log motives. And in order to do this, so let me just write down the definition of usual category of Vodka motives. And then I will list two more kind of relations and get the category of log motives. So I will work with log motives. So I will assume for simplicity that the characteristic of my base field is 0. Well, if it's p, you can do the same thing, but you have to invert p in the coefficients. And then, so for Vodka motives, you do the following. Motives. So you consider a category of schemes, say a finite type over a field. And then you form an additive category, just objects, schemes, all schemes of finite type. And morphisms are a linear combination of maps, no correspondences here. And then I want to take complexes, finite complexes over this. And then I mod it out by certain relations, by subcategory. So this is a, well, if you can do it on triangulated level, pass to homotopic category, then take Verdi-Aqvoshan, or you can regard it as a differential graded category. So and what are objects of teeth? So objects. Well, of teeth. So, well, I will list them. Let me start here. So first object is, well, it's going to be class of objects, right? So it's X. So objects are complexes of schemes, right? So this is first. This is called A1 homotopic. And then the second class of objects is, well, perhaps you have to let me do it here. So this is the second class of objects. I will refer to it as CDH topology. So these are generating kind of sequences, covers. And so there will be two parts. Well, so first, suppose I have the risky open subset and I have in a tile map, this is a tile. And so what are the conditions? Condition is that the map P inverse of from X minus U to U to X minus U, this map P, the restriction, is an isomorphism of schemes. So that means that this is a tile map. And on the complement to U, it has a section. It's actually a bijection, right? So this is the risky open. This is a tile. So in particular, U and W cover X. But it's much, much, much more than that. And in this situation, I want relation. And this relation has the form X, U, W. And here I have the fiber product, U, W. So all these maps. And so this is part A and part B. So I want the following. I consider maps P from X prime to X. These are proper. And I assume that there exists a closet sub-scheme here, closet sub-scheme, such that over the complement, this map is an isomorphism. So P induces an isomorphism between P inverse of X minus Z and X minus Z. For example, Blob. So OK. And in this situation, I want to have the following relation that motif of X prime plus motif of Z. And this maps to motif of X. And here I have motif of prime of Z. And here you must put a sign inside one of those things. Yeah, I have to put sign. So either it doesn't really matter where. So yeah, you're right. So I have to take the difference, otherwise the square will not be zero. So and this calls it right. So and also A, B, C, D. OK. C is that the map from X is used to X. It must be an isomorphism. That's it. It follows from B because you can take Z to be there. OK. So but you're right. So many things in fact follow from others here. So and well, you can so this is not that's not. So you can have. So this is not what's called, usually called, the category of Wojewódzki motifs. It's also defined and studied by Wojewódzki. And it has a very complicated notation, this category, this quotient. So let me give it here. So it's H, A1, CDH. And then here I take Z of schemes. I need Karubian completion. OK. So what is the relation of this category with the category of Wojewódzki motifs? So there is a, well, at least there is a functor. So this Z, the Wojewódzki category, which is obtained exactly in the same way except that you add transfers. So you start with, consider the same relations, but this category is different. You consider schemes and where maps are finite correspondences. And also only smooth scales. Don't think that if you do CDH, the poetry, it makes any difference. You're speaking about now the, OK. So you can do it with this. Yeah. So if you consider smooth schemes, then CDH, the poetry, then B can be derived from A and other schemes. OK. So now I want log motifs. So what I do with log motifs? How I, so let's just consider the same, similar category, but let's start with log. So by log schemes, so I consider, I mean, F has finite saturated log schemes. OK. And then I want to take, so I want to consider quotient of the log scheme by T. Well, and what is, so what is, what is this T log? Well, so T log consists of, it's a full subcategory. Objects, well, I did not mean objects of type 1 and 2, 2 and the following. So I need to do, to impose a bit more, a few more relations. So, OK, so what is, what are the relations? So, well, maybe just before we explain the relation, so what I have here, this, well, there is homotopy equivalence relation. So in this homotopy equivalence relation, X is allowed to be any log scheme, as well as here. So I want everything in this picture, X, well, this must be log schemes. A1 here is just usually A1, but I will add axiom for log A1. And if you speak about closing merchant, perhaps you want the exact one. Yes, yes. So, OK, so what I want is the following axiom. So I have A1 log. So what is it? It's a, the underlying scheme is A1, and the log structure is given by one point. So that my M group is just corresponds to the line bundle of this point. And here I have, so log point, it's kind of the origin. And here I have GM, it has trivial log structure. And I want these maps to be isomorphism in my quotient category, but not only this. I want to multiply this by, and again, X is any work scheme. So, and also this GM times X is valid. Well, there is one additional axiom. It's strange, it just has to do, we already observed that all the construction we have made so far depend only on M group, not on M. M is irrelevant. And I could consider the category of our skin just by the category of extensions. What do you say about them? They are in my category T. So you require them to be here? That's all. That's all. Yes. Do you want the A1 log, is that one isomorphic? Or you, too, like A1 log? Yes, so these are object in T, like, for example, is this those. So, and finally, 4 is very, very strange. Well, so it's very, very, is the following axiom. So suppose I have any map P from X prime to X. These are log schemes. And the underlying map between usual schemes is an isomorphism. And suppose that it induces, the map induces it on M group P up a star to M prime group is an isomorphism. Then I want the following relation, that X prime goes to X. It must be in my category. So this kind of way to say that everything depends on the group. But again, so I could consider just the category of pairs X plus this extension of star, this star. So now, very good. So here is the theorem. When you do block blow-ups, what seems when