Okay, thank you. I apologize for the remote aspect of this lecture. So, okay, let me, then I'll start, I'll try to share my screen as I write so. Let's hope this works. Okay, no, no. Okay, good. So it's, I hope it's visible. Yeah. Okay, so we'll, we'll just, so we'll discuss two topics. One is something that we started last time. So this is a topic of the representation of the diagonal in essentially a self product of our modular space. This is very, yeah, so so we'll be very specific very soon. So, and the second second topic, I'm going to start to say some things about the homology rings of quote schemes. Uh, sorry. Okay, feel free to interrupt anytime in any case. So let's start with one and here for us the basic fact, let me recall it since it's been a few weeks. The first thing was that if we give ourselves a non singular complete variety M, and we consider the diagonal inside M times M. Let's say we have projections P and Q to the two factors. Well, if we manage to write. The class of the diagonal as as a sum of split split classes coming from the two factors. So something like this. Where is alpha, I paid higher just classes in the Chow of M. So this is a representation in the Chow ring of M times M. If we can write this, let's call this star. Then well let's say the alpha eyes but it goes the same of course for the betas. They generate the Chow of M as a Z module. Okay. And so so, so this is just a it's a very basic fact but it underlies basically this whole this whole discussion so let me so in other words if for any X of course I can write for any class X. I can write X as the sum of some coefficients and these coefficients are of course. So these are some coefficients that say AI. Okay. So you can really represent it as a as a linear combination of these classes of I just because we're representing a diet and okay so so then you can also show further and so if if this relation holds then so if you can represent the diagonal is a split, then in Chow, then in fact the numerical and rational equivalence are the same for M inside and the cycle class map from Chow to homology is an isomorphism. So then this M is actually Chow trivial so it's a very strong condition. No, I mean this is not going to happen easily. But in any case even if it does not if the same represent the in in commonology. Of course you can, you can always split everything using the couldn't decomposition so in for what we are for what we're about to say you know this this might at least on the level of common this will shed a lot of light but okay so so this is so the same statement holds in homology homology once you represent the time you can always do it in homology in in this way then the alpha is will generate the homology. Okay. So, as an example last time we considered the code scheme so let me this is a this will be our first example today we're going to we're going to sort of and look at this a little bit more closely. So we had considered what's while we let me denote it in this manner. But of course so our and then are some fixed parameters are is less than or equal to n. So this is just the parameterizes exact sequences. And here we're in the setting of P one. Okay, I will comment on that later but we give ourselves this exact sequences on P once we're concerned it was him on P one. So, this he has a rank R and degree minus D. And of course F then has a rank and minus R and degree D. Okay. So this this this code scheme in the case in the sort of geometrically more significant case when this is a proper grass money so R is less than an this this compactifies the space of maps to the grass money. So in here's maps from P one to the grass money. Which sits as a note of degree D. Okay. So it sits as an open open subset of the code scheme. Just, and what what is a geometrically well we're looking exactly for maps looking exactly at those exact sequences where F is is always locally free the situation but F might have torsion and when F is also locally free, then it actually comes from a map to the grass money. So, I should say before I go a little bit further with this I should say that basically the subject owes a lot I mean the, the, the, maybe the earliest thorough geometric analysis of this code scheme came in work of strome. Exactly this code scheme so from P one and this is a classic paper from the 1980s on parametrized rational curves in grassman varieties. So a lot, a lot is calculated there as I will describe. As we go on. Okay, so. This is a paper from the, I don't know, I don't remember the exact here but it's, it's back in the 80s. Okay, so. So now, what about a code scheme also we have seen the following that if we consider. So here, if we consider two points in the code scheme. So let's say, given by two exact sequences to. What's nice in this setting and which you don't have actually now in a strictly in a modular theoretic state when you when you're only parametrized sheeps here obviously we're parametrizing quotient of a fixed sheaf. But when you only parametrized sheeps you don't have this. There's a nice total logical map here so let me. So between E one and F two so. So what you can do is you. You know this. You use the, the first inclusion of the one and CNN and then you use the second. Surjection onto F two. So this gives a completely naturally a morphism whenever you have two sections let's say, well, let me actually sigma one two from E one to F two. And this homomorphism is zero exactly when the two points of the course him coincides exact coincide exactly when you have. In fact, the same you're talking about the same portion. Okay, so it's it. Yeah, so you can consider it is a non zero homo homomorphism which is zero if and only if the two sequences coincide. And so what we also saw last time. Was that we calculated. We calculated that X one. So this is calculated on P one between E one and F two in such a setting is always zero. Okay. So this is this uses the fact that we're on P one it does it's not, it's not always true right I mean if we were on a curve of higher genus this would not be true. This is simply H one. One P one of you want to do a left to know just to. That's what we're talking about. So, so we calculated that this is zero. So this of course, I'm using the same sequence. This means so let me also. I also saw that. So this is for all for all to for. Yeah, so for arbitrary points, arbitrary points in arbitrary pairs of points I should say in the code scheme in QD. Okay. So we also saw that if we were we talked a bit about the tangent space. So we saw that this is equal to X zero. This is true for any code scheme in any setting of E into F. And because of this vanishing of X one, we actually obtained that the code scheme is smooth. Since this X one vanishes then. Okay, so we have these smooth smooth projective variety since I should have said I mean they're this is a projective this is a projective variety but it's a smooth projective variety in the case of P one. Since X to one. So anyway in that case as a as a sheaf of course I can write that the tangent sheaf is. This will reacquaint us with the universal sheaves here. So here I'm using the universal sheaves. There's a universal sequence on the code scheme. And this is the projection. I mean I have the projection to QD and roll projection to P one. Okay. So. So now we just to carry through this with these observations so we, we may also consider on the complex. Let's call this w. Well, I mean I can look at. Yeah, let's not be restrictive on the product. So this. So here, the setting is that you know this is to the, the twin this is mean that we're looking at, so looking at a pair of code schemes. And this is the universal sub chiffon QD on the first factor times P one and you have the universal quotient on the second. Okay. And buys the projection to just the product. Okay. Yeah, so then this w is on on. So what X one as we saw will vanish so in fact this is this is a this is a vector is double is a vector bundle. This is this vector bundle. Okay. So, and so, of course it's on QD times QD and what's nice about it is that it has this total logical section that we were discussing. Yeah, so for for a pair of points in the code scheme, you always have this morphism. So this is a homomorphism from this. The fiber over a pair of points of doubly is precisely the homomorphism group from E one into F two, and there is a canonical one. Okay, so the code schemes come with this canonical section canonical section. And as we saw the so we saw what it is on on every we saw the value of the section on each pair of points at every point of the product. So, in particular, we have that the class of the diagonal is precisely the zero locus of this section sigma. And therefore this is the same as the top turn class of w. Okay. So now it takes. So again, we can calculate the class of the diagonal by the remark theorem so well. So, so the remark theorem says that now, if I can calculate the turn character of this double you know because this is just a push forward shift. So, well so the turn character of two is just and minus turn to. Okay. So quotient shift. And then I have the top genus of P one here on plus the class of a point. This is it. So now if I, we may write, of course, if I. So let's think just of homology now explain exactly how. So. So you may write. This is important for us with fixing some notation for us so we're going to write the turn classes of the universal she sub she. Well. So this should come in terms of a as a community composition in terms of the homology of P one so that's just the fundamental class and which is one and the class of a point on P one. And this is for I between one and are so there are our such turn classes. And now a I is in H2I of QD. And of course if I is in H2I minus two. And here you may this notation is classic I'm using it because it's the classic notation that at the end bought used in their study of the endless equation of Riemann surfaces so I'm just sticking with it as well. Okay, so this is for the community composition. Okay, so notice here that this F one so if one is just D. Yeah, so if one is a. Yeah, there are two are minus one classes of positive comological degree. So then if we, if we do this then. Well then, then you proceed with the calculation and it's clear that you know the churn character of W is written as a, you know, as a sum of say poly polynomials of homogeneous degree. I mean of homogeneous polynomials of certain degrees of these are the churn pieces of the, the pieces of the churn character.  