OK, so thanks a lot for letting me speak at this conference. And also thanks a lot to you for coming. I realize it's the last hour, and you must all be pretty tired. So I try to not give it too hard talk. And also, I have to announce that at the end, my talk will be a little bit experimental in the sense that I cannot answer the main question I raise. Anyway, let me tell you what the talk is about. The talk is about graph complexes, which have been maybe not introduced, but at least popularized by Maxim Konsevich. So graph complexes, in general, are complexes of vector spaces, graded vector spaces with a differential, where? Excuse me? You think that he produced it. So OK, yeah, so there's ever some of some you introduced. And I have to say in my defense that I titled my paper, Maxim Konsevich's Graph Complex. And so on, so I. But yes, so the complexes I'm going to speak about today were introduced by Maxim Konsevich. So these complexes in general, so the underlying vector spaces are spaces of linear combinations, or of series of certain isomorphism classes of graphs. And you can put a differential on these spaces, and the differential is usually defined by either contracting an edge, or duly by splitting a vertex. Edge contraction or vertex splitting. And in the literature, there's a whole zoo of that graph complexes, because there are a lot of different types of graphs you can take, ribbon graphs, or ordinary graphs, or directed acyclic graphs, or otherwise decorated graphs. And these classes will give you different complexes a priori. I will talk today about the simplest version, where you just have ordinary graphs without any decoration. And these types of complexes were introduced by Maxim Konsevich. So let me give you a little bit more precise definition. Let me define a z, let's say, nk, the set of graphs. So they're not isomorphism classes of graphs, set of graphs that they are connected, and the vertices are at least wellened. And I say that the vertex set are the numbers from maybe, if I may change it, make a capital N, because I will use the lowercase n later, numbers from 1 to n. So you have n-numbered vertices, and k-directed edges. So each edge is just a pair of numbers. So you have a list of k pairs of numbers, and this is what I call a graph. Now let's also assign to each such graph a degree. And the degree, of course, is just a set, but the degree will be used later when I construct a vector space formally spent by these things. So the degree of a graph, this is some number n, which I fix, n times number of vertices minus 1, minus n minus 1 times the number of edges. So some number little n, which is a degree of every vertex, times number of vertices minus 1, minus number of edges, times degree minus n minus 1. So this is the degree of one edge. Then you have an action. So this is n for a sum n. Then small is equal to n. Possibly not equal to n capital N. OK. It's like for E n operator. Yes, so this n is the dimension. If you wish, these are vacuum graphs and some field theory, topological field theory, this n is the dimension. So maybe I should call it d, but there will be an E n operator. And usually you say E n operator and not E d operator. So this little graph and curve, the set of graphs is acted by some group. So the metric group in n letters acts by just permuting the labels on the vertices. Then you have action of sk by permuting the labels of the edges and an action by s2 to the k by permuting the direction of edges. Then we define the graph complex. The graph complex subscript n will be defined as a product over all capital N and k of a vector space, spanned by the set gra and k. And here without marking it in the notation, I assume that a graph with so many edges and vertices is put in this degree. And then I take invariance or coin variance. It doesn't matter much, just two different rotations. So coin variance, let's say, under this group action. And here I fix certain sign conventions. I'm sorry for being a little bit pedantic about the signs. Usually just skip over. But it happened to me many times that later people would ask the question anyway, so I just do it. So here I say that I let Sn act by permutations of the decorations of the vertices with sign if this little n here is odd. So you give the vertices an odd degree, so it's natural if you permute the labels on the vertices that you get a minus 1 if the permutation is odd. And these two things act by permutations of this k acts by permuting edges with plus minus if n is even. That also makes sense because we assign, in this case, an odd degree to the edges. So if I permute to edges, I should have a minus 1. And one piece of the sign convention is that if n is odd, the permutation of the directions of the individual edges also comes with a certain sign. For the moment being, if you don't care about this so much, you can just ignore the details about the signs. But remember that here we define two different complexes, essentially one for n even and one for n odd. So the signs matter modulo, sorry, the n matters only modulo 2 with respect to the signs. Let me give you my n deep, and then small, so a nice n. Small n, yeah. So lower case n matters. And your k is changing form. Your k is changing form. It's changing form. Our kids write in the tail of change, age, and so on. Yeah, like this. S e to the power k. Yes, it should be k. So maybe, yeah, the students always complain when I write this k in my lecture. So maybe, so let's just give some example. So elements of my complex are just some linear combinations of these morphism classes of graphs. For example, this one plus, I don't know, 3 half times this one, let's say. But one thing to notice is that if the graph has an odd symmetry, and odd symmetry using these sign conventions there, then the graph is 0. So for example, for n even, we know that the edges are odd. And this graph has a symmetry by interchanging two edges. So this has an odd symmetry, and this graph will be actually 0 in GCN for n even. So it's important to keep in mind that not all isomorphism graphs can appear, but only those with. OK, let's say k is, for all that I will talk about, let's say the characteristic of k is 0. But you're right for characteristic, not 2. Anyway, so the important thing to notice is that whether n is even or odd gives you a different complex. So different isomorphism classes will be present in this complex and others not.  So if you want to apply the differential to some graph gamma, what you do is you sum over all vertices of your graph. Then here's your graph. So here's the vertex you have. Then you delete this vertex. In place of this vertex, you put two vertices connected by an edge. And then you sum over all this of reconnecting these edges to these two vertices. And these designs above have been chosen such that delta squared is equal to 0. So you can check that with these nine conventions, this equation holds. And then the graph homology is just the homology of this complex GCN with differential delta. Is there any reason why in a definition take direct product and not direct sum? Yeah, there's some reason, because I want certain statements that I'm going to present later to be true. But there's no reason in the sense that I could have equally well taken a direct sum. So we will see, maybe it's a good remark. So we want remark. So this differential does not produce bivalent vertices. So vertices are valence, too, if they were none before in the graph. So delta does not produce bivalent vertices if they were none before. So basically, let's say here, I draw some portion of the graph. And now you split the vertices on principle, you could produce something like this. But an equivalent picture is also obtained, or the same picture is also obtained by splitting this vertex. And if you compute the signs here, you see that there are always such that these two terms cancel out. So it does not produce any bivalent vertices. And there is some result or proposition or theorem, which was already in Max and Conceivages paper, that if you compute, if you want to compute this homology of this graph complex, it can be written as the homology of the at least trivalent part. So all vertices are required to be at least trivalent, plus the parts that are spent by graphs with all vertices bivalent. So these we call, let's say, wheel or loop graphs. Let's call this loop graphs LLM, and over here we have M vertices. And here you have some more product that doesn't really matter. I mean, I don't want to get into this. Let's say products, we don't have a discussion. So M equivalent to N plus 1 mod 4. So you have those wheel graphs and the completely trivalent piece. Furthermore, the grading, it's that graded, yes. So the grading is the degree is N times the number of vertices minus 1, minus N times minus 1 times the number of edges. That's the degree of. So for me to take direct product, it's not a gradient, right? Well, you can take a, let's call it a complete grading.  But in the definition of a graded vector space, we place direct sum by direct product. So the statement I'm going to make now will probably settle this. So this delta preserves the Euler characteristic of the graph, right? I mean, betting number of the graph does not change if you split one vertex. So that means that your complex decomposes into a direct product, according to my definition, of pieces for each Euler characteristics. So Gc N greater or equal to 3 to product of Gc N greater or equal to 3 comma E, where E denotes the Euler characteristic. And these pieces are actually finite dimensional. So actually, you have a direct product of finite dimensional complexes. And so the difficulty is whether you take direct products or direct sum are then relatively non-severe, right? So if you take a chronology of this, you take a chronology of every finite dimensional piece. And then afterwards, you can take either direct sum or direct product. It doesn't matter much. And the main problem I want to talk about is this. What's the graph chronology? It has been studied for a while, but currently, nobody knows. We do not even have a conjecture of what it is. And I'm going to talk about some constraints. I used to have a conjecture, but unfortunately, it turned out to be wrong. So I'm going to talk about some hints only. But let me maybe state one thing. So why should we care? So here I presented it as some combinatorial games that you can play. But many people considered it and why is it relevant to more grown-up mathematics, let's say. And the answer is that these graph complexes, so the GCN governs the deformation theory of EN operas. So