Punkeray's work on topology. Thank you very much. So it's really just a great honor to be able to come to Institute on Read Punkeray to speak about Punkeray's work on topology. And well, so these papers are Punkeray's, Annalise C2 papers. I mean, that's Annalise C2s. That's what they call topology in those days. And there's, well, there's several Comperondu announcements and five papers, but actually six, the original paper and five complements. But really the hardcore topology and the stuff I'll mainly talk about is in the first paper, the first and second and fifth complements. So John Morgan, in his lecture yesterday, said that most topologists think of Punkeray as the founder of topology. And part of the goal of this lecture is to make this argument, not that he's the first mathematician that did sort of impressive results in topology, rather Punkeray was really the first person. Well, he really created topology as sort of a separate field of mathematics, a field which has its own internal problems and issues. But Punkeray demonstrated that topology is a field that gets a lot of input and inspiration from other fields of mathematics and science, and in turn gives a lot of sort of contributions to other subjects. So John, yesterday sort of gave some hints about what topology is. And well, I think I'm just refrained from giving sort of a formal definition. But rather I'd like sort of Punkeray in his own words to tell us, rather not the technical definition of what topology is, but sort of what its structure is. So in the introduction to his first paper, he says, geometry, in fact, has a unique raison d'etre as the immediate description of the structures which underline our senses is above all the analytic study of a group. Consequently, there's nothing to prevent us from proceeding to study other groups which are analogous but more general. So I think what he's saying is that he was looking at, well, before he had the study of Fuxian groups, he was looking at these very special things. And Fuxian groups are the groups underlying hyperbolic geometry, the non-Euclidean geometry of the plane. And now he recognized that there's really other groups which describe sort of some more general objects, manifolds. So but then he makes this statement, which I really like, is, perhaps these reasons are not sufficient in themselves. It is not enough, in fact, for science to be legitimate. Its utility must be incontestable. So many objects demand our attention that only the most important have the right to be considered. And then he goes further and gives some examples of why it's important to study topology. But I'd like actually to quote, which actually John paraphrased yesterday, but just give the direct quote from this other paper, which he wrote in 1901, which was sort of a summary of the scientific works. And he says, it has been said that I've written it in the preface to Analyst of Cetus, which he did. That geometry is the art of reasoning well with badly made figures. Yes, without doubt, but with one condition. The proportions of the figures might be grossly altered, but their elements must not be interchanged, must conserve their relative situation. In other words, one does not worry about qualitative properties, but one must respect the qualitative properties. Sorry, one must not worry about quantitative properties. One must respect the qualitative properties. That is to say, precisely those which are the concern of Analyst Cetus. Then he mentions that there was an early stuff studied by Riemann and Betty, but no one really is followed up under works. And now here, he gives this long, just incredible reason which drove him to think about topologies. He says, well, as for me, all the diverse paths which I was successfully engaged in led me to Analyst Cetus. And he goes on and on. Finally, I glimpsed in Analyst Cetus a means of attacking an important problem in the theory of groups. The search for discrete or finite groups contained in a given continuous group is for all these reasons that I've devoted to this science a fairly long work. So that was the introduction. And before I go on and talk about what Ponqueray actually did, I want to just give you an idea of what the state of topology was before Ponqueray. So this is the first page of Euler's famous paper on the bridges of Konigsberg. And actually, this is sort of a picture in that paper where the problem is, well, here is like the city. And think of it being in four parts. And the question was, can you just take a walk starting at one spot and just go over all the seven bridges without going over a bridge twice? And Euler sort of solved that problem. And maybe that was the first serious result in topological type of argument. So Euler also discovered the Euler characteristic. And Gauss discovered this idea of linking numbers.  Of course, he did a spectacular Gauss-Benet theorem, which found sort of a connection between geometry of the surface and its Euler characteristic. Riemann, well, he introduced the idea of a manifold. And in general, but in practice, he just looked at the two sphere and looked at really branched covers. But for surfaces, he had this measure of how complicated the surface was. He called it the order of connectivity, how many cuts you need to chop a surface up into a disk. And then there was Listing, who discovered the Mobius band and actually coined the word topology. The topology is spelled in English. It was first used by Peter Tain as a bituary. Well, Mobius independently discovered the Mobius band. Cayley and Maxwell independently discovered this idea that if you have an island, then if you look at the high points and the low points and the saddles, they syncs minus the saddles plus a sum equals 1. And then there is this Jordan curve theorem, which said that if you have a closed curve in the plane, it separates into two pieces. There are various works in knot theory. And then there is a very influential work by Betty, which tried to generalize what Riemann did to higher dimensions. But all these works, and this really summarizes the whole extent of knowledge of topology before Pocherey's works. I mean, they're sort of very interesting isolated results, but not really part of a general theory. So now I'd like to just say some things about, well, what did Pocherey do in his foundational paper, which actually was preceded by two announcements? Well, to start with, well, he actually gives a little sharper definition of manifold, which was just along the lines that Betty and Riemann did. But another thing which actually John Morgan mentioned yesterday was the current, I mean, well, the standard definition now of a manifold is just being built up by charts, by pieces. I mean, that sort of is an innovation in this paper. He defines this notion of orientation. Well, actually, the idea of orientation existed earlier, but using sort of the termines, so between the transition maps, of course, the spectacular contribution of defining the fundamental group. So if you're given a manifold, then associated to that is a group, the fundamental group. And he defines it both sort of as a group of covering transformations in universal cover and generated in terms of loops. And this itself is quite revolutionary, because previous to this, to topological things, there is just sort of numbers. There is invariance. But here he's associating a group. Now he defines this idea of Betty number, which, well, in this form, it was 1 plus the maximum number of the kth Betty number is 1 plus the maximum number of k-dimensional orientable sub-manifolds, so that over the integers, these sub-manifolds are homologically independent. So in other words, if you just take some linear copies of this one and copies of that one and copies of that one, and if they all bound a manifold of one higher dimension, that's what a homology is. Well, more or less, in modern words, he recognized that homology, H1, is the abelianization of pi1. He defines this idea of algebraic intersection number and shows that if you have a manifold of dimension five and a manifold of dimension three living in a manifold of dimension eight, they'll intersect in points. But rather than just counting number of points, count number of points with signs. And you get a number, which if you just take the intersection of m and n versus n and m, they differ by a certain sign. And these intersection numbers are invariant under homology. And I should say this, for those of you who aren't mathematicians, these are just incredibly fundamental concepts that it's just amazing that just in one paper that they're introduced, he uses integration theory to distinguish homology classes, generalizing methods of Betty. He gives really interesting examples of manifolds. I mean, the examples that existed through Betty, through Klein, and students were not really too exciting. But I mean, it's amazing that he just, for example, looked at tourist bundles over the circle. And of course, he had a spectacular, where all this stuff is spectacular, but the punkerate duality theorem that says that if you have a manifold of dimension n, then the Betty numbers that are, in his words, that are sort of equidistant from n, the kth Betty number and the n minus kth Betty number, those are equal. And while he thought about this because he had some, well to him, he had this idea that a class was homologically trivial, if in all of you it's algebraic intersection number with classes of complementary dimension or trivial. And I should say he was very much inspired by Picard, who noted that the first and third Betty numbers were equal for complex surfaces. So, right, he defined this idea of cellulation, which, I mean, was very similar to, I mean, this idea of he just takes some space and just sort of decompose it into cells. I mean, that's, it was just a variation of an existing theme, but a very important sort of psychological way of looking at things. Of course, the famous Euler-Ponqueray characteristic relating to classical Euler characteristic is the alternating sum of Betty numbers. So, in this one paper, just incredible, truly incredible, just one after another, just absolutely fundamental seminal ideas. So, I'd like to mention a quotation of Darbell in his eulogy. He said, I saw a Ponqueray at the Sorbonne, the Bureau of De Launcetudes at the Academy. Whenever asked to solve a problem, his answer came with the speed of an arrow. When he wrote a memoir, he wrote by a single drift, making a few changes without returning to what he had written. I should say I made a serious attempt to read Ponqueray's paper. And I believe what Darbell says is true. But this is actually, to me, a very interesting point that his writing style might have been just one go. But his working style, completely different. And I'll try to say just by quoting his own words that he constantly came back and rethought about central issues. And you'll see in the case of topology that each time he sort of rethought the subject, just incredible sort of the new breakthroughs that he was doing. So, well, du Donné was a little bit more direct. He said, it is often necessary to guess what he had in mind by interpreting the context. For many results, hardly a single argument does not raise doubts. The paper is really a blueprint for future developments of entirely new ideas, each of which demanded the creation of a new technique to put it on a sound basis. So, well, I mean, just have a list of things here. I mean, for example, this idea of just thinking of classes as sub-manifolds, well, that's actually a very delicate issue that took, I mean, there's really sophisticated algebraic topology and was finally sorted out by Rene Tom in 54. As far as using integration to understand classes, well, I can't do better than quoting sort of the anonymous author of the Samir in Volume 6 of Pancras' Collected Works, where he said, paragraph seven introduces cohomology. He posed problems that Elie Cartin explained and George Durom resolved. So the famous Durom theorem, which relates sort of the Durom cohomology based on forms with cohomology based on in real coefficients. And anyway, Cartin sort of inspired by what Pancras wrote, sort of conjectured these Durom conjectures, which Durom proved. Anyway, there's also other things, topological invariance