Thank you so much. Thank you for all of those that returned to this third and final lecture online and also here at Yashua's. So this is lecture number three. And the title, it's Applications to Geometry. So let me recall you what we have done so far. So we have been working always with the perfect base field of characteristic P, P greater or equal to 0. And in the first lecture, we saw this theorem saying that if you have a smooth proper case kin, then you can look at the conjectures, the celebrated conjectures for x. This non-commutative counterparts for the associated DG category of perfect complexes, we saw that there is no difference between these two. And also that we can more generally consider not solely the DG category, but also the corresponding non-commutative child motive, even with rational coefficients. And this, for any C, the conjecture, the one of Grottendijk, Weyvotsky, Veilinsen, Veil, and all these variants of the Tate conjecture. OK, so this is what we have seen so far in today. So what's the idea today? So today what we will explore is the following. So we want to find, we can look at these non-commutative motives, even with rational coefficients. So given any two x and y smooth proper algebraic varieties, you can look at the corresponding non-commutative child motives, even with rational coefficients. And also I can look at the conjectures for x and the conjectures for y. And I would like to find today a relation between these two. I want to find a relation in such a way that that relation will imply an equivalence between these conjectures. So that's the main idea for today. So what can we do? First of all, the first case, the very first case where we can find this relation is when we have a derived invariant. So suppose that the categories of perfect complexes on x and on y, they are even equivalent. Equivalent via Fourier-Muckay equivalence. Then in that case, well, that implies that the corresponding motives of x and y are equivalent, are isomorphic. And of course, if you just use the above string of equivalence, that's going to imply that the conjectures of x and of y do not change. So the conjectures x and y for x and y do not change if x and y are derived equivalent. Let me make some remarks about this. So first of all, it is known that if the canonical or anti-canonical bundles of x and y are ample, then it's a very interesting result of bondale n or log that in that case, the varieties themselves are isomorphic. So it's a very strong restriction that we have here under this assumption. But of course, there are cases of non-isomorphic algebraic varieties, for example, and a billion variety. And it's dual, a billion variety, for which the corresponding derived categories of x and y are equivalent. And this was this pioneering work of Mukai. So our formalism that we, our results that explain automatically imply drive the invariance of these classical conjectures. But so this is a very strong relation. And there are many other cases where we actually have a relation between these non-commutative motives. And one machinery to establish this relation is called homological projective duality. So we usually write HPD. And this is a theory that was developed by Kuznetsov. So let me explain how does this work. So the idea is the following. So you have an algebraic variety equipped with a map towards a projective space. You can think as being an inclusion. But it doesn't need to be an inclusion. Then you can look at the associated line bundle, where you pull back along this F, the line bundle on this projective space. And then what you want to do is to study hyperplane sections of x. So you have hyperplane sections of x. And if you want to study them, you can study them all together simultaneously. So you can first look at the incidence quadric inside of the projective space across the dual. So you can look at this incidence variety. And then you can look at the universal hyperplane section. And this is simply the fiber product of x with this incidence quadric over the projective space. And this sits inside x cross the dual projective space. So this carries information about all possible hyperplane sections of x. If you fix here a point, you are thinking about an hyperplane. And so when you look at the corresponding fiber over the projection over PV, that corresponds to the hyperplane section. And so our goal would be to understand this category of H, the category of all hyperplane sections. And the result is that suppose that we understand the category of x itself. So suppose that the category of x has a very specific form. It is what is called left sheds decomposition. Suppose that it admits a left sheds decomposition. So that means simply that you have a sequence of triangulated categories inside in such a way that when you twist them using this line bundle. So here you have a 0. And then you twist one with this line bundle, et cetera, until ai twisted i times. Then you get the semi orthogonal decomposition, the classical semi orthogonal decomposition of your variety. Suppose that you are in such a setting, then you can say something about this drive category. So inside of it, what do you have? Well, so let me get some extra room here. So what you have here is that all these blocks will also exist here. So you have this. And then, of course, you need to do the box product with the perfects on the dual projected space. And then it turns out that there is something orthogonal that is still missing. So here you have an extra category that appears. And this category is called the HP dual category of X. So what I've done so far is something very formal. You start with a scheme. You keep it a map towards a projected space. And suppose that this scheme has a semi orthogonal decomposition of this very specific shape, like a left shape's decomposition. For example, that's what happens with the projected space. For example, we'll have o, o1, twist it by 1, o2, twist it by 2, et cetera. Then you can say something about this category of the universal hyperplane section. It has all these pieces in its interior, box time this part. And then something mysterious, something orthogonal that appears here. OK. And now what's interesting about this theory is when this very abstract category is HP dual category, it's in fact geometric. Sometimes it turns out that this category, it's geometric. What do I mean by that? So I mean that sometimes this category here, it's actually equivalent to perfect complexes on a different algebraic variety. And sometimes it's not actually just an algebraic variety, but it's twisted by a certain shape of algebra. So not very far from being an algebraic variety. And in both cases, we call this y. We call it the HP dual variety, dual variety of x. And in particular, it comes equipped with a map towards the dual projected space. And suppose that we are in such a setting, then what you can do is that if you have a subspace of the dual of v, well, then you can consider its orthogonal, which is just the kernel of this induced map. And then here you can do two things. First of all, you can do the linear section with respect to this subspace. So you just take your original x and do the fiber product over the projective space with p, v, or orthogonal. Or you can do the linear section of y. So where you do the fiber product over the dual projective space with p of v. And now the theorem, which I call the HPD invariant, stays the following. So what was upstairs was the derived invariance of the conjectures. This is the HPD invariance of the conjectures, stays the following. Suppose that these linear sections are, in fact, smooth. Suppose that they have the expected dimensions in the sense that the co-dimension of this linear section is equal to the dimension of l. And also that the co-dimension of this linear section is equal to the dimension of l perpendicular. And also let's assume that our conjecture, the non-commutative version, is true on this largest piece, on this a0. Yes, because you see this thing is defined in this sense. So you can think about x inside the projective space, for example. And then you are taking a look at the hyperplane section. So and you assume that this conjecture for the largest piece holds. So some remarks about these assumptions.  So they are quite mild. And the last assumption, it holds, in fact, in all the cases, in all the examples so far, because in all the examples, these categories here that appear in the left chance of the composition are quite simple. In particular, they often admit full exceptional collections. So assuming this, it turns out that the conjecture for this linear section and the conjecture for this linear section, they are equal. So this is the content of the theorem, simply saying that, OK, under these assumptions, the conjectures do not vary. So what is the idea here? So just a brief idea of the proof. What's behind of this is that when you look at the non-commutative motive of this linear section and the non-commutative of this linear section, they encode. So there is a common piece inside of them coming from this mysterious C. So you have a certain category here, which is common in both of them. And then you have extra things, extra factors. But these extra factors here, they all, the conjecture, this conjecture holds for all of these pieces. Because these pieces are the pieces that are coming from this one. They are, in fact, direct summons of this one. And since the conjecture holds here, it will hold for direct summons. These pieces are not necessarily the same. But well, this tells you that, well, the conjectures hold here, hold here. So in fact, the non-commutative conjecture for this linear section is just the non-commutative conjecture for this non-commutative gadget. The non-commutative conjecture for this linear section is just the non-commutative conjecture for this. So you get an equivalence between the non-commutative conjectures of these two. And then you use the fact that the non-commutative or classical conjectures are equivalent. So somehow, you want to relate two geometric things, XL and YL, both of them live in the world of geometry. And what you do is a zigzag. You go towards this mysterious non-commutative thing.  You pass from X to L, from L to Y, via a zigzag, via something truly non-commutative. OK, so that's the idea behind. So now there are a lot of HPD dualities in the literature. So there are a lot of HPD dualities in the literature. Let me just give you an idea of two of them. So we have examples of HPD dualities. This, for example, is a Clifford duality, the Grassmanian-Pafian duality, the Spinner duality. The Determinant Hall duality, and many others. So I propose to look at two examples to look at this one, where in that case the HPD dual variety will be of the first form. So we twist it by a certain shift of algebras. And then the second case where the HPD dual will be actually geometric, given by just an ordinary algebraic variety. So let's look at the Veronese Clifford duality, so HPD duality. So this is built from work of Kapranov and Kusnetsov. So what is the idea here? You start with a vector space of dimension V. And you look at V, the sin2 of V of W, sorry. So this is your V of the theory. And then your algebraic variety is very simple. It's just a projective space on W. But then the map here, it's a non-trivial map, going to P of V, in other words, to P of sin2. And the map, it sends W, in other words, it's the Veronese embedding. So this is my algebraic variety. This is my projective space, and this is my map. So in this case, if you look at the universal acroplane section, and you project to the dual projective space of V, in other words, you project here. It turns out that what is this is, in fact, a quadratic vibration. So here, let's simplify and work nothing characteristic to. So what you have here, you have a quadratic form, and above it, the fiber is precisely the associated quadratic. So in fact, this thing, in this particular case, it's a quadratic vibration. And if it's a quadratic vibration, I can build out of it a shift