you do the operation of block blow-up, I think that the space, I don't remember now, the space X log doesn't change? No, it changes. OK, space X log, yeah, it changes, but it's the same problem. So here is the theorem. So, well, I have a category A1, CDH, this is my category. And here is the name for this. So this is Z of schemes. So there is, of course, a function to this larger category. We are going to consider A1, CDH, and here I have Z log. OK, so this function is an occurrence of categories. So what does it mean? So what are, for example, functors from this category to, say, the category of complices? These are homologous theories, right, that satisfy these basic properties. The claim is that any homologous theory can be extended uniquely to log schemes provided that it has all these properties. OK, so let's see. So in particular, well, of course, here you have map to functor to usual Weyvotsky category, and then you can compose the inverse and get Weyvotsky motif. Now, so the construction, the proof is very little, uses very little geometry, in fact. It's more or less linear algebra.  Let's call it here. Yes, fully faithful, homotopically fully faithful, if you think of this as G-functor. So fully faithful. And B, so essentially, subjective. Well, and in fact, so easy step is that A implies B, and therefore, so all you have to do is to prove A. So and that's because you can do it by induction on dimension. So you need to show that any motif of any log scheme is in the image of this functor. So we have enough relations to express a motif of any log scheme in terms of motifs of usual scheme. So that's easy. So you do it again by dimension of your log scheme. So if it's zero-dimensional, then, well, it's fine saturated. So it means that my Manoid M group is just z to the n. And so the corresponding, so if I have point and take its, well, its motif, for example, is motif of GM. And if I consider Cartesian product of any scheme of log point with itself, then of course it will be GM times GM. This follows from this axiom. And so using this property, any zero-dimensional log scheme has the same motif as product of this. So now what you're doing, one-dimensional case. So you have some curve. Well, now, generically over an open set, the log structure is trivial. It just corresponds to trivial extension. M group is just trivial extension of z to the n by your star. And therefore, OK, so you know what to do over an open set. And then you can use this CDH axiom to see that this log motif of this curve is also in the image. So what do you think? You have missed my phone, sir, have you? No, I used because, so let's see. Well, if you look at this CDH axiom, how it looks like. So you have some key inverse of z. And then you have z plus x prime and this maps to x. So I want to show that this object, so knowing that this object and this object are in the image and also this, I want to conclude that this object is in the image. But then I need a map from x from this square bracket x to this guy. And I need to show that this map exists in the usual category of Levi-Wadzky category. It exists by definition. So because it's an exact triangle, there is a map from square bracket x to this guy which is shifted by 1. And I need to show that this map actually exists. So what do you do for? Do you assume that the log factor is a risky local trivial? I use it as a risky local trivial, right? So I could, yeah. And so you don't have motives for a tile? Then I need to work with a tile typology rather than be a risky and, well, at the end, I will get a Natal Levi-Wadzky motive. Well, some applications that I had in mind have to do with this integral weight filtration which exists only for realization of usual Levi-Wadzky motives, not a tile. So, okay. So what you do for A? So what do you need? It's enough just by formal nonsense. It's enough to prove the theorem. It's enough to do the following. So given any object of this category, usual category, A1, CDH, maybe I will just say the following. So let me, because my time is short, so I claim that it's enough, it suffices. I will sort of suppress the completely formal part, so it only uses the fact that the category of Levi-Wadzky motives is rigid, duality. It suffices to show that the functor, home, Z of n, from this usual category of motives CDH schemes extends larger category, this category A1 CDH. And what you do here, so you just sort of, you want to define motivic homology. It's not quite motivic. It's home in this category with no transfer, so I don't want to call it motivic homology. It would be motivic homology if I can consider this category with transfer. So you want to do it for any log scheme. And the idea is very simple. So you have the same group. It can be evaluated, it can be considered as a motivic shift over this motivic shift, shift over the underlying scheme. That means simply that you can evaluate it over any scheme which is smooth over this guy. You simply pull the log structure. If I have a math like this, then you can pull the log structure, this log structure here, and take the same there. So and then what you do, you just compute, you take a homology of x, these coefficients in symmetric powers. These are operations in the category of motivic shift symmetric powers. Well, they're defined by Weyvotsky. It's characterized by the properties that if you take x as that motif of a scheme x, is the symmetric power of motif of a scheme x is the motif of the symmetric power of x. Is it n bar group or n group? Just n group. So for example, what happens if you take n as 1? Well, when you pull it back, you don't make it a log structure on Y, you just take, you don't enlarge the units.  There are n large units?  So for example, what is first, well, motivic homology is n equal 1. This is just homology of n group. It's kind of analog of the p-carve. So, okay. Now, I want to finish by- Which category? This is the homology of what? So, well, you- From the base of this homology works. Yeah. This is nisnerich homology of this material shift. So, well, I want to finish by a very explicit formula that I promised at the beginning, just very geometric, for the motivic homology of the limit motif in the case of semi-stable degeneration, and also for the, for the tripler-nubrum. It will be just in the case of semi-stable degeneration. And it comes from this, I just, well, it's- This formula is here. I just want to- I will make it explicit, which is trivial from this definition. So, the formula is the following. So, here is my setting. Well, now I will have, again, I have the log structure coming from semi-stable degeneration, but now I can have multiple intersections. Well, but it's still semi-stable. Maybe that's not a good picture. So, this should be planes rather than lines. So, okay. Probably I should not put it here. Yeah. So, it's confusing. Okay, semi-stable