more precisely, I write it a little bit sloppily like this. So you can take some cofibrant replacement for this EN operat. You can take the complex of derivations and you compute its homology. And this can be expressed through this graph homology. So it's some completed symmetric product space in one class plus the graph homology up to some degree shifts that I will just insert. So here you have a degree shift by N plus 1 units. And then you have to shift back afterwards. So here we take derivations in operas. That's kind of intentional because I don't regard them as very important. But let me know. And then you shift again by N plus 1 units afterwards. So S plus means it's completed and you don't have a 0's term. You don't have a K term. Does this require N is at least 2? Yes, certainly. The deformations of the associative operata are relatively trivial, so I don't. And there's quite a recent result which taint in collaboration with Victor Turchin and Benoist Fress. Now this looks a little bit odd that you have this big product. And in fact, if you consider derivations not in operas but in Hopf operats, be a little bit careful how to define this, then this is just the primitive part of what you see here. So this is the main motivation for studying this graph complex because these N operats are relatively abundant. So whenever you have an N operat in the theory, you're expected to see some shadow of its deformation theory in what you're doing. Yeah, so I should be a little bit careful. So these N operats exist in various versions. First of all, it's a topological operat. You can say, and then you take chains on this operat. So here, by chains, I mean rational chains, I'm not aware of that or anything. And this will be an operat in dG vector spaces. And there you take a co-fibre replacement, take the derivations in operats. But from the topology, because it's a topological operat, you get a little bit extra. You get a co-product in each arity. And if you also consider this and then your space of derivations changes, so this is from the point of view of rational homotopy theory, this is a better object. But this is more complicated to compute. And the question is, if we want to attack this, so we want to compute this open problem, how do we do this? How to get information? So one relatively simple source to get information is that you can derive certain degree bounds. And for each of these pieces of fixed Euler characteristic, you can get an upper and lower bound where the homology lives. So in general, just from the fact that the graphs are at least trivalent, you get an upper bound. That's kind of trivial because there's just no, well, the complex is just 0 above a certain degree. And so the bound you get for upper bound for H of GCN greater or equal to 3 is fixed Euler characteristic. And the upper bound, if that's a degree, has to be less or equal to E minus 1 times 3 minus N minus 3 if I have computed this correctly. So here you will say it's very trivial. But already this gives us some interesting information. If N is at least 3, this is already negative degrees minus 3. But that already tells us that these EN operas for N at least 3 have very few automorphisms. And there are almost no derivations in degree plus 1. So plus 1 is where the obstructions land if you want to construct maps, for example, the formality morphism. This bound already tells you that the only possible classes there can come from these wheel classes. And you can check that at least. E is negative, H is positive. E is positive. No, E is positive. I thought H is positive. Sorry, I'm negative. First passing number? I had it. Let's say first passing numbers. Yeah, absolutely. My calculations I usually define as E is the number of edges minus number of vertices. But you're completely correct. This is only correct up to sign. So this is interesting already. But you also get a lower bound. And to obtain the lower bound, what you actually do is you take this more or less as a definition and you use a different model for this EN operator. If you use a different model, you get a lower bound. I will not discuss it. So second source of information is you can always do computer experiments. Can you turn on the beamer? So the results I'm showing you are computer experiments mostly by Barnett, Tan, and McKay. And some are run by me. I also wrote a program. I don't know which of the numbers were computed by them and which by me. But let's just look at it. And of course, invalidating the Bible codes. This was invalidating the Bible code. I'm not. Ah, OK. Yeah, that may be. So here I have taken n equal to 2. As I already told you, we only have two cases to consider, n even or n odd. So I just took two representatives of an even and odd number. So for an even number, I allowed myself to take 2. And for an odd number, I will take 3 in a second. So here this is a picture for n equal to 2. So these are derivations of the EE2 operator, if you wish. So this accounts the genus.  So what I mean by genus is the first betting number. For me, genus is defined to be the first betting number. So here you have one loop, two loops, three loops, four loops, five loops. So for physicists, it's a loop order. So you have all these loop graphs we had before. They are spaced by four units. They live in loop order one. And then you have many things in higher loop orders. What you should recognize or see is that in degree 0, we have many classes. Then there are some on this line, and there's one on this line. And here, unfortunately, we cannot go on much further because it takes too much computer time. Actually, the thing, so what takes most of the time is not enumerating the isomorphism classes of graphs. So setting up the differential, but actually solving the linear system. So that's a bottleneck. It's not computing automorphisms of graphs. Let me also show you the other slide here. In loop order one, you have again your loop graphs here. I omitted some numbers. So they are spaced by four units. Then most of the homologies is in degree minus 3. And then here, there are some things in minus 6. And these numbers are different. So it's not just the same. And there's also no obvious map between these two. I'm confused, Thomas. This seems to contradict your upper bound for b equals 1. But here, n is equal to 3. Right. And then minus 3. The degree is less than or equal to minus 3. And it's only for the non-loop part. So here's at least trivalent part. Oh, and there's wheels. All the left colleges. Yeah, these are just the wheel pieces. Those we already have. And here I indicated the bounds actually by this red line. So everything beyond these red lines must be 0 except for this wheel piece. And can you switch it off again? Maybe. I'm sorry. Can you switch it on again? Because there's one thing I wanted to show. So one thing we can explain is that line over here. I want to show that this line is just this Grotendijk-Teichmuller Lie algebra. So compute h0 of GC2 is the same as the Grotendijk-Teichmuller Lie algebra. And instead of giving you a definition, I tell you a conjecture about what it's supposed to be. So it's supposed to be. It's called the Lien-Drinfeld conjecture, or Lien-Drinfeld-Ihara conjecture. It's supposed to be the completion of a free Lie algebra in generator sigma 3, sigma 5, sigma 7, and so on. And there was a very remarkable theorem due to Francis Brown, who recently showed one half of this conjecture. The Grotendijk-Teichmuller contains this. And if you look at this line over here, so here there's sigma 3. I mean, the number here is the sigma 3, sigma 5. It coincides with the loop order. So the sigma 3 is here, sigma 5. Here's sigma 7. Then you can make a bracket, sigma 3, sigma 5. It's of loop order 8. So it lives here, and so on. I didn't try to co-collect commons, which was the generators of the cell. So they can make complex free Lie algebra. You can see the generators come all the way to the gates. So I can give you an explicit formula for these elements in the graph complex. No, no, no. I mean, because it should be simple, complex. These come all just in sigma 5, sigma 7, yeah? Because for any Lie algebra, you can make this, you can do bar-constructions. And people plot these graphs in this bar-construction. Yeah, I tried that, but I couldn't show that it's actually just a generator. So the Chevrolet complex is relatively difficult. I don't know.  I don't know. But you not only have GRT, I love it. You have Pazen, you have 3, 7, 6, 7. Yes, you have things above. And you have 1, 1 famous conjecture due to Maxim Konsevich and independently Drindfeld I said, here in the first line, you have all 0s. Fortunately, you couldn't show that, so you had to create this approach to deformation quantization that I did my PhD thesis on. Now can you switch it off? So if you want to get some further information, you can get it by the following route. So on these graph complexes, you have some extra algebraic structures. The most trivial you see, or I mean not the most trivial, but one you see by this realization as derivation. So there's a Lie algebra structure. And it is obtained as follows. So if you have two graphs, gamma and gamma prime, and you want to take the bracket, you take the commutator with respect to some freely product. And to compute this, what you do is you sum over all vertices of gamma. Here's gamma, here's the vertex v of gamma. And you delete this vertex, you plug in gamma prime instead, and you reconnect the edges in all possible ways. Well, it uses the same algebraic structures, actually. So the dual thing is just you identify a subgraph, you contract it, and you take it out. It's just that here we encode the same structure a little bit differently. Here you have a DGD structure, the concrimer. They set up some Hopf algebra. So for me, this is a little difference. So the main difference is that here this is for topological field series. And the difference is that you have a differential. You don't have a differential in the concrimer story. So this gives you a way to cook up at least co-cycles from known co-cycles by just taking the brackets. But you have a priori no way of knowing that these co-cycles are non-trivial. Actually, the differential can be written as a bracket with the Morakato element, which is a two vertex graph. And one more thing you can notice that there's an extra Morakato element, let's say, up to a degree. Namely, you can consider this graph just a tadpole, if you wish, for physicists. You can check that. Yeah, so it's a tadpole who narrowly escaped the fish. And you have these equations over here. And this means that you can define a new differential, which is just the sum of these two. And to make it the right degree, let's take for my even number, let's take 0 instead of 2. So we consider it dc0. We define the differential bracket with this Morakato element over here. And then relatively, not so deep statement, let's just call it proposition. It's that h of dc0 with this extra differential, let's call it delta tilde. It's one-dimensional with just this one class represented by the tadpole. So it means that that adding or deforming the differential like this kills almost all comology. But this gives you information, because in order to compute this, you may take a spectral sequence the other direction, that in the first page of the spectral sequence you take, for example, take the spectral sequence on the genus. And then this changes the genus by 1. That leaves the genus invariant. On the first page, you just have the ordinary comology. And then on the extra pages, you will see things that turn by turn kill all comology except for this. So what you learn from this is that all comology classes that are there have to come in pairs.  