of algebras, which I denote like this. So let me explain what it is. So let's make a parenthesis here. So suppose that you just have a quadratic form on a vector space towards your base field. Suppose that you have a quadratic form. Then what can you do? If you have a quadratic form, you can look at the tensor algebra of V, and then you could mod out by V tensor V. If you do this, you just have the exterior algebra. But then what you can do is that you can quantize this by deforming it by this quadratic form and get this new algebra, which is called the Cliffer algebra of your quadratic form. But you see that the way these relations are set up, it's not graded, but it is Z2 graded. So you have an even and odd part. So you can look just at the even part. So you can do this for any quadratic form. So here you have one of those on the base, and then you can vary that, and actually you can get a shift on this space. So you actually have a shift of algebras by doing this procedure over the base. You should be non-degenerative. No, it can be degenerative. Oh, okay. So that is precisely... So let me just say that the notation, let's denote by Z, just the singular locus. So inside here, the singular locus of the singular locus of your quadratic fabric. Okay, so above those points, you actually have singular quadrics. And now it turns out the key point is that the HP dual variety in the story, HP dual variety of X is the following. It's just this dual projective space, but equipped with this shift of algebras. So we are in that setting where the HP dual variety is not just an algebraic variety, but it is perturbed by a shift of algebras. And then what can we do? If we have a subspace on my dual, then I can do, as before, I can take linear sections here or linear sections on the HP dual. And if I do sections here, that corresponds to do the intersection of the quadrics, the quadrics in my projective space, which are parameterized by L. Okay, so intersect as many quadrics as the dimension of your space L. And on the other side, what you do is just that you do a restriction. And you restrict here this shift to the P of L. Okay, so we know that to solve the conjecture for intersection of quadrics is to solve the non-commutative conjecture for this gadget. So let's understand this gadget a little bit better. So it turns out that this category with this shift of algebras, it's equivalent to a category perfect complexes on the on a certain double covering of the projective space and this with an azomai algebra. So what's happening here is that you have the projective space and you have this double cover, twofold cover of this, which is defined. So what do you do?  Okay, so this is what you get and you get the twofold cover, which is ramified on this singular locus. And that is what's happening when D is even. Okay, D upstairs is even. So D it's actually equal to the dimension of the quadric that you are considering, the quadrics that you are considering. In the odd case, in the odd case this category is equivalent. Now what you have, it's a root stack as we saw yesterday. It now equipped with a certain shift of algebras which is also an azomai shift of algebras and this root stack that you have above your P L, it's in fact this two root stack where what you do is you get the singular locus intersect with P L over P L. So it's the root stack that we saw yesterday. And so as a corollary, so as a corollary what do we get? We get the following that the conjecture for intersecting quadrics, that's equivalent while we know that it's the conjecture for I of L. And so this turns out to be just the classical conjecture for this two-fold cover of the projective space, this in the even case. And here it becomes the conjecture becomes the non-commutative conjecture for this perfect complexes on this root stack equipped with this shift of algebras. So what does that imply? That implies that, for example, when D is even, in other words, when you are intersecting even dimensional quadrics, so this conjecture about intersection of quadrics holds when, for example, when you are intersecting three or less quadrics for the conjecture of Grotten-Dicken-Weiswitzky, when you are intersecting two quadrics for the other conjectures of Bellinson and Tate, and of course for any dimension for the Vail conjecture. So of course you already knew that Vail conjecture is true, but here you give you like an alternative way to see it. And also you get, for example, when D is odd, so when you are intersecting odd dimensional quadrics, that the conjecture for this intersection holds when, for example, when the dimension, when you are intersecting two quadrics and moreover, for example, when you are working over a finite field or over an algebraically closed field, because in that case is the Broward group of curves disappears. So in that case what you get is that this, this sheaf of Azomai algebras goes away, you just get a root stack, and then root stacks we saw yesterday how to manage them. Okay, so this is just an example. It gives you an alternative way to prove these conjectures for intersection of quadrics in an alternative way to the one that was done by Miles Reed in his thesis which was geometric. In the even D case, you don't need to consider to worry about the Azomai algebra. Because we saw yesterday how to attack the Azomai algebra, when you have an Azomai algebra, the motives with Q-q coefficients are the same, with or without an Azomai algebra. But when you have an Azomai algebra over a root stack, that is not the case. But over an ordinary scheme, there's no difference, but over a stack there is a difference. So now I propose that to look to the other example of the determinantal varieties. So that's the example where the HPDUO variety will be actually a variety. So determinantal HPD. So this was established by Bernard Dara, Bolo, Menzi, and Tanzi. So how does it work here? So you have two vector spaces, W1 and W2, of dimensions m and n. Let's assume for simplicity that m is less or equal to n. And then what is our V? Our V is this tensor product of the two. And then I choose an integer r between 0 and n. And out of this, I can look at the variety rmn inside the protective space, consisting it's the determinantal variety, m by n matrices, which rank is less or equal to r. So let me maybe give you a down to earth description. What do you do? You look at this matrix of indeterminances. So you have a matrix like this. I'm going to xn1 xmn. And then what you impose here, the relations that you impose is that the r plus 1, r plus 1 minors are actually equal to 0. So you have all these variables and you have these relations and that's going to give you a protective variety. Okay? For example, so are those varieties that are defined by equations that are coming from minors? So, for example, if you fix the rank to be 1, then these are nothing but the saver varieties. And for example, 1, 2, 2, this is just you look at those quadruples such that this relation holds, this determinant relation holds. And that's a surface in P3. Okay? And in the same way that you can do this determinant, define this determinantal variety, you can define it's dual. So you have something inside the dual projective space. Okay? So it's the determinantal variety of m by m matrices. But now we co-rank greater or equal than r. And it turns out that these things are in fact singular. So we cannot work with them, but they admit the very canonical resolutions of singularities called springer resolution of singularities. So we have this one admits a resolution of singularities. And the key fact is that x and y are HP dual to each other. So that implies that if I, whenever I have a subspace in the dual of v, I can take one linear section or another linear section. Okay? And now what's so interesting here, you see the following. So we get this corollary consisting of two parts. So first part, so let's suppose that, so we see that in this definition, we have four parameters. We have m and m, the size of the matrix, that are the rank. And we also have the possibility of choosing my L. And so we have the dimension of L. So we have four parameters. And now let's assume that we have the following relation between these parameters so that this is, so this number that it's here, it's actually the dimension of this linear section.  This is the dimension of the other linear section. And so let's suppose that they have dimensions less or equal than one. Then in that case, what does that imply? That whenever the parameters satisfy this inequality, well, you get for free that the conjecture for the other linear section holds. And so let's explore this. So let's explore, for example, the first implication. So the first implication, let's explore it, for example, in the case of Segel varieties. That means that r is equal to 1. Well, when r is, so in the case of Segel varieties, they are already smooth, so we don't need the resolution. So we are really taking linear sections. And so in that case, that number becomes m minus n minus 2 plus the dimension of L less or equal than 1. Then I know that the dimension of XL, in that case, is equal to m plus n minus 2 minus the dimension of L. So what's interesting here is the following. So suppose that I enlarge, so I'm in this case, and suppose that I enlarge the size of my matrix in the same way. So I replace n by n plus i and n by n plus i. And I keep the dimension of L fixed. So if I do this, this number does not change. But in contrast here, this augments us by 2i. So you see that here you have infinite number of infinite family of algebraic varieties, all of them satisfying the conjectures. And they are of arbitrary high dimension, simply because the dimension of this is fixed and the dimension of this is changing. And the conjecture for this one is true. So is it geometrical that you are taking ample line bundles, tensile for twisting the ample line bundles with high enough power? Does it mean that? Because this 2i comes in this dimension of XL, because maybe I'm not very precise, but is it geometrical in this you have enough embedding because you're working with several varieties and you're embedding this variety to some big variety space? It's not that sure with that. We can discuss after this. It's not... And the other example, for example, of square matrix. So in that case, that means that the dimensions m and n are the same. In that case, this you have this. But in this case, the dimension of the dual variety is 2rm minus r square minus 1 minus dimension of l. So again, you see that if you change...  This number does not change, but this increases by 2ri. So again, you see another family of algebraic varieties, all of them satisfying the conjectures and they are of arbitrary identity. And interestingly, these cases, it's not known to the experts how to prove the conjectures for these cases using just algebraic geometry, just classical algebraic geometry. Another interesting remark is that, for example, in what regards the veil conjectures, well, they are known, of course, thanks to the limb, but you see here that in the case of curves, so this is the dimension of yl. So I'm assuming that it's a curve. So for curves, the veil conjecture was originally proved by veil using elementary intersection theory of divisors on surface. So here you are bootstrapping this result of veil to higher dimensions without using the limb, for example. So it gives you an alternative proof of the veil conjectures that doesn't use the limb's techniques. And of course, these results are much more refined. This number one is here because we know that all the conjectures that I'm talking about, they are true for curves. But if you want to be more specific, for example, if you want a veil votsky conjecture, then you could put a tool here, et cetera. So to the biggest board, for curves you have to show some veil positivity in the intersection number. You have to show that this is positive. Yeah, that's the... How does this for the curves means this for the veil positivity here? No, it is exactly the point. The way that I prove it is like the drawing that I mentioned to you is that the conjecture becomes from a curve in this higher-dimensional variety. The conjecture is equivalent to this non-commutative gadget.  