degeneration, and it's strict, right? So, I want really, that's, I want log structure for the risky topology. So, strict, strict, strictly semi-stable degeneration. So, I have components, D1, D2, well, so, so, DI. I, I, belongs to sunset. I have this GM torsors. So, first of all, I have Li, which is of DI. I just want to, I want to, I just want to, I just want to, I just want to, I just want to, I just want to, I just want to, I just want to, I just want to, I restrict it to X0. And then I have the corresponding GM torsors. And I have UI, which is the complement of X0 to DI. So, okay. So, now I will produce, construct the material homology. So, well, first I will produce a complex of smooth varieties over X0. The fibers will be algebraic tori. So, what are these varieties? So, so, step one, complex, very simple, complex of smooth varieties. So, this will be product of all this Li. So, this is product over X0. It's a, it's a, it's a torsor over, over an algebraic tori of dimension for cardinality. Now, what is the next term? So, you take a sum. Let's consider it as a, what's it kind of, I want to, it's not really, it's, in fact it's a, I want to consider kind of an additive category. I want to make sense of sum. So, it means that it's, you can think of this dejoint union. So, of products of i in i, i is not equal to j. And here I will have L-circ i times Ui over X0. So, what is this map? Remember that Li is trivial over Ui. Therefore, I have such a map. It's just given by, well, it's a section. Now, it's a long complex, and here is its last term. It's sum i over times intersection j not equal to i Uj. It's again over X0. And so, all I use here, all the differentials come from the sections. So, for that Li is trivial over Ui. So, this gives me such a, again, this should be dejoint union. So, this is step one. It's very simple complex. Now, form, define a complex of pre-sheets on X0. Well, what you do? You call this z dot, and then you take the following. So, if you have a scheme over X0, then, well, the value of my complex of pre-sheets on X0 on y is the following. You call this correspondences or X0 from y to this complex. So, well, informally, you just take sections of this complex of varieties over y, and then you make it homotopy invariant by applying the system construction here. So, let's call this f, and my material homology of X0m, z is just CDH homology of this X0 with coefficients in f. That's it. That's all I have to say. So, there is one, well, there is, as you see, you can ask whether the log geometry here, and in fact, there is no log geometry. You see it's just linear algebra, and the log geometry appears if you want to prove, for example, that if you have a smooth log scheme, then it's motive. It's isomorphic to the motive of the open part where the log structure is trivial. This I don't know how to do. I know how to do it in the case of, like, normal crossing. Normal crossing situation, but in general, it really requires some geometry. Thank you very much. Was there anything in notation of the logical homology did you say you have several zn for different n? Yeah. So, here I defined only this one index, right? This index is absolute value of this set of indices, i. So, if you want to define it for larger, for larger n, right? You have to just add, in the whole construction, empty divisor formula. And to define it for smaller, you don't... Yeah, yeah. You don't... You don't need to define it for small by consolation. It suffices to define this for sufficiently large numbers. This follows from the books. Yes. No, no, no, just material homology. So, if you want it for... You have consolation. So, you can express material homology of something with coefficients in z of n, in terms of homology of the twist, these coefficients in z of n plus 1. Which is the product of this GM? Yeah, yeah, product of this GM, for example. Yes? So, I just was curious. Where is n? Should we have... Yeah, yeah. This twist here, right? No, no. This n means the lord of monodome. Yeah, it's... That's a very good question. It's this whole complex of schemes. It's this over GM. If you have... It's exactly as in the picture I started with. This gives you the tubular neighborhood. If you want the vanishing cycles, you have to take the fiber over. So, it's a... Yeah, it's a unipotent material shift over GM. But how can you define the map to GM if you're even just... You're in the fiber. No, there is a... The map to GM comes from the trivialization of the tensor product of the swine bundles. So, each of these smooth schemes over X0 admits a map to GM, for example. Because the other one... The product is... Yeah. This is implicit when I said that you were going to... You started talking about how to define the weight filtration. Yeah. Does this come out easily from this? Yes, so there is a... Well, yes, it comes thanks to the work of Bandarka. So, if... Betty homology, or the Ram homology, or the Tal homology of any wave-wise motif is equipped with integral weight filtration. So, that is equivalent to... Rational. Yeah. To what? Yes. He has defined the weight filtration. Yes. But after, you have to show that it's equivalent to the others. Well, but here you don't have... Well, a priori, you don't have the others. What you have to show is that the basic homology of this log-motive that I... of this wave-wise motif I defined coincides with the homology of this... As defined by Kat and Nakayama. But this is obvious because Kat and Nakayama homology theory satisfies the list of all my axioms. And therefore, this factor from log motifs is uniquely determined by its restriction to usual motifs. And for usual schemes, there is nothing to prove. Yes. And... Sorry. Last question. In characteristic P, this was everything characteristic... Yeah, you have to invert P. And always with zariski? Well, yeah, for zariski again. So, the only reason why I work with zariski is that I want wave-wise motifs really for Nisnevich topology, as opposed to wave-wise motifs for Taltopology. So, it is enough to help Nisnevich locally... Nisnevich charts for the work start. Yes. Yes, yes, yes. Though I don't really know... No, maybe that way. There are... Yes. You need to figure it out. Any more questions?