Okay. That's it. Let's say this is degree. And so then you just, you just expressed the top turn classes expressible in terms of the churn character so we also obtain this so this is the top turn class and the top means. Wow. It's also expressible as a polynomial in, in exactly in these classes yeah coming from the two factors. It is a standard transition from turn turn turn from the turn character to the turn class. Okay, and this is the diagonal and you see how you we've done exactly this we have written the diagonal. In terms of just classes coming from the two, the two factors. So, so then we, we have obtained that so we have obtained in fact that let's call this a proposition, the tautological classes, AI and fi generate the homology of the code scheme. So now, I just want to remark on the difference between China and co homology because obviously this argument as I presented it is just in common you use the community composition right of the of the turn classes of the universal sheaf, which you may not have, you may not have in child. I mean, in this case, you do, but as I, as I would say, but okay, so the point was, let me just, so as a remark, and here this is remark concerns child versus chronology. So it comes with this fact, well, we had to, yeah, so we, we consider this push forward. Yeah, I mean, that that's what got us started. Well, and this is the top genus of P1 here somehow. So this came from looking at M times M times P1 and projecting to M times M. Okay. Also, you could rewrite this a little bit with the, and so just to see clearly where the distinction between child and chronology comes, you can give yourself, we can give ourselves two copies of P1 and really consider things on the universal sheaf on one and then the universal quotient on the other. And I can do the same calculation if I just multiply by the class of the diagonal here. Well, so this is the same as, so, so pi star and now, yeah, so I use the tablet is miserable. Okay, so, so this is the same as pi star, the same thing. And now I have, you know, I have two classes. I have this thought of P1, the first P1 and the second P1. So I have two copies of P1. And of course, I have to put in here the class of the diagonal. And so now you see, it's, it all depends on this class of the diagonal. If the class of the diagonal itself in P1 times P1, which is the underlying variety splits. Well, and it does in our case, splits in Chow is written in splits in Chow as a sum of, you know, as a sum of factors from the two, from the two copies of the variety, then the whole product will split. Yeah, because you're genuinely pushing forward, you're doing two separate push forwards, two completely different worlds. So what you get on M times M will split. So, so then I want to say that it all depends. So if, so if the underlying variety is Chow trivial, which P1 is the diagonal splits as a sum of hyperplanes on the two, on the two factors, then, then the diagonal will also split in Chow on the, on the space M. Yeah. So this is again an observation of stroma. So that goes back a long, a long time. Yeah, so if, but this, this will fail. For example, if we look at, if we look at an elliptic curve, you know, here instead of P1, the diagonal will not split in E times E, which means that, you know, you cannot expect this reasonably on the modular space side. Yeah, so, so, so somehow. Yeah. So, so if the underlying variety, in our case, P1, the simplest possible varieties is Chow trivial, then the modular space will tend to be Chow trivial as well. That's just what I wanted to say. So, so if Delta splits inside one, so as Delta splits, maybe I should say then so does Delta inside the code scheme QD cross QD. Now, this is the remark. So then in particular, this shows that, you know, then the code scheme is Chow trivial. Yeah. So, so Chow and cohomology agree in this case. There's no, there's no odd cohomology. Okay. So this is the discussion of the diagonal in the code scheme on a curve. Okay. So, so now I will, I will talk about a modular space of stable sheets, which sort of, it's more aligned with the, with the, you know, that Lothar has been talking about in his lecture so far. So let's say that M to see, to see what we can, what can carry over in that setting. So, so this is a modular space of stable sheets, stable sheets on a variety X and this is either a smooth projective curve or a smooth projective surface, projective curve or surface. And if we're talking about a curve, there's no C2, you know, but, and I'm going to assume there are no semi, no strictly, no strict semi-stables sheets. Okay. And I'm also going to assume there is a universal sheath just to see how this flows, this argument. There's also polarization. So the stability is with respect to an ample ample line bundle on, on X. Okay. So there's a universal sheath on the X and project to X or to M. Okay. So let's see what we can say about the diagonal in this setting. Okay. And there's a bit less structure floating with a code scheme. We have a lot of structure with a modular space. There is less, but we have stability though, so which we don't have on the code scheme. So here, let me note. Yeah. So I also assume that this is, yeah. Okay. So no strictly, no. So it's a situation when there's no, there are no strict semi-stables. So this is a, is also projective. So the smooth projective variety I'm dealing with here. So if, if I'm trying to calculate homomorphisms between a pair, I consider a pair of sheaths in M. So this is, there are no homomorphism unless, actually, like this, unless the two sheaths are isomorphic. And then they're just the trivial, the trivial automorphism side. You have it. Okay. So the only automorphisms of a stable sheaths are, of a stable sheath are just to see starry scaling, scaling. Okay. So let's assume, and this assumption is stronger than what we need, but let's, let's see what it means. So it's a bunch of assumptions to set the scene. So we're still, we're still setting the stage here. So let's assume also that X2 for, for, for any pair of sheaths, E1, E2, parameterized by M. Okay. And so this is, okay, this is automatic if you're on a curve, of course. On a surface, it's very restrictive, of course. And so, yeah, so this is automatic. This is X, I'm sorry. If X is a curve, and this is restrictive, if X is a surface. And so, but how can we understand it a little bit? So this X2 by, by seriality, this becomes on a surface. This is X0 times the canonical here of the, of the surface. Yeah, so dual, of course. But so when might this be zero, this X0 that we understand better homomorphisms than, yeah, than this X2 group. So, so this is, for example, this is zero. The latter is zero if, for example, if the polarization times kx is negative. So this is by stability then. So by stability, you can never map, and I think Lotta also touched on this last, last time, you cannot map a stable sheath of higher slope to a lower slope to a, to a sheath of lower slope. And this multiplication by kx, if h times kx is negative, lowers the slope. Yeah, so then by stability. So you cannot have homomorphisms from higher to lower slope, basically. Well, so that happens, for example, on take p2, but you know, it is restrictive, so it's, it's not gonna happen a lot. So, but let's, let's, and I'll comment a little bit on that, there are ways you can strengthen this, but this is the, this is the kind of the perfect, and I'm setting just the perfect scenario for this, for this representation of diagonal to work.  So yeah, so, but, but if this X2 is zero, that that's why we want it to be zero because then you can, okay, so we can consider, well, I'm getting a bit ahead of myself. So, sorry, so I consider as before, not quite as before, in analogy with, with our first example, okay, the code schemes, we're gonna consider the complex, and here I'm gonna stick a minus on m times m. So this is the same, the same scenario as before, you have a universal shift on one factor and universal shift on the other factor. Okay. And in the context of this vanishing of X2, in fact, well, the X2, so this, the X2 sheaf in which appears in W is zero. So in fact, you can resolve the point is that under our assumption, we can just resolve W by a complex of locally free sheafs. So by a two term complex of locally free sheaf. So you can, so under our assumption, we can resolve W by the complex of locally free sheaves. So I will have a bit to say about this resolution. So, so this then, so then obtaining something like this, so let's talk about these as you can do it in several ways, there's a concrete way to do it, which I will point out, but you basically will have the following. So here is what you obtain. Let me write this. So this is an exact sequence on the product m times m. And I wrote this first term just for inspiration, because in fact, this sheaf is zero. Okay. Zero, it's, you know, the, so you'd, you'd expect that you see something along the diagonal, of course, the torsion free sheaf is zero, but it inspires you because then you understand that it, the diagonal defines the, the, the locus in m times m, where this map from A to B fails to be injected. Yeah, which is where exactly this X1 sheaf, the X zero sheaf is, is zero X1 is not a locally, it's not a locally free sheaf. Yeah, so it, and, and, and where it will jump rank, it has a generic number, where it will jump rank is exactly where this map from A to B. Let's see. Yeah, let's say that it's called is fee is, is a fee fails to be injected. Okay. The fee is not injected. Yeah, so the, so then there would be what we would put, would have to check. So this is a degeneracy locus. So then the, this is, this happens on the diagonal, right? Because unless you're on the diagonal, the X zero group is equal to zero. So X1 is constant is given by minus the Euler characteristic of E1 into E2. Yeah. So, so then this jumping locus is precisely the, the diagonal. And so then you would have, you would hope to write if things were not degenerate. So you may hope to write the degener, the degeneracy locus of fee, which is definitely fee. You try to write it as a, as a, as a class as a child class. And in fact, the portious formula tells you what it should be. Let's say the ranks of A and B are little A and little B. This, this is by portious, kind of portious formula tells you this. So, yeah. So now what is, how does this compare to the, well, the diagonal we know is co-dimension M where M is the dimension of the modular space. But this works out very well in fact, right? Because B minus A is the generic rank. So B minus A here minus chi of E1 into E2, okay, which is a constant here. And, and this in turn is the, is the dimension minus one. Yeah, the modular space minus one. Okay. Okay. Because the X group on, yeah. So it's the dimension minus one. And so then, so then this, then, then this works out pretty well. And this is okay in fact, because you, the degeneracy locus is exactly the expected co-dimension, which is exactly M, the modular space. So this is actually okay. It's not just a hope. It's, it's true. You still have to check something. So this, yeah. So you, you have to check the degeneracy locus is actually reduced, let's say, you know, so the, the porous formula tells you, tells you that the, the, the, the, the, this turn class is equal to the, the class of the degeneracy locus with its natural scheme structure. So you have to check that this is exactly the diagonal, but just a smooth structure on the dial. Okay. But, but that's easy. So, so then this is exactly, of course, this B minus A is precisely the, the complex W. Okay. So it's CM of W, because this resolves. Okay. So, so, so then we're back where, you know, we're in the same situation as before where we had to work a little bit harder. I mean, on the code scheme, it was easier. This was a top turn class of a vector bundle. The, the diagonal was the zero locus of a section of a vector bundle. So it was a beautiful setting. This is just a little bit more work, but not, but it's, it's not bad. And yeah. So then, of course, so finally, as before, by Groten di Creman Roch, you can calculate the turn