So you do this exact, this step where you use the non-commutative world. So it's a not geometric proof and that's the interest that you can go to higher dimensions. Okay, so in the remaining of my time, there are many other examples, many other HPD dualities, many other cases where you have proven the conjecture in this perspective for new varieties. But just to finish this lecture and the course, I wanted to talk a little bit about the Riemann hypothesis. So let me recall you that if you have a smooth, proper scheme over a finite field of dimension D, okay, then we defined in the first lecture it's also the LZ function as the product over all closed points of 1 over 1 minus Q degree of X minus S. So this is actually the cardinality of the residue field at that point. And this converges when the real part of S is greater than D. And then we saw that by combining the links work on the veil conjecture with the work of Bertolou in crystalline homology, you have this homological interpretation of the Asa-Vael Zeta function using the Frobenius and acting on the crystalline homology. So we wrote it like this, omega plus one. So in what follows, I will, these pieces here, so this piece here, I will be noted by the Asa-Vael Zeta function of X of weight omega. Okay, this will be my notation. Gonzalo, it's hard to see what you have written on the bottom. This red chart. So it is the Asa-Vael Zeta function of weight omega. Okay, just this piece. So the ordinary one, it's an alternating product of Asa-Vael Zeta functions with different weights. So this is over a finite field and that's what we saw last time. So now we go to a number field. So to simplify, let's just go to Q. So we can go to Q. So take now, it's a smooth and proper Q-skim, okay, of dimension D. Then we know that there exists a smooth model, a smooth, proper model over the, so away from a finite number of bad primes. And so let's assume that we have good reduction. In other words, let's assume that there exists a smooth, proper model. So X i over each one of these bad primes. So localize that P i. And this for i between one and n. And if this is the case, if we have good reduction, we can do the following. So if you choose an integer, a weight between zero and twice the dimension, what you can do is do the L function of this weight of X by definition. You just do the product over all primes different from the bad ones. And here you do the Aseville Z function of this weight on the fiber. So this stands for the fiber of this model at P. So that will give you an algebraic variety of graphonite field. And then you multiply by the remaining bad primes. So, and here you do, by this I mean the fiber of this model at the prime P i. Okay. And then it turns out it's a result, a theorem of Sarah that in fact, this function actually converges on this health plane where the real part of S is greater than omega 2 plus 1. And it's more over different from zero in this region. So you have the following picture. So over C, you have omega 2 plus 1, omega 2 and here in the middle we have this one. So you know that in this region it converges and it's not zero. Okay. And now what regards this L function so there are associated with this conjectures. So the first one is the conjecture M of X that says the following. So whenever you have a weight between zero and twice the dimension first of all this function admits a unique meromorphic continuation to C the entire complex plane and moreover this extension has no poles has no poles in the critical stripe. So consisting on the complex numbers whose real part sits between so here you have this critical stripe here in this interior the conjecture is that there are no poles so not only you can extend it to the meromorphic function but there are no poles here in this critical stripe and then if this is the case you have the conjecture R of X so maybe it's called a generalized Riemann hypothesis that says that if this function vanishes at a certain complex number and this complex number belonging to this critical stripe then necessarily this number lives in this vertical line so it is necessarily in other words all the zeros of this function they are here so zeros they are necessarily on this line and why is it called the generalized Riemann hypothesis it's because it generalizes the classical Riemann hypothesis so if you take let's see the following example let's take for X just a point so per Q the simplest example that you can think of which is of dimension 0 then of course that you have that there exists a smooth proper model smooth proper model even on the entire over Z which is speck of Z of course and in this case when you take there's only one way 0 so you look at the corresponding L function here and this is just a product over all primes of this Asavel Zeta function of the fiber at P so this fiber well you know that it's precisely the speck of Fp so it turns out that this is just a product over primes of your 1 over 1 minus P minus S well and that you know that you can rewrite in terms of Dirichlet series as fault so it's the classical Riemann Zeta function which we'll see so in this case what's happening is that you have 1, 1 half and 0 and so you know that this function it's well defined and norm 0 on this region first of all and secondly what we know about this function is well the conjecture M of X in this case it holds there's no problem here so this function actually extends uniquely to the entire complex plane and there are no 0s on this critical stripe and then the other conjecture this well this maybe it holds maybe it doesn't but what it's called it's nothing but the classical Riemann hypothesis okay so the simplest example is the Riemann hypothesis and of course this can be more general you can think you can take here a number field and then you would also have a model which is just given by the integers okay and so in that case here what you have it's a product over all primes and then you need to do the product over those prime ideals above P and it becomes 1 minus the norm of that prime ideal minus S and so you can rewrite this in terms of the sum over all possible ideals in this ring of integers of 1 minus the norm of I S so what you get in that case is the classical that can set the function which is also known to for this conjecture to hold and this conjecture is something called the extended Riemann hypothesis in that case Bansala we have received a question that's not a smooth model at the ramified primes yes you can do that also what I'm talking about in terms of finality continuation the bad primes don't count for the third function exactly right it's just a finite amount of information to put them there to correct where the zeros will land etc if you don't have a good reduction well you still can do it but in that case you need to use comology inertia etc no it's not I don't need it and that's a key point here I'm not using the primes at infinity and making it complete I don't need it because when you are putting the primes at infinity what you are doing with the gamma function is that this when you do the extension there are zeros that appear here and then you put the gamma function in such a way that the poles of the gamma function will kill these zeros so that the only possible zeros will land here but the way I'm phrasing it is that I'm just considering zeros in the critical stripe so I don't actually need to complete it so you don't need this big zero is completed at infinity that's why I don't need it the way I phrase it so my point is now is that this still works in the non-commutative world so now we can talk about the non-commutative women hypothesis so if you have now a smooth proper dg category over the finite field so we saw in lecture one so we saw in the first lecture that you can define this as a zeta function associated to them ok and now if my a is over q so a smooth proper dg q-linear category so this still works still exists a smooth proper model a smooth proper model which I'll write like this over so away from the bad crimes and I will assume as above that we have good reduction I will assume there exists enough smooth proper model over my localization of p i and this for every i between 1 and n and in that case we can just use what we have done in the first lecture to define a l function so in fact as usual it's not just one but two so I have this l function defined so I do the product over all crimes different from these bad ones and I do the as above zeta function for this fiber here and then I multiply by the the remaining bad primes I do this as above zeta function p i and where this is the fiber in the sense that it's doing the drive transfer product over fp width and similarly here I'm doing this model and I'm changing it to fp over zeta and you can do of course the one version of it in a similar way for every prime it's this again and I do the product also I put in place the bad primes and this it's this and now what's the point here is that we have a non-communicative counterpart of series result so the theorem is that let's assume that let's assume that the non-communicative well conjectures hold for the fibers hold for these fibers okay this for every p different from the bad primes for i between 1 and n suppose let's assume that this holds then in that case this l function it converges on this off plane whose real part is greater than 1 and it's moreover non-zero on this region so I have c and I have one half and one and here I have this region where my function is infinite product converges it's well defined of course I don't need this assumption because this is just a finite amount of information and similarly here in the one case this function converges on this half plane where it's greater than 3 over 2 and it's moreover different from zero so here again over c so I have one half one and three over two so it's in this region here that my function is well defined okay and of course in this setting we can also we can also conjecture that we have meromorphic continuation so we can conjecture that first of both of these functions both of these l functions they admit a unique meromorphic continuation to c and secondly also that these extensions respectively of l0, l1 so it has no poles in this critical stripe going from the real part between zero and one respectively when the real part is between one half and three over two so on this critical stripe on this critical stripe I conjecture that there are no zeros there there are no poles there and then we can also phrase the conjecture of Riemann that says the full length so suppose suppose that this function vanishes respectively this function vanishes with a complex number in this critical stripe in this critical stripe respectively here and this implies that this number it is necessarily leaving on this line necessarily leaving on this vertical line so the zeros must be here the zeros must be here okay and so what is the point of all this is the following so I think I need to finish so it's my very last blackboard so let me just mention that the result is that if you take X a smooth proper scheme over Q this conjecture holds then you can look at the Riemann hypothesis for it or you can look at the non-commutative version of the Riemann hypothesis for this so this conjecture to hold will imply that that this conjecture for perf of X will hold also and so I can talk about this and it turns out that these conjectures are equivalent as in the first lecture okay so possible applications of this of course we cannot use it as I did today to prove new cases of the Riemann hypothesis because there are not even cases of the Riemann hypothesis the Riemann hypothesis over a point it is the classical Riemann hypothesis but you can use it to establish connections between two algebraic varieties saying that in fact the Riemann hypothesis for them which are very different algebraic varieties