One announcement from our friends from VOC here. Please, as this is the radio talk, please switch off all radios that you should have in your hands. Please switch them off. We have interferences with our microphones here and we cannot start the talk. So please switch them off just as a matter of safety. Before we start the usual announcements, be nice to the people of Zigeli. We want to be welcomed here again.  Save water wherever you can, except when drinking it, drink more water. Lower the noise for midnight. We are more than 4,000 guests, 180 villages, 1,000 active angels, thousands of hours already worked. One more announcement. You will see a phone number on the slides for the translation. If you want a translation on decked, you must dial 8012-8012, not the number that is displayed on the slides as this is wrong. So it goes. Welcome to our speakers. We will also have a special guest. We all got these famous radio devices and many of us are keen to get more of them. We will have a talk that will last approximately 45 minutes. Thereafter we will have 15 minutes of Q&A and then I will announce a special procedure regarding all of us who want to get their radio. We will have a special procedure that ensures that everyone gets one and that we don't have accidents or manslaughter when going to the point of access. All right. Welcome to Sek, AlfGuy and Schneider from CCC Munich. Thank you. All right, thanks a lot. Thanks a lot. As many of you might guess, we have been under an immense amount of pressure the last week, so please forgive us if we forget what our slides contain and what we're talking about. We have prepared this presentation today, like a few hours ago. Okay. Many of you, I guess, were at the CCC camp four years ago in Finnofort and at this camp we had, I guess, the first large-scale rollout of an electronic name batch at a CCC conference. It was the rocket and was actually also done by a team of the CCC Munich. And I think many people had a lot of fun with it and we still see that thing around on international conferences when we travel the world. Every now and then someone has one around their neck and that's really great because the goal of the rocket was to have a conference batch which gives people the opportunity to play with microcontrollers, play with embedded systems and still use it after the conference. That's why we did put on a rechargeable battery and a nice display so you can play with it and have some fun afterwards. Now, four years later, we're here and there's another batch. But the fact that there's another batch isn't just a given. I mean, one year ago we were thinking about, hey, shall we do something for camp again an electronic name batch? Yeah, probably, but not a rocket again, not the same thing again because we would turn in a circle and do the same thing again and again. We wanted to raise the bar a little bit higher still and have something which has an actual use still after the conference and harvest the opportunity we have to do something like that at the camp. And we are thinking about different stuff but none of it was really that good. We didn't think that we can come up with a concept which really satisfies us also in learning something and producing a batch which is useful. But thankfully, at the same time, second me, we were working on the Iridium satellite stuff and we came in contact with SDR. And so we got into that in the beginning of 2014 and worked our way to receiving some satellite data in summer of 2014 and we got hooked. We really thought that SDR is a thing that everyone should play with and it's not actually that hard to do anything with it. And we came to the idea that maybe it would be a nice thing to have an SDR in the form of a camp batch which sounded interesting but also it's a huge challenge. I mean, it's high frequency stuff and all that black magic which is involved. So we started looking around, hey, maybe there are designs which are open source or which are at least somehow accessible and not that complicated and do something with them. And what we came up with is, okay, so there's the Hacker F and I guess the most prominent member of the Hacker F team is Mike Osman and it's open source which makes it very accessible but it's also a quite complex design with lots of parts, lots of also expensive parts and huge capability though on the other hand. Then you have these RTL-SDR sticks. They're simple in terms of circuitry but also very limited in terms of frequency range and you can't transmit with them. And back around in 2014 there was also the portable SDR on Kickstarter. I think it can also transmit but it's limited to I think the lower part of the spectrum and us as to be satellite hackers wanted to something which can also go on to higher frequencies so we can play with satellites using the badge. So we had a look at the different designs and we also reached out to the members of our local Hacker space what kind of contacts they have to chip vendors because obviously that stuff is expensive and you have to get support from the chip vendors to somehow donate parts and we realized, okay, we have a very good contact to Maxim which is chip vendor and NXP which is a number chip vendor and the HackerF is actually using lots of chips from them or at least we can replace some of the chips on the HackerF by parts from Maxim for example. So we contacted them and it took some time but we got a very positive feedback from both of them and so we continued onwards and started to modify the HackerF design a little bit to make it into a badge and of course that's only possible because the HackerF design is open source and it's accessible and you can look at the schematics you can look at the artwork of the PCB and you're actually free to manufacture it, modify it, do something new with it and that's what we wanted to do and now actually Mike Osman is here, he came to camp after he heard about the radio badge and he's one of the core members of the HackerF team and I think he wants to talk to you for a few minutes. I think it's on, oh it's definitely on. Thank you so much, thanks guys. This is HackerF1 and it was something that I spent years of my life working on. When I first learned software defined radio some years ago, I started using it for wireless security research and I immediately had the thought that more people in the hacker community need to know about this kind of tool and how to use software defined radio for all kinds of wireless security research and experimentation and just developing new radio systems, the sky's the limit literally and early on I started trying to give talks at conferences and I started developing a training program and to this day I still teach very often a two day, very intense course on SDR that I teach at information security conferences and I try to help people in our community learn more about SDR and how to use the power of such a flexible radio system for whatever you wanna do and at some point I started working on the HackerF project and one of the big motivators for me was to have a platform to use for my class and to have a platform that people could use to teach themselves how to use software defined radio and how to do creative things with radio that people have never done before and I made it open source hardware, I make everything that I do open source whether it's hardware or software or the content like I'm currently producing a video series that is based on my two day class and I'm putting it online under an open content license and