Thank you very much. It is a great honor to speak at the conference dedicated to Masaki Kashivara. I have, since I was a student, I was exposed to his work and his influence indirectly while in Moscow. And I will talk about two subjects which were he contributed on a fundamental way, which is, first, perverse sheaves, as Pierre said. And second subject is categorification. So the talk is based on joint work with Tobi Dikkerhoff, Vladimir Schechtman, and Jan Sodimov. So both of these concepts and subjects are, by now, classical. Let me just fix notation here. So if you have the category Perf XS corresponding to a complex stratified space. So this is the category of certain constructible complex as F. And the conditions, let me write the conditions in the most suggestive way that the i-th caramology of the sheave is supported on co-dimension i. So the caramology kind of dies down as we go further. And an example is, as Pierre said, is the complex of solutions of a d-model, our home over d from n to o. So if we take this as an example of perverse sheave, that this is exactly the normalization. So in the meaning that it is perverse means that, at least generically, the correspondence between models and sheaves is exact. So whatever obstructions there are, they kind of sit on higher co-dimension. And this is a such a fundamental concept that appears in many areas of mathematics. And it seems that it will appear also in many other areas. So and here, the second subject, categorification, it is very prominent now in representation theory. It is a passage, so saying briefly, it is a passage from vector spaces. And the relations in those vector spaces of the form a equals b plus c to triangulated categories. So suppose vector spaces v and triangulated categories v. v script, and it can be appeared as grotting the group of the category, say, tensor our field, so vector spaces over the field. And the basic identity is lifted into something like this into an exact triangle, b, a, c. What's remarkable is that there are so many situations when algebraic structures for vector spaces are naturally lifted into data of triangulated categories in which the identities are lifted into triangles. So those structures, they basically ask, please categorify us. If you look at some point, your eyes are opening and you see that all the identities has to be lifted. And the theory of perverse sheaves seems to fit into this subject. So let me discuss, first of all, the absolutely classical example of this, and then our approach to extending this to a geometric theory of shift-like objects, but of this type. So of course, the classical example is perverse sheaves on the disk. So we have a disk. We categorize perverse sheaves on the disks with one singularity at zero. And as well known, it is given by two, such a perverse sheave can be described by two vector spaces and two maps, u and v, such that the transformation is 1 minus uv and 1 minus vu. Suppose this is transformation for one psi, and this is transformation of phi, are invertible. In fact, the vector space is a finite dimensional that only one, if only one is invertible, then the other is invertible. This is kind of a conceptual refinement of Picard-Lefschitz theory. And this categorifies to the concept of a spherical functor. And this was the starting point of our approach. And this is due to unknown logunyanka. So instead of two vector spaces, we have two triangulated categories, g0 and g1. Now when I say triangulated categories, I need to be more precise, because in order to perform the constructions, we need to do enhancements. We need to, let me just write, say enhanced. And there are two ways of enhancing by DG structures or by stable infinity categories as proposed by Luria. And in fact, more systematically, it's actually better to use this formalism. But I try to not go into those details so much. Suppose we have a functor, f, so that the triangulated categories, f and the exact functor. And suppose it has an adjoint, f, the right adjoint, then we have the adjunction maps. We have something like the identity of d0. Well, the initial transformation is called the unit of adjunction, I think, to f star circle f. And the co-unit is f composed f star to the identity of d1. And if we have sufficiently flexible formalism, then we can take the cone of those natural transformations of functors. Cone of this one and cone of this one. And call this t1, and call this t0. So those are, again, self-functors of those categories. And the functor is called spherical. I simplify just a little bit, because in the correct definitions I also another adjoint appears. I simplify just a little bit to the comparison. So f is called spherical if t0, t1 are equivalences. So this is completely parallel to this algebraic identity. And the adjointness condition means that we have the maps which sort of materialize those identities. So the goal of my talk would be to kind of develop this idea to a more geometric theory. So here I must say that, again, everybody knows this very well, that this phi and psi are not canonically determined by the perverse sheaf. We need to choose certain data. So this depends on choices. So for instance, we should choose a direction, or we should choose a coordinate, or something like this. And in reality, those are local systems, not just vector spaces, but local systems on the parameter spaces of those choices. So my goal would be to say things cleanly enough so that one can pass to the categorical analog. So the goal is develop a geometric formalism, because this sort of generalizes a particular way of describing perverse sheaf, the quiver description. And so define an analog of the global sections of a categorical perverse sheaf, which then would provide as a sort of candidate for fukai categories with coefficients. And this idea of introducing coefficients in fukai categories was suggested by Maxime as a categorification. So I don't think. What am I writing here? As a candidate, fukai category was suggested back in search. So why is it natural here? Because fukai categories at a very rough level is categorification of homology. And this is sort of allow ourselves to switch between homology and co-homology and be with coefficients so we can ask if there is something similar there. OK, so now let me just stick on this board. Oh, there's a third one. OK, so what I will do in the next maybe five or 10 minutes, I will just pound on this example. This is a very, very classical example. However, since I said the concept of perverse sheaf is so important and there are many consequences. And even this classical example, if you look at it carefully and systematically, it reveals more than we expect. So that's what I want to do. Let me call it. This part perverse sheaves on a disk invariantly. Perverse. You may ask what is there left to say about this, but it seems that the subject is completely inexhaustible. So we can look at this for many, probably many years. So let's consider a part of the structure. Suppose we have just a map like this from Pc to Phi. So this data, well, it can become, it is just a linear operator. Or we can look at the two-term complex. Now it is a classical construction of the grotating school of algebraic geometry that with two-term complex, we can associate the Picard category or Picard groupoid. I write it like this, Psi to Phi Phi. It's very common in the theory of stacks. So Picard, let's say Picard category. It's a category of which objects are formed by elements of Phi, so objects equals Phi. And morphism, home between two such objects. Yeah, all those Psi which map into the difference. Set of all those Psi, for which V of Psi equals Phi, say Phi prime minus Phi. So it's a Picard groupoid in the category of vector spaces. Now if we write all morphisms, so like this, that's all more of this category which is this joint union or Phi Phi prime, home, Phi Phi prime. So in doing this, we'll count some of them multiply. So every Psi will enter several times and it's clear how many times it will enter. This is going to be Psi plus Phi. Now it's a category, so let's form the nerve of this category. It's a simplicial object. In this case, it will be a simplicial vector space. Simplicial. I'll just call it N. So the Nth set of Nth simplices of this, it would be, as again, everybody knows, set of composable arrows. And if you write it like this, it would be Psi to the N plus Phi. So this is a simplicial object. So there are face maps, the N and minus one, the del i, the degenerations, S