character of W. And so then you can express the turn class in terms of the turn character PC. So in terms of, in turn, the, the QNET components of the, of the universal shape. So whenever this is possible, then in homology, so you can then conclude the QNET components of the turn classes of E, which naturally, of course, they belong to the homology of the product, you know, decompose in terms of the basis for the homology of X, be it a curve or a surface, generate H star when Q multiplicative. And of course, as remarked before, if the diagonal is factors inside X times X in Chao, then this also works in Chao, if not not. So, right. So I should also remark that then, you know, you can, this argument, of course, was given with, in this simply, with this hugely simplifying assumption that, that X2 was equal to zero. So this argument was, ah, okay. So first of all, I should say that this argument is also due to strone, the argument above and maybe Boville, Boville kind of, these are early 1990s, okay. And it was adapted by Markman to work in the case of a K3 surface. It's 2000s for X, K3 surface. Okay. Yeah. So there, of course, you don't have, then the, this, you don't have this vanishing of X2. So E1, E2, or this is, this is the case of a K3 surface. The canonical bundle is trivial. So, ah, so this is then zero. Okay. So this is, so it's zero if E1 is not isomorphic to E2, but of course it's C if E1 is isomorphic to E2. Okay. But in any case, it's a, it's a small variation and then one can deal with it. So the argument, this is just, it's just an adaptation of, of strome's argument. So Boville's argument. Okay. So one thing that I did not say as I move away from this subject is to, yeah, how do, how do you obtain the resolution? Yeah. So this relies on this resolution here. And I mean, you can always obtain it, it's a, okay, but it's, you can actually do it in, and it's sort of instructive to do it very concretely. So it's not, you know, that such a resolution exists. Can you actually write a complete one? Yes. So I, well, let me see if I really want to say something about this or not. Yeah, maybe, maybe I won't actually. In fact, it's a, it's a nice, it's a nice construction, but I see that the time is actually a bit short. So unless I don't know it, I can go either way, depending on what the audience wants. So my inclination is to skip it at the moment. So let me just maybe just write the remark. So you obtain A2B from the geometry of the modular space itself, from the geometry of the universal sheaf. So sheaf. So, so, so, and the key point, then you can sort of think about it. So the key point is that you can choose a large integer, M, so that the push forward of the universal sheaf twisted by a large multiple of the polarization given by M is equal to zero for, so that the higher, the higher direct images are zero. Okay, so this is actually a vector bundle. So if I call this, and moreover, it's a vector bundle so that if I, so this is a vector bundle on M, but if I pull it back to M times S, it surjects onto E twisted by H to the N. So this is true on M times S, M times X. Okay, and this is true. And so this is, this is, it's sort of, it's built in deeply into how you construct a modular space. So sheaf, this boundedness is part of it. Yeah, so the fact that you can, you have this, it's, it has very much to do with how stability plays into obtaining a bounded family. And anyway, so if you call the kernel K here, then this helps you get the resolution, basically. So on M times M, so let me call this, you use star for E2, for E1, let's say, and you take text with values in E2. And then, and then this precisely gives you the resolution. Okay. Okay, so you get, get precisely this, get the desired resolution, resolution of X, of the X complex. Okay. So, yeah, anyway, so this is, this is, so with this, I'm, I'm ready, I think to, so we leave it, I leave it to the audience to finish this, this little argument. Okay. So, so, so now I think I'm done with, yeah, I said what I, you know, was reasonable to say about the diagonal, I think, in general terms. And I would like to go back and time flies, I'm not here. So I'll just, let me at least get started on my second topic here, which much more is to be said, in fact. But so, so this is the study of, now that you have this result of generation, it was a study of, of the cohomology of QDGRM in my original setting on P1. This is instructive, it's sort of a, I view it as I'm sort of toy model for what, for what you might expect to happen in, in a, in a setting which is not as simple as these are after all quotients on P1. Okay. So, chief quotients on P1. So it's sort of a simple setup. Okay. But it's, it's, it's still, it still has some interesting feature. So, so let me start by discussing a little bit the Poincaré polynomials. So, so again, this is, you know, so we're back to this setting. So where we, we're just parameterizing short exact sequences on P1. And here, the degree, is D would, and so what's, what I think of as fixed are these parameters are an N. So the dimension of the trivial sheaf that we take a quotient of and the, and the rank of the, the rank of the sub sheaf which is fixed are, I think I'm going to, we're going to think of this D as moving. Yeah. So this is N minus R D. Okay. So the Poincaré polynomial. So let's say, well, okay, so if we, for every quote scheme, we're indexing them by D. So there's, remember, there was no odd homology. So, so let's write them as like this, the dimension and the dimension is linear in D. Yeah, I mean, it's easy to, so it's, it's N D. And then, of course, you have the dimension of the underlying grass mania here. But anyway, it's linear in D. That's important. Okay, so, yeah, so then we formed the full series. So we include all these. So we formed the, the full series, let's say T. Okay, so Z here keeps track of a homological degree. And this T, the variable T of the, the quote scheme, which, which space you're, you're looking at exactly the maps of quotients of which degree. Okay. Okay. So we sum over all quotes, quote scheme degrees here. Yeah, so this Poincaré polynomial, the Poincaré series was calculated by Linda Chen. And the year was 2000. And it's a beautiful, it's a beautiful expression. So let me write it. So there's a prefactor here. Okay, so here, this P zero is just it's just Poincaré polynomial of the grass mania. It's classically known. So let me write this. So this is Poincaré polynomial of the grass mania. Okay, so, yeah, so we'll do a little, a few, we just get, so it's, yeah, well, so let's, let's take a little bit of a closer, closer look at this formula. So first of all, I want that you can deduce immediately. So what we can observe is that just to get us started a little bit is that B two of QD is equal to two. So for all the RN, of course, I hear these at least one, you know, otherwise. Yeah, so this is just one just says to read off the coefficients of, the coefficient of Z times T to the D, okay, in the above series. So one can do it. And it plays a bit differently. I mean, here, you'll see this, sorry. Yeah, so this plays a bit differently. There are two cases, we'll sort of look at two cases. One case is when we're talking about a genuine grass manian, so R is less than N. And that plays a little bit differently in this case, because, well, I mean, somehow, yeah, so there's a, you know, this Z here appears with this coefficient Z to the N minus R plus I. And when the, when R is equal to N, in some sense, the formula is simpler. And you also don't have this P zero. So the, there's this pre factor. So when R is equal to N, you're talking about a point. Yeah, so this grass manian GNN, it's a point. In any case, in both scenarios, B2 is equal to two. So then you conclude that, oh, sorry, A1 of the code scheme is spanned by these two classes, which, well, we knew this, the only chance was that they would be linearly dependent somehow, but they're not. Yeah, because I'm sorry, A1 plus F2. So remember, we do have, at this point, we have the Poincare series, but we're also looking at it knowing that these classes, A1 through AR and F2 through FR, generate the homology. Okay. So this is the first, yeah, so let me, it's already, my time is already up. Let me just write one thing, which is amusing and sort of, then we can pick it up next time with, because this deserves a more, a more thorough analysis. So, so let me write this as a remark. Remark is that the homology stabilizes as D goes to infinity. Yeah. So more precisely, like we'll see this on, what does it mean on the level of betting numbers? And so more precisely, we see that the stabilization starts to occur for D greater than or equal to K. So if we fix, so this means that if we fix a certain homological degree, then if we look for code schemes of sufficiently large D, and these has to be at least K, then this, these betting numbers with the degree of the homology, I'm sorry, the rank of the homology degree K stays the same, as you move on. And so this is a phenomenon which, is more sophisticated, a lot are analyzed, for example, in the case of the Hilbert steamer points on a surface. Yeah. So some, it's a phenomenon you see there as well. And of course that series is a lot more sophisticated, but this is some sort of, you know, a very simple version in some sense that you can play with and its geometry is much simpler here. So as we'll see, as we develop it. Okay. So how do we see this? Just to, we see this. Yeah. So if we recall it, we have this, we have to, we can read it off in the Poincaré polynomial. Let me explain briefly how, and this will be the last thing I do. So it won't be more than two or three minutes. So yeah. So let's say that we write this, okay, V2KD, this means that you're looking at the betting number in the D-quote scheme. Okay. So if we consider then, so if we write, we can write, to notice this stabilization, we write 1 minus T times PZFT. So this is PZFT minus T, PZFT. The full series. So, you know, there will be some initial, so I, okay. So I'm, okay. So this is the part of degree zero, which I write here. And then starting with degree one, of course I have exactly this difference, which I want to notice is zero. Yeah. So I have B2KD minus B2KD minus one, Z to the K, T to the D. Okay. So this I would like to observe that it's zero. So in other words, what we need to see is that the coefficient of Z to the K, T to the D, in this modified series where we multiply by one minus T is zero for D greater than K. You know, that's what we would like to see. Once D is greater than K, we just want to see that this is zero. But here is, well, this is sort of manifest. If you look at the form of the series, well, look at the original. Let me just point this out in the, yeah, in the series as I wrote it, you see here, this starts when i is equal to one. I'm looking at this particular. So you can, so you have basically two types of two types of factors here. And if I look at the first type that starts with one over one minus T, you know, when i is equal to one, that's precisely what you won't see anymore once you multiply by one minus T. All right. So this is just P0Z. So you have the product of one minus TZ to the i from i is equal to one to r minus one. And then the product from i equal to one to r, one minus TZ to the n minus r plus i. Okay. So notice what's important here for us is that whenever you have a factor of T, it's accompanied by a Z. So it's a very easy point in this multiplication then you see that every T is accompanied by at least a non-zero power of Z. So you cannot simply buy Z to the a for a greater than zero. So that's the argument. So then you're done. I mean, the coefficient of Z to the k, T to the d when T is greater, when D is less than, when D is greater than k, it's just zero. So coefficient of D is greater than k is zero. Right. So there is there is homology stabilization. And so then you can also ask, so what does it stabilize to? So in other words, and then I'll finish on this note actually. So so if you set, let's say, B to k infinity to be equal to B to k of QD for D greater than or equal to k, then the stable Poincaré polynomial of QD is, well, so you, you just form this series with the stable betty numbers. And the fact is that which is easy to see, I will, fact is that is that you calculate this by evaluating a T equal to one, the product of your, of the original Poincaré series with one minus T. Okay. So I can briefly explain this but not now. So in any case, you get the following because now we're running out of time. Yeah. So I will, I guess end here because unfortunately I imagined I was going to cover a lot more than I actually did. But I want to point out one thing that if you set this formula is simplest when n is equal to r, n is equal to r is the, so for n, let me just write this one, this Poincaré series. Well, there's this P zero is one in that case.  