Thanks so much Michael and to all the other organizers. I'm very happy to have the chance to speak here about my work with Steiner and Cagudin on, as you said, the supernorm problem in the level aspect. So we'll begin by recalling some background on the supernorm problem. So just to keep things rather concrete, we'll take M to be a compact Romanian surface and then we'll let phi be an L2 normalized Laplace eigenfunction on that surface and we'll think about what happens when the eigenvalue tends to infinity. So this is a problem in quantum chaos or semi-classical analysis of understanding how big the size of such eigenfunctions can be. So there's something called the local bound due to Horminder and Saga that just takes into account how the eigenfunction behaves in small open subsets of the manifold, which tells you that it's bounded by t to the half, where t again is something like the square root of the eigenvalue. And one way you can think of that that proof, there are a few perspectives on it you could take is that one can understand averages like I've indicated here, where you take t in a window of size a bit bigger than one of the squares of these values rigorously. You can prove asymptotic formulas for them that tell you they're of size roughly t. If you drop all that one term in an asymptotic formula like this, then you recover the bound I've indicated here point wise. So yeah, so this this bound is sharp in some situations. So for example on the two sphere you have eigenspaces where all but one of the elements will vanish at the north pole. And for those examples, only one thing contributes here. So it has to be as big as the bound suggests it could be. But there are some cases for example when M is negatively curved or hyperbolic where it's expected that these these these bounds can be improved. But you know, since this is a number three seminar, we come to the corrupt, which is that the improvements have been made in a significant way, meaning in the exponent rather than just a logarithmic factor, only when the manifold is an arithmetic manifold. And when the eigenfunction phi is also arithmetic in the sense that it's a hexagon form. So there's a pioneering result in the subject going back almost 30 years now, due to invaniation Sarnac. So what they consider is, for example, the modular surface that I'll call M, which is what you get by quotient upper half plane by the modular group. And they take fee to be a cuspital hexagon form. So it'll continue to be a Laplace eigenfunction in the sense of the previous slide, but it'll it'll now satisfy an eigenfunction condition under the heck operators. So this in particular tells you that you can actually determine fee up to a scalar by the eigenvalues that we know about it. So it kind of throws out the multiplicity issue that causes problems when you try to understand the super norm problem more generally. And so assuming these conditions they managed to show the following improvement where you replace the exponent one half by something a bit smaller, something smaller by the fraction 112 up to something that we can take shrinking as to your grows to infinity. So their result and their method kind of kickstarted the whole industry. I mean, I think the last time I checked there were some there's somewhere on the order of magnitude of 100 papers that have cited this and built upon it in various ways. So for example, people have generalized it to the level aspect, the subject of the talk, where you don't vary the manifold, you don't vary the eigenvalue, but you instead vary the underlying manifold. And you try to understand what happens there. Many people have generalized these results to other spaces such as other quotients of more general groups by arithmetic groups. And there are also many results where people don't just bound values of eigenfunctions at points, but instead integrals of eigenfunctions over submanifolds, for example. So it would be kind of impossible for me to summarize, but there are lots of papers that have generalized this in many ways. So this talk will be specifically about the level aspect of the problem, which will kind of say what we mean by in a bit more detail in a second, but the methodology will kind of play a big role in the talk. So I want to kind of pause to explain in some broad strokes what their argument actually was and what that argument is a prototype people have generalized and then indicate very briefly how we're going to kind of depart from that before we go into the details of what the results are. So the argument in a nutshell considers what we now call amplify second moments, which are expressions kind of like what we had on the first slide, where we had a sum over fee with parameter in some window of size roughly one of the squares of its values, both an additional weight factor introduced here that are called amplifiers following the work of Ivaniich and Duke Freelander Ivaniich and then Ivaniich Sarnak. And the idea here is that the coefficient cl are maybe real numbers between negative one and one that can be chosen to kind of conspire with the signs of the eigenvalues of a specific eigenfunction fee that one cares about. And the idea here is that if one can prove an asymptotic formula for an expression like this, much like one could when there wasn't any amplifier, then one has the hope of kind of choosing these signs in a way that conspire to amplify the contribution of a given fee at the expense of some other fees. And so then the asymptotic formula by kind of dropping all but one term and expression would then give a better than trivial bound for the values of that eigenfunction. So to actually make this kind of argument work, one needs a few inputs. So one, for example, one needs to know that these eigenvalues, the Hecke eigenvalues are not all zero for L in the range under consideration. And one needs that in a quantitative form one needs to know that they're kind of all pretty big. And there's a trick that's now standard in the subject going back to some of these pioneering works and application that I mentioned, which is to make use of the Hecke multiplicity that relates the values of the eigenvalues at a prime and the square of that prime. So this identity shows that like you can't have both of them being too small. And then it gives kind of a source of examples of Hecke eigenvalues that are provably bounded away from zero. So that's kind of the main leverage one has to show that these things can be made large. So then, okay, you can make the amplifier large, you're gonna need to actually bound this expression. And this is something you do kind of using, well, using what's called the pre-trace formula that I've written down here, where, so things like on the left hand side are what you get by say majorizing the condition on T by some weight function H that maybe is smooth and big on this interval and pretty small otherwise. And then expanding the square here and using Hecke multiplicity to collapse the Hecke eigenvalues multiplied together into individual Hecke eigenvalues. So the right hand side is what's called the geometric side of the pre-trace formula, which involves an integral transform K defined in terms of H, and then a sum over two by two integral matrices of given determinant, the number n that you're taking the eigenvalue for here. And then K you evaluate on something like the distance between where gamma moves the point Z that you're evaluating in Z itself. So there's kind of some analytic problem of estimating K in terms of H, and then there's some diophanting problem of actually estimating how the various gamma contribute here. So for instance, one needs to understand how many gamma have a given determinant and have distance in this sense at most delta, for various ranges of delta that we should think of as being pretty close to zero. So these are the problems that they kind of introduced and then solved in their paper. And what can we say about this? Yeah, I guess the main thing is that so their paper is 30 years old and somehow no one's managed to improve this exponent since then. So it kind of seems like one runs into a wall here. People have thought about this, there doesn't seem to be so much room to improve here. But there's a good bit of inefficiency actually that comes from having to impose this condition here. So if we knew something a bit more robust about these eigenvalues, like if we knew that they were typically bounded away from zero or something like that, then Avonius and Sarnac even remarked that they could then improve their exponent quite a bit. But we don't know how to do that. So it's kind of an open question to find any way to do better here. So all of these other directions that I've alluded to considering the supernorm problem use kind of the same basic sketch.  And so this is kind of an archetype for a lot of the literature on the problem in many directions. So things changed a few years ago when one of my co-authors, Raphael Steiner, introduced a new approach to this supernorm problem in these arithmetic settings for surfaces where instead of using an amplified second moment like in the previous slide, you consider what would happen if you tried to understand just a fourth moment on amplified. So in some sense, the point of an amplifier is you want to increase the contributions of the bad fees, the ones where the supernorm is large so that you can prove that they don't exist. And the best possible way to do that is just to put the value of fee in there. But then the obvious question is can you actually make sense of the asymptotics of expressions like this? Can you understand them rigorously? So he introduced a technique for doing this kind of in a, and I think what could be fairly described as like a test case not directly related to many of the problems that people have considered previously, where he showed that you can rewrite this kind of fourth moment over a family of eigenfunctions as I've kind of just indicated that schematically here as something like an inner product of a pair of theta functions which you can then maybe hope to try to estimate in some way using geometry of numbers techniques. And I'll go into more detail about what exactly is meant by that later in the talk. And then once you have something like this set up, you can try to estimate individual values by dropping all but one term and just using that everything is positive. So he wrote a very short paper, maybe it was six pages or something kind of introducing this technique and apply it in some some basic example. And a few people or teams of people have applied that technique in the intervening years. So first, the other two of my co-authors, Ilya Kiyudin and Raphael Shiner applied it to the weight aspect on arithmetic surfaces. So kind of like the Avani Sarnak set up where the weight is varying. And so they got a very strong bound there that's now the world record. I guess in the non-compact case, so for example, for SL2Z, it kind of just reproved a record that was already established by a different method. But at the very least, it kind of showed the promise of the technique to, you know, see things differently and also to extend and to compact quotients, things that had already been known for non-compact quotients. So it kind of plays a role substituting Fourier expansions in Shah's argument. And then I've indicated your Blommer-Hakosh Magan-Milisevich recently applied this to something involving hyperbolic three spaces and their quotations for something I just kind of called the K-type aspect. And