i, satisfying well-known conditions. So it's all very easy to write in terms of this map V. So now, it's a simplicial object. It's a factor from simplex category delta, with the contra variant factor, to the category of vector spaces. Now the category delta is embedded into various categories appearing in cyclic homology. And this turns out to be relevant to the problem of perverse sheaves. So let me say include this category delta into what's known as a paracyclic category. It's a version of the cyclic category of Alamcon. Paracyclic category. So here there are faces in the generation and there is a new, so let me just say that there are objects named by, labeled by natural numbers here. So new automorphism. Automorphism will be Tn from N to itself. Which kind of rotates faces and degenerations around the circle? The conjugation with this rotates, let me just write rotating del i, S i. So it's written in any book on cyclic homology. And the actual cyclic category lambda is obtained by imposing the condition that Tn to the n plus one is the density. And here we don't impose this. So there is a bigger category which sort of involves cyclic symmetry of things allowing us to moving them around. And I want to formulate the following proposition. Let's suppose we have this which is a part of a data of a perverse sheaf. Just one map V. For a given V, we have a bijection. So the following two things, sets I in bijection between, first, all the possible ways that the maps in the other direction which define a perverse sheaf. They do define a perverse sheaf. Maps, maps U from V to psi. Such that this diagram, U V, so corresponding to a perverse sheaf on the disk. And second, ways of extending this simplicial structure to a bigger category, to the data of a simplicial vector space to a paracylic vector space. So ways of extending, extending. I'll just write N dot to a paracylic. So in this situation, so in cons category, we have TN to the N plus one equals identity. Here TN to the N plus one for all N, they form a central system. It's an automorphism of the identity function. It's commute, they commute with everything. And this thing would correspond to the monodrome. Somehow correspond, it combines all the monodromes. So the corollary of this is that the category of perverse sheaf on the disk is equivalent to the category of paracylic vector spaces which obtained as simplicial objects, they are nerves of something. So paracylic spaces which are as simplicial ones are nerves of something. And this being nerve of something is a well-known condition on a simplicial set or a simplicial vector space known as the Siegel condition. And it's convenient to sort of qualify it and say that this is one Siegel condition. So basically the data that the Simplex is determined by its sort of outer skeleton. Okay, here's only two of them. Okay, I see. Okay, now this can be understood a little more geometrically. And this is where the point of view of around spaces and around categories comes into play. So consider the circle. So the whole somehow drift of the cyclic homology is to work on the circle. So consider the circle as one. And let's consider the, let me call it the run poset, partially ordered set of S1. It's a version of the category of exit paths of the run space. So it's a set of posets of disjoint union of arcs. So disjoint, A, which is disjoint union of closed arcs with a natural inclusion. Ah, not empty, yeah, not empty. Not empty. So on this poset, it is a category. In particular, the morphisms are embeddings. So there are morphisms which are homotopy equivalences, which sort of biject, so it's homotopy equivalence is bijection of pi zero. So, and let's call it run of S1. So this is this poset, and we invert weak homotopy equivalences. So in this, it is not difficult to prove. It's the same as the paraciclic category. Find it, find it, find it. Yes, not empty, and find it, yes, yes, yes, yes. It's a paraciclic category, and this way is sort of geometrically clear. So now we can, if we have a perverse sheaf, we can geometrically produce a factor on this set. So we have, suppose we have several arcs. So let's form a sort of cone over this set of arcs, some kind of propeller. So it's a K of A propeller. So if now we have F, a perverse sheaf, to function, which takes A into the first homology, relative k-perc homology, that K support K of A of disk. With coefficients in F. So in this case, only one, so this is the only one non-trivial, so all the other hyper-chromology will be zero. So this also shows that with respect to F, it's an exact function. So in this one, this how one can see that thing directly. So in this description, we already don't use any choices at all, or we sort of take all of them simultaneously. So you have, I want to know, so of course you cannot take everything. Yes, yes, that's also not allowed. Yes, it should be contractible. You cannot take everything, you cannot take the empty set. Yes, but points are allowed, close points are allowed. Points are allowed, it's okay, it doesn't really matter. Yes. Yes, points are okay. Okay, so now let me discuss the next part. We'll be still about perverse sheaves, but let's describe them invariantly on a surface, on a topological surface, again, invariantly. So we have S, an oriented surface, possibly with boundary, with boundary, okay? So something like this, and we have, so a stratification would consist of a finite set of points, interior points, and inside the stratification, and we have the category of perverse sheaves on the surface with possible singularities at this end. So we want to get a description of this category in a shift theoretic way. We want to describe, sort of say, perverse sheaves as sheaves. Of course, one can say, let's use the demodule language, but this is harder to, it's not clear how to categorify it. So let's sort of play a game similar to this one, but allow ourselves to move the central point, the center of the propeller a little bit on the surface. So let me first, or rather let me make a definition. Let's call basic, instead of basic pairs of open sets. Open, opens. So it's a open set U inside U prime, like I said, an open set U prime, with the following property. Let me first make a picture. It would be a sort of curved version of this. So such that U is topologically a disk, or maybe we can say that the closure of U is topologically closed disk. Second, U prime is topologically disjoint union of disks to find it, non-empty.  Let's call it K. So it will be this part, it's the curved analog of the propeller. And it meets the singularities in at most one point, may either meet or not meet. So this is a version of this picture. And in this case, then this implies that hypercromology with coefficients, degree is not equal to one of U modulo U prime with coefficients in F is zero. And F lies in pair. So it's the same situation, except now it is a poset with respect to embeddings of pairs. Again, it's a poset. So the disks are open or open? Open, open, yeah. So this is an example, this is what we are allowed. So this is the disk, and those are topologically open disks, so it's an example. Or maybe I'll do it here. We can prove, if you want, it's a theorem, but it's really a proposition. On the same time, it's a clear description of perverse sheaves without any choices. And as such, it is a peeling pair of Xn, as equivalent, to the category of contravariant functions. That's called E. From this poset, so let's call this poset, let me call it run of Xn. It's a version, kind of global version of the run category, Xn, two vector spaces. Satisfying, the following two conditions. First, homotopy invariance. So basically if we have an embedding, so when we have v prime embedded into u, u prime, such that, well, embedded in the obvious sense, such that v to u, sorry, u is homotopy equivalent, v prime, v minus v prime to u minus u prime homotopy equivalent.  