So you have these two distinct products, I viewed them as coming, having a slightly different flavor. So that's why I write them separately. So n is equal to r is the case when you were looking at the code scheme of rank zero quotients. Yeah. So the sub-sheaf has the same rank as the CN as the trivial middle sheaf. So then the quotient is pure, is pure torsion. So it's the geometrically the simplest, most accessible case. I mean in, and so as you, what this suggests, of course we know we have these generators. We have these atia-bot generators.  And what this formula explains in fact is that these are atia-bot generators actually become relation free. Yeah, as D, as D increases, because in fact this stable Poincare polynomial, if you look at it, this is just, this is just the Poincare series of just the polynomial algebra in these generators. Yeah. So p infinity of z is the Poincare series of the polynomial algebra. So no relations in these generators. Yeah, precisely with the correct degrees, yeah, because, yeah, so, and you can see that the two products, one would correspond to the A classes and the other one to the F classes and the F classes are of course by, yeah, by one, by one less. So yeah, so I, my plan was to explain why essentially, you know, so it's an interesting thing, but I think we'll have to leave it for, for another day. So I'm going to stop sharing. Yeah, so, so yeah, I apologize. I went over time and yeah, it's, it's, it's an interesting this where we left it off is sort of an interesting point and I hope to resume it. I have one question. So first of all, thank you for the beautiful talk. I wanted to ask if the space QD has a cellular decomposition or a fine paving or whatever it's called. And because this would, so the actual question is, does the formula for the Poincare series become a motivic and this would be implied by the affine paving? Yeah, yeah, it's, it does. I mean, it's this in, even in the initial analysis by, by, by Stromed and, and also in, in Linda's derivation of this Poincare series, of course what's used here is a torus action. Yeah, so, so it admits a full torus action.  So in fact, you have finitely many fixed points and you have this Bielinisky-Biroudi composition as well. And this is how, in fact, this analysis, I mean, that these were reduced, so yeah, you can sell a lot more. And also I should say that this thing with the torsion code schemes, this analysis works on any curve, you don't have to have P1 there. I mean, I'm, I'm keeping it a bit more on P1. I'm interested in any grass mania, not just the case of torsion sheeps, which is why I, I assume that we're on P1 to simplify certain things, you know, but, but if we are just interested in torsion sheeps, then, you know, any curve would do. Yeah, so, but my point is to actually not just calculate, my point is to sort of understand which I didn't get to, but I will hopefully in a future lecture is to understand geometrically why that is, why this becomes relation free and what, what are the relations in fact, you know, and there are two ways to approach it. And yeah, so to have a basically a kind of a detailed geometric understanding of what this series means. But yeah, there is a, there is a serial decomposition you can, you can study. And it's been studied much from this point of view, but not so much from the point of view I want to emphasize. So, you know. All right. Thanks a lot. Sure. Good question. This tank, Alina, again?


In this step, we're going to set about creating a material for the scroll and getting it placed precisely, which is quite important for this particular material. The first thing we need to do then is to make the material. So let's get our hyper shade open, make sure we have a clear workspace and then let's go for an AI standard surface. We're going to use the clay preset again and then we need to load in the textures for it. So remember, if you want to use my textures, then you can get them using the link in the video description below. That will give you access to my project file. If you go into my source images folder, you'll be able to see all these textures. Just copy them into your source images folder and you'll be ready to go. So I'm going to load in scroll underscore diffuse, which will give us the color. There you go. Let me just put that back on the sphere. So you can see there is some white on the top and bottom of this, which is why UV placement matters so much. And then we're going to load in the roughness for it. It's going to be a file as well. Scroll roughness. And finally, we will load in our normal map. So that's a file. Don't forget to set it to tangent space normals. And then I'm going to load in the bump value, which is going to be our normal map for the scroll. Now that that's complete, then I'm going to drop it on the scroll. Oh, actually, I don't think I've named it yet. Let's do that first. There we go. M underscore scroll. And now I'm going to drop it onto my scroll, but it won't look like it's on there. You see the color changed slightly. What has happened is it's showing this part of the material, not this part. So we're done with the hyper shade for now. And we need to look at why this is not showing our material. So we'll drop back into our UV editing workspace. And when we click on our scroll, you'll see that nothing has actually come up here. And that's because the way we created this scroll, which was using curves and nerbs, means that there are no UVs at all. We need to create some from scratch. To do that, then we're just going to start with an automatic projection, which will give us that. You can see that's given us loads of pieces. Let me just shade that. Loads and loads of pieces. That's not useful. So what we're going to do is go into edge mode and we'll select every edge in there. And then I'm just going to get it from my cut and sew menu up here in my UV editor. I'm going to click on move and sew. There we go. And we can see that that has actually stitched it together and opened it out like a big piece of paper. What I'm going to do then is just get hold of this UV shell and try and get it so that it's the right size. And for me, I already know that it's not going to be because I've rehearsed this step to see what my problems are going to be. And I'll just make sure that it all fits within the boundaries, which it does. That's pretty good, Shane. Nice one. OK, so I just go back into object mode over here and let's have a look at how this is coming out. So it's a little bit stretched. That should really be circular. And the problem I've got is if I go into shell mode and I scale it so that this is going to be circular, which is about there. The edges have come off, which means I'm probably going to get, let's just go into object mode. I'm probably going to get like a white bit somewhere. There it is, which I don't want. So I've got to do this slightly differently. So the way I'm going to go about it is I'm going to go into face mode and I'm just going to select this middle strip of faces here. Let's try that again. This middle strip of faces. And then I'm going to do shift and full stop to get a larger selection than that, which is this. So this is what I want to have the writing and the drawings on it. To make sure that I get that then, what I'm going to do is just do a UV projection, do a planar one on the Y axis. Make sure width and height ratio is turned on. And that now is going to create a new shell for me, which I'm going to have to rotate. I don't want to get this perfectly straight. I don't need to get it perfectly straight. Just close will do. And then I'm going to let me just turn this on so you can see it better.  And then I'm just going to go into shell mode. These two shells here, I'm going to move off to the side for now. They're fine. I don't need to do anything else with them. But I've got to be happy with this one before I move on, which I think I'm about to be. Yeah. Okay. So that's good. I'm happy with that. What I need to do now is bring this shell back in and make it fit in the remaining space of the scroll. So you can see it's too fat. So let's just scale it on this axis to make sure it fits within there. That's good. And I'm just going to put it fairly close to the edge of my other shell. And then this shell here I'm going to bring in as well. I'm going to make that thinner like so. And then to avoid getting any issues, I think if I go into object mode and now look, I might actually be getting away with it already. But I want to avoid there being any seams here. And the way I'll do that is by going into edge mode. I'm going to double click on the top edge and I'm doing it on my middle shell. So double click on the, no, click once. Sorry. I'll click once on the top edge and then go down to the bottom hold shift and double click on the bottom edge. And then I'm going to go into cutting so of my UV toolkit and choose stitch together. And I'll do the same on the other side, stitch together. And that now is a completed UV map. So let's go into object mode and that's going to look terrific. Okay, we can just turn that colored view off. So that now is our scroll with some very kind of old school wizardy looking right on it and some runic image and whatever this guy is. That's ready to go. So we've got one more step in texturing and UV mapping which is going to be for, we'll do one of the books and I'll let you guys do the rest yourself. But that's going to be how we can assign two different materials to one object. That's what we'll be looking at in that step. So I will see you in the next step for some book action. Game Dev Academy is graciously supported by these absolute legends. If you'd like to offer your support then check out our Patreon page using the link in the description below.