yeah, what I'll talk about today is a pre-print that went up a couple months ago, I guess, joint with me and Kiyudin and Shiner, where we apply this technique to the level aspect version of the problem. So then what I'll do in the talk is I'll say what I mean by level aspect, I'll state our results, and then I'll try to say something about like what we actually did, like what kind of analysis actually went into making them work. And I should mention that as of now, this technique does not seem so hopeful in attacking the kind of motivating question here where you just vary the eigenvalue. So the Avani of Sarnac problem, it seems very difficult to improve upon that or even to improve upon the trivial bound using this technique, but maybe just some new ideas are needed. Okay, so yeah, with that kind of overview, what do we mean by the level aspect? So for the talk, I'll let M be a natural number that we'll think of as coming off to infinity, and I'll always assume that it's square free. So I guess natural numbers kind of come in two extreme classes. So they're the square free runs or maybe the primes, and then they're the ones that are powers of fixed prime. So for example, two to some large power. For the latter examples, it turns out the supernorm problem is a rather different flavor that is kind of more closely aligned with the spectral and holomorphic aspects that I indicated previously. And there's a whole different discussion that, you know, many people have worked on. So it's a particular Abhishek Sa'a and Yuki Hu of many papers going in that direction. So here we're going to take N to be square free. You can think of it as just a prime and you won't lose anything for the talk. And we'll let M be the quotient of the upper half plane by the standard congruent subgroup Gammonata then. So this is a quotient whose volume grows something like N as N tends to infinity. We're going to assume as before that Phi is say a Laplace eigenfunction, Cuspital now defined on this varying manifold M. I'll always assume that it's again a Hecker eigenform. I'll further assume it's a new form in the sense of academic letter. And I'll assume that the eigenvalue is kind of bounded to some fixed window. So if we kind of fix an advance, I'm bound on the eigenvalue and we require it to lie in that window as the level N varies. For the sake of normalization, I'll assume now that the L2 norm squared is equal to the volume of the manifold. So what this says informally is that on average in an L2 sense, the values of the form are one. And that's a convenient normalization because it motivates what I think is the folklore conjecture, which says that the L infinity norm should likewise be bounded by something like one or something that grows very slowly within. And that's to be compared with the analog of the local bound that can be again proved pretty easily using a pretrace formula of into the half. So just like in the eigenvalue aspect, we have some gap to bridge between the trivial thing where the exponent is a half and maybe the optimistic conjecture where the exponent could be say zero. So yeah, many people have worked on this question. So I guess Avonius Sarnac was in 1995 and the first improvement on that, at least the publication date is 2009 by Blomer and Holowinsky, where they improved on the exponent by the fraction one over 37. And yeah, they introduced a lot of new ideas into the into the subject. So in particular, unlike in the eigenvalue aspect, in this aspect, they're kind of much more serious diophantine considerations that go in. So it matters a lot whether, for example, the real part of the point that you're evaluating at as well or badly approximable by rational numbers, they give different arguments according to the two cases. But I guess the basic prototype of the proof, so the overall method was like in Avonius Sarnac, and that's the case for all these results here. They all use an amplified free trace formula, but they came up with kind of better and better ideas to handle the diophantine analysis, or perhaps to construct the amplifier, and then to do all the necessary counting. And eventually the exponent kind of shrunk down to one sixth, which you can think of as kind of one third of the way from the trivial bound to the optimistic bound. And it might remind you of some other natural barriers in in analytic number theory. So for instance, in the subconvexity problem, a third of the way from convexity to lindelaw through the zeta function is what's called the vial bound. And that's kind of known as like a very hard bound to improve upon many people have, but still just by a little bit. And there are many settings where something like a vial type bound is the best known, and it kind of feels like a natural limit. So okay, I've emphasized again, all these results use this second moment amplified approach of Avani of Sarnak, improving the diophantine analysis that goes into that method. So yeah, so Steiner, Cajunin and I tried looking at this question using the fourth moment approach. And we didn't really know actually whether it would have any chance of succeeding, because by then we had seen that, okay, it succeeds pretty well in the weight aspect. It seems to fail pretty miserably in the spectral aspect, the eigenvalue aspect. Level aspect for square free levels is kind of intermediary between those two aspects in certain respects. So it seemed for about six months that it was definitely going to fail, but we at least had the hope of kind of coming up with a good reason why it would fail in the level aspect that maybe we could, you know, write up and share with people and say, hey guys, you know, here's something to maybe try to find some new idea to improve upon. Then we ended up actually making it work, so that was nice. And so what we get here is a further improvement from one sixth up to one quarter, which is exactly halfway between the trivial bound and the optimistic bound. So we were quite surprised that this actually worked out. Well, it's a preprint you guys can tell us if you believe that it worked out, but okay, we do. And yeah, it's kind of a rare thing. Like I mean, for example, for the zeta function, this would be kind of like proving a bound of t to the one eighth, that's which is kind of hopelessly out of the questions. This is a situation where you apparently can prove kind of halfway like that. And yeah. Okay, so that's the result that I'll try to say something about what went into the proof of in the remainder of the talk. As you mentioned, maybe a little bit about like a little bit more about why people care. So I've indicated here a few applications kind of a bit a bit internal to the subject. So for example, you can interpolate this L infinity bound with L four bounds proved by other people to get better LP bounds in general. You can make Wolfin's estimate for twisted additively twisted sums of Hecker eigenvalues quite uniform with respect to the the level of the eigenform. You can improve certain sub convexity estimates in some cases. So some people how in Chen had proved a sub convex bound in some kind of hybrid twisted case conditional exactly on the super norm bound that we're considering here. So just by plugging in our new exponent to the result, you get a better result in in their setting. And then one of my co authors has applied this to improve the known bounds and the diameter of certain arithmetic hyperbolic surfaces. Okay, so maybe that's that's it for now on applications. Yeah, before I go any further, are there just any questions on kind of what we're doing, what the result says, anything else? Peter, I have a question. If you take the sort of the attic quotients instead of this continuous question, so you'd get a graph, and there are a lot of people in studying their infinity norms of graphs. So I assume your results applied there and give all, you know, these Ramanujan type graphs some bound. Have you worked that out? Yeah, that's a good question. So the answer is yes. And it'll be in fact on the one of the slides coming up. Okay, thanks. Excuse me, just a follow up question. Does it give any bound on diameter of Ramanujan graphs? So I think what he observed is that it gives the bound that follows from Deline or Eichler or whatever, but without appealing to that. So it kind of recovers two times log of some, so it recovers the same. It recovers it, but it gives a proof that doesn't need that. For example, for some reason, we want that. Paul, I had a quick question. Sure. The folklore conjecture you mentioned, enter the epsilon bound. I seem to remember that there was a paper by Tompley that in some setting that's not true. What was that? Yeah, so the setting would be if you, for example, you allowed non-trivial central character. So if you work with Gamma 1 of N, then their examples were kind of the most optimistic thing would fail. Was that enter the quarter that he got? That sounds, I'd have to think to remember, that sounds kind of, no, I think it might have been bigger than that even. I don't want to kind of be wrong, but that happens for kind of well understood reasons related to the Fourier expansion and kind of behavior near the cusp. It's like one term kind of contributing to the Fourier expansion in certain regions or something kind of of that flavor. And that just doesn't happen for the class, for the example we're considering here. For Gamma 1 of N with N squared for you, that kind of thing won't happen. I just thought in case it's a quarter, then I was going to ask, are you proving the best possible in that setting? I don't remember. That's a good question. I seem to recall it being a third. Okay, if you want another coincidence though, so the analogous estimate over a function field was proved essentially by Will Sawan a couple years ago where, so what he proved is that you could take delta to be something that tends to zero as the cardinality of the underlying finite field tends to infinity. So at least if p is sufficiently large, you get something kind of of that shape. But for each individual value of p, it seems likely that one could probably adapt our proof to the function field setting and then give a better bound there. So maybe that's one example where kind of the two bounds kind of match up. So what he gets using a lattice homology and all that versus what we get by just averaging. Okay, so yeah, so I've indicated already in my response to one of these questions that there are results holds a bit more generally. And I mean, I would have been happy just for the sake of kind of giving an informal talk to present the proof in the case I already described with gammonadevin. But as it turns out, the proof is a bit simpler to describe for a different specialization of the general result. So I'm going to state the general result and then I'm going to specialize it in a different way in a way that makes the proof it easier to go through. I think, I hope at least. So what's the more general result? So it's going to concern a quaternion algebra over the rational numbers. So these are classified up to isomorphism by their discriminant that I'll call db, which will be some square free natural number. And a good example is if B is the algebra of two by two matrices, then db is one. That's kind of the example relevant for what we have been talking about so far. So in this example, you can define trace and determinant maps, taking values in the rational numbers that satisfy a bunch of natural properties. And I mean, if you don't know what quaternion algebras are, they're basically