homology. So this business with intersection numbers, well, to really put that in a firm foundation, you really have to understand sort of general position, which was done by Whitney. And of course, incidentally, Whitney proved this embedding theorem, which showed that actually all the manifolds that Hunkray considered are actually just takes here of all the manifolds. So Heiguard, in his 1898 thesis, well, he had some complaints, too. And in particular, he noted that RP3 was a counter-example to Punkray duality because the first betting number is one, the second betting number is two. Now, so in one due paper of 1899, well, Punkray responded to that by pointing out that his definition of betting number is actually different than Betty's definition of betting number. And well, the first approximation, well, definitely his betting number was just a rank of homology and Q coefficients, while Betty's number was approximately, well, to some extent, the first approximation, the rank of just in Z coefficients. So in particular, for RP3 rationally, it's just homology is just trivial in dimensions one and two, while in Z coefficients, of course, you know that betting number is one, and the second betting number is two. But going from Betty to Punkray, just looking at Betty numbers, Punkray had this huge breakthrough where he was allowing to add and subtract and divide homologies by integers, which, well, and today we think of that. I mean, that's just sort of in rational coefficients. But this is Hegard's objection. But I quote a gift because Hegard was really the first person to really look at what Punkray did. And I should say that Punkray, to his credit, he could have just blown off Betty by just this, sorry, by Hegard, just sort of dismissed Hegard by saying, Hegard, look, you misunderstood what my definition of betting number was. But Punkray took this as an opportunity just to sort of rethink the whole subject. And right. So then he just quickly followed up with the first and second complements. So here's a quotation from the introduction of the second one. It says, nevertheless, the question, that is, topology, is far from being exhausted. And I shall doubtless be forced to return to it several times. This time I shall confine myself to certain considerations that are likely to simplify, clarifying, complement the previous results. So in this one, he really just goes back and just really drops this idea of homology classes being represented by manifolds and introduces what we now have the standard thing of simplicial homology. And so in particular, if you have a space, it's built up by cells. Say there's CI cells and CI minus 1, I minus 1 cells. And he recognized how to compute the homology by just taking boundary because he sort of understood orientation, boundary orientation, from his first paper. And therefore, the boundary operator is this CI minus 1 times CI matrix. And then just by elementary linear algebra, then the ith betty number is just the number of I cells minus the rank of the ith boundary operator minus the rank of the I plus first matrix. So therefore, there's this nice, clean definition of homology, and therefore, he just gets really clean proof of the Euler-Punkray formula because when you're taking the alternating sum, well, you can see that the number of cells alternating some of the cells, which is just what Euler's definition is, well, in the low dimension case, is these bi's, they just cancel each other out. And in this paper, he recognized that there's the torsion part. And what I should just do a little side point is that it's interesting that although Punkray introduced the fundamental group, the first time a group is associated as an invariant of a manifold, nevertheless, he and for the next 10 years, some very talented top level topologists thought about homology not as a group, which we do now, but in terms of just numbers and torsion numbers and betty numbers. And she just made this just a very simple observation, which psychologically changed the way people thought and just really a big advance, which was that you should just think of these things as groups. So right, and there's certain things that had to be cleaned up later, going from smooth, the PL, and invariance of these as topological invariance. And then Punkray goes on to just, again, completely fundamental ideas, which are the idea of barycentric subdivision, star of vertex, dual salulation. Anyway, well, if you're a topologist to recognize this picture where there is the black, which is, say, the original salulation, and there's the red, which is the dual salulation. And so these are two different salulations of the same manifold, but they both sort of subdivide to the barycentric subdivision. And anyway, staring at this picture and thinking about it, you get sort of a clean proof of at least in the simplicial world of Punkray duality. And well, in here, he sort of announces his first version of the Punkray conjecture, that he thought that if you have a manifold and all its bedding numbers, well, in the middle, except for the top and bottom dimension is zero, then the manifold's a sphere. And I should say, actually, this idea goes back to Riemann, the idea of if you have a manifold, try to find some invariance that just determined that sort of uniquely. And one of his big motivations was with these tourist bundles. Those were examples of manifolds which had the same bedding numbers, but were different manifolds. And so this is sort of, again, searching for the right sort of criterion. So now let me just go to the fifth compliment. So again, in the introduction, he says, I now return to the same question. Persuade that one can come to the end only by repeated efforts, and it's important and sufficient to justify further effort. This time, I can find myself to the study of certain three-dimensional manifolds, but the method used without doubt are of more general applicability. So of course, this is the famous paper where he entered, finally, after this long process, gives the right form of the Punkray conjecture. But ignoring that, this is just an incredible paper. And in this paper, he basically creates the Morse theory and handle-body theory. So in Morse theory, you have a manifold and you have a function from that manifold to the real numbers. And that's a way of slicing up the manifold using this function. Think of it like some type of height function. But there's certain singularities. And in the Morse theory, well, you show the function can be realized so that the singularities are all of certain types, and which you can then build up the manifold by just understanding these singularities. And what's incredible is all of that is in this paper. So here, you can't read it. But there's, well, it's really, it's right there. I mean, well, if I could actually make it bigger, it's just incredible. I mean, because, well, I don't know. Maybe it's the French education. Everyone knows this. But to me, I'm just totally shocked to see this. I mean, right here, it basically says that you have this height function on this manifold. First, you make a perturbation. Then you change the coordinates. And this function looks like a quadratic function. It's exactly Morse theory. And then sort of here's like the standard picture of sort of the index one singularity on a surface. Anyway, that just, that's, and so when he, in his introduction where he says this stuff, I have more equitable ability to higher dimensions. Well, this is exactly what sort of smells starting point for proving the high-dimensional Poincare conjecture. So, right. So anyway, so Morse and Morse didn't actually come out and say this isn't Morse theory. This is Poincare theory. But he does, in the introduction to his book, The Calculus of Variations, he gives sort of a clear acknowledgement to Poincare. So just, so he says at some point, such conceptions are not due to the author. It'll be sufficient to say that Henry Poincare was among the first to have a conscious theory of macroanalysis. And of all mathematicians, was doubtless the one who most effectively put such a theory into practice. So, that's more, so here's sort of other results from the, from this fifth compliment. He recognized that you could, there's a symplectic form and you use that to compute algebraic intersection number. He had a criterion for showing when a homology class is represented by a simple closed curve. Another criterion for when a homology, when a simple closed curve, sorry. Here's another criterion when a homotopy class is realized by a simple curve. And this to me, he just says this just casually in a couple lines, really incredible. So he just says when you take a curve, just homotopic to a geodesic, lift it to the universal cover. And if you just see that these, these are all just disjoint curves, just assuming it's not a power, then this is, it's gonna be, it's simple. On the other hand, if you homotopic to a geodesic and you see in the universal cover that these things are crossing, then it's not really simple. That is, it crosses itself downstairs. And I mean, to me, this is really incredible because the fact is for him to make this statement means that he must have known. I mean, he says these things if it's obvious, but he must, it means that he really understood this idea that if you take something, you do a homotopy. Well, that sort of look, might be look like a radical change in the surface, but the homotopy is going to just nevertheless, you start with this curve, you do some crazy homotopy, you're still gonna get some other curve which has the same endpoints at infinity. So this is probably the first time that the apology of infinity of hyperbolic space is used to do topological stuff. Anyway, he just showed how to compute fundamental group. Again, this is, I mean, there's really, I mean, this is just the primal form of the well-known Cyford-Van-Kampen theorem. Of course, then there's the, his famous thing of showing the punk ray homology sphere, this sphere which is counter-exampled to his, his earlier form of the punk ray conjecture, first the famous picture of the punk ray homology sphere, and the final statement of the punk ray conjecture. Actually, just an aside, you know, he states so the punk ray conjecture, so this one question remains to be dealt with, is it possible for the fundamental group of this manifold to reduce the identity without being simply connected, then he just gets some more explanation. And then the last statement of the paper is, however, this question will take us too far. Now, you know, I never understood what does that mean? So, but you know, I have my computer, I have volume six, 1,000 pages. So I said, okay, well, why not just give this a shot? And so I just, you know, just type in on the, sort of the find feature, I type in, you know, the, you know, entran, entranter-ray-tro-loin, and I get one hit, and it comes up with that expression is actually used in chapter seven of Nalicitis where he uses sort of that same expression except sort of he says these conditions are quite easy to construct. That would take me too far away from my subject. So if he really meant the same thing here as there, then, and I think what he meant was that, well, whatever more thoughts he had on the subject was really a little distracting from the content of this paper. So anyway, this again, just incredible, amazing things that did, and fundamental seminal ideas, just independent of not including what he did about the Poincaré conjecture. So that sort of summarized his analyst C2's papers, but what he did in topology is just outside of that, just amazing. I mean, there's, he had a, this is just thinking just purely in terms of functions, but I mean, the modern way of constructing the universal covering space of a topological space in terms of equivalence classes of paths, well, that appeared in some paper in 1883, the Poincaré-Hoff index formula for calculating, showing the Euler characteristic of a surface could be relayed in terms of vector fields. Well, I mean, he did that for surfaces and Hoff got his name somehow because 30 years later, he proved the same theorem in higher dimensions. Well, he had this theorem at the degree one maps. Well, the idea of degree one didn't exist then, but he had a map of a sphere which had, which, well, somehow mapping, anyway, so he had proved something, a version like that in this, he, of course, he computed, understood isometry's hyperbolic space and had his models, which are just completely fundamental, of course, to modern day hyperbolic geometry. Now, I'd just like to mention just his dimension theory where in this philosophy paper, he introduces, he asks the question of, well, why is three-dimensional space three-dimensional? And from the point of view of sort of, well, a coordinates to us, well, it seems obvious it's three-dimensional. From the point of view of just as sort of, as a smooth manifold, while you do a diffeomorphism in modern day, we have its dimensions because of the tangent space and a smooth manifold's rank preserving. So, but on the other hand, should it really be three-dimensions because Cantor had observed that if you look at three-dimensional space, I mean, it has really, has the same number of points as the circle, which is one-dimensions. So what intrinsic about three-dimensional space makes it three-dimensional instead of one-dimensional? And, well, then he makes this incredible statement. He says, I'll base the determination of the number of dimensions with the notion of cut.  