Hi everyone, Sean with Jaspys case breaks comm here doing 2019-2020 Panini contenders optic team all two box break pick your team number three Where we're giving away the pelicans all you have to do to be entered to win the pelicans Let's have two or more teams in the break. So even though it says there's two left. It is sold out All card ship. This is the team all China edition How to be entered by two or more teams this break get entered to win By two teams get one entry four teams two entries six teams three entries so on and so forth We're looking for the season ticket gold and red wave parallels in the team all as well as all the other great stuff That comes in contenders optics. So Here is our list of customers from Eric Carangela with the Hawks all the way down to Barry LaFranco last spot mojo with the Wizards To figure out how many people are going to be entered into this randomizer We're gonna take this list of customers We're gonna alphabetize it see how many spots each person got so Barry with last spot mojo got two spots So that'll get him one entry Eric gets one Eric K gets three Joe gets one Matt gets two you get five spots total, but four will give him a Obviously odd number, but you'll get two spots on there Nick gets three Six spots overall Steve gets one Tony gets one and Tyler gets one so 14 spots in the randomizer and name on top dice roll After a two and a three five times Fifth and final time congratulations Matt Lieber Get yourself first and second spot, but obviously the first one gets you the pelicans. There you go, Matt He also was one of the last spots available took the Knicks too, so thank you very much Matt So let's go back over here and enter you in for the pelicans So let's print and rip so You can see the case in front of me It's 20 boxes Now We're gonna do to figure out which two boxes we're gonna do one on top here eight on the bottom nine on top here 16 on the bottom you can see one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen okay, so we're gonna go back over here to the randomizer And let me turn on the Nick cam just so you guys can see that there's no funny business with the the shuffling of boxes Boom so there you go We're going to One through sixteen random number generator first box is box seven So one through eight on the left. I'm gonna pull this one out a little bit just so you can see that that is box seven and next box is Box three so Here we go so you can see one two three four five six and seven There you go, so the rest of these boxes will be for the next what will be seven breaks We have 14 boxes left So you go Here's our final list last spot mojo Barry LaFranco with the Cavaliers and the Wizards and Matt with the pelicans that he won Let's find some nice stuff in here guys So same setup just this has exclusive parallels of the red and the orange or sorry red and gold wave Parallels Is there not always a auto I guess not maybe Okay, so they're not guaranteed an auto like the original or the regular version of contenders optic Kemba Walker uniformity silver for the Boston Celtics and Matt Lever season ticket Carson Edwards also for the Boston Celtics and Matt Lever Clay Thompson season ticket Golden State Warriors Matt Lever DeMar DeRosen season ticket San Antonio Spurs Tyler Rutledge and our first Red Wave Alfred Payton for the New York Knicks Eric Jock And Red Wave season ticket Seiku Dan Boya for the Detroit Pistons and Tony Barkey There you go, Tony Not numbered but like I said those are the exclusive parallels for team all nice rookie one there for you And box to get a die cut in here. Can those be red wave? Oh Trey young superstar die cut Atlanta Hawks Eric Carangela Carson Edwards season ticket Boston Celtics Matt Lever Mark Gasol Toronto Raptors Nick Stover Russell Westbrook Houston Rockets Nick Stover Kelly Ubre Jr. Red Wave one of the Phoenix Suns Steve Locke and Our last red wave Christian Wood also for the Detroit Pistons and Tony Barkey And guys that was 2019-20-20 penin contenders optic team all two box break pick your team number three four and five are in the store now and I believe they are in like the teams. So let's get those going. We're gonna do another couple boxes tonight I'm Sean Jaspies case breaks calm. Thanks for hanging out. I'll see you next time


Welcome back to my home and welcome back to another what we eat in a day. So today is going to be a bit centered around just kind of recouping. We went through a sick week this past week and so I feel like I'm focusing more on just eating a lot of really good nutrition and making sure that we are rebuilding our systems after being sick and all of that. So I am starting my day out with some lemon lime water just to get good and hydrated. I'm probably going to try to drink electrolytes as well and even give some to the girls. So I'm sipping on this and I just got these cute little heart shaped straws that I've been loving. I have not gotten ready. You can see I just got water on my shirt but I have not gotten ready at all today. I just threw a hat on. This is the shirt that I woke up in so we're going to try to get breakfast accomplished and then probably get ready for the day as well. I grabbed this at the grocery store last night and I actually had two of them. I drank one last night. I got this one and I have another type of one that I want to take later today. This one is called Wellness Rescue. It's by Vive Organic and it's like basically a wellness shot. This one is oil oregano ginger and elderberry and whoo you can really really taste the oregano in this but I will admit after I took this last night I felt a lot better so I think it is definitely worth getting and using. So I think I'm gonna go ahead and do this along with my water and then we are going to do some waffles up for breakfast and I've been wanting to get waffles done. You all know that a lot of times I prep them for the freezer but I want to show you guys how you can do freezer prep kind of along with your day. You don't need to have an entire day for freezer meal prep or for prepping a whole week of food, a weekly meal prep. You can kind of prep things as you're going and that's really what I want to show you is how you can make prepping and being prepared with your food for your family kind of a lifestyle. So we're going to make up some waffles and we're going to make extra to pop into the freezer. So these you have to shake up before you take them because a lot of the goodness settles in the bottom but since I had one of these last night I know how bad they really are. If you are not an oregano person which most people I don't think like oregano in huge quantities then you yeah. Cheers wellness. I'm gonna get better. I'm gonna get better. I am getting better but I just want to make sure that it leaves and stays away. Let's say thank you to ButcherBox for sponsoring this week's video. ButcherBox sources their meat from farmers and fishermen who meet the highest standards for quality. You choose your box and delivery frequency. They offer five boxes, four curated box options as well as the popular custom box so you get exactly what you and your family love. ButcherBox ships your order frozen at peak freshness and packed in an eco-friendly 100% recyclable box. Their delicious high quality meat is 100% grass-fed beef, free range organic chicken, pork raised crate free and wild caught seafood. You all know that I'm always looking for a great deal and the average cost is less than $6 per meal. Right now ButcherBox is running their Nuggets Burgers and Dogs deal. New members receive one pack of gluten-free chicken nuggets, six grass-fed burger patties and one pound of uncured hot dogs in their first box. You won't want to miss this deal so click on the link in the description box to get your hands on your first box. If you all are completely new around here then you may not know but I make a lot of gluten-free friendly recipes and this is one of them. I will leave the recipe that I was inspired by in the description below but this is a great almond flour waffle. It's a really quick and simple and we did use all natural local to us maple syrup on top of these but you could also make your own maple syrup or pancake syrup with a sugar substitute if you are trying not to eat very high carb. And then I like to keep a nice stash of frozen orange juice in the freezer so I just mixed some of that up to go along with our breakfast. Okay I'm about to go get ready for the day but before that I'm going to go ahead and put this beef stew freezer meal into the crock pot so it can simmer all day and I get so many questions about how I take things out of the freezer and reheat them or like how I cook a freezer meal. So this here I actually got out of the freezer last night and I let it in the refrigerator overnight and I was hoping actually it would fall a little more than it has. It's pretty frozen still so I'm probably gonna run a little hot water over it just to soften it up enough that I can dump it in here it's gonna slow cook it's gonna thaw in there it's gonna be fine so I maybe should have left it in the refrigerator last night and then when I got up first thing this morning left it sit on the counter to thaw out a little bit more so for the next time I do this I probably will do that but for now I'm just gonna pop it right in here and that will help part of dinner be prepared when it's time to start making dinner. Alright so I took a shower I washed my hair which if your mom you know that that always makes you feel better and I ran and got water out of our Berkey filter we have it in our basement just because I don't really have a lot of space I want to take up up here for our Berkey water filter so I refilled our water dispenser in the refrigerator and I've got the water rolling I'm about to use I've been loving this it's called the Fixer and it's from EOS and it's their medicated lip ointment and it's just I don't know it's so soothing and I feel like when you're sick you're always fighting with your lips just being dry and everything the Sun is starting to come out it's been a little bit of a cloudy day hmm that feels so good on my lips I didn't really put a whole lot of makeup on or anything just letting my face breathe did my skincare so before I make some lunch I'm going to take this second this is not sponsored or anything this is just literally me trying to get better and trying not to be sick but I got this one and this one is a little bit similar to the the one I took earlier and it is their elderberry and ginger and it doesn't have the oregano that was like the worst part was the like swat drinking that down so I think this one's gonna taste a little better so let's give it a try it does however have black pepper and turmeric so I don't know it may have a little bit of heat oh oh wow heat it does have I did not realize it was gonna be that spicy oh my goodness oh if your grocery store has these I do recommend them though because I feel like every time I take one for the next like two hours I feel such an uplift in how I'm feeling so I definitely think that there is something to them working oh my goodness now that we've managed that so I was had a little bit of a different plan today I was going to do some bell peppers and I've had a pretty big stash of canned tuna just from like Costco runs and stuff like that so I want to find ways to use it but I just forgot that I have some leftovers of some pulled pork in the refrigerator so I have some baby bell peppers I was gonna do kind of some like tuna melt bites but since I've got this pulled pork I'm going to go ahead and stuff the baby bell peppers with that put a little bit cheese on top melt that down and I also want to use some of the butcher box bacon that I didn't use for breakfast this morning to make a really yummy broccoli salad so we are going to have a veggie loaded lunch I feel like all of the good nutrition and just refueling our body will be so helpful and the girls really love those baby bell peppers as much as I do so let's get preparing this meal and digging in using my salad spinner to wash smaller veggies and fruit and it just makes it a little bit easier and quicker to get the water off of them and I love using bell peppers I know there's a big trend of using them in replacement of bread to make sandwiches right now but I personally prefer to kind of roast them or cook them just to soften the outside shell it makes it a little bit easier to eat and a little more palatable as you can see I used our cast iron skillet and it just popped it into the oven basically until it was