are equivalent so for example suppose that one of them would be zero-dimensional and the other would be higher-dimensional this would say that the Riemann hypothesis for the higher-dimensional it's equivalent to the Riemann hypothesis for the zero-dimensional but for the zero-dimensional it's just that that can set the functions so you can somehow reduce the complexity to get consecutive functions which are very well studied okay I think I'll stop here thank you and sorry for going over time okay many thanks for a wonderful mini course any questions or comments the last point you were making when you stopped after that here so here so you see in the first lecture we had this result for the conjectures right exactly this result I'm saying that the Riemann hypothesis I could so put it in this package where it can be extended to the non-committative world in such a way that when you plug this kind of DG categories coming from schemes you recover the original conjecture so now I'm saying that if we played the game of today of having two very different algebraic varieties with geometrical are very different but in terms of the motives are related then I can relate to the conjectures so this I could relate the Riemann hypothesis for two different algebraic varieties suppose that one of those algebraic varieties is zero-dimensional for example then this would say that the Riemann hypothesis for the other one which could be higher-dimensional is equivalent to Riemann hypothesis for dead-kin set of functions of course this doesn't allow you to prove the Riemann hypothesis because the simplest case of a point is the classical Riemann hypothesis but allows you to establish connection between Riemann hypothesis of very different algebraic varieties another question from Remy is the reason that you are only considering L sub-node and L1 that you have tape twists what's happening is that if you the L-node of the perf of the scheme it's actually going to identify a product of all the even weights of the classical L function on X but here you need to shift it by this so you grab all the L functions for all even weights and you shift them to plus them precisely in that position there that's the relation that you have and you have a similar relation for one and now it will be a product of odd and now it's a shift by 1 minus 1 over 2 so this is the link between the non-commutative world and the commutative world as usual what you do is that you trivialize the tape motive so somehow you get lost of the individual pieces you only keep track of the parity thank you another question from anonymous attendee last talk you mentioned that in the non-commutative world there is no tape twist you want to say that such an object does not exist in the non-commutative world or just that you did not find a good way to define it yeah I I would say that it doesn't exist it makes no the tape twist comes from what's happening with the projective line and the projective line by additivity is just two points somehow it is not there any other questions or comments if not done, grand merci for a wonderful lecture mini course many thanks indeed thank you for having me, thank you


All right, Lady, what is this? Hey, I'm making more Stem-AQT boards. I did get a big shipment of AT-Tiny817s, which means I can make these Stem-AQT to sensor breakout. So this is a slide potentiometer to I-squared-C converter board, and there's four neopixels. Now, my controllers have ADC, so you may not need a board like this to convert it to I-squared-C, but a single board computer like a Raspberry Pi, or an Onion Pi, or whatever, Linux machine, often don't have ADCs. And so if you wanna add just like one or two slide pots, this can be a really easy plug-and-play way to do it, because you just do it over I-squared-C, plug-and-play, and then you get the analog reading. So this is the board, and you can see those nice neopixels underneath, testing it with a Metro Mini, and I'm programming it over UDPI with a USB to serial converter. And these are the values. Looking good, ready to ship.


My name is Sarah Fiena and I'm a student here in Geneva, Switzerland, the home of the International Telecommunication Union. ITU is the United Nations agency that manages and promotes information and communication technologies, or ICTs in all no language. That means your mobile, tablet or even just a plain old telephone. I've come to ITU this morning because today is Girls on ICT Day. That's the day when ITU staff show girls from local schools how interesting a Korean technology can be. I want to see what it's all about and meet some of the participants to talk about their experiences. The first person I've found to talk about the day is Mr Hu Lin Zhao. He's the secretary general of the whole ITU. Mr Zhao, why did ITU start Girls on ICT Day and what do you want to achieve? As you know, ITU is a specialised agency of the United Nations that is responsible for ICT development in the world. Our mandate is connected people, connected world. ICT will offer tremendous potential to help our girls to develop themselves in their career. And we also found that girls have a lot of fantastic ideas to contribute to the ICT development in the world. Therefore, ITU would like to organise this special day to invite everybody to come together to celebrate ICT and Girls. We wish our girls a great day of this celebration. Thank you very much. I've tracked down Mr Senu. His unit leads the Girls on ICT Day each year. Mr Senu, this seems to be a very popular event. Why do you think so many girls get involved in Girls on ICT Day each year? This event is really inspiring. And we are gathering every year all the young girls to make sure that they make the difference in their life and the life of humanity through ICTs. We want the young girls and the women to become ICT creators instead of being just ICT consumers. Thank you very much, Mr Senu. My pleasure. Here at ICT today, you will get to see and experience ICTs first-hand in practical workshops, encoding mobile applications, satellites and robotics. In this workshop, Hanan from ITU is teaching the girls how to programme these very cool robots donated by Lego. Hanan, how hard is this and what can you get the robots to do? It was fantastic to see what the girls have achieved today. They are learning how to programme and they are experimenting with robots, programming with fun and it was really fantastic. Can you give us a demo? Yeah, of course. Let's demonstrate this first demonstration. We put an object here and the robot should detect this object and stop near it. Let's go. Thank you very much. May I talk to some of your students? Of course. Thank you. Can you tell us a bit about what you've been doing this morning? Basically, being programming and controlling the robot with this programme by Lego. Thank you. What about you? They've also been showing us different tactics and how we're in control of the robot but also how the sensor makes them also reply to us. Thank you very much. I thought I'd check out another of the workshops. Can you tell us a bit about what you've been up to so far? Hi, we are doing a workshop on data visualisation. We are from CERN. At CERN we have huge amounts of data and we have to visualise it and we have these tracks of particles that we generate billions of times a second. What I'm showing them is how we can generate those tracks and make dots where they pass by and connect the dots. We are letting girls actually programme and see the bowels of the visualisation engine, how that works and it seems like they are having fun. Is working with ICTs like what you expected? It's a lot more interesting than I thought it was going to be. I thought it was going to be really boring and just open numbers but it's a lot more fun. And there's also this great speed mentoring activity where you get to hear from real-life tech role models about what it's like to welcome the ICT sector. It's time for the girls but for the Geneva diplomatic community it's time to hear a debate about some of the issues and about some of the success stories already out there. It seems to me that the reporting as a school subject in the future in 2016 would seem to be relatively wide area. Most of the technical skills are such. The debate has to happen between the generations. We've heard from several panelists that we need to impart skillsets from early ages and to go back to the company question or the entrepreneurship question many, many educational systems don't embed entrepreneurship and leadership in their teaching. Technology innovation is changing our world. It's at the heart of many of them hard problems that we have to change in the next 50 years. We want girls at the table creating technology or we encourage you to listen to learn, to do, to make things and consider to participate in this really important field. Acura Chex is a non-profit based in Nairobi, Kenya and our vision is to increase the number of women who use technology to create solutions. With that kind of definition our members include any woman who is interested in using technology and it does not limit to whatever career that she has chosen to have. I'm here with Gareth Baldworth from Lego Education. Gareth, Lego sponsored the equipment for one of the workshops today. Why do you think girls on ICT Day is important? Well, firstly at Lego Education we believe that it's really important that we enable every student to succeed and with this we include girls as well. In my job as someone who's talented students we meet are girls and if we can give lots of opportunities for girls especially in ICT then that will be a job well done for us. Thank you very much. It's been such fun spending the day surrounded by all this cool technology. Girls on ICT Day is a great way to spread the word about what a fantastic career you can have in ICTs.


A formal agreement between Beltrami County, the city of Bemidji and the Bemidji School District for roundabouts near a new elementary school is expected to be agreed upon. The County Highway Department met with the Beltrami County Board of Commissioners to discuss the estimated 6.2 million dollar project. Under the agreement, the school would have to pay a certain amount of money based on the percentage of increased traffic to the area. The County Highway Department says it has considered other options such as traffic lights for those intersections. The other big thing is timing. You know, we might not build all four at once. It might be one or three or one might be saved for the future. We're just kind of, I guess, again, looking at the corridor and the needs out there. The cost would include widening of certain streets left and right turn lanes, milling overlays, and engineering for four roundabouts. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


A further high court in Abuja has ordered the Department of State Services, D.S.S., to produce the 12 detained associates of Yoruba Nation activists Sunday Iqbal Ho on Thursday next week. Justice Obyara Egoa to give the order after counsel to the applicants moved emotions seeking their presence. The judge also ordered the D.S.S. to show reasons where the applicants should not be granted bail. All 12 were arrested and detained by the D.S.S. on July 1 during a raid on Iqbal Ho's residence in the Shoka area of Iqbal Ho's state. Two of Iqbal Ho's associates were killed during the raid. Meanwhile, after three sessions lasting about six hours, the hearing of the case against Yoruba Nation activists Sunday Iqbal Ho in Benin Republic has been adjourned until Monday. Iqbal Ho's wife was allowed to go home but the activist remains detained. The case against him is immigration-related as is alleged to have attempted to travel with a fake passport. But the Nigerian government failed to submit charges against the activists that could start an extradition process. The Nigerian government wants Iqbal Ho for his secessionist agitations and for allegedly illegally being in possession of arms. Don't forget to hit the notification button so you get notified about fresh news updates.