everything I do is open source and I wanna tell one little story before I hand it back over to these guys. When I designed HackerF I was able to get some funding to work on the project early on and a big part of that funding was a beta run and does anybody out here have a HackerF job breaker? Nobody? A few? There's a hand? A couple. HackerF job breaker was the beta board of the HackerF project. It predated HackerF one but it's very similar and the original concept for HackerF job breaker was that we would make several hundred of them and give them away at tour camp, the US hacker camp and I was so excited about giving away hundreds of these to a bunch of hackers in a field and see what they could do with them and then that didn't happen because the project fell behind schedule and I was so disappointed that we didn't get to distribute them all the beta boards to a whole bunch of people who are all present in the same place and talk about SDR and see what people could do with them and now years later, thanks to the fact that everything I've done has been open source, this team has been able to take the design and provide you with the radio badge which is an amazing adaptation and I couldn't be happier. I am so excited to actually be here when my dream is realized that we are giving now not just hundreds but thousands of hackers, SDR platform in a field and I can't wait to see what you all come up with and before I hand it over, I just wanna say because I brought too many of these and they're really heavy, I have throwing star land to business cards and I have a lot of them so if you see me tonight or anytime through the weekend be sure you grab one of these from me so I have less to carry in my backpack back with me to the airport, thanks guys. Thanks Mike, we're really happy to distribute that stuff and now comes the part where we actually wanna thank someone and that's the CCC for supporting us and covering the remaining cost of what was left after we got an enormous amount of donated parts from the chip vendors so lots of RF parts from Maxim, the main CPU from NXP, some transformers and coils from CallCraft and Infineon is providing the RF switches on the badges. I mean it's at least for example 60,000 RF switches which is quite a number. Now we are a team in Munich who has done the rocket batch so we have a little bit of experience in doing larger runs of electronics or with large I mean like a few thousand which for some people is like nothing but for us it's a lot and I wanna talk a little bit about the timeline. So last summer we thought about the project and it took us until winter that we started talking to people about it and then it took another like one or two months for people to make decisions about if they wanna support us or not. Which led to an insane timeline which led to the fact that on Saturday our transporter was leaving from Munich and on Friday everything was finished. I mean the last PCBs were falling out of the factory. It was like just in time, it was a very stressful time but we somehow managed it, I'm still not sure how but it worked. So we on the way had all obviously some fails in the prototypes and we were running so fast that almost any failure at the first prototype would have stopped the whole project right there because we wouldn't have any time to spend a second prototype before the production starts and but the thing was the first prototypes came back and nothing worked, nothing at all and after debugging for like two hours we realized hey, looks like the pinout in that eagle symbol which is our design program for the PCB has a problem. There are a few pins swapped and we didn't know why and what but in the end we realized okay if we drill a 0.25 millimeter hole at the right point of the PCB by hand through to the other side on the backside of the PCB of the chip we can open up a connection and make it work and thankfully that worked and the first prototype started to working somehow which was almost a miracle so some advice, read the latest version of the data sheet because for some reason NXP decided in February 2015 hey, maybe there's a problem in our data sheet we have to swap some pins in there but they didn't update the library and eagle and we just used that so we had to redo that but yeah, word of advice, look at the latest version of your data sheets. Now after the first prototypes worked we had to do a lot of modifications on them and time was so critical that we had to send off that PCB to the fab house which was going to produce them and the lead time was around four weeks and we didn't have any time anymore for a second prototype so we shipped them off, they were going to be manufactured the same time we started to do another prototype though still to verify the layout and make sure that we don't populate bad stuff. Of course the second prototypes didn't work either. Now there's a special part in the design and it connects these two big blue ground planes, this is one ground plane, this is one ground plane and there's a little piece of copper in the middle of the PCB you can't see it, it's inside the PCB which connects these two parts. Now in the prototypes they were missing somehow the board house managed to delete it from the data set and we were going crazy we were thinking that we have to fix four and a half thousand PCBs to make this thing work, it was quite a stressful night and I was in the US at that point, driving in the car having phone conference with Germany and trying to figure out what's going on, almost going nuts but it turned out it's a problem with the prototypes not with the final PCB so everything well. Now therefore some advice start earlier than us it led to crazy stunts to get this thing going and the lead times for PCBs and components can be really long and you get pressed hard to make this thing happen. We had to resort to like over same day shipments of prototypes starts to squeeze out one or two days to get the fab house happy with the deadlines it was not good, the stress level it's peaked above any sustainable limit. Then another thing, now okay everything worked first prototypes somehow worked we shipped off the PCBs to the manufacturer did some second type round prototypes and then the manufacturer of the second prototype says hey by the way your pads for the small components are way too big you need to change that to get this thing done, what but the first one didn't and now you what's going on and we realized okay our layout tool has wrong footprints for the small components there and you can see that in the picture in the final board now we had to reorder some components in the bigger layout package therefore some advice check all your footprints every single footprint even if you think it's so simple that it can't be wrong and your cat package has it right probably it doesn't and that's what happened to us. Now that