Well, that's two-dimensional. Why is that? Because if you have a point on the sphere, you take a little neighborhood of that, boundary of that's a circle. That's, well, that's a circle is one-dimensional. And why is that? Because if you have a point on the circle, a little neighborhood of that's two discrete points and discrete points are zero-dimensional. And he just says that sort of casually, but this sort of, you know, right away, Browler just tried to get sort of a more sort of mathematical definition. Well, that is mathematical actually what he said, but which is more ultimately formulated by maybe Manger in your zone, maybe 10 years after that. But this, you know, it's huge, well, subfield of mathematics based on this dimension theory. So let me just mention that it's just incredible what Punkeray did in topology. And yet, well, as I mentioned in the very beginning, I quoted from the introduction, that was about, took up, well, like a full page of Punkeray's study, well, view of his own view of his own scientific works, which was 100 pages, about 100 pages. And so of those 100 pages, about three and a half pages were devoted to topology, those three and a half pages felt the need to spend like a full page just explaining why he's, he'd wanna do this stuff. And so you might say, well, that doesn't seem like very much. And, but, you know, Punkeray actually, you know, offers a disclaimer for why he shouldn't be sort of overwhelmed by these numbers. And so there's an introduction, well, just a little two page O lecture paper written by Mittag Luffler, who sort of solicited this paper from Punkeray. He says, well, in the letter I wrote, which he agreed to my request, he wrote characteristically of his powerful capacity for work and activity. Punkeray wrote, I would point out that there is the disadvantage that too much time will last between when the proofs are returned and the publication is given. Making the record seem more complete than it actually is. So, right. So, the next thing is, so I wanna say a few words about Punkeray's sort of influence in topology. Well, of course the influence was just overwhelming, just in the Punkeray conjecture, the stuff that the mathematics that it led to in high dimensions, low dimensions, work in hierabolic geometry. But independent of that, there's just incredible amount of work that these papers sort of stimulated. And of course, there's the famous Punkeray question, Punkeray conjecture question, but here's sort of three questions that he asked from his analysis, C2's paper. It says, it would be interesting to treat the following questions. One, given a group defined by number of, well, basically it says given a finally presented group, does it correspond to a manifold of n dimensions? And if so, how would you create that manifold? And three is, if you have two manifolds of the same dimension, which have the same fundamental group, are they always homeomorphic? These questions will require difficult study and long development. I will not say more here. But so these were in his 1895 paper. Now, I should say that a lot of English version. Now, if you just take these questions literally, the answers are relatively simple. In fact, Cameron Gordon noted that Punkeray himself could have answered question three because these S2 cross tests, two and S4 are different manifolds of the same dimension four, but they both have trivial fundamental group. And there's also sort of relatively simple, I mean, clever, but simple examples, in particular for question one, given any group you could find and any dimension bigger than equal to four, you could find a closed oriented manifold of that dimension which has that group. So every group is realized by all manifolds of dimensions bigger than equal to four. But I'd like to take this point of view is that Punkeray, he did stuff and he sort of rethought it, rethought it, we find it understood it better. So I don't think that we should be frozen in 1895 with sort of the statement of these questions, rather that with the sort of the increased sophistication that these questions really should have evolved appropriately. And if you just modify them just a tiny bit to put it in sort of a more modern sort of understanding, then these questions are just, well, they're only at best sort of partially understood. But in particular, this question three, does the group determine the manifold? Well, if you restrict to manifolds of which have the property that all the higher homotopy groups are trivial, that's also known as a spherical, and you allow yourself sort of a weaker condition of what's known as homotopy equivalents, then Whitehead in the 40s noted that manifolds which are a spherical same fundamental group in fact are homotopy equivalent. And so these as spherical manifolds include sort of a wide class. But if you take the question three of, does the group determine the manifold and then restrict yourself to as spherical manifolds, well, this is what's now known as the Borel conjecture, that is closed as spherical manifolds with the same fundamental group or homeomorphic or sort of in different sort of just form, it's what's also known as topological rigidity of as spherical manifolds. So just said another way, I mean, what does the Poincare conjecture say? It says that if you have, say a three sphere and you have another manifold, which, well, is homotopic to that, so if you have a three sphere and another manifold homotopy equivalent to that, then the Poincare conjecture says that this manifold really is the three sphere. So you could just say the same exact thing if you have a manifold which is as spherical, another one the same homotopy type or has the same group, then the Borel conjecture is that in fact they're the same. And this has led to just so tremendous amount of mathematical activity. Chris Punker I knew this in dimension two. The famous Moss-Dahl rigidity theorem says that if both those manifolds were hyperbolic, then in fact you could homotopic to an isometry and that's a, well, theorem in all dimensions bigger than or equal to three. And in high dimensions there's sort of a sharper form of this Moss-Dahl rigidity due to Farrell and Jones and very recently Bartels and Luke sort of generalize the Moss-Dahl and then Farrell, Jones theorem to grow of hyperbolic groups and cat zero groups. So, but actually just as an aside, let me mention that you could sharpen this question a little bit further is that if you have two homotopy equivalent manifolds and you have a homeomorphism, how unique is that homeomorphism? And well certainly you need at least unique up to isotope and in low dimensions, at least dimension three it's true that two homotopic, homeomorphisms are isotopic, but so this is interesting in high dimensions, it's actually false that you could have you could have a homeomorphism of a hyperbolic manifold to itself but the isometry of homotopic to it could very well not be isotopic and that could happen in dimensions 10 and higher now. So that was, so question three is very open for many contexts and so okay, that's just a situation there and now here's a formulation of question one which our question one is given a group is it the group of a manifold? Well, if you restrict your attention to manifolds which again have this asphiricity property then again this is something that just stimulates this tremendous amount of work and well it's maybe it's known as the wall conjecture that basically these punk or a duality groups these if you have a group that when now you look at from the point of view of well a complex which has somehow given a group you could find some topological space which has that as the fundamental group and if that space has well certain properties then that group is called a punk or a duality group and those are the groups that are candidates for being groups of asphirical manifolds so this is I call this sort of the modern form of punk or a sort of first question and so again this is now known in dimension for punk or in dimension two and it's ready for dimension three it's still very much not known and there's been a huge amount of work in this progress in this direction but it's been a consequence of if you have a group which satisfies certain properties that you can do various things well basically it's all been reduced now to two interesting problems which are the weak hydrobalization conjecture which is whether these PD three groups are hyperbolic in the sense of Gromov and well, seemingly they have sort of some what's known as atroidal and then this other thing which is the cannon conjecture which is a very interesting conjecture which you have a group which in some sense again you look at its boundary like punk or a was doing in the fifth complement and if that boundary is a two sphere then this group is actually the group of a, well, well if it's torsion free that's the group of a hyperbolic three manifold so this is extremely interesting question which is basically saying that you have a group of such and such type can you actually sort of uniformize it and there's been various partial results and maybe just point out this result of Kleiner and Bonk which is that if you have a space well in certain circumstances the answer is yes if the certain space satisfies what's known as like a certain punk array inequality so right, so I just want to just briefly just to indicate just a direct consequence of punk rays initial paver and topology already there's these very interesting questions that are just very open and so anyway this, if you want to learn more about punk rays work on topology there's really a lot of really great resources I mean and I should thank, I just had a huge amount of help in preparing this lecture from Michelle Brawlow and John Stillwell and most of the translations were direct from Stillwell's papers on, well it's not his papers but it's, he translated the analyst Cetus into five supplements to English and gave some annotation and where I, and there's Sarkarya sort of did one of that I mentioned power graphs in the introduction and Google Translate helped out a little bit too. So anyway thank you for your attention. We have time for some questions now. Is the question here? No. Yeah, in your introduction you show briefly the notice of punk array on this motivation for analysis Cetus and in that there is, there was one big motivation which was to understand more the differential equation in the three body problem and also the disturbing function in the planetary problem and these were very, he was very much motivated for the expansion of this perturbing function which involved very complicated algebraic equation. So he had a very concrete problem to solve and my question, and a difficult problem. So my question is whether, how much discount in the success of his development? The fact that he has this very difficult problem to solve. That I have no idea. I mean clearly he was, I don't know. You certainly covered a lot of territory there. Last minute chance. Okay, well let's thank David. Goodbye again. Thank you.