So by taking spectral sequence on genus, quantity classes have to cancel in pairs for even n. First of all, there's an analog story for odd n. Can you turn it on yet? So let's see how it goes. And I can just tell you by just looking at the degrees and where these classes live. You see, here you have your Grotnik-Taichmanou-Lea algebra, which is conjecturally free. Here you have the real classes. Now what you can show is, let me maybe write this as a proposition or remark, the loop in the spectral sequence, you can show that these loop classes, so the things we have on this line, exactly have to kill the generator of GrT. These are found quite a nice picture, actually, quite pretty. So we know that, for example, maybe I can give you one example to make you believe it if I have enough time. So I have time until 15 minutes past six. OK, that's very good. To motivate this remark, just make one quick calculation. So the sigma 3, just believe me, is represented by this graph over here. We can start with the 5 field. This is the first 1, 2, 3, 4, 5 non-trivial one. And let's just check where it goes under the spectral sequence. So this is not closed under this extra differential coming from here. So if I break it with this, I add an extra edge. So I get up to a pre-factor, which I omit. I get this. Now, this is exact unless the other differential. And you can check it's up to pre-factor. It's killed by this. And now, if I apply this differential again, I just get this. So I've just shown that this 5 loop kills this sigma 3. Anyway, so here you have these loops.  And you can see that in GRT, not everything is a generator. You have a lot of brackets also. And these brackets are killed by whatever is above. So for example, here's the first bracket. This is the bracket of sigma 3 and sigma 5. And you can check it's killed by something in degree 3. Actually, this is something you can give a formula, right? So sigma 3 is killed by this 5 loop L5. So the bracket will be killed by L5 bracket with sigma 5. So this is what you see here. And similarly, you can just check and these classes all match. So these classes here correspond exactly to brackets in here. Also here you have a higher bracket. I think this corresponds to this. I mean, I don't really know because this should correspond to the commutator. This should kill the commutator of sigma 5 and sigma 9. So from this picture and this extra differential and this result, you get a very nice picture. You can explain all the graph homologies that has ever been computed. So very nice. We had a very good conjecture. I already started writing a paper about it. But yeah, I will talk about it in one second. Unfortunately, not in a very positive way. But let me also spend two minutes about the odd case. So this was all for the n even case. What about the odd case? So on the line 0, you have these classes which are raised to gt. And so they relate to some numbers, like multiple value numbers. And so is there any relation to any kind of periods? It's not a number. So you should be given a form of high degree of rule dimensional cycles. It should be a sum no need to co-object in the higher case.  So it's just combinatorial game, what's the motive for that? Higher cycles, I can't say. I mean, there are some. So for n odd, you actually have a very similar story. Namely, you can deform your original Maura-Katoa element in this manner to another Maura-Katoa element. So here you have sums of all graphs with two vertices and an odd number of edges connecting them. So for example, for j equal to 0, you just recover this graph, which was given the Maura-Katoa element, which yields the original differential. And the rest will be some perturbation. And again, the nice thing is you can show a proposition that if you take a homology of GC1 with this other differential, this is also one-dimensional and spent by, well, I mean, this is just a leading order term, but spent by one class. And you can check that also for n equal to 3, you observe these cancellations. So I mean, if you know that this is 0, then by the same trick, taking some spectral sequence, you will see that all classes come in pairs. And for example, you have these loop classes here. And I can check up to a certain degree that you can just rule out that they cancel anything below the line minus 3. So they cancel something here on this minus 3 line. Ah, sorry, this is for n equal to 3. So here I choose a different representative of an odd numbers than this one over here. But it should not confuse you. And one question or one conjecture is that these wheels always cancel something on this line minus 3, but I can't show it. So I don't have an analog of this remark in the odd case. Although the question is, I mean, in the even case, the guys that are canceled by these loops, they have the special meaning. These were conjectually generators of this group. What's the special meaning of the classes that you find here? I don't know. Given that you have an upper or infinite sum there, is it even clear that it cancels the lonely maps to a finite character? Yeah, you have to be very careful that you complete right. And yes, I mean, it's a valid concern, absolutely. But if you just compare these things and you see these kills something on the minus 3 line, minus 3 line kills something below. And this minus 3 line, is it related to a significant variance? Not, yeah, of three manifold, so of rational homology field. This is what this is, yes. You can understand the cycle. It's finite of invariance of 2. So this is dimensions of dimensions? Yes, these are the dimensions, yes. And so these things are well studied. But I think there's no formula for what the dimension is, right, there's no. Anyway, so here we have a nice conjecture of what this graph of homology is. So in every case, you have one kind of, yes, your first conjecture that I raised. In every case that you have one dominant degree where most of the homology is, plus you have certain things that, I mean, they are partners in the other dimension. So here you have, it never happens that, for example, something below cancels something below. It always happens that something cancels something on this line, or something on this line cancels something else. So you kind of have two copies of whatever is here. So that was my conjecture. But in five minutes, and maybe I can make, no, I don't make one more conjecture, one more remark. But then there's a different source of information. Namely, you can count graphs, right? Graphs are just some combinatorial objects. And the combinatorialists, they have been, I mean, they have invented methods for counting graphs long ago. So other source of information, one can count the graphs. So count the dimensions of these graph complexes and compute the Euler characteristic. Maybe one remark is, of course, not my idea. So this Euler characteristic has been previous work, for example, for other types of graph complexes. So for the ribbon graph complexes, a nice formula for the Euler characteristic has been obtained by Ketzling-Tapranov. And for the graph complex, we care about formulas for, how to call it, a virtual Euler characteristic. So virtual Euler characteristic means that you count a graph by weight 1 over the symmetry group of, 1 over the size of the symmetry group of this graph has been computed by Maxim Konsevich also. But now we don't want this virtual Euler characteristic. And the reason is that there are far too many graphs with symmetry. So it's true that in high dimensions, of course, most graphs don't have symmetry. So the number of graphs with symmetry is roughly, I don't know, square root of the number of all graphs. But the homology is much, much smaller than this. We will see some tables soon.  But really, we want to count these isomorphism glasses of graphs. And you can do it, given that I have three minutes of time. I think I will just give you the formula. So here we make a generating function for the number of graphs, essentially. I mean, the notation here I took from our paper doesn't quite match with what I said before. So read number of isomorphism classes of graphs without these odd symmetries and without vertices of well and less or equal to 2. And by the standard combinatorial tricks, essentially, you can compute this generating functions. They are relatively complicated. But if you compare with this Polyas function for counting the number of simple graphs, it's very similar. So you have the sum over partitions. And then in this Polya function or Polya formula, there is one piece which is kind of linear power in these j's. And one piece which is quadratic in these j's that forms a petition. And the only difference is that here in the simpler formula, there's just some very simple polynomial, like 1 minus st to the something. And here it's replaced by some, let's say, in a physics language dressed version of edges using this cube Pochama symbol.  