So lately on this program, we've been talking a lot about how Donald Trump's approach to COVID-19 has been to functionally pretend like it's no longer a thing. His staffers have reportedly said that they just hope people grow numb to the deaths eventually. So, you know, if you can't beat it, then just pretend like it doesn't exist. That's been his strategy. And needless to say, this strategy has been a colossal failure because people are dying. And regardless of what excuse you want to use for cases rising, people want this to go away. They want you to be a leader and take action. So if you actually want to have a shot at being reelected, you can't pretend like COVID-19 isn't a thing. You have to at least pretend, do window dressing, but you have to at least make it known that there's an inkling inside of you that you care. So now, because his numbers are on freefall, because his approach to this has been such a huge failure, you can't even really describe how harmful it's been to his re-election campaign. He is now forced to do a 180 and actually start trying to at least pretend to take it more seriously again. He resumed daily press briefings again this week saying, I think it's a great way to get information out to the public as to where we are with the vaccine, with the therapeutics, and generally speaking, where we are. And after weeks of his own supporters making matters worse because they refuse to wear masks because Liberty, well, he tried to encourage them to wear masks by tweeting out a photo of himself in a mask and suggesting that it's actually patriotic to do so saying, we are united in our effort to defeat the invisible China virus. And many people say that it is patriotic to wear a face mask when you can't socially distance. There is nobody more patriotic than me, your favorite president. Now he may be insufferable in the way he promotes people to wear masks. He may be racist, which I unequivocally denounce. But you can tell here he wants to get this under control. He knows now that he's not going to stop hemorrhaging support and votes if he doesn't at least pretend to try. But it's not just Donald Trump because other Republicans know that if Trump's in danger, they're in danger too. And even Mitch McConnell is changing his tune, now suggesting that the next COVID-19 relief bill will in fact include another stimulus payment to Americans. Now, I want you to understand that these actions are being taken. These statements are being made out of necessity, not out of concern for the American people. The reason why they're doing this is because they are terrified that not only they're going to lose the White House, but they're going to lose the Senate possibly. They're really close. Like if you watch some of the ads, some of which were featured possibly before this video, there's an ad of Chuck Schumer, excuse me, of Mitch McConnell fear mongering about how Chuck Schumer only needs four seats to get the majority. So they're worried. They know that if they don't turn this around at least somewhat before November, they're going to lose and they're going to lose badly if nothing changes. So they don't actually care. Like what we're seeing, even if you can argue like the encouragement for his supporters to wear a mask is a good thing. This is nothing more than political theater. This is window dressing because they don't want to lose, but make no mistake about it. They're not actually trying to solve this crisis. In fact, behind the scenes, they're making matters worse because during this unprecedented crisis that we're facing, they know that 32% of households missed their July housing payment. They know that 23 million families could face eviction come October because of this pandemic. That's why they're changing their tune. That's why they want you to think they're taking this seriously because they know you're suffering and they don't want you to blame them. But they're only going to do what they can publicly so you think that they care about you. But behind the scenes, they're trying to actually make matters worse. Because for example, because of this pandemic, because so many people are now unemployed, well, the demand for food stamps has increased by about 17%. And as a result, food stamp benefits have been expanded to accommodate the increased demand. But Republicans, rather than trying to keep this demand or expand food stamps further, well, they're trying to end the expansion that was made during this pandemic to accommodate people. That means people who are newly unemployed will have less food on the table. They may go hungry. People may die because of what they're doing and I'm not being hyperbolic. And that's not all because as cruel as Republicans are, they at least try to expand funding for COVID-19 testing or at least that's what they want to do. But Trump has made it very clear he's not interested in doing this, presumably because he really does believe his own bullshit lie that more tests equal more cases. So as Republicans try to get this under control, which requires testing, Trump is saying, No, I don't want to do that. This is all happening behind the scenes and you can tell that they're scrambling because they don't know what to do. They waited so long and now there's four months before the election and they're trying to hold it together. But it's all coming apart. It's all unraveling before their very eyes. They waited too long and their lack of empathy for the Americans they're supposed to look out for.  This is damage control. And even if you want to give Donald Trump credit for recommending that it's patriotic to wear masks because that's the idiotic message that will resonate with his supporters, like he's not willing to actually be serious about it. He's not willing to take it a step further to actually stop the spread of the virus because in an interview with Chris Wallace on Fox News, he was asked, would you actually institute some sort of federal mandate? To whatever extent you can do that legally speaking. And he said, no. Then there are masks. From the first day that the CDC said that people should wear masks on April 3rd, you said you weren't going to. You wore a mask for the first time in public at Walter Reed this weekend. Question, the CDC says if everybody wore a mask for four to six weeks, we could get this under control. Do you regret not wearing a mask in public from the start? And would you consider, will you consider a national mandate that people need to wear masks? No, I want people to have a certain freedom. And I don't believe in that. No. And I don't agree with the statement that if everybody wore a mask, everything disappears. Hey, Dr. Fauci said don't wear a mask. Our Surgeon General, terrific guy, said don't wear a mask. Everybody was saying don't wear a mask. All of a sudden everybody's got to wear a mask. And as you know, masks cause problems too. With that being said, I'm a believer in masks. I think masks are good, but I leave it up to the governors. Many of the governors are changing their more mask into, they like the concept of masks, but some of them don't agree. I do say this, schools have to open. Young people have to go to school. He still makes matters worse because he says, I want people to have a certain freedom. And I don't believe it. So on one hand you say, hey, everyone, let's wear masks because it's patriotic.  Therefore you won't mandate it. So you're saying please wear a mask, but you're also right that it violates your freedom. I mean, he can't help himself.  And he said, you know, I just want to leave it up to governors. As he put it, they're more mask into. Okay, well, what if the governor in a particular state is a complete moron endangering his or her people? I mean, take Governor Brian Kemp of Georgia, for example. He's literally trying to block local governments from mandating masks. What then? Well, I'm assuming his answer would be, well, that's just freedom. States rights. So I mean, he's not serious about this. Oh, and also he said kids should still return to school.  He wants to ameliorate your suffering. Republicans are looking out for you finally. But then he says, no, we're going to send your children to school to act as guinea pigs to see how far this is going to spread. If we continue acting like it's normal.  Are you seeing the pattern here? Even as they do political theater and try to get people to think that they care at all, they still end up showing their true colors. They end up revealing who they are.  I mean, it was already mask off when your staffers reportedly were saying that they hope people grow numb to the deaths. Right.  People know about that now. And we know that you don't actually care. We know that this is all for political purposes. But if somehow you stumble upon, you know, the right strategy that actually makes you effective at combating this, that's a good thing. Like I'm not hoping Trump fails at stopping the spread of COVID-19 because of the election. I want to stop the spread of COVID-19 because this is a highly contagious, deadly pandemic. I'm removing political considerations from the equation here because dealing with the pandemic seriously in and of itself is a good. It's a good for America and it's a good for the world. But Donald Trump can't help himself. He doesn't know how to seem authentic. His actions will be driven by what he believes is going to best help him get reelected. And currently, I mean, it's statues using federal agents to occupy democratic controlled cities under the guise of defending statues. That's exactly what he thinks is going to help him get reelected. And the same is true for Republicans.  It's not necessarily unusual for politicians to act this way. But I mean, they're so bad at pretending to care that they can't even hold the facade for like five seconds before they end up showing their true colors. We care about you. We want to give you another stimulus, but we're also going to roll back them food stamps. We're also going to not going to extend that $600 bonus for unemployed people. I mean, they cannot help themselves. That's how little they care. So I mean, it may be too little, too late for Donald Trump. Like it's certainly a good thing that, you know, there's this inkling within his administration that you have to at least try to take on COVID-19, even if you're pretending. And maybe if you pretend you accidentally end up being effective in some way, I don't know how. But I mean, going in this direction to try to take this seriously is important because at a minimum, maybe this will signal to your supporters that it's not a hoax and that they should wear masks because if you take it seriously or at least present yourself as someone who takes this seriously, maybe they'll follow you. But I mean, who knows? So I just, I can't see this getting under control. And I think that he waited too long. Like functionally speaking, just pretending like this isn't a thing hurt him so bad that I don't know that he's able to undo the damage that he caused, but we'll have to wait and see because this is America. This is 2020. Anything is possible. But it is interesting how quickly he abandoned that strategy, how, you know, this shouldn't even be surprising. But of course you can't just pretend that a pandemic isn't a thing when this is unprecedented, when people are losing their jobs and their loved ones because of this pandemic. Like of course that's going to fail. What are you thinking? Thank you.