Homotopy equivalence, first condition. It's kind of clear that it would, for this fun car out there, it would hold. And second, the exactness, let me do it properly. So I simply write the exact sequence of triple, but in the case when all three terms are admissible. So let me write it here and then explain. E of u, v intersected with u prime, E of u, u prime, E of v, v intersected with u prime, zero, this is exact whenever all three, whenever all three triples basic. So a good example of such v would be, suppose this is u and this is u prime, this is u, this is u prime, and suppose we have v like this, then if all three are admissible, then it would be like this. So I should say that this is kind of mindful in the particular case of sheaves on the surface. Right here to the approach of McPherson to perverse sheaves via the concept of what we call fairy functors. Except his approach is more general and it's not precisely at the level of vector spaces. But it's a similar sort of general approach. Anyway, it's just a completely shifteretic description of this, of course, a very elementary category. No, no, no, if all three are basic, so if all three pairs, sorry, suppose you have all three pairs are basic. So in the definition of rank category, you don't require that they're basic. Rank category just keep- No, no, no, no, no, no, so only basics, sorry, only basics. The morphisms in the rank category are in which direction the inclusion goes exactly for morphisms. So if we want this to be contravariant functors, so that's actually embedded like this. So we want this to be the functor. We want this to be the functor. F would associate this functor H1.  Yes, yes, yes, both of them. Well, let's write U prime less or equal than V. V prime means that U is contained in V and I think U prime is contained in V prime. Now in the homotopy invariance, you stated the condition of the complement. And then for the complement, first of all, you don't have a MA. Yes, yes, we need to say, sorry, about V prime, yes. But for the, for the, but this condition, we need anyway. This condition is important. So the complement, you don't have a map, directly a map between V and V prime and U and U prime. Yes, but if it's already sort of homotopy invariant in the naive sense, then we have this map. So if V prime and U prime are homotopy invariant in the equivalent, if this is homotopy invariant, then you can by looking at it, get a map up to homotopy invariant. Yes, okay. So why don't you just say, whenever all three pairs are basic, if you require the basic homo-basic pairs, then you get it. No, no, no, I'm saying if I have U, if you have U inside U prime, suppose this, and we have an open set V, such that, if you just drop superimpose on this, an open set V, that it not necessarily will be like this. But if they are like this, yeah. Okay, so now having such a clean description, we can with more sort of, more ease, define categorical analogs of such data. The next part will be called Schrober's on surfaces. So first of all, let me discuss the analog of the nerve of the Picard group point. So and this is a categorical construction known as the Waldhausen construction, Waldhausen S construction. It actually appeared in K theory a long time ago. It's relative Waldhausen S construction. So we start with an exact function B to C of pre triangulated DG categories, or just DG function, sorry, DG function of pre triangulated categories. Or we can do it in the other formalism. So we have a new DG category called SN of F. So let me write how it appears. It appears as a fiber product SN of B, SN of C would be SN plus one of C. It will be a fiber product, which is the same in this case as homotopy fiber product. So SN of B is by the, so the simplest way to say is a category of representations of A and quiver in B of representations. Something like this B1, Bm. Or it can be also viewed as a version of exact triangles. For N equals two, we'll have B1, B2, but we also can think of this as an exact triangle. So anyway, this is this category. This is the induced map. And this is the same category with label N plus one. And this map del takes, let me say C0 to CN, like this, diagram into the diagram of quotients, which really should be understood as cones. I'll write C1 over C0, CN over C0. And those are really cones, not quotients, just for simplicity of notation. So what's important about this category? So first of all, they form a simplicial object. So the simplicial object. And there is complete analogy with the formula Psi to the N plus Phi in the sense that this category SN of F has a semi-artogonal decomposition. It has N copies of B, that's semi, which means that have several copies of categories, isomorphic to B, it's kind of clear out of this presentation for the ion quiver. And one copy of category equivalent to C, they form in one direction, but not in the other direction. And everything is generated out of those copies by forming the cones. So on the level of growth in the groups, we get this. Similarly to the theorem about parasyclic vector spaces, we have a result that if the function is spherical, so the theorem is if F is spherical, then S dot of F, a priority simplicial object becomes parasyclic, if formulated properly. Yes, and I'm about to say some particular case here. So this sort of, as I said, indicates rotational symmetry with respect to two dimensional geometry. So let me just, let me consider the simple example. Suppose N equals to one. Then S one of F, it has semi-arthogonal decomposition made out of B and C. It's simply, so this is actually a canonical, particular case of the canonical way of gluing semi-arthogonal decompositions. If we have two categories, B and C, and the function from one to another, we can produce a new one in which there is a B and there is a C, and somehow the natural pairing between them is given in one direction, is given by this factor. So if you have the semi-arthogonal decomposition, presuming that the factor has adjoins, then we can form, so C is B-arthogonal. We can form a B double-arthogonal, which is C-arthogonal. So in such case, there will be an economical equivalence from B to B double-arthogonal, known as the mutation. We can continue and form a C double-arthogonal. It was a B triple-arthogonal. So it begins to look a little crazy if it starts doing those orthogonals. But there is, where was to say it? Yes, there is a theorem of Harper and Leitster and Schiffman, Schiffman, sorry. That if the factor is spherical, or if the factor is if and only if it is spherical, then the fourth orthogonal will be equal to B. So f-spherical, the orthogonals are fourth periodic. If you look into this, it is not hard to prove this, but it's a remarkable statement. So if there's a fourth periodic, there is a mutation from here to here, and there will be a mutation from here to here, and the composition will be self-equivalence, which will be exactly what happens in the context of a spherical factor. So already in this case, we have this situation. So now we can get a definition of a perverse Schauber. How much time do I have till 50? Yeah? Still five minutes. Ah, okay. So I still have 12 minutes. Yes, still. Oh, I still have 12 minutes. So a perverse Schauber. Something is wrong. A perverse Schauber on Xn, which is a categorical analog of a perverse sheaf, is a contravariant factor called S from the run poset of Xn to dg-categories. Or one can do the stable infinity-categories. Satisfying. So first, homotopy invariance. Second, the analog of exactness is, for a categorical level, is the concept of Rekolmann or a semi-artisanal decomposition, if you like. Exactness. So exactness one was exactly right there. So for, let me say admissible as before. Admissible u inside u prime and v. We have three categories.  So it's, sorry, intersection, yes, here intersection. And actually I think it's united. It should be united in both here and here. And I think it's like this, yes. So basically it's the condition in which you can write the exact sequence of triple. So there is no way to, v is a subset of u, yeah. So an example would be this. So suppose this is v, this is u, this is u prime, this is u prime, this is u prime, this is u prime. Yes, I think it's okay, yeah, I think it's okay like this. Yeah, anyway, so it will be, it will correspond to sigma of v. Very difficult, it's okay, yeah, if you take union of v. Union of v, no, no, yes, yes, yes, yes, yes, yes. Yes, you probably should touch bound, yeah. Anyway, so there is only one way of doing this, just to write the, yes, we should touch bound or something like this. To write the long exact sequence of triple. v intersected u prime. So and this would be, would be a recalman or semi orthogonal decomposition. So that would be this category, we embed it here, it will be projected here and there's some other map, naturally we'll embed it back. This is property number two, and it's almost everything, but there is one more property which we need to impose, which does not follow in categorical case, which is the Myer-Vittorius property number gluing.  