Anyway, I can't see much in this formula, so I just skip over it. But you can feed it to the computer and say compute me the number of the dimensions, compute me the Euler characteristics. And this is what comes out. But then you need many more variables, can you take some more numbers? Yes, here you have sum over many variables, so it's computationally expensive. So I hope it's not the best formula you can find. Actually, I hope you can find a simpler thing. Is odd the n-odd case? Or is it? Yes, odd is n-odd. Yes. And this is what the computer finds. So we computed it as though this B is a loop order. We computed it up to loop order 30. And so here everything looks fine. Now the problem is, if you go to a very high loop order, these numbers grow much too fast. If you just believe this conjecture about the Grotendic Teichmüller Liegebar, this cannot explain these high numbers over here. So my conjecture, therefore, is unfortunately false. And even more unfortunately, it appears that it really, really in high degrees, you see how false it is. But the problem is, for example, here in loop order 30, so number of graphs is number with 50 digits or something. So you cannot expect to compute anything on the computer in this regime. Although something that's very interesting is if you remember the tables I had before, this n-even-n-odd case, they look very different, actually, in low degrees. So the even-and-odd theory of this n-operate seems to be very different. But if you go to high dimensions, these numbers are almost the same up to conventional sign. So the sign here is pure convention. You can get rid of it. But otherwise, these numbers are very similar. So what this picture actually suggests is that the process I conjectured before is only one piece of it. So there's one process, and there seems to be some other process contributing the bulk of the homology classes, which is the same in both cases. And another feature that is quite astonishing is the sign. So here I really pushed my student to make sure that this program was correct because I couldn't believe it. I thought before, yeah, well, high dimensions, maybe. You see, this is contributed by some family of graphs without symmetry, so they appear in both complexes.  But in that case, this can't explain this strange flipping of signs. So the signs, they do not flip every second time, but somehow, I don't know. So this is really not explainable. Does it move forward? What? Move forward, something like that. No. No? No. No, it's weird, though. No, that's my wrong. No, no, no. I think it's not sensible. If you, in a full positive, take the sum of pro-eurocroticism, it's something very small now, but not more than 15. If you just take it. So just take these sums. Take the sums. Get very small. Yes, absolutely. That's a very interesting thing. So it means that conjecture is that there are many classes which appear in the even and odd case. And I don't really know how. But there's signs also that don't have any regularity. Yeah, yeah. The sign also has random signs. Yes. Yeah. So unfortunately, now I don't have time to explain why it is the case. Honestly, I don't know why. No, I don't know why this happens. And this is a question I have to leave open. So that's the end. And yeah, thanks a lot for your attention.  Yeah. Can you explain why the signs are opposite? This is just a convention. You see there, if you. They both switch at the same time. Even if you have a convention, but they both switch at the same time. So why do they tend to be the same? If you change the convention, why are the signs the same? Yeah, that's a question. Yes. So the conjecture is that there are many classes which appear both in the even and in the odd complex. So for example, given by graphs which don't have symmetry. That would be one conjecture. But I don't know. Maybe. But I mean the number of graphs with symmetry in these loop orders is much, much larger than these numbers. So we cannot really say, I mean, of course, most graphs don't have symmetry in there. Yeah? Can you try taking the pletistic logarithm and see if that's easier to conjecture something about? No. Well, that should be made a little better. So what kind of computation resources that you used to get inspired? So you mean how long it took? So my student wrote some program. I don't know how optimal this is, but I think for loop order 30 it ran for a few days or something. Just one PC, yeah? Yeah, yeah. Just one PC. Yeah. I have a person next to me here. I think so by computer. No, no. We don't have. OK. Yeah. No, no. We don't have. We don't use supercomputers, no. Is it something about the beginning of getting a new proof of formality and you need three operas? Yes, that should follow. I mean, I didn't want to be too precise about this because it's really work in progress. And in order to, I mean, the statement that would follow is that the n operas for n, at least three, are intrinsically formal. So that means when you have a hopf operat that has homology, little e n, then it is quasi-asomorphic to the n operat. And this what should follow, there are a few technical points. So the most important thing is that you have to set up the deformation theory for these hopf operats correctly and the obstruction theory. And that's why I don't want to make two bold statements because it's technically relatively complicated. So we use Benoit-Fress formalism for this. But really it's not easy and I wanted to avoid having to answer technical questions about this at the end. But that is what it says. Yes. So you have one small thing to notice that sometimes there can be some homology in degree one, but you see n operats, they have a flip action. You can say flip one dimension and these extra classes, they are odd. And I think that shows there cannot be it. This computation via spectra sequence or...? This computation is just taking this formula and expanding. So...


Hi everyone, Joe for Jaspy's casebreaks.com. Happy Sunday, happy Father's Day. Thanks everybody, you've got into all the Father's Day sale breaks. 2019, 2020, Panini, Mosaic, basketball coming out to two boxes. So it's two of those cello pack boxes. So 24 packs total in this break. This is Ram Team Break number 16. No vet commentship except for Luca, Giannis, LeBron, Per usual. Big thanks to all of these folks for getting into it. There are the teams right there. Let's roll it, let's randomize it. 10 times, I guess. After yesterday, Ram.org's being extra careful. Four and a six, 10 times for each list. Your names first, one, two, nine, and 10th and final time. Four and a six, 10 times, after 10 times, we got TJ Leonard, down to Austin Carr after 10. 10 times for the teams. 10th and final time, after 10. Good luck everybody, Knicks on top, down to the Toronto Raptors. All right, so here's how it shakes out. TJ Leonard with the Knicks. Oliver with the Hawks, Justin with the Spurs. Nick Lali with the Warriors and the Bulls. Rocky O with the Jazz. Daniel with the Kings. Jesse with the Cavs. Quinten with the Heat. Marissa with the Lakers. Roy with the Pells. Nice. Quinten with the Magic. Timberwolves and the Grids. Nice. TJ Leonard with the Pistons. Brendan O'Neill with the Rockets. Danny with the Pacers. Greg with the Blazers. Marissa with the Wizards. Fuad with the Hornets. Quinten with the Mavs. Mike with the Bucks. Justin with the Thunder. Zach Paul with the Nets. Greg with the Sons. Daniel with the Clip Show. Nick, last bottom mojo star next to your name. You get the Boston Celtics. Rocky O with the Nuggets. Joe, Sixers, Austin Raptors. Let's get all this on one screen right here. I'm gonna pause the video, allow for a little bit of trading time. And when we come back, we're gonna see if there's any trades and then we'll have the break. Stick around, BRB. All right, welcome back. A little bit of trade chatter, but no deals done. So to everyone on a Sunday, happy Father's Day. Thanks for getting into the action and spending a bit of your Father's Day with us. Appreciate it. Here's the final printout. It's official now. Here are the two boxes with the 12 cello packs inside of each. 24 cello is total in this two box break. Good luck, everyone. Got the feud on the background, of course. Not much else to watch. Game show network on Direct TV. Check your local listings. I'm taking the under on the 200 points for fast money. You've got 88 total points. I still like the under. Kobe White, Silver. It's a nice start. That goes to Nicholas and the Bulls. Silver, Kobe White. That's under. Under's a lock. Got a Yanis for the Bucks. That's gonna go to Matt. They've viewed Kobe White in there too. 147, got the under. MVP's Yanis, just the base version for the Bucks. Got a Kendrick Nunn Green. Kendrick Nunn will go to Quinton Carter and the Heat. Green given go. James Harden, LeBron James. And that's a Serge Abaka, Genesis. Super short print, parallel. Going to Austin Carr and the Raptors. Tried to trade, couldn't trade Mojo. Didn't want him. You can tell by the black and blue, swirl, pattern, parallel in the background. There you go, nice. All right, let's see what's in these pink camo packs, exclusive to this set. Dentist. There you go, who wants to receive Harvey's job? And MVP's pink camo, Yanis for the Bucks, Mike Freese. Fries, it's not, it's not Genesis. No Xions, no Jamarans. No other sort of significant parallels for the top rookies, except for that Kobe White Silver, which was really nice. Let's see what's in this box here. All right, next box, good luck. Parallels are the key in these cello packed rakes. The autographs are pretty rare and stuff like this. Where's that guy going? Second box, let's roll. Here we go. Takes a second or two. Need some more excitement in this box here. Let's get like a Silver Tyler hero, something like that, to get that Genesis RJ Barrett or something, let's find something. Jimmy Butler Green, there's a Luka Dodgecich. Bradley Beale, give and go. MVP's green, Steph Curry, that's not too shabby here. Gonna be for Nicholas and the Warriors. Got a Silver Deer and Fox, Jackson Hayes. There's a John Morant, just a base John Morant for Quentin Carter and the Memphis Grizzlies. We've got a Yanis, Will to Win. Is that a different parallel, maybe green? I don't know, bucks with that one, Mike. Will to Win, Luka Dodgecich. Drew Holiday, give and go, Deandre Hunter. Kobe White Green. LeBron James. Calliola Nick Silver and Talon Horton Tucker. All right, so a few things there at the end. Nicholas with the Bulls. All right, now the Pink Camo's. Also, I think I've seen this Family Feud episode before. Or at least this family before. We need to get live sports back, ladies and gentlemen. If I start remembering families from Family Feud episodes. All right, so the final set of Pink Camo packs. NBA debut, PJ Washington, Seth Curry, Seiku Damboya, Darius Garland and Zion Williamson on the very back. Wow, Pelicans, Roy. The very, very last card in random team number 16 of Mosaic basketball is a Pink Camo, Zion Williamson. There you go, we have to wait until the very end to get a big one here. And that's nice. There you go, boys and girls. Thanks for watching. Thanks for breaking with us. I'm Joe, I'll see you next time for the next one. Bye-bye.