was a little overview I had took part in basically every little aspect of the project and managing stuff but our F guy knows the RF parts of our hardware in and out so he is going to take over and explain a little bit about the hardware. Yes. So first one as far as the idea for me so I know to make a heck of it's easy to lay out you make a very similar design first one I use another layout tool as Mike do so I have put the complete schematic at new and also we use another controller to ask any space or we need a controller first one we try to use the same controller as a hack af and he told us yeah you can get this controller if you're end of this year something like this we don't have how many in stock and then we ask yeah we can have another controller and now we have four, three, three, three this 180 pins so first of them we have more eye-opens so thus we make additional parts you don't use only a software defined radio although we like to have a batch so you need a display was also very nice to get ones this reassembled uses Nokia 6100 displays from a shiny factory was Schneider tried to get them when we get prototypes was also very interesting story to get this display by the way we have the same five buttons like the rocket on this part and also other controller have two USB ports so maybe this is also a nice part so we add an additional USB port this is our schematic of our radio batch we look at the components from the hack af and see there's a chip that's have inside a mixer and a voltage controlled oscillator and a PLL this is think very expensive this I mean is about 60 dollars so the chip are cost and we have this very nice apart from Maxim's you have also a Fouse CEO PLL by controller so he tried to use this and also I tried to find and mixer this have a very wide frequency range this is from linear they have about one megahertz about six gigahertz so we redesigned with another people this is called next called Feldwig we this meet together we designed a completely RF card in you we look over sides what you can get so we have exchange a low noise amplifiers to a Maxim type we have exchange arrow switches also we need the transformers you have all the look this transformers is on USB three transformer was also very works very nice in the application here so you start the layout and then when I think this is the layout with an 100 pin BGA to try to lay out this is the pain absolutely the first one say okay layout is easy I make many layouts also in my job and say it's no problem overall to make a layout at this and so we done okay it tried to make six weeks as one was three months aligned to get this very nice design as far where we hope now we got finally get this finished a second thing was so the second prototype see ask our supplier I can make a second run of prototype oh yes we are on holiday and within three days I get a new manufacturer many thanks to them that you get this prototype very fast or many thanks to them they say okay you have a problem with your footprints this is not zero four or three or two so this is a zero three six is a zero three all done it's a very nice design cost me a lot of time but it's working we think we have some errors inside we have now 40, 4500 developers try to play with the device and here's a basic error specs so we have Eric's and takes range about 50 megahertz to four gigahertz we have started okay we make a final measurement of this so we get a very nice spec to you but the time running absolutely out I'm here on the campsite August two to get the camp running many thanks to people from unique they get this project to run without me you have an eight bit ADC this is the same and deck this is about 40 DB dynamic range and the maximum output power depends on the frequency range is about five to 10 dBm we have some a little harmonics problem from the PLL at frequency above 2.7 gigahertz and yes you have to do with our measurement and with an inverted inverse EQ demodulation so maybe we can shift out some harmonics so onboard antenna is hope fuel each unit it doesn't measure and met at the moment at around 2.5 gigahertz we'll do it here at the camp we make a measurement on the antenna and this will be around 2.5 gigahertz what is easy come out and standard SME connector and move a resistor and we also make an antenna workshop that is not terminated at the moment so I give to Zach he makes something with usage and about Q-Radio and we make a live demonstration here as I many times our team hope to check okay I'm more the software guy so I'm talking about the software there's the batch has basically two modes the one is the camp application which starts when you turn it on when you get it the first time it's quite similar to the rocket firmware actually we did reuse quite a bit of code it can display your nick you can choose your font and animation as same as with the rocket also we have now a color display so you can choose the color you can also display graphics there are scripts in the git repository to convert any image to the format that this thing needs we are working on a web app so you don't have to do it yourself but it's not finished yet unfortunately we were running out of time a bit the second thing is you can use it as an SDR that's the main thing you want to play with all the frequency stuff have fun with it to get into the bootloader menu hold the joystick to the left while you turn it on then you get a selection of the applications on the badge one is the camp and the other one is the hackrf firmware there are two versions on it hackrf and hackrf old the device identifies over USB with a unique ID and we got a new one but if you have GNU radio installed from your linux distribution it is too old to know about this so it won't work with that ID so we have the hackrf old which fakes and says I am a hackrf one and so all the tools work with it but maybe in a few months the other one will start to work properly yeah, we have two little demos prepared one is like radio transmission and receiving so you just put your badge into the hackrf mode which I already did and then you use a standard GNU radio companion FM receiver so Schneider, do you want to show the other side of the setup? okay as you can see as you can maybe here move this up alright so what we have here is just a Raspberry Pi and it's attached to this radio here and we're just looping a file of music for a Raspberry Pi onto the radio and we're using the integrated antenna and it's right now running at 2.495 GHz and we're declaring this in a scientific experiment so therefore it's in ISM, no problem and some little advice, don't forget when you use to play with a SDR when you use a frequency from 2.3 to 2.7 you use a lot of little power than this mixer so for experiment it's a very nice idea okay, yes, and the radio on Sak's side is receiving the same signal it's an analog FM