all heated through the cheese was melted and the bell peppers were softened a bit and then I started in on making the broccoli salad it was really just an easy throw together broccoli salad I just use my fingers to pull apart the broccoli into small bite-sized pieces I chopped up some bacon and then to make my sauce I used a little bit of avocado mayo some everything but the bagel seasoning I buy that in bulk because we use it for so many things and then a little bit of honey mustard and I just stirred that all together and poured it over top of the salad mixture okay so normally whenever I make broccoli salad I put cheddar cheese in it but this time I wanted to give it a little bit of a different flair so I'm gonna go ahead and put some feta crumbles in with this here it's a very simple salad today but it's gonna help us get some green veggies in and taste yummy so I am about to make my afternoon cup of coffee and there's something that I have been wanting to do and I decided you know what today is the day with fall getting closer one of my absolute favorite drinks is something called a dirty chai so normally you can order like a chai latte which is chai tea with spices and all the goodness but a dirty chai I used to work in a coffee shop and we used to make these all the time and this was like my go-to every single day I worked in the winter time I would make this you basically are taking a regular coffee espresso latte and you are adding the chai spices to it to give it that extra little spicy feeling so it's really like the ultimate fall coffee drinks so I was looking online to find my own chai spice blend and I really didn't find anything that I liked the ingredients of but I did find a recipe on Pinterest to make my own a spice blend so that's what we're gonna do Erin's I got a few ingredients for what I'm going to be making for dinner tonight and I made myself I'm about to actually pull the last piece off but I made myself a little cricket label for my spiced chai spice I always feel like this is the most fun part is pulling the transfer paper off I love this so much and now I think whenever I redo my coffee area back there which I'm getting ready to redo for fall I'm going to do like cinnamon and probably cocoa powder and do the same kind of lettering on it but either way this is gonna be so much fun and I actually did make myself a cup of coffee with this and it tastes so delicious so I will be sure to write the little recipe below in the description box for what I mixed together to make the spice up so I have some fun news we actually had a butterfly come out of its chrysalis if you guys remember I think in the last video or possibly the video before that I was telling you all that we had gotten some caterpillars my mom accidentally cut down a dill plant and there was a bunch of swallow tail butterfly caterpillars and some of them have escaped and we haven't ended with as many as we started but we've had a butterfly this week and I posted about it on Instagram so you guys can go over there and follow me if you want more like daily update type things but it was so beautiful we're pretty sure it was a male that was one of the first questions that the girls had was is it a boy or a girl and so from what it said online a lot of times the males have more orange to them and the females have more blue so that's definitely was very orange and it was just so beautiful and we left the little enclosure open which some of you were asking for the link for that so I'll try to remember to link that below and we went inside after we looked at it and came back out and it was gone so it really just flew away on its own we didn't have to take it and try to get it out of the enclosure to release it or anything just flew away and it was such a neat experience for the girls especially with homeschooling to see the whole process of metamorphosis and just to talk about it and how amazing it really is anyways I'm gonna go ahead and get started on dinner here in a little bit and obviously the main dish is made for me with the beef stew so we're just gonna make up a quick side dish and then I have something kind of fun as a little sweet treat after we are done I don't know if it's because it's the time of year where it's probably the freshest but this asparagus was so delicious we could not stop raving over it it just turned out so so yummy I just drizzled a little bit of avocado oil over it I used my favorite veggie seasoning which I will try to leave linked below because you guys need to try that it is so good I put it on all of my veggies if you watch my videos often you know how much I love using that buttery steakhouse seasoning and then I topped it all with some mozzarella and after the asparagus was ready and out of the oven I dished up our soup and I put the asparagus on some little plates and then I chopped up some fresh parsley just sprinkle across the beef stew I was talking about I decided to make some hot chocolate I know it's a little bit of a weird time of year to do that but my daughters love hot chocolate it's one of their favorite treats and I decided it would be fun to make because we haven't made it for a while and a little side note these cups are my grandmother's tea cups she used to have a huge wall of them at her house and she's since passed away but I love using these and I just think it's so neat that I have three daughters and I ended up with three of these cute blue tea cups so on special little occasions like this I pull them out for us to use enjoying their hot chocolate that dinner was so delicious that's one of Corey's favorites is to do either roast or a beef stew like that and I just think it's such a yummy meal especially going into fall and I'm thinking more about comfort foods and cold weather foods since we live here in central Pennsylvania there is a lot of cold weather a big portion of the year so I'm always looking for foods that will warm us up I am enjoying a nice little dirty chai and I didn't mention this earlier and maybe in the next video because I'm gonna be drinking this is like my favorite fall and winter coffee combination is a dirty chai but I will try to remember to show you my chai syrup that I use you can get it on Amazon and it's just really good and it's a good combination with that spice I made it's just perfect I think that the black pepper in that spice is what really brings the warmth out and gives you that good spicy flavor that is kind of different than a lot of other cinnamon type drinks anyways we are on the recouping mode I'm definitely feeling a lot better than I did the last couple of days so I'm glad about that and I'm so thankful you guys could hang out with me today I hope that you subscribe if you're completely new and as always leave a comment below I read all your comments and try to get time to respond to as many as I possibly can and don't forget to check out butcher box the information and the link is in the description box especially if you've been thinking about it or maybe have been wanting to have a meat subscription or something where you're having meat come right to your door and this is the best quality we love butcher box and have used it for a long time and I know that you'll love it as much as we do so I'm going to go ahead and get the girls and nighttime routine started and just start to wind down from the day and I'll see you guys in my next video


with our show, which is opening tonight. I'm in fifth grade, you are in kindergarten, two one act plays in tribute to Maria Irene Fornes, written by some of these lustrous people I'm standing in front of right now. Let me just get out of the way and just say thanks to the Lewis Center, thanks to, you can look on the website at arts.princeton.edu slash Fornes and get a full list of this weekend's activities as well as our full list of funders. And so thanks to all of those folks and thanks for being here. But I would like to turn it over to my friend and colleague, Ann Garcia Romero. Ann Garcia Romero is a playwright, a scholar and an educator who has been working as a playwright for decades and is also in a very distinctive category of scholars. She is a professional playwright who is also a PhD holder and an assiduous scholar and critic of contemporary Latinx and other traditions of playwright. And so she's an incredible presence in the field and it's an incredible honor to introduce her today to guide us in this conversation of the playwright's pedagogic legacy. So I'll turn it over to my colleague, Ann Garcia Romero. This afternoon, I'll give some brief introductions to my two illustrious guests on my right and my left and we'll talk a bit about their plays, a bit about their teaching and then open it up to all of you for some question and answer toward the end. To my left, Medellia Cruz is a playwright, lyricist, translator and librettist, a new drama alumna. She was a New York Foundation of the Art Fellow and the Helen Merrill Distinguished Playwright. She's been nurtured by Sundance, The Lark and by her mentor, Maria Irene Pornes at Intar. To my right, Mac Belman is a playwright and novelist, a new drama alumnus. He received his third Obie Award 2003 for Lifetime Achievement. He received an award from the Foundation for Contemporary Performance Arts. He is a Donald A. Fine Distinguished Professor of Playwriting at Brooklyn College, where he's the coordinator of the playwriting program. Please let me welcome Medellia Cruz and Mac Belman. Begin today talking about both of your plays that are in this evening, this plays that Brian mentioned, I'm in fifth grade. You are kindergarten, two-shore plays to honor Maria Irene Pornes and your play, the new new Mac and your play, Medellia, The Book of Meow. Can you talk about how your plays were influenced and inspired by the work of Irene Pornes? Well, this particular play because I knew I had, it's a new play and it was a commission play for Princeton. So I knew what my task was but I didn't know how to go about it. So I started, I decided I wanted to take a play of Irene's and work on a script that I worked on when I first met her in 1984, when she accepted me into her workshop, even though she thought it was a really bad play. She told me so. But she said, thought I had potential. So I thought, well, I'm gonna rewrite that play which was based on a short story by Colette called Grubish. I'm gonna take that play and I'm gonna take Irene's play Promenade and I'm gonna write Fantasia Cabaret about memory loss and constellations. So I did it. So I did it. So the way I used Irene's work, I had read about how she had written Promenade on from index cards. So I took all the characters from both sources from the Colette and from Pornes. I put all the characters on index cards and I put all the scenes on index cards and I put lines from each of the original sources on this cousin. I'm just gonna mix it all up and see what scenes are right. And from the random find the specific which is what Irene was all about. So that's, I mean, it's a pretty direct influence. But. Thanks for telling me that. I never took a class with her but I knew her on and off is a colleague in the theater. Actually, I saw, definitely her friends in the original production Broadway on Eath Street. As I was going up to see the show, the elevator stopped in between two floors and I had to climb through the top of the elevator and drag three people out of the elevator to the floor where the show was going on. I got a standing ovation. And I also enjoyed to play a lot. I admire her work a lot. What I particularly admire about her is she's not a pretentious, she was not a pretentious playwright as a lot of people are. And she was very collegiate. Every time I ran into her teaching we would have very good discussions about the people we were mentoring. I ran into her, I think the last time was at the book party for a book of hers. And I happened to have a play called Fulu La Loo being done at Soho Rep. And I said, I really want to come see my play. And nobody would ever come see. I mean, no one does that, but she did. So she came to see my play and said nice things about it. I think I remember. But I remember most of what a wonderful presence she knows. And also have the few directors, who are writers, who's really a great director as well. So I think the world of her. And really in both of your works I'm really struck how your exploring intersections of both culture and history, and you kind of riff on both of those. I know MacDally, you were saying how you use index cards for the various aspects. And in your piece you