If they come over here, we're going to apprehend them, and we're going to close the border. That's not really been done to the extent that I'm doing it, because I mean it, and I'll close it for a long time. Well, I do say, why are they there? I mean, I have to start. Well, first of all, the tear gas is a very minor form of the tear gas itself. It's very safe. The ones that were... I say to the President of the United States that it helps them because we want a better life because we are living in the country, we are dying of hunger. A lot of children are dying of hunger because there is no job. We want a job opportunity to improve our living conditions.


Good morning. My name is Navid Nikain. I'm a professor at Urecom in south of France. Here we want to present you our work related to the 5G RAN slicing. In particular, we want to show you the new achievement we have made in enabling the 5G RAN. If I start by, let's say, key ingredients, one thing that is very important in RAN is how to separate the data plane from the control plane in the radio access network and how to ensure that we could enforce some real-time control from the controller into the RAN. For this, we need to define a control plane protocol that separates the RAN data plane from the RAN control plane and where we could have applications, network applications, to be developed and to be applied to the underlying network. This actually requires a software development kit which we developed for our controller enabling the network developers to use the software SDK, software development kit, to develop the network applications. I'll provide here two examples. One is the monitoring applications. On the real-time, you monitor the radio access network information across all the layers from FI to the RRC layer. But also, you have this policy enforcement app where an application developers could get the status of the network, analyze what's happening on the underlying network and determine which resource allocation policy has to be enforced to the underlying RAN. And this could be done through the controller so the application will push a policy to the controller which in turn, the controller will push the policy into the underlying RAN. Another ingredient of this real-time control to really enable the application developer is the concept of the network graph database. So this is different from just having the standard database like MySQL or NoSQL type, but here you actually represent the network through the graph where you have a node and the links and each node and each link has certain properties. So an application developer, what it can do, it can, for instance, as an example, let's take the positioning app. It could query the controller and the graph database. I want all the node base and all the UEs with only, let's say, RSRP and RSRP information. So this is a query sent to the network graph database and the result would be a subgraph of the original graph which has all the information requested by the user and therefore this user, this app developer, could exercise the algorithm on this subgraph very, very efficiently. So in this demo we are showing all of these ingredients all together to show how radio access network could be sliced and how different policies could be applied according to a specific slice requirement. Now I'm going to present you the demo. So here in this figure you see we have, on the right-hand side, we have the core network, standard 4G, 4G plus core network. We have a radio access network. We have a RAM data plane. We see also the control plane, this real-time controller together with the RAM agent that both of them are actually having this control plane protocol through which the information could be exchanged between the RAM and the controller. We also see two applications up there. One is the monitoring app to really read the status of the underlying RAM. We also see the policy app which enforces the policy back to the underlying RAM data plane. And here we have remote radio units and the smartphone. So here in our example I can show you the UI. Now it's running. The unit is transmitting and now we actually connected our UI to this base station. Now we start the YouTube. We go, for instance, to open an interface website and we start the video. So here we see that the UI is effectively connected to our network. And now we could see these ingredients I was talking before. So through this controller we could retrieve the status of the UI that is here, but also the unit that is there. We could actually retrieve it in the controller. So this allows the network application to use this information to optimize the network to apply some policies, even to create some knowledge, like as I said before, like positioning, crowd distributions, and so forth. So in this example we have developed an application which is RRM application, Radio Resource Management application. This application what it does is that it receives the status information from the underlying RAM, underlying UI, decide which percentage of resource block has to be associated to each UI to each base station, and then through the policy application it will enforce that policy back to the network. So here in this window we see that these are the status and the logs that are happening on the real time receiving the information. So this is all enabled through the SDK software development kit we developed for this real-time controller, allowing to develop a diverse or limitless application. On the right-hand side what you see is that you see not only the visualization of the underlying network, how many node Bs, how many UIs are attached to node B, but also what you see is that you also see the relationship, you also see the properties of the link, properties of the node. So this is not only for a visualization purpose, but also for optimization purpose because actually this is based on the concept of the network database. So each node like E node B or UI are associated with a certain properties that could be extracted from the status manager of the controller, and then an application developer could for instance do a query say I want a subgraph that has the information for each link based on the RSRP, RSRQ information, and this could basically retrive.


And we ask Allah SWT to send his peace and his blessings upon Aba Abdullah, and upon his son Ali Ibn al-Husayn, and upon the family of Husayn and upon the companions of Husayn. We'll ask for those peace and blessings of Allah to be sent to his brother, the standard brother, Abu Fadal Abbas, al-Salam, to his dear sister, Al-Zaynab Al-Kubra, al-Salam, the mother of tragedies, and to his dear daughter, Sakina Bint Husayn, al-Salam, in the dungeon of Sham, where she passed away. And we ask Allah SWT throughout for the service that we've tried to offer throughout these nights and the tears that we've shed with you, during these nights for them to be accepted. And we mentioned that hadith from Rabah al-Salam, where he says that those tears abolish the greatest sins, and insha'Allah, may they be a means of intercession for us, in dunya and in this life and in the hereafter. Tonight we remember the individual who held that group together. We remember that individual who held that religion together. We remember that individual who for us is a source of inspiration and guidance in so many different ways. We dedicate this night to him and to his absence after he left this world, to Aba Abdullah Imam Husayn al-Salam. And we'll try to, whilst expressing the masa'ib to take a pause at different moments to see, okay, this masa'ib of Aba Abdullah, what is it that we can take to us day to day, insha'Allah, and actually apply going forward to ensure this maharam, as we've said many times now, isn't just ten days of mourning, rather a year, a ten year, a lifetime worth of change, insha'Allah. Our poetry is delivered by Aba Abdullah al-Salam. Peace be upon you. Peace be upon you to the dear viewers as well. It's a heavy feeling, the night before Ashura, on the day of Ashura as well. It's a very heavy feeling. It's almost as if a weight is on the shoulders knowing and realizing that this is the moment in which Imam Husayn al-Salam would be butchered on the sands of Karbala. It's not just because he is an Imam, not just because he is the son of Imam al-Salam, and not just because he is the grandson of the Prophet Muhammad sallallahu alaihi wa sallam, upon which all of the Muslims unanimously stood behind. And upon which all of the Muslims unanimously saw how the Prophet would treat Imam Husayn al-Salam, and only 60 years passed between that and the butchery of Imam Husayn al-Salam, that this heavy feeling is because of the manner in which he was killed, the manner in which he would plead out to them and say to them, what is wrong with you? Do you not realize who I am? Do you not realize who my family are? Do you not realize who my children are? And in the way that they were attacked and butchered, and not just, it was an issue of, look, we need to kill youth out of necessity. It was more of a hunger to kill. Revenge. And a revenge, and there was a deep passion behind the killing and the beating of the children, the beating of the women, and the burning of the tents. It's not an issue of, look, we need to take care of this situation in order to get into power. No, there was rage behind it. And that's why it's a heavy feeling remembering Imam Husayn al-Salam on the Day of As-Shu'Allah. And to understand if Imam Husayn was, of course, to stand against oppression, something that we see day to day, something that we see in loads of different varieties of oppression, and it's something that if we attend the Majalat of Aba'ab Dillah, we are giving that promise and that vow that whenever we see this oppression, whatever type of oppression will be the ones to stand up against it and may Allah give us the Tawfiq and the strength to be able to do this. But when we look at the stand of Aba'ab Dillah and we say, okay, I will stand with you against any oppression that I see in the world, it's important for us to identify these different types of oppression because sometimes it won't be as clear as a Yazid. Sometimes it won't be as clear as X, Y, and Z. Sometimes it's a lot more hidden. And it's important that we find it within us to recognize that is haqq, that is bartha. This is the truth. That's falsehood. That's where the oppression is and that's what I need to stand up against. And this oppression comes in different forms as we said, but what's scary is that sometimes we can actually be the oppressors ourselves. So whilst we're constantly searching for is there oppression here or is