sup guys welcome back to another episode of rugby player reacts i'm your host jacob mcdonald and uh well thanks for joining me today we're looking at a buccaneers player he lands at number 43 on the list he's a super bowl ring recipient and his name's levante david is it yeah that's right levante david levon yeah ld for sure playing lb for the bucks but with all that being said we are on the top 50 which is exciting nonetheless it's going to be name after name after name from this point and i don't mind it so guys sit back relax get your beverage of choice i'm going to roll the intro and i'll see you in a minute right then levante david linebacker for the bucks let's see what uh well let's see what tom brady has to say no turkeys what nine points no turkeys and gronk got two turkeys two turkeys in the super bowl we all remember that right the embrace between tom brady and gronk on the field after the super bowl win two turkeys well this is a this is another embrace with the defensive player uh telling him no turkeys so whether it's two turkeys or no turkeys they all contributed to the win if you're not smiling after watching that then you've got no heart just like the tin man on the wizard of us last year man i started out a hundred like what what do you mean what that's all right like come on now right you gotta start somewhere make our mark make a point right now make a statement good these inside linebackers man they are so tough they go in so damn hard with whatever confronts them on the field they are absolute enforcers and they're ready to initiate contact at any moment they ain't gonna the best of the linebackers right the most aggressive of linebackers they ain't gonna absorb contact they're gonna initiate it and when you've got a running back wanting to initiate contact with that linebacker you've got a real collision on your hands not only that but it's exciting isn't it dangerous but exciting i said the number one thing about levante did that made him so good is his consistency you know day in and day out every game we're definitely gonna hear about this guy whether it's practice the game you're gonna get the same levante you're gonna bring the same swagger the same game and nobody's ever gonna be able to count them out his presence is gonna always be felt every time you take the field sorry i missed that one i was just admiring his facial hair and thinking yeah i'm yeah yeah anyways breakouts that could have been interception i gotta switch that oh i gotta turn those interceptions i gotta add that to my stat list i only had one interception last year which is ruggy one but it was what that's cool second hand arrives for the first time good moment of my career man just understanding protection i might have a one-on-one with the back and then understand that the back with the running back understanding that the back is yeah the running back definitely needs to react a bit quicker than that best job in the world gone up against he does his homework you can tell he's in the film room and he's studying schemes and making sure that he understands the positions that the coaches on our end are trying to put him in nice play way to track him across the field way to way to stick with him a big man like travis kelsie but also way to use your patience to break it up what's up other Super Bowl champs wabanta who's been studying in his league quietly for nine years now been some dog days here man first eight years of my career not making it to the playoffs only having one winning season to get to the Super Bowl and win it everybody you know to show love we're going out of history dog legend of you say the tamper legend worldwide legend champion to the world champions of the world feel really good about it i just should go to show the respect i have for those guys you got to put a lot of that you got to put a lot of that success on the back of tom brady right the end of the day if brady hadn't come to tamper bay would they have made the playoffs i don't know don't at me but before we go we're going to look up his stats if he's been with that same team the entire time eight seasons in the league without making the playoffs and he's gone and done it last year but not only that won the Super Bowl i mean as a career does it get any better he's been a tamper bay buck in air for life since 2012 pick number 58 in the second round of the 2012 draft he's certainly a veteran he runs a four six five 40 yard dash he's listed it being six foot one two hundred and thirty five pounds 36 and a half inch vertical jump 9 foot 11 on the broad jump and 19 reps on the bench press the other thing i like to read is their deals so he signed a rookie deal four year 3.47 million dollars in 2015 he signed a five-year 50.25 million dollar contract extension and in 2021 he signed a two-year 25 million dollar contract extension with the bucks worth 20 million guaranteed so the man has secured multiple bags he's secured multiple sacks one of which last year was on Aaron Rodgers and i will say and i will say guys that as far as tackle count is concerned this is the most we've seen thus far 1,125 combined tackles in the NFL in 137 games let me say that again 1,125 total tackles in 137 games 24 total sacks 48 passes deflected two pick sixes 24 force fumbles 16 fumble recoveries and one fumble recovery for a touchdown he's got some bucks franchise records most fumble recoveries in a career with 16 most tackles for loss in a career most assisted tackles in a season most tackles for loss in a season and most fumble recoveries in a season the man is a defensive machine the man is a defensive machine and he's number 43 on the list of the top 100 players in the NFL for 2021 guys thank you so much for watching that brings us to the end of another episode of rugby player reacts and i hope you enjoyed if you want to support the channel hit the like button if you want to go one step further head down into the description box below and check out our video sponsor and affiliate links for certain products that i use and i enjoy on a daily basis and you might too so guys thank you for watching and peace out


Welcome to this Cillium Maintainers Track session. My name is Liz Rice. We're going to have some guest speakers today to talk about how they've been using Cillium and some updates about how you can learn about Cillium. But let's just start by saying welcome to Cillium. How many of you are already using Cillium? Pretty good show of hands. And also put your hand up if you have contributed to Cillium. Okay, hopefully next time you will come there will be a bigger number of hands but thank you to everyone who's been contributing and thank you to everyone who's been using Cillium. So let's just have a quick refresh on what Cillium is. Probably most of you know it best as a CNI, a networking solution for Kubernetes, although it isn't just for Kubernetes. You will probably be aware of Cillium's service mesh and some of the features we've been doing there around Ingress and Gateway API and mutual authentication that we've been talking about this week. How many of you have used Hubble for observing network packets? Yeah, I think it's one of the real strong points of Cillium that you can not only connect, the packets aren't just flowing but you can also observe them with Hubble. And then finally, the Tetragon subproject. Anyone here using Tetragon? Okay, again, that's another one I expect next time. There will be a bigger show of hands. Tetragon is the project that uses EBPF for runtime security, observability and enforcement. And all of these things, of course, are built on EBPF, which is very exciting technology that allows us to change the way the kernel behaves. Did anybody come to see that EBPF documentary screening last night? It's so good. It's a half hour of your life that you will not regret if you watch that documentary. It's really good. So, Tetragon reached 1.0. Give it a round of applause for everybody who worked on Tetragon. So Tetragon is using EBPF to detect events which may be relevant for security purposes. Because we're in the kernel, we can detect file access or network access or changes of privilege, all of these kind of things that are very significant potentially for detecting malicious activity. And the other thing that's really important about Tetragon is that those events are filtered in kernel. So it's extremely high performance. We've done some measurements pretty recently about the performance impact. Normally when you add a security tool or anything that's adding a ton of observability, it might have an impact on performance. But you'll see some really low numbers, under 2% CPU usage for some really useful observability going on. So the performance is excellent. Tetragon is 1.0 and ready for use in production. So we want to hear when you try it. We want you to tell us how you get on. We want you to raise issues and contribute profiles and just tell us how Tetragon has been for you. The other element alluded to this earlier is that Cillium is not just for connecting within a Kubernetes cluster. We have cluster mesh, which allows us to connect multiple clusters. We have Cillium mesh, which allows us to connect with external workloads, have ingress from external traffic and essentially meet all of your connectivity needs with Cillium. I guess that leads us on to the other big piece of news, and I'm sure you all know this, but I think we're going to have another round of applause for it. The fact that Cillium is now graduated in the CNCF. So a massive thank you to everyone who has really done anything at all with Cillium because even just adding your company to the adopters list has had an impact on this and enabled this milestone. I think everyone who has been involved can be really proud. If you're not involved yet and you're thinking, I want to be part of this rocket ship, then there is the Cillium contributor ladder which lays out how you can work your way into the Cillium community, whether that's through code contributions or non-code contributions like educational material or documentation or community management, we're really interested in non-code contributions as well as actually fixing issues and adding features. If you do want to get involved, you have an idea for a feature or you want some advice. There's a weekly Cillium developer meeting that happens on Wednesdays and we also now have a monthly, APAC friendly time zone meeting as well. All the details for this are on the Cillium readme and you also can find all this information in Cillium Slack. How many of you are in Cillium Slack? Okay, if you're not already, it's a really great Slack.Cillium.io or you find the information on the Cillium readme. Really, there's a ton of people there, like 18,000 people who are interested in Cillium and EBPF and it's a great place to share information and get advice. I mentioned this already, I stole my own thunder but if you haven't already seen it, definitely go and watch the EBPF documentary. The final thing that I want to leave you with is I would like you to take a picture of this URL or scan that QR code and fill in the survey and tell us about your experiences with Cillium and tell us about what you want to see next and give us the feedback that helps us to move the project along to its next success. With that, I would like to welcome James McShane and we're going to tell us about how they're using Cillium in the wild. Let's give James a round of applause. Thank you, Liz. The