algebras that have analogous maps satisfying analogous properties. So they come in a couple flavors according to what happens when you extend scalars to the real numbers. So when you do that, you either get the two by two algebra real numbers, that's called the indefinite case, or you get Hamilton's quaternion algebra, which is called the definite case. And in that case, the thing we've called determinant, which is maybe more traditionally called the reduced norm, defines a positive definite quadratic form on B. So something that looks in suitable coordinates like sum of four squares, unlike the determinant on the two by two matrix algebra, which is a signature two two form. So that's some kind of indefinite. So for some arguments or for some definitions, really, it'll be easier to switch to the indefinite setting. Sorry, switch to the definite setting. So next, we're going to again, let n be a square free integer tending to infinity, co-prime to the discriminant. We'll choose an Eichler order of level n. If you don't know what an Eichler order is, you can just focus on this example where it's kind of the order, meaning a ring of rank four, where it looks like this. So an Eichler order in general is something that kind of locally looks like this when reduced modulo n. And then instead of our manifold hyperbolic space modulo gammon out of n, we'll take an adelic quotient of this shape defined using the adelization of the Eichler order and some copy of SO2. So again, if you don't know what adelic quotients are, don't worry about it. Just think about this example. This is kind of the general way to reproduce that example. But then coming back to Peter's question, as Peter knows, and as many people here know, these quotients in the definite case I provided you further quotient out by SO3, we'll give these finite Ramanujan graphs. And so some of the eigenfunctions we consider will be eigenfunctions on those graphs and we'll be bounding the super norms of them. This is some kind of generalization of both certain hyperbolic surfaces and certain graphs are kind of more generally, I guess in the definite case, this would be a union of spheres, finally many, which you can think of as vertices in a graph. Yeah, and if there are any questions on notation or anything for anyone, just please feel free to jump in. I don't mind being interrupted as I go. So, okay, we'll fix some kind of cutoff t that'll bound the eigenvalues of things involved. That'll be independent of n. We will let script F be an orthonormal basis of, again, Hecola plus eigenforms V on our manifold M with parameter bounded by T. It'll be convenient just to kind of simplify writing to introduce the notation V for the product of these two numbers, which is pretty close to the volume of these manifolds with respect to the natural Hermannian metric. So we'll think of V as kind of the main parameter going off to infinity. And then the main bound will prove is, okay, whatever point you choose on your manifold, the fourth moment of that over your family is bounded by a bit more than V. And this is kind of something you'd expect to be basically best possible. So we normalize things in the same way as before, so that on average, in an L2 sense, third size one, the family will then have size roughly V because we've kind of chosen a bounded spectral cut off and the volume is growing like V. And I've only stated here that the main estimate we prove in the compact case and in the non-compact case, we have some additional terms that kind of blow up as G tends towards the boundary. But near the boundary, we have other methods using just the Fourier expansion that'll give good bounds. So in all cases, we get the very clean result that the L infinity norm is bounded by the volume of the quarter provided you have fixed spectral cut off. So in particular, in the case that B is the matrix algebra, this is just this congress quotient of the upper half plane and we get 10 to the quarter like we stated earlier. Here's the minor remark. I mean, everything that I stated here works also in the weight aspect where you don't take Laplace eigenforms but polymorphic things. And in fact, in that aspect, we can kind of make the whole thing uniform in the weight and we get a bound that depends on the weight like K to the fourth, which is optimal and that we're kind of best known in that respect as well. In this Laplace eigenform aspect, kind of the best we seem to be able to hope for is to recover the trivial bound with respect to the eigenvalue. Okay, so that's the result that we're going to present the proof of. Are there any questions on that? So improving this quarter would directly improve the diameter bound? Oh, that's a good question. That sounds kind of believable. I mean, I don't know if Rafael's here and wants to answer that. I mean, I'm sure he's thought of it, but I think the answer might be yes on that. I see. So somehow it's a barrier reason, like if you correct this. I think so. Don't take my word on it, but you can definitely look at Rafael's preprint and I think he answers that. Sure. Thanks. In the introduction. Yeah. Okay. So the overview of the proof, we're going to find some theta function kind of in the spirit of things defined by Shimizu, but we'll call capital theta. It'll live on Gammonot of V. So Gammonot of V is the standard congruence thing of level the product of the discriminant and N. And it'll satisfy something like the following identity. So the fourth moment that we want to estimate will be the ultra norm of this theta function. So if we want to estimate the fourth moment here, all we got to do now once we prove this identity is estimate that norm of the theta function. Of course, it's not obvious that that's any easier, but it's something new to play with. So we're going to try to just get our hands dirty and understand anything about this norm of the theta function by integrating over over Ziegle domain. So we'll say, recall what we mean by that. And that'll eventually reduce the problem to some counting problems of two types, what we'll call type one and type two. And then we'll solve the counting problems. So as it turns out, the type one counting problems will be pretty close to things that already showed up in this table of records that I had here when people, you know, optimized to this amplified second moment approach to this ignore problem. So maybe the main new ingredient will be the kind of type two bounds, but there'll also be some new things just in the type one treatment. But first, I'll say something about where this basic identity comes from to make it believable. So it's going to come from the pretrace formula, just like the study you've amplified second moments did, but in a slightly different way. And to present the proof as simply as possible, I want to go to the setting where the pretrace formula itself is kind of as simple as it conceivably can be. So I'm going to take B to be definite. So then this determinant form is positive definite. And so all of the fibers of that form on this order are will be finite sets. So I'll call those fibers are then that'll be the elements in our Eichler order with determinant and that'll be some finite set. I'll also take the argument of the eigenfunctions, which we bound them to be the identity element of this adult quotient. Just for notational simplicity, we can always reduce to that by conjugating things a bit. And then I'll take the cutoff to actually be zero. So what this means is that the kind of parameter here the plus eigenvalue will actually be zero. So I'm considering things that are harmonic, which means that they're actually constant on the spheres. So we can think of them as functions on these finite sets on these finite or monogen graphs. And so in that case, the pretrace formula has a very, very, very simple form. So the left hand side is just the average of the Hecker eigenvalue weighted by the square of the value. The right hand side is just up to normalization, the number of elements of norm n in the Eichler order. That's quite simple. And then also that the definition of the Shimizu theta function in this setting is a bit simpler, because in general, theta functions are easier to define when you're attaching them to positive definite quadratic forms than indefinite ones. For indefinite ones, you're always going to have some major in the background introduce. So here it's just kind of a standard theta function like in the first course in modular forms, where the coefficients are the number of elements of determinant n in the Eichler order. So this will define a modular form of weight two on gamma naught of v. And so the identity will come down to relating the pretrace formula to the Shimizu theta function. And you can kind of see the relation right away. I mean, the first is the Fourier coefficient of the second.  So let's just see how that goes real quick. So we need one more ingredient to explain it which is the notion of Jacke Langlands or Eichler Shimizu lifts of our eigenfunctions phi. So these are modular forms now on gamma naught of v that you get by just taking the series expansion attached to the Hecke eigenvalues of your given form. So it's kind of a theorem proved by the authors indicated above using a comparison of trace formula that this actually defines a modular form. And moreover that any two modular forms you get in this way are orthogonal to each other. So this is one of the ways that the multiplicity one theorem for these compact quotients can be proved. So we're going to use that in the following very serious way the orthogonality of the Jacke Langlands lifts attached to our forms. So they're basically orthogonal and then the inner product is roughly the volume of or the co volume of that group which is something like v. It's given more precisely by an adjoint L value whose size is known to be pretty close to one. All right so that's where we've used the multiplicity one and we've defined these Jacke Langlands lifts. So there's a basic lemma one can now write down which says that this Shimizu theta function can be written as a weighted sum of these Jacke Langlands lifts where the weights are kind of the numbers that we actually want to bound at the end of the day. And the proof is very simple you take the pre-trace formula you multiply it by e of nz and then you sum over n. So I've written down the pre-trace formula here I've multiplied it by e of nz on both sides and then I've summed over n. On the right hand side we get these Jacke Langlands lifts on the left hand side we get this Shimizu theta function and it's then the lemma pops out. Now finally if you take this lemma you can use it to try to compute the inner product of theta against itself. You expand that first as a double sum over forms in your family of these inner products but we already mentioned that these inner products detect kind of the diagonal condition and so then you end up just getting basically this fourth moment of values of the things that you're interested in up to some normalizing factors. So that's the basic identity so you see that we've kind of used the the pre-trace formula and the multiplicity one theorem in a very serious way here. And after all that the whole point of or what remains is just to prove this bound for this elton norm of the theta function. So there are any questions on on that? I imagine this was kind of fast but I hope it maybe just gave a flavor for like what actually goes into the argument what the inputs are. So if there are no questions I mean kind of where we're going now is we're going to reduce to this kind of probably abstract seeming thing to some concrete counting problem which we'll then talk about in the rest of the talk. So one very very minor caution is that as I've written it these integrals are actually infinite because there's a non-custodal contribution that I haven't indicated in each of these steps. So one can either regularize things by subtracting that contribution or one can work with the differences between two different values a study sums like this instead and these sums are adequate for proving these fourth moment downs. So I'm not gonna I'm just gonna kind of ignore this technicality going on and what I'll explain now is how to actually how we actually try to bound these expressions. So theta is on some quotient like h mod gamma not a v and that quotient so I copied from I think Diamond and Sherman's book via math stack exchange the following image of a fundamental domain for that quotient.  