signal and he's demo-relating it on his PC right now this is one of the things that you can do and the other thing is just you can do like nearly every protocol if you know what to do so we have this remote-controlled power plug and you can of course, if you know the sequence it sends you can even turn it on in fact it's just a five-bit address and I think four bits for the four different power sockets and one bit for, if you want to turn it on or off it's a really simple protocol and of course it's not documented very well but you can also listen to it and just press the buttons on the remote control you get when you buy those and it's really easy to figure out so that concludes our live demo and can we have the slides back? thank you now it's the call for your participation we kind of, as you heard from Schneider ran nearly out of time and produced those at the last minute and also the software is working but not very full-featured we would be very happy if any of you wants to contribute or play with it so if you do something nice with it just send us a pull request on GitHub and we will gladly merge them some easy things to do is like you can write loadables and nick animations for the camp firmware there's this optional RGB LEDs on the badge that you can populate yourself there's still no ready-made software to turn them on besides some test pattern I think or you could write some games at least with the rocket people did that you can also modify the firmware itself we planned to, that's why there are two more holes we planned, you should be able to keep your badge this way but someone needs to write software to turn the display and there is some potential to make this badge safe power by powering down the CPU when it's not needed that much then your battery would last even longer if anyone wants to look in this the other part is with the SDR stuff as this badge has a display and a battery you could can do SDR stuff on the badge we did not have time to do this we have a branch in our Git repository which is called Porta which tries to do FMD code but we didn't quite finish it doesn't really work if anyone is knowledgeable enough and wants to take over or continue there is a thing called PortaPack which is an add-on module for the HackerF which contains a display to plug into the HackerF which then makes it like a more improved version of our badge you can probably steal code from them and implement it on our badge so there is FM receive, transmit, spectrogram batch to batch communication or even like video streaming to the thing you can do like 25 frames per second on this display you just need to get the data to the badge somehow after this talk, after the Q&A we are going to give out the radio badges to those who did not get them yesterday we will have a person next to the exit which will be the start of the line so there's no point in racing to our village right now because if you arrive early you will just get sent away follow this person and you will be fine if you receive it, please read the included instructions on assembling it check the wiki if you have any problems if you find any problems that are not documented go ahead and edit the wiki, it's a wiki tomorrow we will start with something we call the SDR Stokes Avenger Hunt because we want everyone to actually use this thing we've prepared a few challenges where you need to use it and solve some problems or find some stuff we will use our Twitter account to get updates to you there are really easy challenges at the beginning so everyone can join up if you are scared, team up with someone and use of search engines is heavily encouraged you don't have to reinvent the wheel every time the starting location will be at our village you need a radio and some SDR-copable device like your laptop or an Android with an USB on the go adapter the end of the challenge will be on day 4 after dark and the winner will receive some prize and also on day 4 at 9pm there will be the radio meet-up if you do any cool software modification or hardware modification we will give out prizes to the coolest of them and we will also make a photo session so we can document all the cool hardware modifications that people make and last but not least we have to spread out the thanks because people from the Munich CCC really helped out in assembling all the things, getting the stuff here in time and a lot of angels helped in flashing them so they all have software on them and you can just turn them on two days ago and a lot of other friends helped out here and there you know who you are, if you haven't helped us it would not have happened thank you Thank you all very much for the thundering applause you have really deserved it, thank you very much for this nice, kind and good effort to bring us further in our mission before I do more announcements on the radio handover procedure we want to have about a quarter of an hour Q&A we have two microphones on the top of the ails here my guess is we will be able to take two or three questions from each mic so if you want to ask questions please queue up in front of the two microphones now I see people arriving okay we have the first question here hi, my question is just in your estimation is it possible to turn the badge into a decked phone? I think so we don't know enough about the protocol really and you have to always remember that the badge is half duplex so it can either send or receive at a certain time and you have a certain bandwidth limit of 20 megahertz but I don't think that decked will use that much unless it's frequency hopping so it really depends on the specifics of the protocol and I don't think we're qualified at the moment to answer this question definitely so that's the challenge for the congress then I guess so in general I mean you have a headset port on the badge it has support for Apple style headsets so you have a microphone and some audio output if you can manage to get the protocol done you can certainly send or receive decked calls okay next question here okay thank you for all the work really nice I get one and it's very cool and now I'm really interested in where I can find Scott I want to help him with the luggage you know sorry I didn't get that okay where can I find Scott I'm really interested in one of the uh... HRFs Mike Osmond? yes sorry I don't know if he's down now okay so maybe have a deck phone you call him okay okay ah there he is so yes when everybody's waiting in line to get their badge tonight I'm gonna go walk along the line and hand everybody who's waiting some some swag so everybody gets something okay so we have solved that problem thank you next question hi I appreciate your very well-made SDR badge and I'm interested in how software-defined radio will proliferate in consumer and professional electronics over the course of in the future like what possible applications you don't