mentioned it's a Fantasia cabaret. And there's influences of French cabaret, Cuban cabaret. And then Mack in your piece said in Ebor City, Florida you have influences of sort of Cuban culture, Florida culture. One of the ways that those cultural and historical aspects influence the writing of the play, the inspirations for the plays. My play was commissioned by a theater company in Tampa, Florida. So I went down there and snooped around and did a lot of research and found out there are a lot of connections in Ebor to Cuba, but also to the anarchist communities of Spain and Italy. And that interested me a lot. Che Guevara and Castro both came to Tampa. The anarchists were very powerful there. And in the 20s, it was one of the first cities in the south to drive out the KKK. Because the KKK came to town like in 2122 and all the anarchists were up on roofs with rifles and told them to get out of town and they did and they never came back. So all of these weird connections made a huge impact on me. And I just studied a lot of the local history. First up is a play called Why the Why and then I worked on the script a lot more and it was done so a rep a few years later. But she, I never studied with her but I certainly was influenced by her work. And I think at that point in New York she was certainly one of the most influential playwrights. I wish she still were. But she's a remarkable presence in the American theater. Great, thank you, Matt. So the question is what were the cultural? Well, how did the cultural and historical influences that you explore and you riff on in your play how did that inspire the writing or inspire the creation of the world? Well, you know, I feel like it all came out of my head so I would say this is the influence. But it's more like what I know of Irene especially in her, as she got ill with Alzheimer's what I saw that she still reacted to and her sense of music and fun and you know, listening to either Pia off and Compai Segundo and, you know, Astor Piazola those are the things that excited her. When she could still, when she was still talking she would be singing, you know, one Tana Metta alongside East Side West Side all around the town. It was just like, it's like, where are we? Where is Irene's head? And so I sort of focused on what is her head? Like what is going on and what does it mean when you lose your memory? And what are the memories you do remember and what do you remember them completely? And how do you, as a writer, how do you hold onto your story? So that was really my influence. I was thinking about disease and intellect and how they moved in this weird plane once you sort of get removed from the world and into your body, into your head. Yeah, because I'm struck by how memory works in both of your plays. Memory, you said of sort of, in your case, thinking about like what is Irene's memory? But how does that kind of collage of memory also impact form? So both of your plays have songs. They both have a variety of locations. Structurally, they kind of are very expansive. So how, does memory in some way influence the form of the actual play? I think so, but I mean, you have to write using memory. How you use it is up to you. I admire the way she used memory because it was not simple-minded. It was not what gets taught in most schools. It was more interesting and it was more surprising. I think the most interesting way of approaching by writing now is to use epiphany rather than narrative.  In her plays, often do that slap in the face and wake you up, like that. And that to be as interesting, predictable of theater narratives don't do very much for me. And I don't think they did very much for her. I remember talking with her. She said she got into playwriting because at the time she was living with Susan Sontag, who took a great writing course and was baffled by this course and gave an assignment to Irene to look at and was about writing a play. So she wrote a play, and then she turned into a playwright. God help her. And I think it's always things happen to you and it's how you respond to them that's interesting. That is something that interests me a lot. Thank you, Matt.  Things you think you remember. You don't remember them correctly. Then you go back to think about the beginning and you remember another detail that maybe is false, but it seems so vivid. So it's like, for me, memory and dream world are lived side by side. So I think as a writer, you're constantly looking for those, for me, anyway, me as a writer, I'm always looking for those places where they live in a parallel space. And not so much remember things, but re-remember to dream things. Yeah, another notion of sort of epiphany and truth telling, I guess I'm gonna circle back again to kind of issues around aesthetics and form, because with Fornes's plays, every play was formally very different. And she never ascribed to a particular narrative model it was feeling, what does this play have to be? And I'm kind of curious, maybe as playwrights in general, like how does the form of the play reveal itself and how do we have some of these two plays, how do the form reveal itself and the writing? Well, for me, I followed Irene's guidebook to promenade. So I followed that form, but it could have taken any direction because that's the beauty of Irene, is that it can't go in any direction. It could have been a musical, it could have been a monologue. I didn't know, but as I started to write it, I realized that for me, the most important part of Irene's character now is this idea of music and what her music is and what her music used to be and how, and the musicality of her characters. It was less about what shape it was gonna take was more like how it's gonna sound. What's the soundscape inside her head? That's what I was focused on. So that's what informed the form, I guess. I wrote The New London a long time ago and I remember what I was thinking about at the time, formally was a Greek play called The Amenities, which was about the creation of a political state. And the fact that you had Castro, Che Guevara and all these anarchists in Tampa, Florida, that interested me a lot. And I'm very interested in political theater but not in the kind of lectures. I don't think that's a waste of time. I'd rather create plays that get slapped in the face, make you doubt what you think you believe in. But I just let it go where it wanted to go and a lot of it had to do with places in Tampa. Basically the set in the Italian blood, but there were all these incredible places there that are still there. And it's a, you go almost to any place and there are wonderful stories in every look and cranny. So kind of moving towards now, you're both teachers of playwriting. And Fornes's playwriting method, she taught in theaters, universities, arts organizations and she used very unconventional means, a unique combination of visual art techniques, acting techniques such as visualization, drawing, yoga, sense, memory to help her students generate new play material. I'm kind of curious as both of you as long time playwriting teachers, what are ways that you help your students access that unique voice that they have as writers? You know, when I first started teaching, I thought I had to teach them what I knew and since I didn't know anything it made me feel very embarrassed. So I would have them write a monologue with the same number of words as to be or not to be monologue. But as things progressed, I began to get dubious about that. At one point I had an experience. I was offered a commission to write a play and I knew the play would get some attention because of who was doing it.  What if I were Shakespeare or Escalus or somebody like that? And all of a sudden I felt more confident. And I wrote a play and it actually did get some attention. And then so that made me change my notion of what creative writing was all about. I don't think it's about teaching people rules for how to do things. The thing that it's about is getting you to create the ego that can create. The other thing that's happened more recently I began to notice all of these people who were coming to these writing programs. I was trying to figure out what the hell is this all about. I mean it's all over the country too. And then finally it occurred to me when I came to New York, you could rent an apartment for $200 a month on 14th Street. You'd get a job on a coffee shop. You'd have to have a job. That world was long gone. The only way you can meet your own generation is go to one of these programs. And that's why people go to them. It's not to have me tell them how to write a play. It's to meet other people of their generation. Because theater changes every 10 or 15 years. So the thing that I've focused on now is introducing people to each other. And I'm very good at that, but it's important because what my generation wanted to do is we sort of did it. But there's a two or three newer generations come along since then. And that to me is very interesting. I think when I teach, I teach the only way I know that I actually learned from, because I had two degrees in playwriting and I still didn't know how to write a play until I met Irene. Because I learned how to, I don't know, lead people to find their own voices. I don't know exactly how I do it, but I think I do a lot of like, I don't know if it's like conjuring and visualization of Irene. Like I always think about her voice when I teach. And she had a tiny little Cuban accented voice that was just as small as it was, it was fierce. So I think about all that energy that she brought with her into the teaching, into the teaching, into the classroom. And I think about the things that she valued. And I also, the one thing I do that she doesn't do is I also bring in poetry because I feel it's important to start with words you know are good before you start to try to find your own voice. Like listen to how someone, a poet picks precise words in a precise order, at a precise order, at a page. So when you see, when you read a good poem, you kind of begin to understand the value, I think, of imagery and starkness.  Not that many. People like Irene did it beautifully with two words. There are other people who take 25 pages to write the same thing. To me that's not good writing. Then it's sort of like, it's like expensive and it's like, that's a novel, that's something else. But in a play you want it to be alive and you want to create its breathing art. So for me it's like allowing people to find their own voice and dissuading them from thinking that it has anything to do with plot and taking them out of the academy in their heads. Because I feel like what is taught now is how to critique each other in most play.


For us in our normal star jumps training, you know, we're back home, we're in an area where it's pretty controlled, there's no one going in and out of it, it's not the open ocean. So these junior guys who get open ocean training is really good, it's something they won't get back home at all. When the healer door opens, we're looking into the water right to make that leap, what we feel is excitement, excitement because here's a train that are finally being utilized. Once you hit the water, you're feeling a adrenaline rush because you want to try to go as fast and as smooth as you can in order to save this person's life.  What other sea life is around?  Out here, you're at the mercy of getting that healer to you, so you know, you just have to be on your toes at all times. Every now and then, depending on the situation, we'll have to lower a swimmer via the hoist and that could be due to any number of reasons, whether it's an extremely high sea state or if there's any debris in the water, which would be unsafe for us to deploy our swimmers the normal way. If I was put in the survivor's position and I saw the helicopter overhead coming to get me, I would have a feeling of extreme relief knowing that the United States Navy is going to pick me up. These guys are the experts at what they do. And everything, like all the training that we were taught, you're like, man, do I remember this? Do I remember this? As soon as this happens, everything comes back.  You're like, I know exactly what to do. I know how to get this guy out safely. I'm not, you mess this up. Your training kind of kicks in and you just get this guy on the aircraft that we were going to transport into the closest medical treatment facility. I don't think you really think about your actions until a couple days later when you're like, oh, wow, that guy's alive. Because we went and did something about it.