So the way you do it is you kind of you know I guess for the part near infinity you cover it by what's called a zeal domain this thing that I drew a picture of here in red which has the advantage that when you integrate along the horizontal contours you can use use parsable's identity to simplify the integral quite a bit and express it directly in terms of the Fourier coefficients of theta and then you need to do something similar for all these other regions near the cusp zero and you can understand how theta looks there by using for example Poisson summation to work out its Fourier expansion yet. So it turns out that if you kind of try doing this naively okay you'll reduce some counting problems but they turn out to be kind of at least as far as me and my collaborators are concerned very difficult so we couldn't see any way to broach them. So it turned out that like the contribution from this part of the fundamental domain near infinity was quite easy to bound but the remaining ones were quite difficult. So what we needed to do to make things work was to kind of balance out the fundamental domains in a way that makes this this part a bit harder and these parts a bit easier and at the end of the day we found a pretty efficient way to do that which is just to take this standard covering by little fundamental domains for SL2Z and apply the Frickin collusion to it and then after having done that apply zeal domains to the parts of the cover that we get and then unfolding this integral by integrating along each of those. So that was one of these um that that was maybe one kind of at least relative to our ignorance like one novelty in our argument and I don't want to kind of bore you with like ways that one can go wrong in trying to prove this theorem but okay once one has that idea which which turns out we believe to be on the right track the problem reduces the counting estimates. So the counting estimates are for example of this flavor so these numbers are of annual recognize as the Fourier coefficients of theta so it shouldn't be too surprising that they show up in the estimates that we need when we try to unfold an integral like that and we need to know for example that the sum over n up to x squared of the square of the number of elements of our Eichler order of determinant n is bounded by maybe a bit more than x squared so this notation will mean maybe up to some v to the epsilon coefficient and we need this in a range for x going up to about the square root of the volume so um yeah I'll try to get a little bit of a sense of like why this is not like a completely trivial problem after giving a preliminary reduction of it. So the preliminary reduction is that so these orders they have a kind of boring part which is the part given by the integer z and the orthogonal of that boring part is the traceless part that'll call r zero so it's the elements in the order of trace zero and this direct sum is pretty close up to some factor of two let's say to the order itself so pretty much any accounting problem involving an order r can be reduced to accounting problem involving the traceless part which is the more interesting part and so when you actually try you know breaking up this sum which is counting pairs of elements of r in terms of now quadruples of elements where two of them are in z and two of them are now r zero there's a pretty straightforward way to use the divisor bound to reduce this kind of estimate um using this kind of and using this kind of inequality to estimates that now just involve the traceless part of the iCover so sigma one is a first moment of cardinalities in the cycle order and sigma two is a second moment so these are what what we call type one and type two estimates we need to show that each of these are bounded basically by about x I mean just to just to think for a second about what that what is that actually saying so the number of numbers n up to x squared is roughly x squared and each of these cardinalities are integers so we're trying to show basically that at most roughly x of these cardinalities are non-zero in the first place and whenever they're non-zero they're bounded by basically one and if you think if you think about what a first and second moment down together like this are kind of saying that's that's more or less the content um so there's not a lot of room to kind of prove a bound like that if you mess up a little bit as you try so um I guess we could get by in the non-compact case a bit more simply for both of these problems by using very explicit analysis of coordinates but to get this um this bound in the generality we have it where it works in the in the compact setting where you don't have quite natural coordinates in your iCover orders and we're actually you can you can even vary the underlying quaternion algebra so the discriminant can vary freely um we didn't see too many ways to do this other than the kind of systematic way that we eventually found so um for the type one estimates I've already mentioned that like these were basically treated in existing literature on the supernorm problem via arithmetic amplification so Blommer and Michelle wrote a wrote a paper proving this delta equal one sixth estimate in the definite quaternion algebra case where they proved this this bound for the type one estimates or what will they implicitly prove something like this um which is adequate in the range that we need it um and it's approved using things like Minkowski theory and some kind of explicit estimates for the successive minima of our iCover order equipped with the determinants one so the only novel thing that we do related to type one estimates is that we give analogous estimates in the indefinite case which um I guess could have been could be used retroactively to prove the one sixth bound in the compact indefinite case which hadn't been done apparently um and I mean I mean there the statement is just that kind of the same bound holds if you replace the determinant by any majoring for it so we put some work into formula even just into formulating kind of what the replacement is and then we adapted the argument so those are the type one estimates so it remains to kind of treat these type two estimates which I'll try to give some flavor for it so the first the first observation is that the type one estimate follows from the type two estimate assuming you can prove the following thing that I call a fiber bound which is just that for all n in the relevant range these numbers are basically bounded by one so maybe bounded by v to the epsilon that's what I mean by this notation right because then you know the type two estimate is the second moment but if we bounded all of them individually by roughly one then we can reduce that to the first moment and then that gives an adequate bound so um yeah I guess the main the main thing the most difficult point was just to find a way to prove this individual bound show that for any n up to roughly the volume the number of trace zero elements in our Eichler order of norm n is basically bounded by one so if you want to really stupidly simple example of what this estimate means in a case where you can't really see what's going on but just to give some flavor so the whole subtlety here is really that the Eichler order r is actually varying it depends upon the discriminant it depends upon the level n but maybe we if we took r to be the Hamilton integral quaternions for simplicity this will be saying that if you look at integral points in free space just look at z three in the standard way it ends up saying something like that the number of integral points so I guess this is kind of an Archimedean analog of what we're saying here but it would say something like the number of Archimedean the number of integral points in a ball of radius one is basically a big O of one so it's not a very impressive sounding statement but we're kind of trying to prove some kind of distorted analog of that here that's roughly what we're looking at and so let's hope and maybe to end a bit early but I said at a lot of times so I'll say at least like kind of the input of the proof for the fiber bound so so the main thing that we use in the end is that if we have two elements in our Eichler order then we can take their commutator and the determinant of that commutator always satisfies a very strong congruence condition so maybe it's simplest to just look at this example here where we have the matrix algebra and our Eichler order consists of things like this that are upper triangular mod v well when you take the commutator of two things that are upper triangular mod the the result will be null potent mod v and it's pretty easy to see that the determinant of anything here is divisible by v so this turns out to be a pretty robust observation and the way we apply this is to show that if we have one element in the set that we're trying to bound say gamma one then all of the products that we get from other elements in that same set actually lie in some set of cardinality one so I just say set s of cardinality one that contains all these products so in some sense we're using one element and then this kind of strong condition on the commutator with any other element to eventually show that those other elements have their products with a given element highly constrained and hence those other elements in turn are quite constrained so um yeah I have a final slide that just gives the argument for anyone who really wants to see kind of the details of what we do it's it's quite a simple argument at the end of the day but I thought just I would conclude now just by summarizing saying that yeah we improved on these bounds in the little aspect using fourth moments over families studied by norms of theta functions and counting problems and then it's worth just remarking that it's it is still open to improve upon this avanias sarnac bound in the eigenvalue aspect and we don't even know how to actually improve any improve on the trivial down in that aspect using this method and with that I will thank you guys for your time and I think we


Hey everybody, it's Tossos with RF elements. Have you ever wondered how antennas work? Have you spent countless hours wondering how noise affects your network? Maybe you're wondering what makes antenna A better than antenna B. We're surrounded with wireless lingo every day with terms like side lobes, front to back ratio, cross pole isolation, V pole, H pole. What does all this stuff really mean? Well, watch our upcoming video series inside wireless and learn more about how these things work and how they affect you.