If you are articating over commercial disputes even though the law says so here, there is also need to have aptitude, some aptitude to understand commercial transactions, to understand a bit of numbers, so we can deliver fair judgments. Don't misunderstand me. I'm not saying you're not delivering good judgment, but it's just a six. Entrepreneurship skill of some kind.  I think you heard me last time I was delivering somewhere at some platform. I said let's change our curricula as a country so that at an early stage our children pick up financial literacy skills, they pick up entrepreneurship skills as they become lawyers, they become administrators, educationists. They have that basic understanding. It does help. So we support you in that area to make sure that you're continuing education skills development with your mundane legal issues can include some elements of this, including IDESI IT. I think you touched on it yourself. The automation that is essential which will bring efficiencies. So your training center idea, establishment of the training center, you have our full support. Let's just talk what we need to do as central government to support that. And you have support from us including this fellow talking here. And this fellow will do what he can to make that training square reality. I think it's a shared vision. So Chief Justice, we support better conditions of service for the judicial. We support that. I noticed that the biggest and longest club came from that subject. So we support that wholeheartedly, wholeheartedly. Because that will assist in improving the morale. You well articulated that because the judges may not be able to do other things to enhance their income. So well taken, point well taken. I want to attrest that by saying that does not negate and I picked a few whispers, negate the importance of the overall need for prudence in the utilization of public resources. It doesn't negate that. The two are not contradictory. If we save money from corruption, it means we will have it available to support the improvement of conditions of service in the judiciary. That's the story. And it is important that the judiciary understands the importance of prudence overall. If the president doesn't want to ride in a latest Gulfstream 650, which costs the taxpayer $193 million, the judiciary as citizens needs to understand why we do not support that extravagance. Because we could have gotten a plan of capability in terms of range reliability around $20 million. So why did we have to spend $193 million? On that piece of metal, we could have looked after the judiciary in the same ticket. We could have also bought a lot of school desks for the kids. We could have also invested in one or two border posts as Kazungula border posts is now delivering value. I hope the Kazungula council chair person is here and the MP is here. We spent around $240 million on that bridge. That's across the river. 900 meters of the bridge, 900, close to a kilometer. And before we spent that money on that bridge, cheap justice, the river knew we were getting around there was very little. Since we invested in that bridge, we are now earning so much money, including now being able to get the payback from that money within 2 to 3 years. Complete payback. This government wants to invest money prudently and not waste it in certain areas of expenditure. We expect and we know we have the support of the judiciary as the legislature should support us. Because after all we have triplets. No, triplets. Yes. Three is what? After all we have triplets. Legislature, judiciary, executive. So these are things that are important to this government so that we can take care of the needs of the judiciary in terms of conditions of service. But we shouldn't go and spend money like that. It doesn't mean we should not improve the conditions of service of the judiciary. We should not provide vehicles. We should. But the question is that why should we buy a plane for one person and is small in tourist at $193 million. That's why I refuse to use that plane and we'll be selling it. We're just going through the procedures now. It's gone. We can recover what the eye sees, some loss. It's not a loss because the money was never spent on the plane. The money was siphoned out in the process. The plane was just an opportunity to siphon money. The issue of corruption. That's the issue. But when we do so we should be able, if we want to replace it with the proper plane that does the same work, similar work. But not spending that much. And the residue we can spend in two, three other border posts. That's the point I wanted to make. And we can recover the full $193 million with the replacement plane but also two border posts in two to three years. The fourth year will be in profit. That's how this government operates and that's the mind frame. We wanted to share that. We agree you have a backlog of vehicles. We agree office space. We're in agreement. We're in agreement. We're in agreement that you need facilities. We need, actually you don't need, we together need those facilities. It's good that you spoke before me so we're going to have this conversation. It's good. So count on us on the office space. We heard you loud and clear and my team will get a couple of your speech so that it's our input into the work that we should be doing together. Straight forward, isn't it? Straight forward. We also know that the minister of justice is part of the executive. The judiciary is one of the triplets. So we understand that. We think there's a legal issue there how the judicial was administered through the minister of justice. We understand. So I think part of the issue is not to break that but part of the issue is to now create the judicial leadership and the executive must also have regular direct contacts to discuss these things. So which means the chief justice and the president must be talking regularly and comparing them. And that's fine. Then we'll be in a position to tick off, some of the things we raise are mandate. We'll be able to tick off those things and guide each other. Isn't it? And then drop it to administrators, the bureaucrats whom we are tackling every day, chief justice, tackling every day to get things done. So I think you'll be pleased to learn that we are very happy with your speech. We are very happy with the issues that concern the judiciary. We would like to work together within the confines of a treasury envelope that was depleted, which we inherited. Our efforts to rebuild the economy is meant to support the judiciary as well. So it's a self-saving agenda for all of us. And therein lies the issue of teamwork. Bamuami. Judiciary does not exist in isolation. Executive does not exist in isolation. Legislature does not exist in isolation. If they keep on making laws that are creating trouble for you to make judgements when you have cases before you, we must talk to each other and address those issues. Because otherwise the citizens who think the judiciary is inefficient and are issuing contradictory rulings, citizens are watching. And maybe the contradictory rulings are arising from conflicting legislation coming from the legislation. So we the executive are interested to make sure that as the legislature we work as a team. That's my message. If you want to take home message among some, this is one of them. But don't forget to take home on economic reconstruction. Because that will fund what we want. Chief Justice, it is important, dear delegates, and I want to speak to more than the delegates from Zambia, delegates from our neighboring countries, our saddick region, our beloved Africa, and the world. That it's important to note that we the three arms of government, executive, legislature, judiciary work for the people of Zambia. The people that we work for are the people of Zambia. Even as a judge sits to write a judgment, remember you work for the people of Zambia. We are not above the people. We are a creation of the people. The constitution is a creation of the people. Therefore we are subservient to the people of Zambia. All of us without exception. Another take home. Having said that, so I don't convolute the discussion and pollute it, but help to make it clear. So in totality we support the judiciary. We support you. And today we will sit here. We're not rushing out ministers. We will sit here to witness our honorable chief justice as he launches in his launch of the vision for the judiciary. Focusing on building public confidence through enhanced judicial accountability and increased access to justice. We will sit in here and listen to you present. We look forward to your new vision, our chief justice. We look forward to your new vision for an independent and truly indispensable, this indispensable arm of government. This one of the members of the three twins. No, three triplets. Triplets. One of the three triplets. One of the triplets, three triplets. So we look forward beyond your presentation of the vision to walking the talk, to seeing an improvement in the judiciary, to helping society reduce the fights. When a matter is not decided quickly, chief justice, and litigants are looming out there, they end up killing each other sometimes. So we could protect them from deaths by walking the talk, dispensing justice fairly equitably timely. I think it's the right point for me to end this same, very pleased to have this honor to declare the 2022 judicial conference officially open.  I thank you for your kind attention.