Cillium team is really killing it at this conference. It has been, you want to talk about some buzz. They've done a spectacular job in this year in their community and I think that's what really drives our usage of Cillium in the wild. Who am I? My name is James McShane. I'm director of engineering at Super Orbital. We are a cloud-native consulting services firm as well as offering training curriculum. I am trying to resurrect the Cincinnati cloud-native meet-up. If any of you are in Cincinnati, come find me afterwards. We'll make it happen. I've contributed to Tecton, Argo and Cillium, though don't go look my PR at Cillium. I've done a lot of work with the team and getting real production use cases out for Cillium at a couple of our clients. Our team focuses on delivering high-leverage projects requiring deep integration across multiple teams and in large end-user environments. For us, the way that I see it, Cillium has really nailed the delivery and the maintenance across hundreds of clusters, thousands of services and all the major Kubernetes providers and provided it for us a consistent strata on which to build network observability, network security and it makes it really easy for us to build solutions on top of that where enterprises can trust that they are delivering on top of a secure platform that they can then trust their applications on top of. This is where we really started our path of utilizing Cillium is thinking about it from the network security perspective. For us, this has evolved from a set of layer 3, 4, 7 policies now to think about security policies as application. When you think about a large multi-cluster, multi-region delivery, the key thing for us is to be able to say, hey, I've got this policy set that is its own application. I need to ensure that I can modify my policies consistently. I can get those delivered across, validated in a test environment, run a number of validations to make sure when I release this out into the wild for my edge release customers that I know that I'm not going to break their existing workflows. On the back end, we observe that with looking at the network flows it's a little bit difficult, but the key thing is, if you've already started breaking your customers and you're seeing the impact of that, the goal is to validate and ensure that that consistent policy set is enforced before we get there. By treating this policy as applications, it's also really useful for security teams that want to know what's going on in their environments that want to know how is this being enforced. They can view our GitOps delivery model as their place as the source of truth for how is my network being secured inside of these clusters that I deliver applications to. It starts there when it comes to delivery because we really want to, when it comes to these high-leverage enterprise projects, we need to involve security from the start. It's that shift-left mentality that Axilium is at the root of for us when we're delivering these policy sets across multi-region, multi-cluster environment. Then, as we look into the work that's been done in 2023, I really see the buzz of the project, the significant effort that's been done in the community, has immediate impact for us in our use cases. I put this last, but I'll be honest, it's one of the biggest things that has improved the observability and the operational aspect of Axilium for us is separating out the Envoy-Damon set into a separate deployment, separate unit. It's a very simple thing. It's a separate process. It's running Envoy with Axilium for the later seven policy management. But those kinds of usability improvements have been consistent for us as we go from, I was here up in Detroit last year and talking about what Axilium 110 and 111 had provided for our team. I just see that consistent delivery going on in this project. Things like enterprise customers need supply chain validation for their open-source artifacts. These things that are going on in the open-source ecosystem are really critical to delivering secure environments that start from delivery in the repository down to the runtime security environment that you need to be able to monitor and need to be able to enforce. For us, when I think about the use cases that we haven't yet picked up that I'm really excited about, mutual authentication is absolutely like the top of mind for us as we move forward. These are use cases that we've been asked about consistently by our customers for a really long time because everyone wants this kind of transparent encryption from service to service and Axilium makes it so easy. Thomas will talk about that a little bit more later in the presentation. Unified spiffy identity across the cluster boundary with Axilium service mesh is another thing that we can then utilize in other APIs to use that identity for all authorization mechanisms. The BGP control plane, I know Marino is just these kind of improvements are really in line with the kind of things that we've needed to see in the delivery of our applications on top of Axilium. For us, in the runtime, it's about pairing security and observability. We put together the observability of Hubble seeing those network flows, the process flows in that immediate nature that Hubble provides. Tetragon is the tool that we've needed for a long time when it comes down to monitoring and maintenance of SIS calls. That's a really key use case. We were working with a client in 2020 that wanted to do this deep-level integration into SIS calls and we ended up using SETCOM policies that have been around for a really long time, but the maintenance of those types of policies, especially across nodes that have less host access and different host profiles when you get into different operating systems and different architectures, Tetragon enables us to build better visibility around that that enables enforcement. By bringing that centrally and allowing us to view and query and those sorts of things, we can then build consistent policies that enable us to get far more granular about the SIS calls that these containers should do. The next steps for us with Tetragon is to bring that back and treat that policy as code in the same way. Take our network policy approach of delivering that starting from the repository to drive those things and we want to do the same thing in Tetragon as well. What's next for us is very much in line with the things Liz was talking about. Gateway API integration, Syllium service mesh with mutual authentication and then using Tetragon to make that runtime security even more of a reality than it is today. Please feel free to come up and talk to me afterwards about your end-user use cases with Syllium and we're really excited to be a part of this community. We'll go ahead and Hamath will come up and talk about learning with Syllium. Thanks, James. Hello, everyone. We wanted to take some time to talk about some new parts and updates for how we go about learning about Syllium. A quick introduction about me. I'm a senior software engineer at Datadog. Datadog is an observability company and I work at a team called Compute Data Plane which is responsible for managing Syllium for all of Datadog. We run hundreds of Kubernetes clusters and tens of thousands of nodes. Syllium CNCF maintainer. I primarily work on the SIG IPAM which is the different IPAM modes in Syllium. I also spend a lot of time in Azure and AWS modes. You can find me on Syllium Slack, our community meetings, as Liz mentioned, on Wednesdays. For this section, I want to start this off with a quick question. How are all of you learning about Syllium these days? What are some of the resources that have helped you learn Syllium? Anyone? Did not expect that, but okay. Blogs, yeah. Perfect, yeah. So, here's what I had in mind, right? Documentation, docs and blogs, Echo office hours, maybe reading code, running Syllium at your own company or home lab. There are different ways. There are so many resources that you could use to learn about Syllium. But depending on your background, your own path might look completely different, right? And part of what makes it slightly tricky is that Syllium is extremely feature-rich. There are lots of features. I went to the Syllium IO website earlier today and I could not fit all of the features into one single slide. And that's how many features Syllium has. And Syllium is a very fast-paced project. I saw a screenshot from earlier today. In the last one month, we had 90 plus authors making 362 pull requests and there were four major releases. And I can tell from our own experience, it's hard to keep up with the pace at which Syllium is developing and building new features. So, the community has been constantly adding lots of new features. And where I'm getting at with all this is a graduated CNCF project with as much complexity as Syllium needs a structured learning path, right? So, the community has been really excited that CNCF is finally coming up with a Syllium Certified Associate exam. And this is an entry-level certification exam. And the ideal candidates would require some Kubernetes knowledge, networking background, and some hands-on experience with Syllium, of course. And this should allow users to validate their Syllium knowledge and also gives an opportunity for companies to identify Syllium talent. So, we are really, really excited about that. And here's how the blueprint looks like currently. And this blueprint was designed by a set of subject matter experts from different companies. And all of us have agreed on these topics as the first topics that somebody should try and understand when you're getting into Syllium. And so, who's creating this CCA, right? So, there are a set of 15, I think, subject matter experts from different companies. We're all collaborating with each other to try and come up with a certification exam. So, the process is basically all of us draft our own questions and that goes into a peer review process. And we all exchange feedback on those questions and once those questions pass, once you add all that feedback back in, it gets added to the question bank, right? So, here's a sample question. I'll give you all a few seconds to read about it. Any guesses? Hopefully not from the first one. First one? Yeah. Cool. So, the idea of this certification is it's meant to be an intro level certification. You are not required to be an EBPF expert or a networking expert because we understand that there are different kinds of engineers from different backgrounds that are all trying to learn Syllium for their own use cases. So, this is meant to create a learning path for everybody and create some structure around that. So, how do we go about preparing for CCA, right? So, Isovilleant has done a great job at building a set of labs and these labs have their own distinct learning paths. So, based on your background, you can pick your own path and explore different labs in each of those paths and that is a great starting point. And on top of that, there's a course from CNTF called Introduction to Syllium which is completely free. So, check the course out. And, of course, the official reference guide documentation. I know everybody says, read the documentation but nobody really does, but we should. It has a lot of good content in there and that is the official guide for the entire certification and every time you write a new question, we are required to cite things from it. And here's a link. If you want to get notified about updates