Hi and welcome to the session. I am Asha and I am going to help you with the following question which says Prove the following, sin square 6x minus sin square 4x is equal to sin 2x into sin 10x. So let us begin with the solution and we will solve the left hand side of the problem and show that it is equal to sin 2x into sin 10x. So left hand side is sin square 6x minus sin square 4x. Now this is in the form of a square minus b square whose formula is a minus b into a plus b. Thus this can further be written as sin 6x minus sin 4x into sin 6x plus sin 4x. Now let us learn two identities with the help of which we will solve. First is sin a minus sin b is equal to 2 cos a plus b upon 2 into sin a minus b upon 2.  So with the help of these two identities LHS can further written as a plus b are a 6x and b is 4x to 6x plus 4x divided by 2 into sin 6x minus 4x divided by 2. Now opening the second bracket which is sin 6x plus sin 4x it can be written as 2 sin 6x plus 4x upon 2 into cos 6x minus 4x upon 2. This is further equal to 2 cos this is 10x upon 2 is 5x into sin 6x minus 4x is 2x and 2x divided by 2 is x. Now solve the second problem which is 2 sin 5x into cos x. Now this is in the form of 2 a into sin a whose formula is sin 2a. So we can write it as 2 cos 5x taking this 5x here that is we are rearranging these terms such that we get it in the form of 2 cos a into sin a and here 2 sin x into cos x. Now applying this formula now here a is 5x so it can be written as sin 2 into 5x and this bracket can be written as sin 2 into x which is equal to sin 10x into sin 2x which is the right hand side. Hence we can say that sin square 6x minus sin square 4x is equal to sin 2x into sin 10x hence proved. So this completes the solution hope you enjoyed it take care and have a good day.


Our first finalist on the on the Android side is going to be Philip Larson from the Department of Informatics here at the University of Oslo. And thank you. Welcome. He's gonna have seven minutes. So it's kind of brutal, but hopefully he can hopefully he can do it. I'm sure that he can. And then we'll have two more Android finalists following him. And whenever you're ready, take it away. Thank you. Yeah, hello. My name is Philip Larson. I'm a former master student here at the University of Oslo. And today I'm going to present the cold chain monitoring application, which is a sensor based application using the drives to capture app. So I was fortunate to pilot the project in Sambesa in Mozambique, where we implemented that for health facilities, providing tablets to help facilitate the workers and training them using the application for digitizing a manual temperature reading process. So the problem with cold chain monitoring is that people are vaccinated with vaccines that may be unsafe due to insufficient temperature during storage and handling. As immunization programs grow, the complexity increase and the need to strengthen components like cold chain monitoring and logistic management is critical. And the unit cost of vaccines has increased from $1 per child in 2001 to about $28 in 2014. So therefore poor vaccine handling can have significant financial consequences. So how can the cold chain monitoring improve control? This is the current cold chain monitoring in Mozambique, a paper based solution. And we are using a digital Bluetooth sensor to monitor temperatures. It's portable, providing use case where you can bring it to vaccination campaigns and rural vaccination and application prompt real time alerts and provide historical data for analysis in the GIS to recording in progress. Okay. Nice to know. So how do I remove? It's not showing on my screen. Okay, 30 seconds. So the digital solution is two parts. It's the hardware, the Bluetooth sensor from Blue Maestro with the battery lifetime of two years. It costs $35 and when you purchase it, it's no subscription or additional costs like other cold chain monitoring solutions and it's fully waterproof. And then there's the application, which is a custom Android application using the Android SDK and tracker capture to store temperature readings locally in a database, providing local alerts, of course, functioning offline and exporting of the temperatures to a CSV file, just in case. So you can see the temperature flows from the sensor captured by the Android application. And then when you have internet connection, you can upload temperature readings to DJI's to servers, providing analysis for decision makers. And now I'm going to show a demo of the application. So the first thing you do is logging into your DJI's to instance, granting access to Bluetooth and location. And then you synchronize your tracker program metadata and data. And you can start this selecting one it automatically connects to it. And then you can see the current temperature minimum maximum average last 24 hour and you can collect temperature stored in the local database. Further the graph will update when you read things arrive. So the application automatically listens to changes of temperature. And then you can capture. You can see the database, the local database, which are going to and you can set threshold for the alerts with a minimum and maximum threshold. And if you're above or below it will send a local notification. So health workers can improve. You can export the local database as a CSV file. If you lose something so you can upload it manually. And you can also clear the database if you want to have a clean sheet. Lastly, by pressing upload, the data will be uploaded to a tracker program on a tracked entity instance and store the temperatures as events in the DJI's to so you can use data visualizer to visualize the data. So. Thank you. The goal of the cold chain monitoring app is to reduce the number of spoil vaccines to improving temperature control during storage and handling and reduce complexity by introducing cold chain monitoring as a support for DJI's to platform ecosystem and increase the global health and immunization by reducing number of spoil vaccines with a cost efficient cold chain monitoring application. Furthermore, the scaling and further developer development of the app is that the Android team is recruiting the dedicated LMS developer. And this will be one of top two priorities for his Bellamy's team in Oslo. Mozambique is also interested in extending the pilots and application will search for WI show PQS. So thank you so much to the team to start digital to his Bellamy's and thank you for your attention. Thank you very much. Next up, we have. Yeah, sorry. Next up, we have David from JSI. Presenting another Android application. Good morning. Good afternoon. Good evening. I'm David Boone from JSI and the PMI measure malaria project. I'm here to present a new tool, an Android app that we have designed to measure data quality at health facilities. Particularly those, the data in source documents, the client register, client encounter forms, et cetera, those data that are then aggregated and reported up monthly according to precise indicator definitions. This is often an aspect of data quality that is overlooked because it requires a visit to a health facility. So data quality assurance is important. I think we'll all agree. But let's face it, it's no fun. I wouldn't think of it as like housekeeping. No one wants to do it, but if it doesn't get done, things get pretty funky. It's often done by large health facility assessments on a sample of health facilities, which are expensive, so they're infrequent. Sometimes this is done more frequently, more routinely, for example, as part of health facility supervision. For its often lack coordination in terms of what is being assessed, how it's being assessed and when, with little possibility of deriving global conclusions for improvements. Measure at measure malaria, we created the MRD QA in Excel, and we've been using that for a couple of years in PMI countries to good effect. We took the decision to adapt this to Android to facilitate the use of the tool and aggregation of data to subnational and national levels. This way we can compare results at facilities across districts and over time to get a better idea of where the problems are occurring. The app comes with a DHIS2 configuration package, i.e. metadata and dashboards to facilitate the visualization of results. We think this more coordinated and standardized approach to routine data quality checks will yield more efficient targeting of resources for data quality improvements. So let's look at the app, and this is a live demo, so bear with me. First go to the menu, and we would need to configure the app for first time use. You can see here we are connected to a test server at JSI. Come over here, you can see the name of the data set that we're connected to on the DHIS2. You'll see throughout the app there are information icons. If we click twice, we can get more information about the screen we're looking at. And importantly, on this tab we can see the supervisions that have been saved to DHIS2. And this permits us to standardize the approach across supervision teams across facilities and across districts. It is using the same configuration of the app in the same supervisory period, and we can get comparable data. So you see here the two configurations that we use for our pilot tests in Sierra Leone and Cote d'Ivoire this month. If we go to here we can see we can pull down health facilities and indicators from the DHIS2 and add them to the local device. Looking for indicators and data elements as well. Here we can take a look at what's already on the local device in terms of facilities and indicators. So having configured the tool we can go plan a supervision. We can add a new one or we can look at one that existing. We see the name and the reference period for the data quality checks. We can push that to DHIS2 or we can edit it. Here we can see the reference periods selected. We can select reporting periods for accuracy checks, and we can select metrics for the supervision. We don't have to do them all every time. Okay, after having planned the supervision, we can go to data entry. We select our supervision. We select the health facility, and then we can enter data on completeness and timeliness, completeness of data sources and data elements. We can enter data on accuracy. This is the monthly values recounted compared to the value in the monthly report and also to the value in the DHIS2 for the same reporting period. This allows us to calculate a verification factor, which is an indicator of the accuracy of reporting. We can also add reasons for discrepancy. Why was there a discrepancy if one was found? We can also conduct cross checks, which is a comparison of different data sources with similar data, such as the malaria case register against the laboratory register. We expect that the data in there for the same period would cohere. We can conduct consistency checks, consistency over time in terms of annual consistency, the current month data against the same month last year, or the current month data against the average of the three preceding months. We can also conduct a system assessment, which is a qualitative look at the reporting system at the facility or all the elements in place to produce good quality data or not. And then having entered all the data, we can