there oppression there, occasionally it's about getting a mirror out and saying, am I the Yazid of this situation? Am I the oppressor in this situation? And if so, how would Imam Hussein view me? For he stood against any type of oppression. So how would he then view me if I was the oppressor? So to be more concrete, many different types of oppression and if you just take three examples, political is the obvious one that comes to mind. I would stand against those who oppress Muslim or non-Muslim. Our dear Prophet ensured that everyone of different faiths was able to live together in harmony. So is it just that we look towards the oppression against Shi'as or just the oppression against Muslims? Or do we extend and say no, we don't stand for any oppression against anyone, any unjust ruler? But political is always the clear one and it's a question of are we reacting? It's very kind of factual and easy one to see. When it starts to get a little bit more in depth and where it can start to actually hurt us a little bit, is if we look at social oppression, meaning what? Loads of different meanings of this but one element, the way in which you take your community, if they're your social circle for example, are you oppressing your community? Is there oppression going on within your community? Even more closely, is there oppression occurring within your friendship circle? Is there someone in your friendship circle, maybe even a family member who is oppressing someone? And this oppression can be as significant as saying he's holding this person ransom and is going to kill him or to a much lesser extent but still as bad to say this person is making person Zed feel very, very ill of themselves or making person Y feel very vulnerable or make person X feel extremely saddened about this certain situation. This is all different types of oppression and the question is if we sit in this Majlis of Aba Abdullah, are we actually standing against such types of oppression? Or are we partnering with it? Or are we the instigator of it? If we're partnering or instigating it then how will Imam A.S. look upon to us? And that's a very, very scary thought. Social oppression, there's political, there's social, there's a third one that we want to look at which is person oppression as well. The oppression against your own soul. You have these daily fights with your soul, should I do this? Should I do that? Allah SWT gives everyone a soul, pure, clean, blank canvas. And now it's up to you how you want to play with it. Do you want to feed it with love of al-Muhammad and mercy of Allah? Or do you want to feed it with gunge and oppression and animosity and jealousy and backbiting and etc. Cancer of the soul as they're known as. That in itself is oppression. Allah has given you something and you're just trashing it to one side. So can you take the inspiration of Aba Abdullah, the stand against the oppressive ruler and regime and apply it to today? Because if not, the message is really lost. The beat of the chest is almost meaningless if you're not going to do anything. If you're not going to stand up against that person, if you're not going to stand up against your nefs and to say actually let me detach and remove and as we've said in this general theme over these past ten nights has been am I now able to remove and say forget it? Materialisticness and dunya is here, submission to Allah is here and that's where I'm going. Is it an addiction that's oppressing you? And if so, what is your Hussaini mission to fight against it? Have you battle planned? It's not going to happen overnight if you have an addiction, if you have something that is tainting your soul. It's not going to happen by just saying, I'm going to start, I make my intention, that's it, I'm going to try and solve it. It needs a battle plan. It needs something concrete. It needs for you to sit down and write, okay, this is the problem I face. This is why I need to get to.  So the lesson is very simple. Take this notion of standing up against oppression further. Don't just see it as a political thing or don't just see it as a Hussain versus Yazid thing. See it as a truth versus falsehood. See it as your own self in your own social circles. And if you can identify yourself as an oppressor in whatever format it may be, reflect but act fast. Reflect and act fast because we never know when our day is numbered when Allah SWT will say, that's it. To me you belong to and to me you will return. You never know when that moment is coming. There is a hadith from Imam Sadiq, alaihi salam, where he talks about the oppression upon Ali Muhammad and upon those, insha'Allah, us who grieve for them. And he says, the breath of the one who is saddened on our account and is grieved for the oppression done on to us is glorification. The breath is glorification and his grief for our cause is worship. Grief for the cause of Ali Muhammad for the oppression against Ali Muhammad, Imam Sadiq says, is worship. Is ibadah. Don't take it lightly. Don't take the azad lightly. Don't take the rituals lightly. This is worship. But it's worship if we understand why and we've said this many times, it's because you are reviving that message of Hussain Ibn Ali. You're reviving the message of Hussain the grandson of the Prophet.  So, insha'Allah, we are able to be amongst those who revere the personality of Hussain more so than just a surface level. And we can be amongst those as Imam Sadiq that says who side against those who oppressed them and grieve for those who were oppressed at that point facing up to oppression. And he takes his family and he's there at this point once all of his companions are gone, once all of his family are gone and he makes that call of Helmin Nasser and so on. He's calling, as we said, he's calling absolutely anyone but knowing that now is his time to walk towards his fate, to walk towards this moment that the angels, that the jinn, that everyone knew was gone and everyone knew that everyone was going to weep and cry upon this moment when Aba'Abdillah al-Hussain would go and fight for the cause of Islam. And this is the tragedy of Aba'Abdillah. Aba'Abdillah al-Hussain, you mentioned that when you are inflicting oppression on yourself you need to identify what it is and how to take steps to overcome that. So, within poetry as well, especially within this poem, automatically you refer back to Imam Hussain a.s. when it comes to really reviving yourself, developing yourself, seeing that inspiration within yourself, you'll go to Imam Hussain a.s. because it's such an emotional story, an emotional event, crying, weeping, increases that likelihood of being able to be inspired or opening up your heart to be inspired to do the change. And so, in the poem it says, worlds apart I search for the road from me to you, O Hussain. What veils and what worlds exist between myself and Hussain? Can one who the heart has stolen referring to Imam Hussain a.s. can one who the heart has stolen be worlds apart from his servant? Can one who the heart has stolen be worlds apart from his servant? Worlds apart I search for the road from me to you, O Hussain. What veils and what worlds exist between myself and Hussain? Can one who the heart has stolen be worlds apart from his servant? Worlds apart I search for the road from me to you, O Hussain. Can one who the heart has stolen be worlds apart from his servant? Can one who the heart has stolen be worlds apart from his servant? He who wonders the world of love I stand alone at this world's end. My eye searches for your figure so to your woods I can attend. And yet still worlds apart I stand. Even if worlds your love transcends I wish when you stood there my hand to you I could extend. Is it fair that I can't serve you? Is it fair that I can't serve you? Yet to all of my wounds you tend I wish when swords upon you pray that my master I could defend. I stand on the edge of one world crying out your name, Hussain. And my tears that drip down reshape to write your name, O Hussain. Can he whose love destroys reason be worlds apart from his servant? The poet says, is it fair that time can stand still when I'm entranced by your mention? Yet it won't go back centuries to days of your tribulation. Is it fair that you come to me? In each hopeless situation but I cannot return to you and left you there a whole nation. And you stood there amongst the dead.  Tell me how the eye that sees this notices me, O Hussain. How does the man that walks with death seek life in me, O Hussain? Can he whose love time strengthens be worlds apart from his servant? Though time draws us further apart fires in me if created so when my mind recalls your day I feel your pain on me waiting I see your day as clear as day or within my hand my tears tears and images they fainted as clear as I can see this hand on it with heart chase tend to tend and how your daughters are treated now it's not just your eye that saw these tragedies, O Hussain. Millions witness your day and weep beside you, O Hussain. Can he who gives many's vision be worlds apart from his servant? I live in dreams with such deep love some dreams all I see is beauty others my heart stops in its tracks and my eyes see calamity I live in dreams with such deep love some dreams all I see is beauty others my heart stops in its tracks and my eyes see calamity they see the sun on the sky perched they see the sun on the sky perched as it taunts young tongues so thirsty they see arrows thirsty for blood and swords see death as a bounty indeed I'm taunted by your love indeed I'm taunted by your love it can shape the heart as mighty yet it can tear that same heart apart and make me break down the man empty what love that gives the heart joy yet makes the eye weep for Hussain what love that gives the heart joy yet makes the eye weep for Hussain and yet both in smiles and cries all it calls for is Hussain can the cause of such emotion be worlds apart from his servant? I'll mention one last verse when veils between worlds are lifted will you hear me cry out your name? will you search for the voice that calls for its beloved and burning flame? will you forget that your suffering a soul for this voice it became so that each time it sought good deeds your message it longed to inflame will you recall those who served you? will you recall those who served you? will you recall those who served you? is that not why to us you came? oh he who needs servants please know oh he who needs servants please know my need for you is just the same my need for you is just the same when we are judged will you hear the voice that cries out oh Hussain what is judgment if we are not rescued by you? Hussain can he who holds