So in this, actually is a version of, can be seen as the next higher version of the single condition. It's like, we can call it the two single condition. The typical situation would be when we have something like this, would be something like this, and then we have the two single condition. So the typical situation would be when we have something like this, and the sort of, maybe represent this as a union of two things, so this one and this one, and this sort of corresponds to a polygon subdivided in the dual language picture, corresponds to a polygon subdivided into two sub polygons. So then it's a, this is the definition, it's a local data that can be glued, and for a disk it coincides with the concept of a spherical functor, so it's a flexible local definition. So a functor, when you say contrival, functor to the g-categories, you mean in the, not in the same sense, in the sense where you, the composition doesn't go exactly with. Well, there are several ways of handling this. We can sort of extend this, or in the, something over the groten-dick constructions. So if you write it properly, then there are several levels of doing this, or we work in the model category, when we do it on the nose, but sort of assume that such things can be done on the nose as needed, and then sort of proceed to homotopy data. So probably the most, again, the way the most free from various reproaches like this is to do, is to work with stable infinity categories, but it will be just more difficult to give a talk about this, it will be. Okay, so now close to finishing, let me just discuss the last part, that's called topological Foucaille category, category with coefficients in the shoulder. So then again the picture, which is the approach, which is more natural, is simply to extend. So we have some data on pairs of open sets, which have the meaning of sections, or cohomology of the pair. So once we know it for the basic pairs, we can simply extend this by universal categorical construction to more general pairs by con extensions, by the procedure of con extension, REN of XN, those embedded in simply a set of pairs in X. So pairs of all open set V in the prime. We can, so let's say, let's call it con extension, which means that we say S of more general pair V in the prime. This would be homotopy limit over the category REN of XN, over category S of UU prime. So it's like we define cohomology with coefficients in a sheet, which is a priori defined only on small open sets. So what's important here, that the system of this basic pairs, they don't form a groten-dictopology. However, it may be useful to compare somehow. So if you think of what is the analogy between meaning for this REN category, so we can say that REN of XN so it's kind of similar to what appeared in the study of vanishing cycles with higher dimensional base, some kind of vanishing site. It's somewhat similar to the vanishing site of Deline, Lamont, and Orgogosa. For vanishing site for, so this theory is about vanishing cycles with higher dimensional base. They have some Y to X and this is not necessarily one dimensional. It consists of certain pairs. So here is somewhat similar for the identity X from X to X. So it's kind of similar and the construction is more or less like version of vanishing cycles. It's relative cohomology in such a setting when there is only one relative cohomology. So one can think of this as being analogous. Although it's not, of course, completely the same. So now I'm almost finished. Okay, let me raise this. So let now assume that if X has, let's call it the corner structure, which means that on the boundary, we also introduce some set of corners. Will be something like this. Then we define the Foucaille category of X. X in the sense with the structure with coefficients and S, S of X U prime, when U prime is a small neighborhood of actual boundary. So small neighborhood dx minus corners. So in this localizes on, so this is kind of a priori definition, but this localizes on a spanning graph on any spanning graph. So if you have a graph, which sort of legs terminate in the corners, will be something like this. Then this kind of automatically defines a covering of this nature, of the nature that I raised here, to which intersections are of this kind. And we get a presentation of, in this case, it would be, suppose graph, let me call the graph K, will be sort of argama or homotopy limit of K, with certain shape of, did you categories are K of S. And this is the shape in which Maxime proposes to localize the Foucaille category, as we would now say with constant coefficients for a surface. And finally, maybe I would say as an example of this construction, let me say it here, example the Foucaille-Zeidel category, category of a holomorphic Morse function, say W from some complex menu from M to the disk. And we think of disks with one corner, so one corner. So there will be critical values inside the disk. And such a data defines a shubber, let me call it the left shubber called LW on the disk. So in the Foucaille category, Zeidel category is the same as the Foucaille category of this disk, with this structure with coefficient in LW. So it shows that the concept of perverse sheaves is such a universal all permeating concept and probably there should be still further developments in understanding the very basics of this concept. We have time for a few quick questions. And please wait one second, the time I reach you in order that your question is, oh, okay. Yeah, the question, do you have any idea what to do in high dimension like you have C2 and a point? Well, we don't have a clear idea, but this sort of thing that we're working with pairs is the right way to approach it. Yeah, so appropriate category of pairs from some more steritic reasons or from micro-local reasons. So what's sort of special about this thing? If you write something like this, it's almost if we write something like this and something like this has the vanishing cycle with respect to function sum is equal to L plus one of F. So vanishing cycle with respect to any function, not necessarily function with non-vanishing differential, still preserve perversity. So if you sort of idea that we should look, how should we call it? Possibly, let's call them miller pairs, something which mimics the miller fibers for functions with, say, either at a singularity. Yeah, I mean, it's kind of general idea, but final answer, what should be category of, is the service should be critical? No, we don't have an answer. No, that we don't, yeah. There is a simpler equation about the curve, not just the curve. Okay. Can you say something about the construction of this left-shut shrubber? Well, yes, so it has, so locally, we have it, it's kind of implicit in, or what has been discussed in the category, in the literature. So near a singular point, we have a spherical factor. Outside of those points, we have a local system. So question is gluing them, so it's, once we have a local. I mean, but it's not perverse sheep. What? It's not perverse, right? What do you mean? Or, okay, okay, okay, it is perverse, yeah. So, let me say it like this. If we have a holomorphic, so proper holomorphic, so maybe say proper, proper, proper holomorphic Morse function, then we can take the direct image of the constant sheep. It's a complex. We can take, there is one perverse homology of this complex, which is a perverse sheep. So our left-shut shrubber is a categorification of this. So you think it's any perverse homology or something? No, no, this one, which is the most interesting. The middle one. Yeah, of course, the one of which, the sort of the, so outside of the singularities, there'll be a local system, what local system? Well, the middle cardiology of the fiber. Yeah, so near a singularity, that will be a flip side data. What is the fee there? It's the vanishing cycle, the most classical vanishing cycle of left-shuts. Do you have something to say about mixed perverse sheaves from this RAN point of view? Mixed you mean with a hodge structures imposed? That has been sort of, we've been discussed like various people, but we don't have any clear ideas. One idea that was sort of aired was that one can look for analog of the hodge filtration to stability conditions. But again, it has never been formalized. But it's something kind of, if you have a sort of system of categories, and if you have an aboriginal stability condition, look a little bit like a hodge filtration. But that's where this idea is, we don't have any more. Any other question or remark? Okay, if not, let's thank Misha again.