hole of you. Love me some dungeons The whole of youtube so go go check those out Uh again all channels will link down to the description if you guys can't figure any of that out Um, eric, what are you guys going on? Where can they find you here? Yes? That's it? Yes Well at emo 87 90 at twitter, but I mean yeah, he's not gonna read well. He'll read. Oh, I read He'll read He uh, it's funny how I'll mention something happened on twitter. He's like, oh, I know I read He's following all my tweets on twitter. He's a lurker Oh, I'm on camp urges's livestream. I'm gonna say hi. I'm just gonna I had no idea, but thank you eric for tuning in Anyways, you guys you guys know who I am at this point Because this is obviously the nintendo prime podcast show, but if you don't and you're new I'm not really surprised Three days. We've we've gained 2800 subscribers in the last three days. I don't know what's happening Um, but thank you for being here. I appreciate it at this rate. We read it promotion. You're getting Yeah, I'm sure I'm sure Shout out to our slash tears of the kingdom Love me there. I'm their favorite content creator. I see Pop up on that sub every day and it makes my day every time They're pretty silent when he's right though I'm right. They just say I'm a broken clock. I'm like, okay. Yeah, well clock that has a I don't know how that works, but hey, you know what got announced today that uh, I was right on again Just to pat my own back.  I just don't always know what's gonna happen. I just know what's coming. Um Anyways Yeah, look, I don't know what's happening at this rate. We'll be at 100k by next week's podcast I I have no clue if that that the pace is gonna maintain for that But thank you guys has been absolutely incredible, uh journey One thing happened to me this week that I I didn't expect Uh, and I guess it was just the whole I'm slowly like leaving the small youtuber crowd In terms of expectations on my channel And I don't know what to do about that So I'm just gonna keep doing my thing until It doesn't work anymore. Well, you let me know when you find out get lost. Yeah It don't like it's weird because now like there's you're gonna switch up honest I'm so used to being like as dinky youtuber to do whatever he wants now It's like but now I gotta be even more careful because if I say one thing if I take like one wrong misstep It isn't just like one person that complains It becomes like a hundred people and then it becomes this big drama and I'm like Yeah, it comes a whole subreddit like I'm just not used to that because The explosion honestly happened over like the last few months Um, and I went from like a nobody that nobody listened to to now. Um People are listening and I'm getting like 30 000 views on videos and I don't know what to do with that So I'm just gonna keep doing my thing because my thing keeps working. I'm not perfect I make mistakes. I'm really sorry about the mistakes I make. I do want to be better. I do want to learn from the mistakes But uh, thank you guys for joining me on this journey. It's been incredible. The podcast is getting more views than ever You guys are awesome. Thank you to all the guests we have on all the time You know, once you guys have been on multiple times except darin. I mean I used to be on all the time used to be on Well, I don't know all that we delayed podcast for you that you didn't show There was that one podcast I showed up to drunk and then disappeared halfway through. Yeah I kind of figured you were getting late or something. I don't know. I just I'm pretty sure I just passed out In your drink You know, seriously thank you guys for all the support. It's been absolutely incredible Um, you can obviously follow our podcast everywhere podcast to her. We'll get last week's episode I think up tonight. Hopefully this week's episode up tonight, too We'll see. Um, but thank you guys so much for all the support. It's been absolutely incredible The podcast is my favorite piece of content. I do every single week. I want to continue to keep this podcast growing I would like to see this podcast one day hit 30 000 views every episode. That would be awesome Because this is one of this is literally the foundation of nintendo prime for those who don't know We were a podcast before we were anything else before we had a website before we did other youtube content It was a podcast and it's been here still to this day And we're going to keep it going for as long as i'm doing this thing So or I should say as long as I have enough friends that want to come on a show and talk with me because Kind of an asshole sometimes and i'm really sorry about that Well, I think uh, I think you're doing great. I think everyone here is doing great Mike west daniel, I think you guys are all doing great Eric is here Um, but you know, I think uh, I think you're doing good. So congratulations to everybody on all those subscribers So they're getting recently and yeah, yeah, congratulations.  We got to get the next person up So you're you're let me see the other thing if there's ever a channel that deserves more views and more attention It is cabernicus and you need to Check out his His content is so next level Why subscribe to cat It's not too kind it's the truth man. It's like One of my most high viewed videos on the my channel is one that you made back when it was zelda informer, you know, like that whole uh theory about What was the dragon rick theory? um Yes Like that that was amazing and he just makes content like that all the time on his channel um, and he's had success he does as was doing some of this platoon content a bit ago, but um, he deserves so much more attention Uh, he's the smallest creator here besides darin who doesn't create anymore. So my creator here, uh, but I'm creating here It's his content is some of the inspiration for mine and you guys should really just go If you I don't have a massive zelda audience right now because I'm spamming those zelda videos because I love talking zelda Go to his channel, man You're gonna see an in-depth look at zelda in a way I can't do anymore because I don't focus on just zelda I know it feels like I do right now But I don't do that and he focuses primarily on zelda I'm telling you like any of your favorite zelda games Just go he's got videos for you I I kid you not if cab rickerson's not at 20,000 subscribers went into this year. I'll be disappointed. I'm gonna show them on every week My goal was like five Yeah, we're getting 20 we're jumping we're jumping that way 20k by summer Oh, there you go. That's ambitious I mean my channel is pretty new because I did work on like other people's channels Yeah, but I feel like it gave me a head start that once I was gonna once I was ready to like really go all in on my own content I have the skill set to like You know to take with me. So I think yeah, man for a lot longer than you realize I you know You think that but if I like going to watch some of my old videos.  I appreciate it. Just just keep it up man. It means a lot Yeah, yeah Like you guys, you know every time we have them on you're instantly a crowd favorite I'm like and you guys better be subscribed if he's your favorite. Come on now. Yeah, man All right, guys, let's go do it for this week.


I am Satish Arparyani working as assistant professor in Department of Mechanical, Vulture Institute of Technology, Sholapur. Today, we are discussing the first step project risk planning. At the end of this session, students will be able to understand the first step of project risk process, that is to list down the parameters, content involved, what are different steps and the step one in depth. In the previous lecture, we have just noted the different steps associated project risk. Let us refresh our knowledge once again. The step one is to make the list, step two and three as I have combined it to determine the probability of risk occurrence and its negative impact. Step three is to prevent or mitigate the risk. Step four is to consider the contingencies. Step six is to finally the trigger point. Let us understand the first step in depth. Make the list. Make the list of what? Make the list of potential risk involved in the project. How to do that? Brainstorm. Brainstorm with whom? Brainstorm. First, I will make you understand what the brainstorming session is there. In brainstorming sessions, we are involving the different people from different departments and making them work towards that common goal. We have selected and it should not be that we have to select from specific department or specific involved. Many times the company conducts the meetings, this kind of session, brainstorming sessions from their routine factory towards certain area like certain hillstations where they go, work there and then the different risk parameters from different stakeholders involved. It should not be that not involving certain people because of certain budget constraints or something like that. We should not forget to get involved certain people. Make the role who is there in the project has to be involved. There can be formal meetings what I have said you like going somewhere from different place where total ideas are generated, what are risk potential or probable risk involved that have been captured or forecasted. In this, making a list of potential risk to project should not be the analysis but the formal brainstorming session where all ideas are captured. It is important that the entire team gets involved in identifying threats and highlights what can go wrong. This initial step of the process must be collaborate and involve the individuals who are expert at their portion of the project. Work for they are responsible. Leverage the intellectual capital that is smarts in your team. We have to leverage them out. Smart people, intellectual people, let they come out through different ideas, different forecasted risk what they can do it. If one or more members are left out it is likely that some risk will remain unidentified and pose a threat to the project's success. As I told you if many times within organization certain if we do not involve outside people who are the part of the project though because they are expertise in their field and we left them out. Their experience, their skill will not be utilized in our project right now or some experienced person who is going to retire. These are certain things. We can hire them as a consultant if our company or project permits. End number of solutions are possible but if one member remains out there definitely there will be the risk. Now who will remain out who was not involved and at what level they were not involved it depends the type of risk. If certain key member is not involved risk will be higher. If at lower level the people is not involved the risk will be somewhat at certain. But many times it does not happen because generally project at during the project initiation or project kickoff phase all these people will be there. Involve everybody because let us take one example a procurement specialist over Swiss specialist who is purchasing will not be helpful in identifying potential software development problems and vice versa we can say. So software people the people let us say who is involving certain making certain changes in our process system process if not involved as a process as a procurement team a procured manager will not do that work of software development or changes similarly software development people if they are there and if we are doing the work for manufacturing organization they have to involve that person because they cannot procure they cannot they do not know the steps if they know the steps also in depth their experience cannot be there. So these vice versa this is a simple example what I have put in you think of the probability of possibility in the whole project and number of risk will be there. When you work with the support of an informal team you need to be disciplined and realize that certain amount of research is necessary before moving forward. Hence it is generally said when we are going for the meeting this kind of meetings at least some study of previous projects some communication with our seniors some communication with our outside world so that when we are involved in the brainstorming session or when we involve in the formal team we have sufficient amount of research or knowledge so that we can move forward how this can be done these days it is very easy we I will say compared to one or two decades back in 2000s or before that it was difficult because phone charges phone calls phone calls if phones were not there if phones were there that charge recharge or charges were very high email facities was less. So this way involved right now we can do it because the world is in our fingertips we can say this may involve the phone calls call it not only here we can go for overseas we can call for any number of people's end times now the call charges is also been decreased so there is not constraint over that initially people used to think the companies used to think a project manager has to think given in the small budget how can manage this kind of thing so phone calls are there emails continuously good communication way if the other small factories the stakeholders are nearby we can go to their office we can visit them video conferences as we have seen in this covid world video conferences has supported us whatever it takes to elicit the information you need do it simply do it you have to just think and phone calls are there emails are there office visits are there many times even if a project permits let us say I will take one example if you are making one mold mold of what mold of refrigerator and our bold vendor is overseas at China he has manufactured that mode as per our drawings or our dimensions many times it happens to avoid the risk our member should go that take trials on that mold and their machine so our member go there take trial on their machine with our mold what we have produces this to avoid the future risk because he knows what is required here so corrections are there their corrections can be done very easily similarly to avoid future risk further risk it happens that mold maker brings the mold to India let us say and then that mold he helps us to set on our machine now mold he has manufactured because suppose in our machine during placing that mold if certain dimensions outs outer dimensions are fitted or certain things have to be done so that with the help of him this is what the probability list we have to write it very clearly let us see if that these two steps are not done we have given a dimension he has supplied a small and certain problems come and some major correction occurs some major correction occurs again we have to shift that mold from our factory to overseas which involves lot of cost so it is better to make our member visit there get some trials then bring it here and their member to help us at us and offer our machine you typically start with the informal team members or contributors to project initiate the dialogue as what might go wrong usually this discussion identify the ancillary individuals who are to be contacted functional department managers can be helpful in the circumstances either assisting directly or identifying others in the department who can now think in the step one whether my statement is true or false please tell it you should take a holistic approach to establish the list as all types of risk will need to be identified and dealt whether this statement is true or false holistic approach is needed in step one or not in simple sense yes the answer is true because holistic approach is required to make the list of the risk involved references again it are they are used from MPTL and the major book from Himalaya publication written by Narendra Singh project management and control thank you