such a burden be worlds apart from his servant? many thanks of course to Nouri Sardar may Imam al-Hussain on that day of judgment be an intercessor for us may his mother as Zahra Salamullahi alayhi be an interceder for us on that day one of the elements that we take from Imam al-Hussain that perhaps we overlook in the Masaib because of the emotion that we are in in terms of if we recognize it but we don't really draw anything from it the emotional height at that point is this at that time when Imam al-Hussain eventually is going out himself to the battlefield we need to understand the context and rationalize the context that is actually there for him we've all had a dear one to us pass away be it a grandparent, a sibling, our parents, whoever we've all had at least one experience or seen the experience of someone who has gone through this and we've seen the torment that they go through from that time where the person has passed away up until the person has buried those hours are frantic, they're almost scary you know, the feelings are just we've all been there, I don't need to explain it and the point where that all ends or tends to start to have closure is the moment when they're buried and of course we then try and rationalize what happens in Imam al-Hussain the state of mind and the control and the discipline he needed it's almost like when we say we go to an exam and we need control and discipline and focus this exam, this Imtaham was a different level a different level imagine the focus he needed despite the fact that he was having to fight against his emotions of knowing that all of his Ashab are now dead and all of those family members that could fight are dead and all unburied except his dissonant Abdullah-e-Rawih who he himself buried so that closure hasn't come to him yet so the grief that he is at this point is unimaginable no one on the face of the earth will ever have to repeat that level of grief full stop yet he's having to focus there's focus but then there's actually an element of okay perhaps he was actually lonely at this point perhaps this man stood in a land that he was not from he didn't live in he was a traveller in this land he's now in this area far far from home and usually when the tragedy befalls upon you the one place that you have solace is when you go back into your home and you can let down your steam as the phrase is be it you know lie in bed and relax and just reflect for a moment or on the couch or whatever you're in your comfort zone he's out of his comfort zone to a completely different level how does he deal with it how does he have that control that level of loneliness that he must have felt at that point is unimaginable so the question is how did he overcome this loneliness and how can we overcome loneliness ourselves when we hit that point where something so dramatic has happened how do we ensure we have that same focus that on that test and that exam that we then face and it's a very subtle point like I said we usually overlook it in the Masa'a because it's so emotional but there's a beautiful lesson to be found and of course the simple answer is Allah SWT he found this company and this reassurance in Allah and only Allah SWT that's the simple answer but Imam Ali A.S. says something very beautiful about why it is Allah SWT that it is typically to him that we go to and he says in this hadith and it it takes a few minutes even hours and days to really kind of understand this he says when you fear the creator you will escape to him and when you fear a creature you will escape from it look at the difference between the creator and the creation if there's a creation and you're in fear of a creation take a bee there's a bee's nest you're in fear of it you run away from it you escape from it but with the creator you have a level of fear with the creator that you escape to it to Allah SWT so if you have this innocence of fear of Allah SWT but you're killing as to why you fear him you fear him because of his might his power the glory that he has you fear Allah but you run towards him because his mercy is more than the mercy of a mother so where else would you run where else would Imam A.S. look towards when all of this tragedy is befallen around him and he has this mission to go on and he needs to focus and be ready for what's about to come to ensure that intention is clean throughout the whole way it's that he's got fear of Allah and Imam Ali says when you fear the creator you will escape to him so he was with Allah he was going towards Allah so similarly to us if we can instill this sense of fear of Allah SWT that moment when we stand and pray and we look down we're thinking actually what's looking bad at me what's looking back at me right now is power and glory and might and hence I submit hence I go to Sajdan and take the highest part of my body to the lowest part and I submit and by submitting I'm saying Allah I fear you but I come to you and Allah in that time of test that you give me just like about Abdullah I will hold my fear but I'll know that I come towards you and that you will help me in that moment and it's this Masaib of Imam Hussain A.S. where how he managed to overcome that sight of Aideen and Akbar how he was able to overcome the loss of Abu Fadr and hold him in his lap how he was able to overcome the arrow in the neck of Abdullah Herravi how he was able to overcome and this was the test even more so that when he is being killed he's still having to look back towards the camp because he knows what these men are about to go and do to his own daughter and sisters the Masaib of Imam Hussain A.S. doesn't end yes he's now elevated his soul with Allah SWT but he's looking back he's seeing Zainab A.S. looking on he's seeing Sayyid al-Rukhi A.S. within the tent and thinking I'm gonna have to right now just I can't do anything and what was it that he was able to do have to waql in Allah SWT that's what got him through and we ask Allah for us to seek inspiration from that moment when he gives us our tests when he gives us our tests that we have this inherent fear of Allah and hence we go towards him as for the Hadith of Imam A.S. The Masaib of Imam Hussain A.S. is where do you start, where do you end but I want to take an angle from Sayyid al-Zainab A.S. in the sense that we mentioned a couple of nights ago that she saw why they called her the mother of tragedies because right from the beginning of her life all up until the end she saw every single direct family member either be butchered on a foreign lands or struck on the head or poisoned or a door was closed on her mother or her rib broken there's every single type of Masaib for me everything culminated in one event one little scene right before Imam Hussain A.S. was to go out towards the battlefield he first said his farewells to the women and children he gets up onto his horse grabs his shield, grabs his sword just about to go out he's already said his farewell at this point in time women and children are crying for him to return but Sayyid al-Zainab is standing firm and patient and as he rides up as he starts to ride away she calls out to him one more time she says oh Hussain, oh Hussain come back to me come back to me there is one thing I have to tell you and in this is the scene which everything that she went through culminated in one scene which really represented what she was for me he says he comes down from the horse he says I've already said my farewell I'm already heartbroken and it's a situation which is difficult for me and I have to go right out towards my fate what is it? oh Sister Zainab she says I have a request from Fatima Tezahra and our mother and our mother has told us that there will be a day on a foreign land where your brother Hussain is going to be alone and he will say and then he will ride out towards his fate on that day on that moment you bring him back and you fulfill this request and she held onto this request she didn't tell anyone about it up until she saw that Imam Hussain was on the lands of Karbala was alone had already mentioned was about to ride out towards his fate what was the request oh Sister Zainab that I kiss you by the neck and I kiss you by the chest for she knew that Imam Hussain his chest will be trampled by the horses and his neck will be severed by Shimmer and so in the poem I'm going to refer back to Fatima Tezahra as she comes back to see the massacre in front of her and what happened to her dear children in the lands of Karbala she says there is no day like your day oh Hussain there is no day like your day oh Hussain I came from heavens looking for my son I found you alone by you stood no one I found you in blood burnt beneath the sun left here in your thirst son what has been done oh my grandfather your Hussain was massacred lonely I stood alone the flag of your Islam proud me the blood of my neck couldn't quench my thirst I died thirsty left crushed beneath horses my grandfather is mighty there is no day like your day oh Hussain I saw a woman tear soaked her head up one hand on his chest one hand on her rib she cradles you now she once swayed your crib a veiled lioness defending her cup mother my flowing blood apologizes to your search the pupils in your eyes explode as they left the pain of my shattered ribs creaked was burnt mother your pain your past but my pain is my present I see a lion that's all lion's fear rise up from Najaf in his eye a tip he greets his beloved head on a spear the wails of Ali Hussain's head would hit the wails of Ali Hussain's head would hit the wails of Ali presents a vessel should my death be this way I saw a trace stars fall I saw there is no day like your day one of the things that really is just very difficult to comprehend is that despite all of the tragedies that took place in Karbala despite all of the tragedies that took place in Karbala and when it asked, when Imam Sajal was asked what was the most difficult part his response is not Karbala his response is not it was the moment when my father was beheaded his response wasn't it's when Abdullah Herabiyah had the arrow in his neck his response wasn't when Imam Hussain had his own khaybah to deal with with the spear of Ali in Alakabah his response wasn't the first of the children his response wasn't the eye and mace upon Abu Fawal and the fall of Abu Fawal and the fall of the flag of Islam at that moment his response wasn't the burning sand his response wasn't all of these tragedies combined and having to deal with the burning tent his response wasn't even the moment when an orphan child had her earrings ripped from her ears his response wasn't any of that his response wasn't even putting all of those elements