Guys, it is Sunday, it's late. It is, let's see, 5.13, it is late. We're having grocery shopping and stuff this morning. We're in all the errands we usually do on Saturday, but yeah, we're still recovering from our vacation. Let's see, I'm gonna put you down right here, maybe. Maybe, hold on. So while I was on vacation, I did bring some needlework with me, but I also brought this with me. I brought something else too, but we'll discuss it later. So if you all want, I'm gonna film how I made this, but I got the idea for it from an Instagram person that I follow, an art person that I follow, and I'll link her Instagram down below. I don't know exactly how she did hers, but I saw her coloring on one that she made. I think the only thing I know about it is that she made it with indie ink. Otherwise, I have no idea. I didn't use indie ink, I used either a Faber-Castell pit pen or a Ohuhu marker, and both of them work great. I colored them in with highlighter pens, and those two pens don't smear with the highlighter pen, so they worked really well. I did this one while I was on vacation. I liked it so much, I made another one when I got back. I'm a little bit bigger. And this one's with the Ohuhu markers. I did do a test patch on a piece of paper with the pens I like to color it with to make sure that that would work and it did. But if you want a tutorial on how I made these, let me know. And then today I made this little bag because I really decided I liked, yes, having the needle work with me was great and all, and I did work on some things. I really like to just have a small thing. I don't like trudging a bunch of stuff through the airport. And I seem to do that more often than not, but my goal is not. So I made this little, basically a pencil pouch with a zipper and all the journals can go in here. The difference with this one is it's got two pockets on the outside with a flap, with all my pens in it that I would take to color with. And then it's got the flap to keep it closed. Plus, if I am on the plane, there's a little bit of stiffener in the flap to sort of have it up just a little bit and keep the flap out of my way. And the pencil pouch is big enough if I wanna bring one water brush and one of my small mini travel watercolor palettes, I could still do that and fit them in here. And I have three, these are, there's three journals here. This is one Scott watercolor paper. This is a writing journal. And then this is one of the coloring journals. And there's still room. I have these little tiny watercolor palettes. I could still fit that in a water brush in there. And that fits in a small bag and I can just take it with me. So if you wanna know how I made this and I just made it today, this is the test sample. Let me know, because I'll make a video. And I also took my normal daily drawing journal with me, but I did the collages ahead of time and put the words on it, put the dates on it. All I had to do while I was on vacation is do the drawings and do some writing. I left that and going forward, we may, when we prep September, we may really prep September. We may do the cover and do collage on every single page. And then, yeah. So anyway, because that was easy and then really all I needed is a pen in that journal. And I could, that journal won't fit in here, but I could just bring this bag, bring that journal, everything else is in here. Yeah, I like that. Anyway, taught up here. I've got all the windows open because it's hot up here. I think we brought the heat and humidity home with us from Virginia. All right, I think that's it for the moment. I did get a fruit bouquet from my sister for my birthday, which was great. Thank you, Elizabeth, it was delicious. Came with this really cute little plastic bucket, which I'll use for something, but it has a little crack in it. So before I go downstairs, I think I'm gonna glue the crack and then we'll just worry about the mess that's on my table. Manana, maybe. All right, I'll be back. All right, you guys. Well, it's still a little bit of morning left. I guess I better get my day started. I've been putting off, turning on the computer and doing a new video editing, but it's past time. So yeah, anyway, we're also gonna get this cleaned up, get ready for a project and all the things. First, turn on some music. I'll be back. Okay, still avoiding video editing. So I have one of my, what I call hip pockets. I don't really carry a handbag too much anymore. It's not that I don't, but not very often. I started going without one during COVID when it was just easier to not have a handbag to carry along with the mask and everything else. And when I have too much for my pockets or I'm wearing an outfit without pockets, I have sort of a hippie version of a fanny pack. And I have this green one and they basically have two hooks on them and then they hang off of a belt. And this one actually came with a green belt. I bought this one from Earthbound Trading Company years ago. And it is leather with a cotton lining, but it's not the best quality leather and the snap on it was really kind of a pain. And eventually over this last trip to Virginia, the snap was so hard to get undone that it ripped a piece of the leather. So I used some pliers to pull the snap off, both ends, both the end on the top and the end on the bottom. And I sewed Velcro on here.  And I just machine, I made these by hand, but I hand, I machine stitched it to the flap of the bag. And there you go. So now that's all fixed, which it was on the project list to do on, you know, now it's done. So still avoiding video editing, but I think my computer needs a software update before I actually do any video editing. So we are going to check into that. And if it needs it, let it update and then I'll work on the next project, which is gonna be creating some more of these coloring books and working on a bag, a mini art bag to take with me on trips when I go on vacation. I always take bag, I have a lot of bags. I love my bags, but none of them are exactly perfect.   It'll be fine.  Actually, it's heavy. And so I did a mock up yesterday of this bag, and which is basically a pencil pouch with pen holders on the outside. Now, this one's not perfect, but the basic idea behind it works great. The pocket is for all the journals, the outside is for the pens. I don't take much with me or at least that's the plan. So, yeah, those are the two main projects or first projects we're gonna be working on at the table. Once I get the video editing done. All right, I'll be back. I don't think I've turned the camera on all day today. I've been too busy crocheting. Anyway, Jenna Phipps, this is your fault.  Now I'm crocheting flowers. I really, anyway, been doing that all morning. I got a call from the daughter. I have a couple errands to run for them tomorrow because they're out of town. And the house is being cleaned as we speak. She's downstairs. And I have to stop crocheting and dig out the support gloves because old lady hands. Anyway, yeah, I've just been crocheting like a maniac today. That's all I've been doing. I've been doing nothing else. So, can't say I'm too mad about it. Do you know? Anyway, as you can see, my little set up there in the corner. Yeah, all right. That's it for the minute. I'll be back. Morning, everybody. It is 10 o'clock. Almost at 11 o'clock, it's not 11 o'clock. It's 10 o'clock. Been up for a bit. Had a counseling session this morning. It went pretty well. I have to stop talking disparagingly about myself, which is a really bad habit.  We'll pick up some stuff for the daughter. She's out of town. I have a list of things. I wrote it down, including make bread. I've been home since Fridays till I haven't made a loaf of homemade bread, which is weird because I make a loaf for every week. Anyway, when I get back, before I make my lunch, we'll make some bread. Okay. Go ahead. We're in a vlog first. Evidently, he's got something to tell me, but anyway, we're headed out for an evening walk. It's about 80 degrees out. Figure we should get some steps in while we can because next week it's going to be very hot as balls. That squirrel tribe would say. If you don't know who that is, I'll link her channels down below. I'll probably get demonetized for that, but oh well. Our thoughts and prayers are with the people of Maui, and Lahaina, if you haven't seen the news. Basically, most of the island of Maui is on fire and Lahaina's gone. The town is gone, literally. That 150 year old Banyan tree that I just love is gone. Right by the harbor there. Right by the harbor and the old courthouse building, gone. All of it's gone. All of Riverfront area is gone. All gone. So anyway, on that depressing note, I've been crocheting flowers again all afternoon because you know, I had a counseling day. After that, I went and ran some errands for us and the kids. Am I sure I locked the kids front door when I left? 80% maybe? Hopefully I did, I don't know. It's one of those kind of days you guys. Anyway, we're going to go for a walk, get some steps in. I'll be back. I don't think I've gotten on camera yet today, which you know, and it's like two o'clock. Anyway, I filmed a couple of videos this morning, which is why I haven't gotten on camera yet. And one is for the next RT Trio, another one is for a travel art bag journaling thing, like stay tuned. Anyway, I am getting my next sewing project done. And I actually have some typing and document creation to do on that. I don't know if I want to do it right now, but yeah, I have to do that. I may try to do it on my tablet instead because I think I'd rather. Anyway, that's it for the minute. Bob is out at an appointment and running a couple of errands. He took a break from his desk during the week, which he never does, but you know, he had some stuff that needed doing so he's out doing it. Anyway, I think I'm gonna take my little keyboard upstairs and I think I am gonna type that document I need to work on on my tablet. I really just, my desktop is old and slow and I really need a new one, but they're expensive. Anyway, tablet's old too, but you know, everything's old. I'm old, electronics are old. It's all old. Oh, and we're gonna be creating a playroom here in the house somewhere for the grandson. And I'm looking for opinions. So we have this game room in the front, which we don't use much. There's obviously things here that would need to be moved out like China cabinet. We also have some things out here in the family room we could move around. What do you think? I'm kind of opting for a family room. Anyway, what's your opinion? All right, let's go get this document created. I'll be back. Guys, I would say good morning, but it's lunchtime. It's Friday, August 10th, I think. I don't even know. I have no idea. August 11th. I think I've mentioned it on the channel before almost 30 years ago when I was pregnant with my daughter. Actually, 30 years ago. I was in a head-on collision with somebody who ran a red light and I've had problems with my neck ever since on and off. And sometimes I wake up in the morning and I start my day with my neck killing me and having a headache. Today's one of those days. So while I haven't gotten a whole lot done, I did get a start on my next sewing project, which is a sundress project, boho style, T-Mire style, out of an old bed sheet. The basic pattern is the Indie pattern company summer dress. I think this is when I got off of Etsy. I'll find it and link it below. I had this really pretty blue polka dotted bed sheet and I have started the dress here. Yes, she sorta looks like a nightgown. We've got some ruffling lace on the bottom and a ruffle. The lace is from a couple of pillowcases that I thrifted as is the bed sheet. I'm gonna add a couple of faux pleated details on top of the lace. We're gonna add some pockets, because why not? And some of the edges are gonna be hidden. Some are gonna be left to fray. And yeah, I've already taken it in a little bit around the top, done some pleating on the front and the back, done different patterns of pleating, so I know which is the back. Yeah, anyway, I need to stop now and eat some food and maybe take a pain pill. So anyway, I'll be back. I know it's time to stop because my earbuds run out of juice. My ice for my coconut water is completely melted and it's very hot up here. I have other chores to do. I said earlier I've been putting off, but I did complete a project that has been on my list for sewing for quite a while now, since I first started getting back into sewing, to be fair. And it is this dress, sundress, made out of a bed sheet, boho style. And I haven't washed it yet, so some of the edges are gonna fray, but I do love the way it turned out. Love, love, love. And it'll go really well with some other things that I've already made. Yeah, so anyway, I need to stop now. Kids started texting me, my phone started going off. It's another way I knew it was time to stop. All right, I'll be back. Hey guys, of course it's me. I'm trying to vlog for the first time today and it's like eight o'clock in the evening. And here's another thing about me. I did get the music to turn off, but I don't know what I did. I don't know how to operate like that. When Bob is not here, I don't even turn it bother. I just watch stuff on my tablet. Anyway, I haven't vlogged before today because just because I sat down for a little bit with his serger and did another clean and oil on it. And it's a little bit better. I want to do one more project and then I might just have to take it in for service. Of course, old me would rather just chuck it out a window and buy a new one, but the new one I'd really love like my dream serger is a Bernina that's like $1,400. And unless Bernina wants to sponsor my channel and some of my sewing videos and send me a machine, that ain't happening. So Bernina, if you wanna send me a machine, go for it. But anyway, so we had dinner with the family tonight, another birthday celebration for me, for people who couldn't or be here before now or weren't with us on my birthday because we were in Virginia. And my dad came down, so that was really great. Adopted daughter Jenny brought me flowers. She got me some lavender lemonade mix, which is great. Friend of hers is roasting his own coffee beans and she knows I love coffee and she brought me some beans. Yay, can't wait to try them. And some lavender lemonade mix, which I'd never heard before, but I can't wait to try that either. So anyway, can you tell I love lavender? Anyway, and Jenny is one of our kids who loves arts and crafts. She wants me to teach her sewing and book binding. You guys. Anyway, we're just cleaning up from the evening and planning tomorrow with the same kids. I think we're gonna go see Oppenheimer, Oppenheimer. I think that's the one we're gonna go see. Anyway, we're gonna go to the movies with them and then hang out, run a couple errands, and yeah. It'll be a fun day, but that's for next week's vlog. This week's been interesting. I didn't get all the projects I thought I would get done, but I did get more than I expected to get done. Does that make sense? I think it makes sense. Anyway, that's it for today. That's it for this week. If you have questions, comments, or concerns, leave them down below. Say hi, Mr. Bob. Hi, Mr. Bob. If you would like, share, and subscribe, I sure would appreciate it. Above all, go out and have a great day. Have a great week. Do something nice for yourself, because you deserve it. I'm gonna sit and drink my evening iced coffee. I'll see you next week. Bye, guys.