on when the certification would be released, we expect it to be available early next year. Right? Yeah. So, what else is in store? I was told that after Syllium Certified Associate Exam launches, we might be working on a few advanced certifications as well. Hopefully, if everything goes well. And that's pretty much all I had in mind. I know all of you are waiting to hear from Thomas. So, let's invite Thomas, CTO of Isovilleant. Thank you. Thank you very much. All right, we've heard Syllium is a fast-paced project. I have the pleasure to talk a little bit about what is next for Syllium, because we keep on hearing from you what are your challenges, what do you want Syllium to solve next for you. So, let's dig in and give a bit of an outlook what is planned in the next roughly six months. Of course, we will continue evolving the mutual authentication that we have released or introduced in 1.14. We're not fully done with this feature. It's still in better phase. We will continue to evolve this, looking to hopefully market stable in 1.15 that is upcoming, or maybe 1.16, depending on how fast we all write code. We will of course look into fully implementing Gateway API as it evolves. Gateway API itself is not fully complete yet. It has reached a 1.0 milestone, but we're still adding TCP, UDP route support and the SPAC and the standard is still evolving. We're continuously keeping up, so whatever is being put into the SPAC we immediately implement in Syllium itself, but Gateway API itself is also still moving. I'll talk a little bit about NetKit, which was formerly called MetaDevice, or something very exciting. We can still make networking go faster. It's hard to believe at this point, but we keep on finding ways to improve performance. Then we also have a new Syllium initiative that will briefly talk about remove the friction. Let's dive in. Mutual authentication. Very exciting that initially we have been able to do encryption with WireGuard and IPsec, so if you had a desire to just encrypt all of your traffic, that was incredibly simple. You could enable a simple single helm flag, enable encryption, choose IPsec in WireGuard and automatically encrypt your entire network without actually having to manage keys or run an entire service mesh. If you have been looking for purely encryption, this was a great option. But then we have also heard from many of you you also want mutual authentication on top of that and please without sidecars, which is why we have brought mutual authentication for the first time in 114. We also wanted to keep it simple. You can now use a single helm flag to bring in an entire spiffy spire stack. So Syllym will run a spire server as well as a spire agent on all the nodes and automatically generate certificates for all the deployments you are running. And then you can use network policies. As you can see on the screen there, existing Syllym network policy adds two lines of YAML to require authentication and Syllym does all the magic in the background to actually run the mutual authentication handshake. So we're trying to hide a lot of the complexity that exists when running mutual authentication, which is just the necessity of kind of the complex inner workings of handling certificates and handshake and all of that and exposing the user experience and keeping that as simple as possible. I talked a little bit about this NetKit device and it will go a little bit deeper down the stack. So what is NetKit? This was called MetaDevice until recently. It's a new kernel feature and if you want to learn more about what exactly that is, I recommend Daniel Borgman's talk about MetaDevices. So far we have been kind of abusing what's called a virtual Ethernet device, which is a software device, like a software patch cable which is representing a virtual Ethernet essentially. It's not been built at all for container use cases in any ways. I've been kind of just abusing this. There was no actual dedicated network device that was built for container workloads and running containers has become obviously a primary use case for Linux. So why not come up with a native network device specifically built for container workloads? Because a lot of the performance overhead for container networking was that we not only had a networking stack inside of the container, the network namespace of the container, we also had an entire networking stack outside. So far Sillim has been able to bypass quite a lot of that, but not quite all of it. And with NetKit, we're able to essentially remove all of the network stack overhead, and you can see that this Meta, the slides are still old, so the NetKit rename came after the slides were created. You can see that we can now essentially almost directly connect the network interface card of the VM or the server with the physical interface that's leading into the container. And I will show you what that actually means in terms of performance because it gets exciting. You can see a couple of numbers here. We have in yellow the baseline. That's host networking, not running any containers that's simply benchmarking one node, talking to another node. That's the baseline. That's what we want to get to. Then in light blue we see the old stack, virtual Ethernet device, no modifications. And then in red we see the prior optimizations that we have done to bypass quite a lot of that. And you can see the line has went up and we're almost as fast as host networking. And now with NetKit we're essentially able, that's the purple, we're essentially being able to get to almost host level just from a throughput perspective. It gets better because we can do even better. Here lower is better. This means the baseline is all the way on the left. And you can see the representation is the first five on the left. That's kind of what we've seen before. If we can take it one step further and if your application uses a kernel feature called 0copy, that is a special system call which avoids copying the data from the application into the kernel. It's called 0copy. We avoid the memory copy. And at this point we're so fast that the memory bandwidth, the memory, the throughput of the memory in your server is becoming the limiting factor. If you can use 0copy in the application you can go see it all the way down. And that's an improvement of six times in terms of performance. If you're running in particular workloads like video streaming or any sort of data intensive workloads, this is exactly what you will want. NetKit is currently being merged into the kernel and we already have a branch in Cillium to support this and as soon as kernels are released with this feature you can start using this. Cillium initiative removed the friction. Cillium is very feature rich. We are trying to accommodate all of you with all your features from running a Cillium on a Raspberry Pi to data doc clusters of thousands of nodes to heavily regulated enterprise environments and this needs everything from encryption to high scale service mesh, all of it. We are doing our best to optimize both the learning of Cillium, how you discover Cillium, how you learn about Cillium and the usage of it, migration to it and so on. But we have been dealing with this for such a long time. It's sometimes hard to understand what's actually hard. So I would invite all of you to, as you have learned Cillium or if you have migrated to Cillium, if you started using Cillium please give us feedback what was hard. You need to know that in order to remove that sort of friction. So if you started this initiative, there's a QR code, you will also find it in the Cillium Slack. If you have any sort of input on what was hard with Cillium or what we could optimize on learning about Cillium, what is missing, please tell us because we would love to optimize that. Sometimes it's just hard to actually know. And with that I think, first of all I would like to thank all of you for coming today and if you have questions on Cillium, if you want to contribute to Cillium or if you just want to learn more or try it out, Cillium.io is the best way to get started. You will have URL links to Slack. You can find the documentation, you have the contributor letter, you have introduction material, tutorials, labs and so on. That's a great starting point. And of course the code is all on GitHub like Cillium organization, Hubble, Tetragon, Cillium and so on. And with that I think we have a bit of time for questions and you can open it up and ask essentially any question on Cillium. We have a lot of expertise here today. So go ahead. Thank you very much. Any questions? Yes, I can also repeat the question. Questions, how are we making money as I surveillance? We are offering an enterprise distribution of Cillium and if you would like to have enterprise great support you can give us a bit of money. Yes. Could you speak just a little bit louder? Yes, the question is what algorithms are we using for mutual authentication. So mutual authentication we are using TLS of Go. So the mutual authentication handshake is using standard TLS using Golang. That's for the mutual authentication handshake. The encryption is being performed using IPsec and WireGuard and in particular with IPsec you can run a FIPS compliant kernel limit the ciphers to let's say ASCBC and only run FIPS compliant ciphers. But you can use the full cipher set of IPsec, standard WireGuard ciphers and on the authentication side it's go TLS. Other questions? You can also tell me about the friction of Cillium. Yes. Specifically for low balancing? Yes. So the question is what sort of algorithms are available for low balancing. Cillium offers both layer 3, layer 4 and layer 7 low balancing. Layer 3 and layer 4 low balancing is always performed in EBPF and we have round robin, we have weighted round robin so you can send a certain percentage of traffic into one direction. We have session affinity that you can ensure for a particular client all requests are going to the same backend. Then for layer 7 all of the routing is being done using Envoy and you have a wide variety of algorithms, least connected, round robin, maglev, all the consistent hashing algorithms. We also have a standalone load balancer which can run outside of Kubernetes that's maglev based performs consistent hashing. We also support DSR, direct server return so we can preserve the client IP. So I would say we are implementing and supporting the standard load balancing algorithms that you will find in other software and products. I think we have time for one last question. Yes. Do we see a reason to move away from Envoy? Envoy is a fantastic project. As any proxy it does introduce overhead. So if we're talking XDP, EBPF based load balancer we're talking 15 million packets per second in load balancing capacity. If we try to move that through Envoy that's just not possible. So the reason to not use any proxy including Envoy is performance. At the same time we cannot perform all layer 7 load balancing in EBPF at the moment. Maybe we will never can. That's why we use Envoy. The reason, the motivation is performance but in particular things like HTTP parsing and load balancing splicing connections that's when we use Envoy. I think we're running out of time. I'd like to thank all of you for coming and have a safe trip home. Thank you very much. We have one more quick thing. We have two giant bees that Bill is going to set flight. Set them free. So if you're lucky. Brilliant. Safe travels everyone. Thanks for joining us today.