understand you what possible future applications of SDR and consumer electronics do you see yes many of currently uh... devices that you use uh... using SDR just in a cellular phone have a multi-protocol chip that was a real SDR so software-defined radios and many applications will be every more like you can switch radio communication just by a software update will be the future and most of our devices to interject I think in the end software-defined radio will take over most of the radio stuff but uh... from from a hacker viewpoint you can play with everything you see and that's what interested us the most not the commercial applications hi go next question thank you for making this device and giving it to camp attendance my first question is I imagine making this device into an approach sensor of sorts is it capable of doing rather like stuff or measuring approach and outputting those values to a computer or another device and one point is that this device probably does not have the output power to actually do some radar like stuff and the second thing is I'm not sure I think the fact that it's half-duplex will make it very hard to do you would probably need two devices to to do something like radar was it but we have not experimented in that direction so I'm not really qualified to answer this uh... that's also saying the uh... lost uh... you have don't have a clock input design you have to make a hardware modification you have an clock output so you need a uh... small hardware modification to synchronize two of the radio badges so we will publish this in near future I have to interject some of the badges have a clock input yes we have uh... we have a really problem to get the clock generator uh... we have three different versions of this uh... chip on the badges so we have a lucky F1 is half an clock input okay next question hi uh... do you have any idea how the hacker of uh... one compares to the batch in terms of uh... low-frequency applications like for example thirty megahertz RFID is nothing okay uh... there the hacker is most likely much better than our uh... device because first of all our uh... RF switches are specified from a hundred megahertz upwards and also the uh... low noise amplifiers are specified from forty megahertz upwards and also the transformers are more starting at a hundred so I'm pretty sure that the hacker will have a better performance if you go lower in frequency yeah even beyond this uh... switch to stop uh... other at four gigahertz even the power uh... the low noise amplifiers also only four gigahertz you may be working up for a gigahertz but you have just try it as a hacking device okay thank you okay this is probably a million ways wrong but could you technically hook up uh... ESP8266 chip it's a two dollar wifi serial module and uh... communicate with our computer with this maybe send the video you were talking before because this chip can handle up to 320 kilobit second audio streaming maybe you can figure something out with video or other commands what do you think it's extremely hard to understand the what I'm sorry uh... ESP8266 wifi chip two dollars connect to it you can stream 320 kilobit second audio maybe you can stream your video for the board or some other cool things you can certainly hook up such a chip to the radio uh... I don't see any problem doing that I'm not sure if it's the point of adding another radio to the radio to stream something but you I mean at that point it's basically a display driver so most geeks only have one badge at a time that's true uh... oh so that's a good point so many of you get a badge and uh... maybe even after the camp you don't have an immediate use for that but if you're part of a hacker space I'm pretty sure people will come up with the use for these things so we would suggest that you share the radios with your fellow geeks and come up with projects maybe you need two of them but rather have them do something and work on a project than them sitting in your drawer that would be really great last question I wonder if it's probably also possible to watch TV with it like receive a TVBT yes it's already done as some people told me yes uh... already uh... receive TVBT with snu radio okay uh... another thing when we go outside and you get to grab your radio badge please have your entrance tickets ready you need your ticket again as you get your wristband and your wristband uh... to get your radio on only one wristband one ticket one radio thank you very very much


the OpenStack day at Budapest. This is the fourth OpenStack day here in this city. So I'm very, very excited about it because it's growing big and it's really good to see that we have a real OpenStack community around here as well. So not just everywhere else on the globe, but now in Hungary as well. So even more and more companies are joining and they are starting to use OpenStack. They are starting to develop to OpenStack and for me who's been involved and that's a addicted to OpenStack for two and a half years now, it's really good to see that I'm not alone anymore in this business here. We have, I remember correctly, around 360 registrations. So I'm sure that we have around 300 people at least here or maybe even more. The venue is really, really gorgeous. The rooms are packed with people. What I think is really important when we're looking at the OpenStack community is ensuring that we have the same diversity that we're seeing in our user base, in the community as well. So when you look at the user base, we have a vast variety of customers coming from all sorts of different industries, bringing all sorts of different use cases to bear. And when you look at the community, it's very important we reflect that with the same level of diversity, whether it's age, gender, sexuality, ensuring we've got the same broad spectrum of users adding into the code base. Because that's going to ensure that it's useful and valuable to everybody as we move forward. So firstly, it's really exciting to be here in Budapest. It's a beautiful city. They call it the two cities, then they are Budapest. And I think when you look at what we're building here with the community, it's important that we don't focus in on just the key hubs like London and California, but we also go out to where the people are, to where the business is, to where it really makes a difference. And that's why it's very important to come here. If we're going to be diverse, we need to attract everybody from all over the world. And Budapest is a fantastic center of excellence. People here are very efficient, very trained up. It's one of the more advanced areas when it comes to digital technology. The universities are turning out very, very smart educated people. And those are the sort of people that we want to attract into the community so that we build our base and build that diversity that I was talking about.