The White Paper proposes recommendations from the SCI Spaki Science Community to develop a synthetic integrated model of changes occurring at different system and functional levels in animals and humans during spaceflight in order to predict long-term consequences of human adaptation to space and implement medical support plans for long-term missions. This article was authored by Francesca Childe, Austin M. Brown, Corey W. Baumann and others.


This is stock number 10123 we are here at Summit Automotive in Fond du Lac, Wisconsin you're new and use sports car headquarters. Today we are checking out this extremely clean 2010 Dodge Challenger SRT8. This car has the 6.1 liter V8 Hemi motor which pumps out 425 horsepower stock. Hemi orange is the color. We shoot all of our videos in 1080p so if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is definitely the best way to check out the car without actually being here and actually seeing it in person. Very clean down this side of the vehicle I didn't see any dents I didn't see any dings. Comes with the 20 inch Alcoa forged painted alloy rims Goodyear Eagle 245 40 ZR20 tires. These tires have right around half the tread left. Comes with the Brembo brakes in the front. The slotted rotors. I didn't see any dents or dings on that front fender. The lower valence and front bumper are in excellent condition. You can see the front bumper has never been drilled into. Has the projected lamp headlamps. Has the carbon fiber stickers on the front. They are in excellent condition as well. Has the cowl induction hood. The stickers on the hood are in nice shape too. Passengers side fender is in excellent shape as well. Didn't see any dents or dings on that. Passengers side rim no scuffs no scrapes. Very very clean and as you go down this side of the car you can see just how clean the body is. How reflective and mirror like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the car. You can still see the car hear the car and have confidence in the vehicle that you're looking at before even get here. Does have the power sunroof and once more down this side. I didn't see any dents. I didn't see any dings. Very very clean. Lower rockers all look really good as well. This back rim is in excellent condition too and the back tires have just as much tread as the front tires. Coming around to the back of the vehicle rear bumper is absolutely perfect. No dents, dings, scuffs or scrapes. The deck lid is in excellent shape as well. Spoiler is in nice shape too. Chrome tipped exhaust. Down this side of the vehicle just as clean as that passenger side. For full disclosure this back rim didn't see any scuffs or scrapes on that. Has the Brembo brakes in the back as well and once again down this side. No dents, no dings. Super clean car all the way around on the body. Has the power heated mirrors. Inside the SRT package gives you the black leather and suede seats. Has the orange stripe on the back there. There are no rips, there are no tears on the seats. You get a power driver seat. Both of these front seats are heated. The back seats are very clean as well. No rips, no tears and those seats do fold down for extra storage. In fact we're going to check out the trunk right now. This does have the kicker subwoofer back here. Lots of space back here as well and this is where the battery is. Saw those shocks worked really well holding up the trunk lid. Has the auto headlamps, the power pedals. I'm sorry not power pedals. Has the tilt telescope, auto headlamps, power windows, power locks, power mirrors. Apologize for that. Has the sport racing pedals. And as we hop inside the car here you can see that this one has 14,858 miles.  The leather wrapped steering wheel. Information center controls on the right. Audio controls on the left. Cruise controls right there. Comes with the 430N radio with factory navigation. AM, FM and satellite radio capabilities. It also does have I believe a hard drive. So you get up to 16.29 gigs of hard drive.  You can see the carbon fiber dash trim. Pass under seat is very clean as well. No rips, no tears, smells very clean inside this car. And it does have the power sunroof.  Has the pistol grip six-speed manual transmission. Electronic stability program as well. And we'll take a quick look under the hood. I'd personally like to thank you for checking out the video today. Hopefully from this HD video you have been able to tell just how clean this car is all the way around inside and out. I would highly recommend it from a quality and condition standpoint. Under the hood we have the 6.1 liter Hemi V8 motor. Look how clean those strut towers are. Does have a brace on it as well. A BBK cold air intake. Engine bay is very clean, runs very smooth. This car has been fully safe and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off. The car has been gone through mechanically 100 percent and is 100 percent ready to go. To see more pictures of this car, one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, sports cars, you name it, we got it. Go to our website www.summitauto.com. Full pictures and descriptions of every single vehicle we have. From two locations, all at summitauto.com. And if you'd like to check out more HD videos, you can go to youtube.com slash summitauto. Remember to like, subscribe, and share on this video and all the videos that you see there. In fact, in a second you will see a link to subscribe to our YouTube channel on your left. A link to more sports car videos like this one on your right. If you have not been to our website on the bottom, link to this vehicle on our website. Click those, check us out. And we really look forward to helping you with this super clean 2010 Dodge Challenger SRT8. Thanks again.


Why are we called consumers? I get that it's a term of art in the consumer packaged goods business, and I get that they think that the store is the actual customer and that we're just the consumers coming in and out. But if you look in Webster's dictionary, to consume is to destroy often wastefully as in consumed by fire. The thing is dead at the end. It's worthless. It's basically ashes. Now, I don't think that we do that. I think we've never really done that. But now in particular, because we're connected to each other and because we're able to talk to each other and get together, we can actually do things. We co-produce content, you know, all sorts of terms right now about user-generated media or UGM and so forth are hot in the marketplace. But more than that, we're actually talking with each other and we're doing things to better our lives. Now, the old way of looking at us as consumers is actually the language of a military campaign. The language of advertising is just like running a war. You run a campaign against target demographics.  It's it's all a little bit violent. So the other metaphor here is about cattle, the cattle drive, the cowboy and branding and driving traffic. So the cowboy metaphor is in there as well. Neither one of these is about dealing with civilians, with humans, with citizens. And I think what's happening right now is we're in a great rebalancing where companies and people need to sort out that it's no longer company-in-charge inventing mystical products and selling them to consumers by training us with behavioral conditioning. But it's companies making a profit by creating valuable things in conversation with us and often designing them with us and listening to us very carefully and figuring out what this new relationship means. Now that doesn't mean that the call center at Proctor & Gamble needs to call everybody who's ever bought a bar of soap or a box of tide. It does mean that they need to show up as peers. They need to show up more as humans in this environment than as large entities that are kind of mystically behind the scenes and in control. This means transparency. This means vulnerability. This means a lot of other things that are really pretty scary, especially to the legal department. Target and Disney have called these people guests for a long time. Guest is a pretty good word. It implies hospitality. But consumers and eyeballs really not such good words. There's a lot of other good words. Customer and client are fine words. Member, citizen, participant, family, household, student, fan, patient. A whole lot of interesting words out there besides the big C word.