go to our dashboard and for that supervision and that facility, we can check the result of the cross check, the verification factor for the accuracy check, reasons for discrepancy, and then reporting performance and readiness to produce good quality data. We can also export that to DHIS2 or to a CSV file. So I know you're all thinking, where can I get this app? I'm sorry to say it's not quite ready. We just pilot tested two weeks ago in Sierra Leone and Cote d'Ivoire. It worked pretty well. We did find some bugs. So we will be addressing those in the next couple months. We will be developing guidance for setting up and using the tools in countries. And then we'll make that available in the DHIS2 app repository and Google Play Store. We will send around a notification on the community practice for when that's ready. We believe this app will improve coordination of data quality checks and the use of findings for data quality improvement. But there are no shortcuts. Data quality is hard. It still requires commitment at national and district levels to collect the data, track results over time, and develop and implement interventions to improve data quality. We see big potential for use of this in other health and disease programs because the indicators are practically incidental to the app. They can be easily swapped out. And with that, thank you. Thank you very much, David. Next up, we have Vincent Minda from the University of Dar es Salaam. David, I think maybe you moved here. Good afternoon. Yeah, so my name is Vincent Minda. I am a lead software developer at the University of Dar es Salaam, DHIS2 lab. Yeah, if it's one skill that I've had to learn ever since I came to Oslo is to cram down a complicated scenario into seven minutes. I mean, I'll try. Let's see if I've mastered the craft. Yeah, so I'm going to talk about an app called EID Salaam. I think some of you may be aware of an integrated disease surveillance and response mechanisms around different countries where there is sort of you have to track whenever there is an outbreak and things like that. You have to track the occurrences of diseases before they break out into uncontrollable scenarios. One example could be COVID, for example. Yeah, so I'm a geek, so I'm going to start a little bit with the design. Some of you may have already heard about DHIS2 Touch, which is a standard developer SDK. For those one of the geeks, I'm sorry about that. But it's just an SDK to help you create apps on top of DHIS2 in an easy way. And we have created it in Flutter, which is an upcoming UI framework and things like that. So for those geeks, we'll understand what I'm talking about. So we've had to sort of create a mobile app to sort of monitor diseases in Tanzania called EID Salaam. And as of now, for those who are familiar with EID Salaam, there is the indicator-based surveillance where you look at certain indicators which allow you to know what is going on in the ground before diseases can outbreak. But there's also event-based surveillance, which is based on various events that are happening in the community and things like that. The EID Salaam implementation in Tanzania started a while ago where we used certain technology called USSD, which had a lot of challenges in terms of, you know, that's too complicated. I don't have seven minutes. Yeah, but there were a lot of challenges to a degree that we decided that maybe we should go with a mobile app. It will probably help us with, you know, reporting diseases on time and, you know, providing an easy mechanism to respond to those diseases. The second advantage actually is something that we are trying to standardize the EID Salaam. As I said, we've implemented it in Tanzania as of now, and the second implementation is going on in Zanzibar. And what we are trying to do is actually standardize the entire process of disease surveillance. And our vision to a degree is we want to standardize the process to such a degree that if we didn't know about COVID and it happened today, you should be able to customize DHS2 within three to five days such that you can start surveilling the disease within those three or five days. So that is the idea of the standardization we're doing in this EID Salaam mobile app. One of the advantages is the cost reduction based on what we used to do before that. At least for now, the previous technologies were a little bit too costly in terms of the implementation. So this was also built to resolve that. So, and as you can see there, there is also MCBS, which is basically malaria case-based surveillance. This specific to malaria, which is just one implementation that has been done in Tanzania. But the idea is that if there is a malaria case that has happened, it will be reported through the IBS, which is the indicator-based surveillance. And then after that, there will be a trigger to follow up on such malaria cases so that they can ensure that an outbreak does not happen or something like that. So, yeah, so I was going to go a little bit into the features, but I would prefer to sort of, given the time being, I prefer to go directly to a simple demo. This is the app and you also have to enter a code. There were some sort of data needs, data-private needs that were needed by the minutes. So, yeah, so with the indicator-based surveillance, by the way, there is indicator, as you saw, there was IBS, EBS, and STBS. The EBS is still in development in Tanzania. And yeah, so the IBS is implemented already in Tanzania. It's now implemented in Zanzibar. The EBS is still under development in Tanzania now. And with the IBS, as usual for those who know, it is usually weekly reporting and the immediate reporting. So, the Android app basically, as of now, you can sort of report weekly on the various diseases that were chosen to sort of be monitored by the IDSR. But you can also produce immediate reports, reporting immediately for those diseases that need immediate attention, for example, COVID or Ebola and such kind of diseases. So, in the app, we have a little bit of a summary. I'm going to pick here the date. Oh, one minute. Jesus. Okay, so there is a little bit of a summary of the COVID cases that somebody can look at. There is also the functionality of notifications. In IDSR, you really need notifications so as to address any upcoming outbreaks, things like that, you need to do that pretty fast. So, we have to develop a mechanism to notify people so that they can work on them fast. These notifications also involve telling the user, reminding them of notifying the reporting weekly reports and things like that. There are also various features around uploading data, seeking data, offline support and things like that. These were part of what is needed in Tanzania as long as such that because there is a lot of areas where there's not enough internet to sort of work on report instances and things like that. So, this seven minutes. Anyway, for now, the last thing I would go to was through the data entry, but you know, you people already know so much about data entry. So, I don't think just a simple thing that I just decided to create a sort of interface which is easier to enter data. And yeah, I think that should be enough. Thank you Vincent. So, thank you very much to all three of our Android finalists. Remember, you'll have to vote between those three for one of the winners and then the next three web finalists will have a separate winner so two different categories. I'd now like to introduce our first web finalists, which is from the organization Crosscut application about micro planning quite manual will be joining us remotely. So hopefully we can get that up here. I think it should is this is this quite screen now quite can you speak and see if we can. Yeah, can you hear me. Yeah, great. We've got a voice from on a high coming in from the United States, I believe. When are you ready to take it away. Thanks, Austin. Everybody my name is quite male and I'm sorry to not be able to be there in person, but this is the Crosscut app. Can you see my name. Yes, we can. Awesome. What's micro planning. Different health programs often mean something a little different when they refer to micro planning, but generally it's talking about public health planning that's happening below the district level. And that's really the key point to remember. Common elements of micro planning include identifying settlements, creating maps, estimating the populations, usually those associated with health facilities and forecasting supplies and resources. Mapping is an integral part of micro planning and micro planning is an integral part of public health. The most common map that's used in micro planning is the catchment area map. Some catchment area maps show the geographic area that's served by a particular health site. Some health programs create these maps by hand drawing them like the one you see on the right. Some health programs engage in technical assistance in might last weeks or months where external experts produce digital catchment area maps using advanced geospatial calculations. Catchment area mapping, whether it's hand drawn or more advanced techniques, this is happening every year in almost every country where DHIS2 is being used. So now you can create these catchment area maps directly in DHIS2 using the Crosscut app. You've probably seen many of the cool new maps that are available in DHIS2 already. Maybe you've tried to create some micro planning apps like here shows the sites and the district boundaries. These are views that might be familiar to you. Maybe you've done some dashboard maps like those here showing BCG coverage at the district level on the left or the health facility level on the right. So with the Crosscut app, you're actually able to go from this view to this view. So what the Crosscut app does is basically allows you to easily divide up the district into catchment areas for each health facility. So that's what the black lines are that you see here. So instead of just looking at the district lines, you see the catchment area lines. We've overlaid here the locations of where the actual settlements are within the catchment area. That's also a cool new feature of DHIS2 using the Google building footprint. So this combination of catchment area boundaries and settlement locations is extremely powerful. And so my question to you is which of these two views do you think is more insightful? Which one's going to help more? The one on the left with the app or the one on the right without it? Similarly, the coverage maps or the dashboard maps you probably have produced many of these in DHIS2. Now you can use your catchment area map, your catchment areas that you create with the Crosscut app to make much cooler heat maps. That's what you see here. And so same question as before. Which of these two views do you think is more insightful? Which you're going to get more information from the one on the left or the one on the right. So this is what the Crosscut app lets you do. It's very easy to find. It's available with the latest release of DHIS2 2.38 or later. You can find it right in the app hub. So let's check it out. The DHIS2 micro planning app that we developed is extremely basic. It doesn't do a lot of things. It really just does one thing and that's create catchment area maps. So how do you do