You too team keep it clean what's going on the same grave in here with another video And before we get into this video just got to give y'all a big shout out man. I appreciate y'all I appreciate you all appreciating variety Because a lot of times when I when I when I put out the vlog videos. I'm like, okay, we do the vlog we had fun making the vlogs but Ain't nobody really gonna watch them like that because it's vlog It's not the football stuff, but y'all be coming through like crazy. So I appreciate it a lot and I love y'all. So thank you for just supporting in so many different things that we do on here And that just goes back to to also with us just not making Raven videos as well Since we make videos about other teams too, and you all continue to support that. So I appreciate it a lot So anyway, one of the other things that I really appreciate About team keep it clean is a different conversations that a lot of us have Individually in the comment section whether it be Instagram Twitter, whatever And today I was talking to my guy Sirach And what's Sirach brought to my attention? He asked a question He asked a question wasn't for question from subscribers anything, but he asked a question He said, what's up? I just want to know who you think is gonna have a breakout year on the Ravens I think Chuck Clark could take a big step. What do you think and? I agree with him Chuck Clark if I had to name somebody that I think would take a big step forward this year big leap forward this year On the Ravens squad Chuck Clark would be somebody Because this would be this will be his first full year starting His first full year starting last year of course due to unfortunate circumstances of head in front of him With Tony Jefferson getting injured to Sean Elliott getting injured Chuck Clark got thrown into the line up and Earl Thomas early in the season Earl Thomas called Chuck Clark probably the smartest football player on the team or one of the smartest football players on the team and It was just interesting to hear him say that because it was like oh Chuck Clark really But then when he got out then we saw just how the defense jailed how the defense clicked. It was like, oh, okay Make sense Make sense And Chuck Clark he thrived in his role with the team and that led to him getting an extension with the Ravens So that was a beautiful thing. So shout out to Chuck Clark man Again, the versatility Him just playing sort of a hybrid role a safety slash linebacker role and him doing very well in it But there's some other players too Who could be primed for? breakout seasons Now um one of them I don't know if you would really want to if you would really call it a breakout season But just a continuation of what he's been doing because every year. He's been improving as a player every year His numbers have been pretty much on the rise and that's actually one Matt Judo Matt Judo on is somebody who I would throw on that list as Possibly being able to have a breakout year and one of the reasons I feel like Matt Judo on is on that list is because of What's around him and we've talked about this a lot off on here already, but with Matt Judo on he now has a Kalleus Campbell. He now has a dead wolf. He still has a brand-new Williams He got Jihad Ward coming back. He got Matt a BK. He got a daily Matt coming back They signed jelly They brought back pernell McPhee Jalen Ferguson back another year. So he has a lot of different guys around him That can help him He has more help he has better help and Hopefully with pernell McPhee he can stay healthy the entire season this year and hopefully for Jalen Ferguson He can just continue to improve. I don't expect Jalen Ferguson all of a sudden go off this year In his second year, it'll be nice. Trust me. I wouldn't complain if it happened But I don't expect it like that. I expect him to do better and to just build up that consistency as that edge guy But I don't expect him to all of a sudden go off anything like that But I do expect improvement but with Matt Judo He's been consistently Improving over the years. So now with him having a lot of help. I Expect Matt Judo to sort of have if you can call it that a breakout season even though like I said, he's been steady Breaking out year after year after year not all the breakout breakout like that But it's been that steady that consistent improvement. So that's a good thing That's a good thing But so I guess you can add Matt Judo onto the list now somebody who I don't really hear too many people talking about as having a Possible breakout season this year for the Ravens and I can understand why due to various reasons But it would be this guy right here This guy right here Tyus Bowser Shout out to Mario me and Carter my wife. We would we were playing on Super Mario Super Mario 3d world Last night on the Wii U Carter Carter gets down and Mario on a switch on the Wii U if Mario is on any console Carter will play it and he will master it too And it's a weird thing too because last night we were playing and he was getting frustrated Because we kept losing on this one part and then when he got mad He just started running through the level and he was doing it perfectly And my wife was like Carter you need to start your own little YouTube channel because the way that this dude was going through the Levels like he was doing a playthrough and it looked like it looked like he played it like a thousand times already Because he was just going through making every jump perfectly. It's but anyway Shout out to Bowser, but back to this Bowser not Mario Bowser Bowser He is a prime candidate to have a breakout season this year Because a lot of the reasons that Matt Jude on could have a breakout season Bowser could as well biggest thing just the What's around him? the surrounding factors and the all the players that the Ravens have added this season and Two other things one In order for him to have more of a breakout season Then he would need more playing time now that can be a bit of a struggle because Matt Jude on him and Matt Jude on They play the same position They are though they are those outside linebackers those past rushes, but they can drop back as well So they can be used in multiple roles. They can be used in multiple ways And they can be used to they they can be effective in in a different in a variety of roles Which is a good thing and again something that we've talked about with wink Martindale It seems that it is if the Ravens have been really going that route, especially on defense with guys that can do multiple things So with that being said with Bowser one other thing that would really Help him or one thing that could really one thing that could really motivate him To have that breakout season that breakout role Would be contract time. It's contract you It's money. Yeah He is in the final year of his contract And again, I was guilty of it earlier this all season But bowser, he doesn't get talked about too much as one of the Ravens players. That's in the final years of their contract Because he's more low-key He's more like off the radar A lot of Ravens fans know who he is, but there are actually some Ravens fans who don't But that's because he's not such a household name Uh, but with bowser, he got the skills. I think he just needs more opportunity Now and he is a very efficient player because when he's out there, he does create pressure He definitely creates pressure But it's just a matter of him getting out there more So bowser has a lot of different um, or a few different things that are playing in his favor To where he could break out this year somebody else who I feel could have a breakout season this year would be I mean, well He he started breaking out last year, but then uh, when chuck clock took over his role sort of lessened And that'll be lj fort And the reason I say lj fort Is because with lj fort, uh, again Very smart Very efficient the guy was always around the ball the guy was he made a lot of plays He is a very sound football player for the ravens He is a very sound football player for the ravens and Just his thought process and you can see his thought press a process on the field And you can just see how How level headed he seems to be when it comes to the game of football now. There's some players who, uh, they will How do you explain it? Um, when they're younger You can tell when the game may sort of be going too fast for them They may not be able to catch up with the game and maybe passing them by it's like, whoa, man Whoa, this this is all just too fast It's all too fast But with lj fort when you watch him play you can see that He's caught up to the game He sees the game. He knows the game He gets the game He understands the game Therefore that translates to him playing the game at a high level That's why with lj fort. I could see him breaking out Especially if he is one of the starters at inside linebacker I expect him to have a good little rotation But at the same time have a good little set as well Because I