together his response was one word a shahm despite all of that he says the toughest part was shahm I think that speaks enough for itself into the difficulty of Al-Muhammad then how to go through after that moment the Masa'ib of Ahlul Bayt al-Aliya Muslim imagine it doesn't even end there it continues, it continues, it continues and it doesn't even get tougher and tougher and tougher Imam al-Sajjad al-Aliya says it said that he used to cry over his father Hussain ibn Ali for 20 or 40 years and whenever food was brought to him he would cry over Hussain al-Aliya and then one day his servant said to him may I sacrifice myself for you O son of the Messenger of Allah I am afraid that you will die from your grief Imam al-Sajjad replies and he says I only complain of my distress and grief to Allah and I know from Allah what you do not know verily when I remember the killing of the children of Fatima I am choked, I am choked with tears over them the words of Imam al-Sajjad al-Aliya say I'm reflecting on Karbala the dust settled burnt out by a tear through its ashes the eyes of death pay cries that break bone the dead would cries that break bone the dead wind would hear as Hussain's head is raised on a spear no hands comfort gone or all held dear by Zainab no Abbas would appear by Zainab no Abbas would appear over 72 dead bathed by the blood that was shed painted in dust that turned red as away captives are led as away captives are led we ask Allah SWT to accept this little from us inshallah we ask Allah SWT to grant us the intercession of Ali Muhammad in dunya we ask Allah SWT to allow us to be amongst those who avenged the death of Aba Abdullah and the blood that was spilled in Karbala our dear viewers we hope and pray that you have benefitted from these 10 nights of shows and if there was anything untoward that either of us have said please forgive us for this was never our intention any good that you benefited came from Allah SWT and only from Allah SWT and finally we end with this and that is once this Muharram finishes once the day of Ashura comes to an end know that is when your Ashura begins know this is when your test begins ensure this is a vaccination for you that is going to be with you for 5 to 10 years and renew it as regularly as you can ensure that you do not forget the 30th to the 40th where we remember Ashura Zainabiya for that in itself as Imam Sir Judges was the toughest time ensure you commemorate that and inshallah we ask Allah to accept all of our efforts in his way Assalamu alaikum warahmatullahi wabarakatuh


We already know that CNN is a dem of Democrat Party operatives and left-wing activists, but it still boggles my mind to watch them continue to obliterate any sense of journalistic integrity. Not only do they put the unhinged brother of a Democrat Party political family as one of their flagship anchors, but they also get him to interview his brother, the governor of New York. Both men hate Trump and are fiercely partisan. What exactly are we supposed to get out of this absolute farce of an interview? But you're a great interviewer, by the way. Appreciate it. Learn from the best. The point is this. What do you think of him trying to... It would be hilarious, if not so nauseating. What's the point of this interview? To bash Trump and paint Andrew Cuomo as though he's the one that's actually presidential? Of course we're not gonna get a critical look of the job Andrew Cuomo has done in New York from the media. Much less his brother. They'll never judge him by the standards that they judge Trump by, not even if he was president.  What do you say to Americans who are upset with you over the way you downplayed this crisis over the last couple of months? It's going to disappear. It's like a miracle. It will disappear. March 4th, we have a very small number of people in this country infected. March 10th, we're prepared. We're doing a great job with it. It will go away, just stay calm. It will go away. Meanwhile, where's the questions about how underprepared New York was for this virus outbreak? Under Andrew Cuomo's leadership. Why don't they have the ventilators that they supposedly need? It's definitely not Trump's fault. A study commissioned in 2015 by the New York State Task Force on Life and the Law and the New York State Department of Health that found New York would have a shortage of ventilators in the event of a severe influenza pandemic. Andrew Cuomo did nothing. Trump called him out on it. And what do you know? The media circles their wagons around Andrew Cuomo. Sorry to interrupt, but I have an important message for all my viewers. We are facing a global pandemic. Numerous cities around the world are now under a state of emergency. Preppers Peak is offering a virus safety bundle that comes equipped with a mask, coveralls, gloves, and goggles for an affordable price. If you're serious about taking the same precautionary measures as our servicemen and women, and you're serious about prepping for the worst, then you must consider investing in this potentially life-saving equipment. With an affordable price for everyone, Preppers Peak introduces the ultimate safety suit, which includes a medical grade P100 particulate respirator, bound-seamed coveralls, chemical splash safety goggles, and flock-lined green nitrile gloves, which heavily reduces the risk from dangerous viruses. Prepare now, and at the very least, you'll have the peace of mind of knowing you're ready. Let's go to survivewithdronetech.com. That's survivewithdronetech.com. Hilariously, I stumbled on this fact check from factcheck.org, which is probably the rationale that the media is using to ignore this story. Just look at how they rationalized Cuomo not stocking up on ventilators after the quote, ventilator allocation guidelines were published. To sum it up, while the Task Force report did highlight a shortage of ventilators in the event of severe influenza pandemic, it did not recommend whether the state should buy more ventilators and hire the staff necessary to operate them. Yeah, because why would you want to order more ventilators when your study finds that you're going to have a shortage of ventilators? That's just a big Trump lie. Trump lied because the report didn't actually come out and say, go buy more ventilators. This is in fact checking, they're just offering up excuses and deflections in defense of Andrew Cuomo. The report found that they were going to have a shortage of ventilators during a pandemic like this, but since it didn't come right out and say, go buy ventilators, somehow Andrew Cuomo's off the hook. I'm sure that Chris Cuomo gets into all of this during the interview, right? He's saying that somebody's stealing this PPE stuff or that something's being done with it that is wrong, which is the implication is I'm doing the right thing. I'm getting them the right things in New York. I don't know what they're doing with them. My response is, first of all, if I say I don't know what he means, you can't tell me that yes, I do know what he means. You might think. What do you think he could mean other than that? Wrong. Instead, Chris references Trump's comments that Andrew has been getting thousands of ventilators, but has been hiding them away instead of deploying them. Andrew Cuomo's response is that he's just storing them away until they're needed, but he's never mentioned these ventilators before. So that response is suspect.  Get them deployed now so that they're ready when you need them. But back to the sham of an interview. Just take notice of how Chris presses his brother on this question of what do you think Trump meant? It's an utterly pointless question, but it allows Chris Cuomo to appear as if he's being tough on his brother and being a real journalist. He could be. I don't know. That's a very vague thing. It went out the back door. I don't know. It didn't go out the back door. What is it? A stray cat? It didn't go out the back door. He's saying somebody's taking something. I don't know what it is. Maybe it's the door. Well, maybe that's what he means, but I don't know. It's a very vague reference. What in the world are they talking about back doors and stray cats? It's almost as if they're trying to muddy the waters on this issue. Really, just look, Trump found out that Cuomo was hoarding these ventilators while he's screaming about this ventilator crisis, a crisis that he was warned about back in 2015 and he chose to do nothing. Now he and his brother are trying to confuse the issue to the point that anybody viewing just glazes over. Let me ask you something. With all of this adulation that you're getting for doing your job, are you thinking about running for president? Tell the audience. No. No. No, you won't answer? No. I answered. The answer is no. No, you're not thinking about it? No, you're not thinking about it? Sometimes it's one word. I said no. Have you thought about it? No. Are you open to thinking about it? No. Might you think about it at some point? No. I know what I might think about, but I won't think about it. But you're a great interviewer, by the way. Appreciate it. Learn from the best. The point is this. What do you think of me trying to play you against Biden? What a hard-hitting interview this is. He's practically begging him to run for president as they congratulate each other for how awesome they think they are. If the media was the least bit consistent or principled, they'd be hammering away at Andrew Cuomo. But they're already looking for him to replace Joe Biden as a Democrat candidate. Back when this was all getting started, it was New York City officials that were telling people to go to parades and ride subways. Their health commissioner told people not to worry about it and get ready to party for the Chinese New Year. The truth is, nobody was really taking this seriously back in January, February, and up until the end of March. Look, I'd like for all these people to stop playing politics, come together, and deal with this situation. As this outbreak potentially gets worse, they're just going to become more and more unhinged. And that's what really worries me. Just watch the beginning of the original Dawn of the Dead to see what I'm talking about. I hope that's not what we're watching right now. That's all for this episode. Please hit that like button, share, and subscribe. If you do subscribe, make sure to hit that notification bell as well. I doubt you'll see any of my new content otherwise. If you agree with my mission and you'd like to support this channel, you can do so on one of these platforms. You can find all the links in the description and pinned comment. Thanks for watching. Keep coming back.