Thank you, my name is Lyn Ramsey. I'm from Lyrr imagination Institute of Technology and I'm a Head of Teaching and Learning there, I'm also Program Manager for the west-north-west cluster. This proposal is from the west-north-west cluster, we worked together collaboratively already on a number of projects but specifically projects looking at professional development so we can talk to some of those. I suppose for a personal level we're delighted to be bringing a programme at this forward. I know I was formerly head department and had that same sort of panic as head department as I had as a new lecturer thinking I'm in this job and I have no qualifications at all in this space and I suppose in part this is a reaction to that sort of experience. So we'll take you through a sort of roadmap for the day who, what and why is the TLC took a little bit about the engagement and particularly what that means in terms of our region. There's particular perspectives that we think are relevant in terms of how we engage with our target groups. Touch briefly maybe on the alignment with the professional development framework. I think our sense is that the project aligns very well with the professional development framework. Talk a little bit about the implementation plan and in particular the impact on students and then the value for money and legacy aspects. So in terms of the team here I might just hand them over to themselves to introduce them. My name is Maria Gallo and I am the development manager in the office of the president at San Angelo's College Sligo which is a college of MUI Galway. Hopefully to be merged with MUI Galway next year. Hi, I'm Isabelle Cunninghamma from LWIT. I lecture in management and leadership. I'm Korean again. I'm from GMI T and I work in teaching and learning terms and I'm Jennifer Billigan and I'm an instruction and designer in LWIT. So we talked about the region. This is a nice picture of Mockish taken by one of our graduates from LWIT, Rita Wilson. So I think our project is quite a simple project and I say it's based on the relationship we already have across the cluster. The cluster is of five institutions across the west, northwest so LWIT, IT, Sligo, GMIT, MUI Galway and San Angelo's as Maria mentioned seem to be merged with MUI Galway and within the cluster we've already quite a bit of collaboration but in essence this project has two two elements. One to develop an online and blended community of practice bringing together academic and non-academic managers to share experiences of teaching and learning to engage with the digital roadmap and to engage with the professional development framework. We think our project aligns quite nicely with one of the proposals you'll see tomorrow which is the Atlas project and one of the main motivations in having a blended approach is to have the opportunity for first managers from the academic and non-academic areas across the four institutions to network and to share experiences that will help them when they move to the online stage since they'll already have built some whatever relationship. We're going to work with three external partners from Florida, Rohan Joala, from Loughborough University and also from the University of Derby where Isabel has a lot of experience and Derby in particular is an interesting partner because they have a lot of experience of an online community of practice. So that's in essence the first element of the project. The second element of the project is to take the the learning that we've had from this online forum and to help develop a bespoke module for leadership for mentoring for teaching leadership in teaching and learning. The module would be a sort of module in a box essentially a series of digital resources with an accredited level nine module and they would draw on best practice. In preparation for this, Maria and I did a piece of research over the summer where we worked with some of our staff in each of the cluster institutions who are undertaking level 10 studies. From letter Kenny alone we have 32 staff undertaking PhDs and we were very interested to see what the experience of our own staff who were students was. So we know I think quite well the experience of our undergraduate staff and the experience of our own staff who are PhD students we knew less of and the research was very telling and in particular one of the things that struck us most was how isolated some of the staff felt and how they felt that managers and in particular senior managers didn't know what their experience was, didn't know what it meant in terms of time commitment, didn't know the impact it had on their personal and family lives and crucially I think in terms of professional development weren't sure where the research would take them in the future. How was it to be supported by their institutions? So that was part of our motivation to have an evidence-based perspective and we'd hope to similarly extract the evidence of managers through the community of practice in terms of what their experience trying to lead in these areas are. I know in the time that I've been academic manager there's been no PMDS at all, professional development, no professional development but not a lot of mentoring, not a lot of necessarily engagement in a formal way at management or senior management level so we feel there's a gap there. So in terms of target groups, in terms of engaging the managers, we would hope to target at least five or probably up to eight managers, academic and from the functional areas, we're particularly interested in the non-academic managers, I don't believe I'm really comfortable calling that with the managers from the functional areas, the HR managers, the IT managers, the librarians, who's role is crucial in terms of providing a supportive environment for students. We think the registrars will be key in terms of our recruitment. Our operations group within the cluster at the moment is comprised of the registrars, they're very bought into this process and it aligns very well with the strategic plans with each of the institutions and I say each of the institutions is very committed to professional development of their staff, we all have a number of staff undertaking accredited CPD at the moment particularly at the PhD level. So we imagine that the registrars will act as recruiters for us. The regional perspective I think is important here, we're small institutions, we know each other very well across the cluster, we know each other very well so we will champion this programme. Our experience in the cluster has been working with NUI all the way in terms of bringing our own staff onto the structure of PhD, there's been very positive but it works at a very granular level. So when Lucy burned the VP for graduate studies got involved in that project, she came to visit each of the institutions to promote the project, the PhD project and explain what the commitment would be for staff and we think that's the key, it's a personal relationship that we can bring to bear in terms of recruitment. In terms of student engagement so we developed a system where students would be part of the steering and operational group, the issue rep from the BMW region was very keen to be involved in letter county, we have a lot of students who've now been through the the end step the national student engagement project training our own presence part of that so we've got a lot of buy-in from the students reps and I think the question that we got back to the group from the national forum about what other ways are you engaging students was a useful one and paused us to think about the informal and non-formal way we could engage with students, I think it's something that we as an institutional letter can hear very mindful having been involved in the student engagement project that those informal and non-formal spaces are very important so we had a good discussion about how we could engage students and our idea would be to add the TLC days, the teaching and learning champion days to bring student focus groups into both of those days and in that way they could engage in a formal way through focus groups and an informal way through discussions that's one of the things that we've noticed in terms of our engagement with the end step that when we have training days and we've brought managers and senior managers into the informal spaces that work very well till around coffee breaks lunch times it was the start of interesting informal discussions. Crucially the approach here is based on an action learning methodology where the participants would develop different initiatives that they would roll out within their own functional areas or within their own departments and would review with the action learning set. Our idea would be that these initiatives would impact directly on student learning from whatever your area be, either as an academic manager or a non-academic manager. So in terms of alignment with the personal development framework and roadmap, the digital roadmap, our sense is this programme aligns very well with all aspects of the framework in terms of the topology of personal development activities. It runs a range of accredited, non-accredited elements and we've given some examples in that first column in terms of peer networking for collaboration, in terms of self-reflection, in terms of the unstructured non-accredited element, digital badging for participants through the online forum, and Isabella will talk more in detail about how that might work. In terms of structured accredited modules, it was interesting when we talked to some of the senior managers at the design stage about the digital badging, they were saying, I'm not interested in digital badging, I'm a voice scout, was the feedback you got for some, we were interested in the accredited module. Sharing that learning about what digital badging means with senior managers, I think that's a very powerful start of our conversation. Types of learning again, new learning for some, the digital learning will be very new learning for some, first to others not so much, but leadership might be a new aspect of their learning to consolidate where you're at in terms of some of your digital knowledge and move that on. Mentoring is the key element to the communities of practice in those action learning circles and leadership. Very often it's not in the formal roles of your title as manager, you'll know that very often within your own department it's the informal leaders who are key to change, so it's to know as a manager how to walk the walk instead, as also as talk the talk, our managers particularly in the institutes of technology have a three hour teaching requirement, not everyone avails of that opportunity if we call it that, but it is a fantastic opportunity as an academic manager to walk the kind of walk that you want to see. So an investing in your own continued professional development is very powerful in terms of academic leadership and in terms of the five domains we think we cover each of those in terms of the self professional identity professional communication and developing your skills and aligning to the digital world. The implementation plan that we laid out there is very clear, I think there's three quite distinct phases, the first phase in terms of a project development, the second phase in terms of the implementation, key to that would be continual evaluation, I think that would be Maria's role in the project to evaluate the experience of the participants to extract the learning for them to see where there's areas where we need to develop more, to develop specific digital capacity if that's a case, and then the final legacy phase, a number of us in the institutes technology sector would have gone through this, our committee's training was something that the government sponsored maybe seven years ago just at the start where all this change was coming through and what was super about it was the opportunity to collaborate with colleagues across the sector, but it ended after the two days in Dublin that was it, there was no legacy and we would be very keen that the online element of the community practice would remain as something which other institutions could adopt and buy into, which something with their own managers could continue to work to, and then crucially that you're managed as a manager, you could bring it to your own academic staff or your non-academic staff who would support teaching and learning, so we think it's important that there's a legacy beyond just the community practice and beyond the life of this project, equally the development of the module with the digital elements would provide an opportunity for colleagues right across the country to share the knowledge from this project. So we have very clear outputs we think, first and foremost we want to create teaching and learning champions right across our region, we'll have the online forum with the bespoke digital resources, crucially it would be based on the experience of our own region, the needs of our own managers, the needs of our own students, this mentoring legacy and the modules and in terms of value for money and it was something that were asked back, I think the impact across the region will be significant, not just in terms of the managers who participated but then for all the staff that they will work with and the students that they will work with, those distributed leadership impacts I think will be significant. In terms of the costs it's both with comparable leadership programmes, I know for example their committees project was tens of thousands really with very little lasting impact and I suppose comparable leadership programmes for us particularly for us in the west north west if we want to send our guys to the HE academy in England we couldn't send a whole team of staff and when we put on training days we get really significant buy-in from across our institutions, Mark was involved in a day that we ran there recently where we had 94 of the staff turned up for a session on assessment for groups, yeah so I think when we have something that's put on locally we get very good buy-in and we've designed this project so that no one has to travel for more than four hours, the bulk of it is online, the two learning days one's in Lerrkinny and one's in IT in GMIT so no staff member has to travel for more than four hours and I think that's very impactful for our sense.


Hello testing testing Testing testing sound testing hello, hello, hello, hello Event at the SDC so the International Atomic Energy AC has recently target energy by 2030 and net zero Compacts reduced under the energy compacts History and the IAEA has introduced act this past September title As a one of the members the family agency has been working on the AC topic Member states to ensure they are students of nuclear Conducting the secure and the system To the agents in the second part of that is a new source to the climate change Our all activities including our gender equity for secretary So One initiative called married Program to To attract more female So that has been So Through this Thank you the overview on the energy The first of the you seen in the gender we can simply on this flagship that is there my ago now Because a nuclear Is And those show contribution of IAEA Secretary general so show how we can cooperate with our Organization and our partners with this work in a collective manner nuclear was from and the energy unit is in the Specialism for climate billion weakness that is that is rising up. I do think is Why Billions show up in this cup. So in the 40 events to show to talk about in the cooperation with our part We're not alone. We are cooperating with international organization Any questions from the


I'm Bill Lucas, I'm Professor of Learning and Director of the Centre for Real World Learning at the University of Winchester and really for the last decade my focus has been on real world learning, especially on how young people and older people learn most effectively. So practitioners in FE and work-based learning have a really important role in creating a just and socially cohesive society and a successful and prosperous one, but I don't think enough attention has been played to the role of those individuals. We want the highest possible standards and we want to be really explicit about the role of professional learning. Perhaps most importantly, I and all my colleagues would like to see a re-esteeming of the importance of the workforce and of the value of professional learning. So most effective education systems have professional standards. Wales had some, but I think it would be truthful to say that they were quite complex. It's nearly 10 years since the last standards were created and the world's moved on. So the standards have been developed collaboratively over a period of about nine months. We gather together an expert group of both those who practice and those who think about practice and we work together in a series of workshops and we rather amazingly managed to agree on almost everything. So the big changes here are the length of the document. It's much shorter, it's much more accessible but the result is a set of standards that I believe are owned by the sector for whom they're designed. We hope these will be simpler and used widely by the sector. We also believe that they're quite innovative so we hope that Wales will see itself at the forefront of thinking about what it is to be a work-based learning or FE practitioner in this important part of the new millennium.