could see uh him and patrick queen being the two inside linebackers Malik Harrison being brought in back and forth on sort of a rotation But I think it's going to be lj fort and patrick queen as the primary inside linebackers So He's going to have plenty of opportunity to continue to show Why he's been so good And continue to show why I am I'm a big Huge supporter of lj fort and I just I absolutely love his game I love his game And ravens, of course, they loved his game too because they gave him the one-year extension last year They gave him the one-year extension They signed up to that one-year deal in the middle of the season And then they said, oh, you know what? We liked you so much. We're gonna run this back And that could have served uh in a different couple of ways because That could have served as a safety net A safety blanket for the ravens going into the offseason going into the draft because they knew what inside linebacker there was a little Uh a weakness Because josh binds. He was leaving um Who else left? I think he was only one that left, but they they knew they needed to upgrade the interior Interior interior linebackers, excuse me So they extended lj fort. So it's like with that you get somebody that can play But then you also need somebody that can hold it down Because we don't know how the draft is gonna go So it served as a safety net for both of those situations So they end up drafting well end up getting to the really good linebackers coming out of college And then you still have lj fort. So that's a it's it can be a beautiful situation So i'm looking forward to that um As far as uh secondary I mean we talked about chuck clark chuck clark would really be the only one who I feel would really be breaking out with marlin humphrey um his name Is starting to not necessarily be a household name But people people who aren't care like I feel with household names household names in my opinion are more for casual football fans Football fans who they watch but they know they don't like watching detail And they don't know they don't know every player over here and over there They know the big name guys Like on the rave and somebody that that they'll know obviously would be lamar jackson Besides that They probably wouldn't really know that many people They'll know the brady's they'll know richard sherman's they'll know who gronk is Um, but they won't really know like the all the other players And i'm not saying that i'm i'm some super knowledgeable football fan Who knows this guy and that guy and that guy and that guy and that guy but I feel like for more casual fans. They don't So a lot of people they don't know and but I feel like marlin humphrey He wouldn't be known to somebody who's just a casual fan So but he's been getting more recognition within the nfl Because the nfl is really they really starting to see like hold up this This dude is he's really good He's really good. He does still have his struggles now Again turning his head around for the d-ball tracking that d-ball. That's that's marlin humphrey's biggest problem But if that's his biggest problem And we see the way that he plays Hey, we'll take it because we know he can improve all he got to do to fix that That's it. That's it That's it And it's easier said than done obviously but We've been seeing him I oh, I don't know if y'all been seeing uh the the workout videos with him and tayvon young and matt judon With the foot doctor. I think it's with is it jp the foot doctor. I forget what his name is, but I've been enjoying those a lot I've been enjoying those those a whole lot One of my guys he's been sending them to me on instagram. I'll be like, okay. Love it uh and approach a's been in there too and um, I think the foot doctor I think he even said that he said something like the ravens. He said the ravens are gonna have A top three defense and I ain't talking number three He said something along those lines But anyway, um So, yeah As far as marlin humphrey Would I consider him breaking out? No, not really. I think marlin humphrey just gonna continue to be marlin humphrey And that's been a really good cornerback and marcus peters continue to be marcus peters. He's already broken out We all know marcus peters. We know what he does Earl thomas, uh, why I don't expect him to break out because I feel like it's too late in his career to break out But I do expect him to have an even better season than he did last year. I do expect him to give up some more plays though But I expect him to make more plays too Because I think he'll be even more comfortable in this second year in this Raven sister Like we said, so Anyway, y'all let me know who you think your breakout players are gonna be on defense I know we pretty much went through everybody. Well, we didn't talk about the defensive line too much, but I don't as far as breakout players Derek wolf is a possibility, but I don't really see any breakout players On the defensive line because again to me What a breakout player is is a player that hasn't necessarily hit their prime yet or somebody who's They're there that you you could see the potential But they just haven't Broken out yet. They haven't broken out of that shell yet They haven't broken out and it's like, oh, whoa, there goes that dude Somebody who's like right there though and you could tell they got something but you just want to see it Uh on a consistent basis and you you just really want to see them Take over Sort of like it mattered when they get that x-factor But anyway team keep it clean. I love y'all. I appreciate y'all Thank you so much for again supporting so many different things That we do. Um, I really love y'all for that. Seriously. So thank you I hope you're having a really great day whenever you're watching this and we out


The 40 OT podcast. And what I mean, what you need to inform me on is, because some advocates don't like me, is what are those advocates wanting out of life? Now, obviously not to be discriminated at work and things like that. Obviously. But I think they're kind of what they want is different than for me. I think it's, I would agree with you, and that's why I asked a question earlier about how autism advocacy has changed. And it seems to me that it's a lot about specifics of language use that is the gateway to people either liking or disliking you in the autistic community. Like, for example, my name on YouTube and my name on Instagram is currently Asperger's Grove. Now, I can agree with that because just in my own case, I keep learning more and more. How many people say to me, the older I get, the less autistic I act, and that my talks have gotten better as I got older. So that would be Asperger's Grove. Yeah. And you know, it makes sense, doesn't it? And the message is clear. But a large chunk of the amount of comments or messages or emails that I get, it's about my name. It's about my choice of name rather than what I do, you know, and it's really, it's really depressing sometimes. Really language based. You see, because I'm, see, I'm an object visualizer.  Yeah. There's the pattern, math and music. And then there are the ones that the history lovers, where they are word based. So which I'm definitely not. And so they're really into the exact language. And I'm trying to figure out, okay, what language to avoid using, what language should I use, what are the rules tell me I'll do it? Well, I can send you my videos on autism language explained, if you'd like to explain it in very, maybe explain me, give me the elevator speech. Yeah. Yeah, give me the elevator speech right now. Okay. People don't like Asperger's. They're moving away from the term ASP. God, that I knew that because of the bad background of the doctor that I knew about. Sure. We're also moving away from, we're moving more towards neurodiversity related language. So neurodivergent is the name that people have given to people who are neurodiverse. Well, I understand that because you get autism in the, well, fully verbal forms, it would just be a personality variant. I can go along with that, use those terms. Now, one thing I got bashed about was using high and low functioning. Now, I can't change old stuff as in older books. But now, in everything new, I'm calling it, okay, once they get past age six or something like that, fully verbal, partially verbal, nonverbal. Yeah. Those are the words I'm using now. But I can't do anything about the older publications. You can't go back and change a book. No, exactly. But I, now sometimes I still got some stuff where I have to use those terms. Because if I don't use them, then people don't understand what I'm talking about. Exactly. So I'll say, we'll talk about Asperger's, I'll just say they don't use that term anymore, but that's socially awkward, no speech delay. Yeah. In a nutshell for explaining what autism is to other people, it's, you know, even explaining to other people, but also in medical settings, in social care settings, in teaching, you know, some, it's important to have, to have some kind of language that distinguishes people, not because we want to hate on a certain group, or we want to be more superior or, you know, that that's kind of stuff that people say. But to actually explain what explain what groups of people were talking about. And I don't use high functioning and low functioning. Well, I have stopped using it. I'm calling it fully verbal, partially verbal, nonverbal. And when I'm talking about auditory language coming out of the person's mouth, that's fine. Those are the terms I'm using now. And then also in my talks, making it very clear about some of the nonverbals that can't control their movements and look really severe, the books written by people who type independently. And when I do a full autism talk, that's in all my slideshows. I make sure people know about those books. And the crazy thing is about this whole thing is that people would be a lot more likely to accept what you say if you say in those terms, if you use that language, but you're basically saying the same thing. Well, that's right. It is the same thing.  