it? You basically click the button. You pick your country. We'll use Sierra Leone and do a test. Then you pick the level where your facilities are and click create. That's what's involved in creating the catchment area maps. So part of our vision and our hope with this app is that we can rapidly speed up the time that it takes to produce these types of maps. So right now while we're waiting on this to run, because that's what's happening right now is it's literally producing the map. So it's running hundreds of thousands of calculations. It factors in the land cover, the elevation, the road network, the location of rivers and roads to really try to produce accurate depictions of where the actual catchments are in the areas that are serviced by an individual health facility. So it's not just drawing a line across the middle of a mountain. It's factoring in the mountain to the travel time and actually trying to calculate something a little more accurate. So what that also lets you do is get a better estimate of the target population for that particular area. So there you see that it's run and then to push it in the DHIs to do all you do is push publish. Our DHIs to app is available today on the app hub with 2.38. You can also come to our website check out the full featured app, which includes travel time heat maps, renewable map downloads and boundary adjustments and more. I've got a little time looking at the clock here, so I'll mention the boundary adjustments. All of our boundaries are calculated automatically. But if you don't like these for some reason and people always don't like them completely, something will be wrong about how the calculation was done based on the local knowledge. You are actually able to easily edit these without any need to for any sort of you don't need to know QGIS. You don't need any sort of advanced geospatial analytical ability. You just need the ability to kind of paint the lines differently. So that's not currently available in the DHS to app that's available on our website, but the two are synced so you stay in alignment at all times. So we really hope that you all are able to check it out and try it out. And I really appreciate the opportunity to demo. Thanks. Awesome. Thank you. And I'm glad that we can see your face now quite so so you can wave to everyone in your last 30 seconds. All right. Hear me. Yeah, everyone. And I'm here to tell you a story. I have only seven minutes and I'm from Spain. So you see the issue here. We have really a problem there. And I will try to do my best really sorry if I'm not able. And so if you do this story is about this story is about all of you, because all of you are instances you don't have only one user. You have more than one user and you need to do like big configurations in those instances. Either you are the one that is doing the configuration or you are the one asking for someone to do it. Please be kind with this guy because it's having a bad day. So actually we are not only doing we love doing generate gaps that are also open source. We really love open source and everything is there. So please contribute. It's not not the only one that you know that you will see from us. So maybe we you know us from any of these training up to build trainings or to sing metadata build packages. Export import into Excel. Create with a couple of comments at the test to instance with you to docker import from Google a thing in any data or or maybe the same principle that I'm going to show you with predictors is also about. And so you when you get to it, like the information that you're going to use the exercise to your super happy. First thing is super happy and now that no one from the test record can hear us. Seems like there is an issue with understanding the user roles and the authorities and all that. And time matters actually. So we use that you say okay I got it everything. Now I can do it. You put everything in place and then the big boss arrives and say you know what. These guys from Afro ending the net user name by X and being data visualizer they need to be added with this particular authority. And that happens and that keep happening and you get a mess in your data test and actually that's a big problem for many organizations you use we have seen many different user configuration paradigms like. People like to use user role as a user profile people that like to use user role as a group of authorities, no matter which one you are using maybe we're missing in the test to something called user profile or something like that. Like to apply template for one user to another. Actually, this is what one of the things that you can do with user extended I'm going to try to I feel lucky so I am going to try to do a demo and yeah. And I don't have a session. Okay, so when you access user extended out actually what you get is the least of your users. Is your you're trying to operate on your users. First thing that you want to do is okay let's try to filter to locate my user. So maybe you want to look for the it guys and so you're filtering real time. You might want to look for the managers. Anything you can you can by clicking here decide what is shown in which columns are shown in in the what in the list so you can add you can remove whatever you you need okay. But yeah, sometimes you you don't know the username you need to look for like apply a more complex filter. We have thrown on that. So actually you can filter by the active users you can filter by role group you can put about the organization unit. So the, the idea of locating a user it's more, more than something that we have found in the past. We understand you, and, and then in user extended out you have to type two different type of actions I'm not going to explain all of them because I think, whoa, and I'm going to explain only a couple of them. And actually you can do single actions and you can do both actions. So the single actions are almost anything that you can do on a normal edition of a user like changing the properties and enabling disabling removing anything like that. Something I want to focus your attention on is this copying user. So sometimes you have a user template, and you want to propagate that user template into many users. So you just take the template you say copying user, you decide which user will be applied with that template and, for example, all these.  And then you can decide if it is user or groups, whatever that you're going to be copying. And sometimes you also want to replicate just the user so you can do something like, okay, I'm going to replicate three times that user, but it's not exactly the same user that I want. So I want to change the organization unit or I want to change the organization unit for visualization or anything the username whatever you want, what you want to replicate. Okay, and then immediately you get a copy or three copies and and copies and that's fine. But it becomes even funnier when you you execute a book action and there are two book actions I want to show you one is that you can edit on a table. So actually you can click on it and you see a table and you can change property for all those users that you have selected one minute. And then quickly, I hope I will have the time. And the latest thing and that's one of the good ideas of all we've seen are users extended habits that you can actually export that into a CSV. You can open that CSV. Okay, you are seeing exactly the same columns that you are seeing in the web app, and you can even add more properties like I want to change the password. If that property exists in the user, that will be changed actually you can change whatever you're however you want. There is a validation when you upload it back and and will tell you if that is okay or not. And I'm going to very quickly show you. And then you can import it back by selecting the file. You get an intermediate screen where you still have a last say like, okay, there are validations all the validation from details to apply on the slide. So all those user exists already so I do I want to override them and then change the configuration. And you can decide to just create new news. And that's it. Thank you very much. Next up we have one more remote participant from his from his Tanzania. And gifts and go will be joining us remotely, hopefully you can share his screen. You have to hope you can hear me and can share your screen. I'm surprised this is the first time. There we go. Can you can you speak so we can make sure you can hear we can hear you and then share your screen. Yes, hi Austin. Hi gift. Okay, yeah, I'm just. Okay. Let me share my screen. And please tell me if you can see it. Can't see it yet. There we go. Perfect. Okay. Yes. Sorry. Yes. Let me just finish up setting up. Hey. Yes. Can I start? Yes. Go ahead. Okay. Thank you. Hi, everyone. My name is gift. I'm a system developer from his Tanzania. And I'll be presenting to you the program indicator this aggregator. The program indicator is a custom which is to application that enables automatic generation of this aggregations from a generic program indicator based on different categories. So, despite being crucial for tracker that analysis program indicators configuration has been sometimes required to have this aggregation for different categories based on specific data elements. Attribute constant or variables that achieve this multiple program indicators are configured with the same consideration with a with a consideration of the intended segregation. This is normally done by duplicating it and modifying it for each disaggregate. Now this might not be an issue for smaller number of disaggregations, for example, gender. But in some cases, we may have many disaggregates that may be needed to be generated and this may be tedious. And so we thought of a useful way to automate this process. And this is where the program indicator disaggregator comes in. So the program indicator disaggregator collected is collectively allows management of disaggregated program education from the app. You can see a list of already configured program indicators from which you can select a generic indicator. The off the app also allows configuration of automatic desegregation based on data elements and program attributes. It also allows propagation of updates to disaggregations in case the generic program indicator has any updates. With a current app implementation, the app has proven to be efficient in resolving this challenge. But we are planning to expand its functionality by adding support for disaggregation by variables and constants, adding support for more operators like greater than less than ranges and more. We also plan to add support for disaggregation by multiple data items. And of course, we also plan to support an elaborative program indicator dictionary explaining more about the indicators. But apart from that, we also expect to have some use cases from the community for those who are interested or who are interested to use the application. And now maybe let's jump into a very quick demo. So the app can be accessed through the app menu in DHS2 and its name program indicator desegregator. And when opened, it will show you a list of program indicators that are already configured in the system. And here is where you can select actually a generic program indicator