Going on everyone Sam here with late in sports cards doing a nine-box mixer for Johnny H We got 7 22 at tops tier one baseball and 2 at 22 a Panini capstone baseball. So good luck here Johnny see what we got buddy We're like crying We were crying New age Lou Bob Got David Ortiz nice one there. Wow on the Jersey auto peak There you go. Congrats on that one there Johnny good start big poppy. I don't believe that is numbered Nice hit. There's Joe Ryan rookie dual jersey for the twins Think you need some more prism racing Kyle if you order it now it'll go Probably I mean we could sneak one in for you if you want it tonight Yeah, I kind of know what you mean on that table. So New age Boba chef plan bought a Kevin Harvick full size There's Carlos Rodin one of ten on the black nice one there Jaren Durand Nice one there rookie Jersey.  It's a good product Yeah, I want to see that for sure. That sounds cool I know Tyler McGill base auto for the Mets not numbered Bobby Whit new age rookie. I was Korea Show you Tony on the crest. All right, that'll do it for capstone box. Number one. Let's do capstone box number two now Bojack Yeah, I agree Kyle got any Bojack Edwin Diaz Looks kind of like Zenith. It's like Zenith and recon put together There's ten or how for the Red Sox on the summit auto Manny Machata Eating Sean's over there eating Seth beer for the Diamondbacks on the dual jersey. I'm eating sleeves Literally eating sleeves there. What are you? Yeah, what are you free? Come on What are you three I know honestly, yeah, someone get him as binky is right upper pool halls new age materials for the Cardinals That is game more nice. How's there Amiris? So Lane really is fetic. Yeah, you do need a spider-man water bottle Sean. Do you has one I can tell you I do not You know what I do not have It is a three-year-old spider-man water bottle That I can assure you Nolan Arnato 3 out of 25 on the autograph very nice Artist proof Alex Monella that is six out of 49 Alonzo. All right, that'll do it for both capstones Up next. We've got tier one Let's see what the odds were Whitmerefields the 399 Jersey guard That's wisdom that is 212 out of 299 and we've got Brandon Lau 8 of 10 game use memorabilia for the raise Don't know where that would be on a raise Jersey. That's purple Maybe the wrong patch Gonna send you an empty box and wrapper Johnny because that is definitely not a raised patch I mean never brownling Brandon Lau was ever a rocky So still a nice one there though Yeah, right He's Monty Grande all 297 out of 349 Could be a throwback devil's right devil raised Jersey, but I don't know I don't think so Because I don't even think the devil raised jerseys that they wear now like the throwback ones are purple that is Spencer walk-ins 69 out of 299 and Joey vato 23 out of 25 to color to color hatch auto. I don't think it's I don't think it's purple right now Yeah, even the throwback that they wear it's not purple Like here's the mate here. I'll take you to the main camera. It's a Like that's this is the the one that you guys are all thinking of right here That's not that there's no purple in there and there's no purple with like a white cut either So so yeah, we're gonna send an empty box and wrap her there. There's Javi bias the 399 Air patch even one of one honestly dude Lars New Park 22 out of 25 and nice one here Jose L To base 63 out of 75 for the Astros There's no purple in this. No, it's not purple. They don't have a purple jersey that they wear now Trust me. I am if what it comes to uniforms, man, I Will take anybody on had to had one of one on one with that stuff There's Yachty to 299 game use Jersey for the Cardinals. There's the franimal fran mill race I had so sick 169 out of 299 for the Guardians This one's so nasty. How about a Jeff Bagwell 25 of 25? Game use three color patch and bat patch. I Have not yet Kyle I'm gonna do that my next day off. I've got like four straight now three straight days off this weekend and I'm gonna take that and because Heather got me a lids gift card, too So I'm gonna be buying a new couple new hats for sure Walker Bueller to 249 Auto Lopez 16 out of 25 figure out something. There's George Springer 28 out of 75 on the Jersey auto Black cruise to 399 TJ Friedel to 299 rookie auto for the Reds and tier one talent Jim Rice 212 out of 299 for the Red Sox We got an extra hit in here So we do John Carlos Dan to 399 Josh Peter to 399. There's Aaron Ashfield to 299 nice one there It's a great way to end the break right here, man. Here you go Johnny. How about to 125 Juan Soto? Boom Congrats on that there Johnny. That's awesome, dude That'll do it for your break there Johnny. Congrats on all the hits buddy. We'll get those right out to you my man Thanks as always


Fy glwnaeth y trafodi沒事 yng Nghymru. Felly, yn gwael i ddim yn wirthgurff fel Rhyf'r Rhyw Llyfr Hôl yn yng structures, yn yluodol, ac yn y Llyfr Heliwyr, yn y Llyfr Hôl, yn y Llyfr Heliwyh Llyfr Hôl, yn y Llyfr Heliwyr, yn y Llyfr Heliwyr yr Aelodau Biddrug, yn yr Aelodau Llyfr Heliwyr yn y Llyfr Heliwyr, yn y Llyfr Heliwyr, yn y Llyfr Heliwyr, yn y Llyfr Heliwyr, yn y Llyfr Heliwyr, yn osud, yn yr Aelodau Biddrug, yn y Llyfr conservation number 2, order 2021, urgent continuation order 2022, SSI 2020, slash 39, and I refer members to paper 1 and 3. No motion to another instrument has been lodged. Does any member have any comment on this instrument? Could you please raise your hand, or if you're remote, please type R in the chat box. Go ahead, Mercedes. Thank you. You might be getting some feedback. I can hear a bit of an echo, sorry. It was just a comment about the type of fishing that's been restricted. I understand that, when the Government announced their public consultation on the proposals, they have confirmed that hand-diving for scallops will no longer be prohibited, but creeling will still be prohibited, along with dredging and trawling. I wondered if we could seek some clarification from the minister as to why those different types of fishing have been treated the same way, despite the fact that the Scottish Government categorises dredging as severe, whereas creeling is lower impact. I know previously that they have said that they want to take a precautionary approach, but then they chose the smaller of two possible boundary areas. I'm just confused as to whether it's precautionary or not, because it seems that, within the smaller boundary, everything will be prohibited. Outside the boundary, everything is allowed when we have different types of fishing with different impact levels. If we could seek some clarity from the minister as to why they have been categorised in the same way, I'd be grateful. Thank you, Mercedes. The committee can certainly ask the cabinet secretary for clarification on the scientific evidence. Rachael Hamilton. We'll make sure that we're right for clarification. Are members content to note the instrument? Our second item of business today is consideration of the Organic Derogation Amendments Regulations 2022, and I refer members to papers 2 and 3 from page 8. Under the protocol between the Scottish Parliament and the Scottish Government, the consent notification has been categorised as type 1, meaning that the Scottish Parliament's agreement is sought before the Scottish Government gives consent to the UK Government making secondary legislation in devolved competence. I refer members to paragraph 2 on page 13, which sets out the recommendations to the committee. Does any member have any comments on the recommendations or any aspect of the consent notification? Please raise your hand or type R in the chat box. Rachael Hamilton. I just wanted clarification from the minister why they had chosen to go along with the same policy as the UK. I believe that there's an issue in supply of some of the material for organic pollets. However, there's no explanation in here. Every time we do some legislation, there's never an explanation as to why the Scottish Government chose to not take a different route from the rest of the UK. I was just wanting some clarification on that, if I may. We can write for clarification on that. Any other comments? Is the committee content that the provision set out in the road vocation should be included in the proposed UKSI? Raise your hand or type N in the chat box. We do not agree otherwise. I'll presume that members are content. Thank you. We are content. Finally, is the committee content to delegate authority to me to sign off a letter to the Scottish Government informing it of our decision today? Thank you. That concludes our business in public and we now move into private session.


I just got a comment from one of our actually a question. He messaged me personally through our security mentor Facebook and the guy said Hey, dude, I'm dealing with some negativity. People calling me out some things happening in my in my business in my life I'm dealing with a lot of personal negativity He said you have a tendency to respond really well to negativity to haters to bad comments to people hating on you in the group. I said dude, I Can't control what they do the only thing that I can control is how I Respond and when I respond how will I be remembered and Dude, should we even waste time on people that hate our guts? Who cares? Focus on developing a personal brand that people respect that hey that dude's ethical. He's positive.  I get other people in this industry And I try to collaborate.  They don't realize things that I've done They don't realize that hey I may make more money than they do or that you know in eight months I made a hundred and seventeen K, you know door knocking and cold-calling dude. I've I've past proven myself So I don't need to respond to those people. It's irrelevant Ignore the negativity focus on growth focus on blowing up your brand focus on creating long-term wealth and Ignore the haters or if you want to kind of like I do use them as fuel To surpass them if you haven't already to put them out of business and to freaking destroy them