And I can think words I said, I'm not going to repeat because the two controversial that I said as a young child that everybody did, I didn't even think that it was wrong. I just didn't know. But the thing that I want to see, I'm finding the people on the spectrum that are happiest have got jobs they really like. So one of my big things is helping adults make the transition to work. And one of the big problems I'm seeing is this kid's overprotected. He's never gone to the store and bought something by himself. And he's fully verbal. Like you got to be kidding. So I have to talk about shopping. Yeah. But it's I also think about and I've done a lot of stuff about identity is when you look at a lot of last names of people, they are jobs, Smith, Baker, Minor, Mason. These are jobs. So what that tells me is that a lot of people's idea of their identity was tied up in their work because their last names are names of jobs. That's really interesting. And and he really all I can say about the English language. Well, I haven't done it in any other language of English. And so what I'm thinking is, for me, my sense of identity is not the autism is important as to who I am, but it's secondary to a scientist, designer, inventor. Sure. And you have your own, you have the own right to choose that. Whether you want to say, for example, what kind of language you want to use, whether you want to use person first or identity first language, I think it should be something that the individual chooses. Well, I would agree with that.  And I didn't think about what kind of language it was. Then I had educators or educators who were pushing person first, you should say person with autism. So I started doing that. So that I put autistic in there. Then I get questions from educators. Why aren't you using person first? And then I just explain that a lot of activists don't like person first. Yeah, I just explain it. So sometimes I use a mixture because in writing, it's not good to just keep saying something the same way all the time.


Sales of Marines from the amphibious transport dock ship USS Arlington conducted an amphibious landing as part of Trident Juncture 2015. The landing was conducted alongside Portuguese Marines at the Panera da Cruz Range in Portugal. Trident Juncture is a NATO-led exercise designed to develop cooperation among participating NATO and partner nations. Deputy Assistant Secretary of the Navy for Energy Joe Bryan presented six 2015 SecNAV Energy and Water Management Awards to several Norfolk area commands. During his visit, Bryan emphasized that energy efficiency within the Navy is about increasing combat effectiveness. The kill of the future USS Paul Ignatius was authenticated during a ceremony at the Huntington Angle Shipyard in Pascagoula, Mississippi, October 20th. The ship's kill was authenticated by its namesake Paul Ignatius, who served as Secretary of the Navy from 1967 to 1969. His initials were welded into a kill plate to symbolically recognize the beginning of the ship's construction. For these stories and more, visit navy.mil.


Ladies and gentlemen, stop giving needless pressure to the young ladies, to the young men to be married. It's good to raise a genuine concern at a certain stage, but sometimes some even don't want to come to church because everybody who meets them is asking them have we gotten somebody? Every when the year is ending, our daughters are under pressure, our girls are under pressure. Ladies and gentlemen, singleness is not a cry. If that is clear, somebody scream and say an amen. Hey, it's like they're hungry. It's your problem.


The National Industrial Court of Nigeria and ICN has a joint fee sued filed by the federal government challenging the ongoing strike by the academic staff union of universities ASU dated 16th of September for full dimension. At Monday's proceedings, the socio-economic rights and accountability project SIRAP sought to join the suit as an interested party as its lawyer, Ebon Oluwa, said that his client had filed a similar suit asking the courts to compel the federal government to honor his 2009 agreement with the striking vaste lecturers. The action of the federal government is totally condemnable in trying to abandon the negotiations that commenced already and not allowing that process to go through. We have filed an action on the 8th of September before the same national industrial court asking the court to compel the government to respect and enforce the agreement that is pending and binding on the parties because we are not giving a good impression to the entire world if you really enter into agreements and then for one reason or the other one party to that agreement is not willing to abide by it and is trying to use force and that's why it's important that we believe that the court would intervene to ensure that that agreement remains enforceable and then once that is done we can then talk about how lecturers can go back to the universities and then this course will open because the state of the universities presently is totally decrepit. I am working with a lot of alumni in my own former university building hostels doing a lot of things to ensure that the welfare of students and lecturers is something that can be proud of. We can allow a system whereby government abandons its own responsibilities and then the money that is supposed to be used for infrastructure and the education of our children are being embezzled. How much is that so asking for? What does it take to build the universities? So we believe that those of us who went through those universities it was because of the commitment of government that we were able to attend those schools and we came out. But if other governments lie to Johnny Gizali or so a senior advocate of Nigeria opposed Adeburua's application to consolidate the suits when he told the judge that Siraab's application was premature as the case was built for mention on Monday. Of your various organizations, you can't dictate to your organization how you would debate.  One of their major issues is the issue of payment through either IPKS or UTAs. We are saying that that cannot be dictated to government. We reserve the right to pay the way we believe is most appropriate in the circumstances. The 2009 settlement has been resettled in 2020. They are avoiding that of 2020 and always talking about the 2009. By the time we file all the necessary things, you will have each to see. Realting to Adeburua and Gizali's arguments, Femi Fallana, another S.A.N. who represents ASU, said that he was aware of efforts by the lawyers to file court papers in pursuit on Monday. Addressing journalists shortly after Monday's proceedings, Fallana said the Nigerian government often adopts dietary taxes that have a way of prolonging its strikes. We have new business coming here because the matter ought to be resolved by now. And the government has just set up another committee of 14 members. That was done last week. So we're expecting the report. When we just suddenly told that the government had rushed to the court. I hope it's not a reaction to the suit by Sarah. What the law envisaged was that if you didn't work, you shouldn't be paid. But if I'm saying I am going to work, you know in the past, when ASU details arrived, the members always covered lost ground and they're going to decide this time. So they shouldn't be any blackmail. Yeah. Because when the government says there's no money, but you know there's money in the country. But it's a question of priority. Does the good man, has the government given attention to education? Have we not thrown a country where agreements are served by governments under the rule of law? Because once the government has signed an agreement with ASU and is registered in the Minister of Labor, it's binding on the government. But the government has a way of violating its own commitment all the time. And that is why you have this right.