from which to desegregate from. So for example, in our case, we're going to see an example of COVID case. Disaggregated by different outcomes. So for example, we can have, we can search the surveillance. And then we can now choose the COVID case indicator. From here now, I will see the chosen program indicator along with different explanations. And then from this page also, it's where you can add your desegregation configuration. And here basically it is done in three steps. So first of all, you choose what you desegregate by. And so for example, in our case, we want to desegregate by data element. And then you choose the program stage in which you want to desegregate from. And of course, the data specific data element. The second stage basically you choose what values should be desegregated for this specific indicator. So if, for example, in our case, this data element has option sets tied to it. So automatically your option sets will be shown here for you to choose. And then in case you chose a data element that is probably a free text, you can specify a custom value. So in our case, we're going to select all. And then the last step is basically to choose a name prefix that will be appended on the name and the short name for the generated desegregation program indicators. So in our case, we can just say outcome. Yes. So after that, you just simply speak safe. And just like that on the fly, you have now five new desegregations for these indicators. And you can actually see them here. Now, let's see these desegregations in actions. So if you open our data visualizer and navigate to program indicators and then select our program, you can actually see now COVID cases as these desegregations that we generated. And yeah, we can also select a peer that has data so I can see. So let's choose this year. Yes. And just like that, we now have desegregations for the COVID-19 cases simply in age. But at some point, there may be updates to this generic program indicator. So for example, we want to change maybe an attribute of this. We can simply, let's say, we're changing the short name to case. And then if you save, then if you move back to our application and refresh on this. So basically what will happen, you'll get enough notification that the generic indicator has been updated. And if necessary, you may need to propagate those updates to the desegregations that have been generated. So you can easily do that just by giving updates. And just like that, all the updates will be reflected to the different desegregations. I think that is all from us. If you have more questions or if you want more discussions, we have a posting in the community of practice. We can visit through this link or the capture. Or you can contact us through the email info at his Tanzania.org. Thank you. Thank you very much. And I think we are just about on time. This is kind of amazing. Thank you very much. Gift for sharing that and to all of our finalists for the great presentations. I'm going to share my screen now. And we will move to the most exciting part, the voting. The stakes are high. This will be automatically filled in with the link in just a minute because I have a great team working with me. The stakes are high. So the winners of this year's app competition will get a sponsored trip to next year's annual conference.  And you can talk with them and they can experience the conference atmosphere. And they'll also get lifetime recognition on the community of practice with a badge that has been designed by a Gassim, our community manager. Austin, this link will actually fill in. You're online, right? You're trying to. Yes, I need added access to the doc. Sorry. I should have given it to you. Recording stopped recording in progress. I think you should have it. If not send it to me and I can fill it in. There you go should be there. There we go. Okay, it's on it's on this one here. That's fine. Okay, great. I also wanted to mention so on the right side of the screen here you have a link. So I'm actually also going to start a timer for this. Oops, too many, too many things. Sorry. Too many things. You have three minutes ready go. So you have three minutes for the voting here. And as this, as this goes forward, I will try to bring this back onto the top of the screen. But I also did want to mention three honorable mentions from our submissions for the website of the app competition here today. These are great applications. A few pieces of feedback that we had for, and we'll be sharing with the developers. But there's a hopefully we'll see them next year. Potentially if they, if they submit again. The first of these is from PSI. It is a, an application to significantly simplify the configuration of programs. The second is a very exciting collaboration with the University of Alabama and Huntsville and NASA to import Earth observation data into DHIS2. And the third is tracker data cleaner, which supports de-duplication of users in DHIS2. We've got a lot of noise going on here and some questions maybe. Too many requests. How many of you are there? We might, we might be able to. Extend the time just a little bit, but hopefully keep trying. You can get in. Don't vote too many times. Don't ask your friends to vote. That's not cool. Don't, don't set a bot network to vote for you. Yeah. These three honorable mentions are hopefully we'll submit next year and you'll, you'll, you'll hear more from them. I also wanted to think while we have a minute left here, I wanted to thank the great team that has helped to put together this annual conference for you. It's not working still. Oh, no. Oh, no. We have a too many requests error. The voting is taking place on the DHIS2 community of practice. And if you're in the zoom meeting, you'll see the casino has posted the link to the COP thread there. We can vote. Can I, can I put that on the screen? We're voting through the community of practice. If you're on the COP right now, you can find the thread to vote. And if you're in the community of practice, if you're on the COP right now, you can find the thread to vote. And if you're on the zoom meeting for this session, you can also see the casino has posted the link in the chat there. The community has too many requests. I know a crash in the community. So you should be able to find it on the community of practice. Don't refresh too many times. You might break everything for everyone. But we do have lots of votes coming in. So thank you all for, for those of you who have voted. Keep trying. If you haven't gotten in yet, it will come through. I wanted to thank again the, the team that has been working with me to put on this annual conference.  We're viewing applications, communicating with applicants and finalists and, and putting on the show here tonight, which I have one more minute before I have to turn over the stage to, to someone else. So we should have a, hopefully every, most people have gotten into vote. No, no. All right. We'll still, we'll still pause for just another minute. Keep trying. Please keep trying. I think we might, we might need some, some new servers for this community of practice. If that were a DHS to server with the up and running. So we're reopening the voting just in case you haven't gotten in yet, please try again. Apologies for the technical difficulties. I think we should probably do some horizontal scaling and load balancing on this community of practice for next year. This is going to do most controversial results ever, right? Thanks. You want to hand out these? In the meantime, one of, one of our, the developers on the core team made these really awesome. DHS to magnets, 3D printed DHS to magnets. That are going to be. Prizes for all of our finalists. Hopefully we can get them to the finalists that aren't here today, but for those of you who are here, if you could come up here and, you know, collect your, your finalist prize of these DHS to magnets and let me know how many people are on your team. If you want a few of them, we have, we have a few extras. Yeah. Thank you. Yeah. Sure. One more. Wait, wait. One more. Okay. You can take maybe these for now. Okay. Yeah. Thank you. How many, how many do you have? They're little magnets for the DHS. How many are you on your team? Yeah. Great. All right. How are we doing? How are we looking? 130 votes. All right. We have about 130 votes total. If you haven't gotten in yet, raise your hand. Keep trying. All right. Thank you. Thank you. Thank you. Thank you. Thank you. I haven't gotten in yet. Raise your hand. Keep trying. Good question. Good, good suggestion. So if you, if you get off of the conference wifi, if you have a phone and you have a mobile internet connection, that will let you get in. Because it's coming. So everybody that it thinks we're hackers that are trying to hack from one, one place and overwhelm the system, which maybe we are, I don't know. So if you, if you having trouble getting in and you have access to a data, a mobile data connection, please try that. We're going to give it another 30 seconds. And then I'm going to turn over the stage. So try to get in. If you can. You want to be dramatic. Austin. Austin, can you hear me? Hello. Do you want to say something? Yes. Yes. We have a comment in the chat saying that the UDSM app should be all these are up. I think that we use the, the old name in the voting, just for as a clarification. Okay. So there's a, an older name for the UDSM application in the voting, I believe. But the one is by UDSM is the, is the UDSM application. And our community coordinator, Christine would like to make a clarification that the lifetime recognition badges are actually designed by our expert. UX designer, Joe Cooper. Joe Cooper. Joe. Joe Cooper. Joe Cooper. Yeah. Nice credit credit where credit's due. Joe design the badges, guessing had the idea and put it into action. So great, great team effort there. All right. Five, four, three, two, one, zero. Let's close the voting. I think we have 150 votes or so. So that's, that's a good number. Hopefully. Hopefully we have a clear winner. Yeah. We have winners. You want to just show it? You want me to say it? Yeah. Go ahead. Yes. All right. So our winner for the category of Android is the CCM app by Phillip Larson. And that's not all. The winner for the web app category of the app competition. We have a winner for the category of Android. The DHS annual conference 2022 is the program indicator disaggregator by his Tanzania and gift and go. Again, thank you very much to all of our people that submitted applications, all of our finalists, honorable mentions, and the team. Great work. And thank you all for putting up with terrible voting experience. We'll turn it over to the closing of the DHS to annual conference 2022. Thank you all very much.


The study found that IPSC lines derived from the same donor were highly similar to one another, but genetic variation caused differences in the expression and methylation profiles of the cells, which could affect their functional capabilities. The researchers suggested that integration-free, bona fide IPSC lines from fibroblasts and blood could be combined in repositories to form biobanks. Since genetic variation can cause differences in the ability of IPSC lines to differentiate, it is important to include cells from many donors in biobanks.