So with the final WTA 1000 event of the year in Beijing, first time in four years that we're coming back to this tournament, we've got some massive names playing because a lot of players are still trying to get qualified for the WTA finals in a couple weeks time, but let's go see who's not playing in this event. So some big names not playing, Begu, she's not playing, Benchich also not playing, Collins, Keyes, Mukova's not playing, and she's currently in the top eight for the race of the finals. So that's really tough to see that she's not there because her spot is up for grabs now. Plischkova, Stevens, and Svetlana all not playing in Beijing this week. Let's go to the top of the draw with the number one seed, Sabalenka, for the first time in a tournament as the world number one, but she doesn't get a buy in the first round because of course performance buys are included in this Beijing tournament. So she has to play Kennan in the first round. That is an absolute nightmare. She lost to Kennan earlier in the season, so that's going to be really tough. Winner of that match will take a qualifier on in the second round. Then you've got Yuan taking on Mertens. Winner of that will take on either Paulini or the number 15 seed to Dagdmire in the second round. Then you've got Krajikova, number 10 seed taken on a qualifier. Winner of that will take on Pavlia Tchenkova, who gets a performance buy after making the semifinals in Tokyo. So she won't have to play that first round. Then you've got Trevisen taking on Maria. Winner of that will take on either Zheng or the number five seed, Rabakina. In the second round, that is a blockbuster first round match. But what a start to this section of the draw. Rabakina, Sabalenka, Krajikova all in the same section, not to mention both Sabalenka, Rabakina playing against Zheng and Kennan. Nightmare first round and then the performance buy comes back and Pavlia Tchenkova gets the benefit. So it's a really weird section of the draw and a really tough section. Going to the next section of the draw, you've got Pagula. The number four seed gets a buy in the first round after making the semifinals last week in Tokyo. She'll take on the winner of Vecic or Blinkova, who are going at it in the first round. Then you've got Tien taking on Nuskova. Winner of that will take on either a qualifier or the 13 seed, OstaPenko. Then you've got the 12 seed, Kavitiva taking on Wong. Winner of that will take on either parks or Samson over in the second round. Then you've got Kostruc versus Chucky Areto. Winner of that will take on either a qualifier or the number seven seed, Jabur in the second round. Of course, OstaPenko trying to qualify for the WTA Finals. But an interesting section here. Pagula's been playing really well. She's been playing really well this week in Tokyo, especially making the semifinals. Possibly could make the final even win the title by the time this comes out. Jabur looking for a spot there, but that top half of the draw is really tough. Of course, this section of the draw will take on the Sabalenka. Rabakina section in the semifinals. So we could be getting Sabalenka, Pagula in the semis. We could be getting Sabalenka, Jabur in the semifinals. We could be getting Rabakina, Pagula, Rabakina, Jabur in that semifinal lineup. If you want to go a little bit different, you could get Krajikova taking on Kavitiva, for example, if you want to go really wild. But that top section of the draw, that top half is really stacked. Bottom half of the draw now, we've got the number six seed, Sakari. She gets a buy in the first round after having a good week in Tokyo. She always the winner of Fruvatova and Roo. So we're going out in the first round. Then you've got Wong versus Vonorava. Winner of that will take on either Sharif or the number 11 seed, Kazakina in the second round. Then you've got the number 16 seed, Kudamatova getting a buy in the first round, a performance buy after making it to the semifinals of Tokyo like the other three ladies already. She always the winner of Sharenko or Zhu who were playing in the first round. Then you've got Kosteja taking on Mardic. Winner of that will take on either Alexendrova or the number three seed, Goff. Very tough round for Goff in that first round. The first match since winning the US Open as well. So really tough start for Goff. But interesting section, you know, Sakri Kudamatova playing well this week. Kudamatova just beat Shviantec and Sakri is on such a great run. Kazakina also isn't someone to overlook either. And playing Alexendrova, Goff in the first round, very tough, but man, it's going to be interesting section. Sakri's the player in form. It'd be great to see Sakri, Goff, potentially in a quarter-final. Then the bottom section of the draw, you've got the number eight seed, Vonorava taking on Kalanina. Winner of that will take on either Saval or Sinyakova in the second round. Then you've got Buskova taking on a qualifier. Winner of that will take on either another qualifier or the number nine seed Garcia in the second round. Then you've got the 14th seed Azarenka taking on Lynette. Winner of that will take on either Brady or a qualifier in the second round. Then you've got Potapova taking on Gracheva. Winner of that will take on either Tormo or the number two seed Shviantec who by losing to Kudamatova in the quarter-finals of Tokyo gave away her buy in the first round. So now she's got to play first round in a 1000 event for the first time for the entire season. So it's going to be really tough for Shviantec after some really weird performances lately. But again, interesting section, you know, Azarenka, obviously Shviantec, Garcia, Vondrusova. Some really tricky names there. Of course, this section of the draw will take on the Sakari golf section. So we could be getting a rematch of Shviantec versus golf in the semis. That'd be great. Or maybe if we want to go with some more Asian swing form you could be going Shviantec taken on Sakari. Which would be really interesting to see that one as well. Seeing Sakari's in such good form. Or we could get a rematch between Shviantec and Kudamatova potentially in the semifinals. Or if we don't trust that Shviantec's going to win maybe Garcia Sakari for the third week in a row. We could be getting that. Or maybe even Garcia versus golf if you want to go with something a little different. But man, really interesting section, especially now that Shviantec is not playing as well as she did. It's going to be really interesting to see how she can recover after a couple of weird weeks and a couple of strange matches in Tokyo. So there it is. That is the China Open. The first time in four years we're going back to Beijing. It's a stacked event as it should be. It's a final 1,000 event of the year. We've got a couple of spots left up for grabs for the WTA finals as well. And there's a lot of players there that are trying to get those final four spots. Let me know down in the comments below. Who do you think is going to win this event? I mean, Pagula's look great. Sakari's unstoppable. Shviantec's looking a little shaky. Sabalenka though is really good in Asia. Or at least she was four years ago. So she might be the favorite to win this whole event.  It's going to throw up a lot of upsets, I reckon.