Put immediately the goal that I was announcing last time, right? Today our goal is to prove this theorem original due to Watanabe and Yoshida which generalizes celebrated Nagata's theorem to Hilberg-Kunz multiplicity. We will show that a local ring is regular if and only if it is formula unmixed and Hilberg-Kunz multiplicity is equal to one. So again formula unmixed means that it's equidimensional and there are no embedded components. For the completion. So one direction is not easy, but it's already done due to Kunz. We discussed that if it's regular rings and Hilberg-Kunz function is identically one and we will fight to get the other direction. So our strategy will be similar to what we did yesterday for F-signature. We will do induction and we'll use equimult multiplicity. But things are going to be a bit more challenging because F-signature leaves in a strongly irregular ring, but Hilberg-Kunz multiplicity not. So we will need to work a bit with tight closure. But I think it's quite appropriate for this conference to talk a bit more about tight closure and honor Melon Craig in this way. But first let me say what is the key tool? So the key tool for the theorem of what the Naby-Ushida is not surprisingly lm of what the Naby-Ushida is. So if Hilberg-Kunz multiplicity of R is equal to one and I is an primary ideal such that it's Hilberg-Kunz multiplicity is greater or equal than its co-land, then R is regular. And I need to put one more assumption so we also need I to leave inside M bracket P. Just simply, if we know that Hilberg-Kunz multiplicity is one and we can find a special and primary ideal then that's enough to deduce that R is regular. So let me prove this lemma. For that I will need two simple ingredients. The first one is a slight version of the result we discussed last time. So last time I proved this for J equals to R by a filtration result. We took just the definition of co-land, well in this case we'll take the length of J mod i, we'll take the composition series and we apply the Frobenius and then we can't think and we'll get this inequality. Last time we did it for J equals to R so there was no Hilberg-Kunz multiplicity of J but here we filtered not all the way to R but to J. The second result is also very simple, we say that the Hilberg-Kunz multiplicity of a bracket power is going to be P to the D original Hilberg-Kunz multiplicity. So this is an easy result coming just from changing index in the convergent sequence. So what do we have by definition here? We'll get on top IQP but in the denominator we have something slightly scaled. So we multiply both sides by P to the power D and we'll get the original Hilberg-Kunz multiplicity. It's just a formal consequence for any convergent sequence. If we, with such normalization, if we change the index it's going to pop out. Same way how it works for the usual multiplicity. So two simple lemmas to prove the lemma for the NAPI and your shape. So let me give you the proof. Well, we need to use that this ideal i has all these wonderful properties. So I am going to use this lemma for i contained an m bracket P. I have Hilberg-Kunz multiplicity of i and it's going to be less or equal than Hilberg-Kunz multiplicity of r times length of m bracket P over i plus Hilberg-Kunz multiplicity of m bracket P. And I can compute many things here. So I know that Hilberg-Kunz multiplicity of r by the assumption is one. Well, the length, I don't know, it still stays. What do I have here? By my lemma I get this P to the d goes in front. Then I get Hilberg-Kunz multiplicity of m left, but that's by definition. Hilberg-Kunz multiplicity of r again equals to one. So the other part is P to the power d by combining with lemma. Good? All right, now what else we know? We know that this is going to be greater or equal than the co-length. So length of r mod i. How can I write the length of r mod i? Well, I can still use it. I have a bigger ideal. So this is length of m bracket P modulo i plus co-length of m bracket P. I just made an extra step in the computation of co-length. So what do we see from this chain of inequalities? This is the same length as here, right? So the inequality between those two quantities will imply the inequality between P to the d and the co-length. So I get that the length of r mod bracket m bracket P is less or equal than P to the power d. And now we look at this. We remember the Kuhn's theorem, the computations that we did before on Tuesday in the first day of classes. And we see that this immediately will imply by the Kuhn's theorem that r is regular. So we know that actually the inequality goes the other way around. And if its equality holds, then r is regular. This is the equivalent characterization of flatness that we discussed. So as you see, it's a very simple lemma, but somehow it has a strong punch. I don't know any good way to prove the Watenabe-Ushida theorem without going through the Watenabe-Ushida lemma. Somehow it is really, really crucial for all the proofs that I know. Because you could ask, we have a very easy proof for a signature. We can get as easy proof for Hilbert-Kuhn's multiplicity if we assume that r is regular, r is stronger than regular. But then, if you could prove from Hilbert-Kuhn's multiplicity equals one that r is stronger than regular, you could, may as well, just prove that it's coin Macaulay. And then, this is what Watenabe-Ushida did in their original proof. Once you know that the ring is coin Macaulay, you can just take i to be a parameter ideal deep enough, right? Because we know that for parameter ideals in coin Macaulay ring, we have the equality. Because Hilbert-Kuhn's multiplicity equals multiplicity for parameter ideals, and that's the characterization of coin Macaulay rings. But proving that it's just coin Macaulay from this condition is not an easy task. Other ways to do it, well, we could use integrate closed ideals. And the other way to prove this, and basically some of the ideas that I will present, they come back to the paper of Craig Hewneke and Yanwei Yao who did induction, the same way how we do induction, and then they choose a special i to be symbolic power of a smaller prime ideal plus parameter element. So we will do something similar, but our construction of i will be based on induction and equimultiplicity. Okay, so let's proceed. So I want to start building equimultiplicity machinery. So last time we built, we understood when f signatures are equal, right? That was the equimultiplicity. Today we need to understand what happens when Hilbert-Kuhn's multiplicity doesn't change when you localize. And to do so, I need a little bit more about tight closure, so tight closure. So I'll mention some of these things that we already said, let me remind you the definition that x is inside tight closure if and only if there exists c, which is not contained in any minimal prime, and c sends bracket powers of x into Frobenius powers of i for all q large enough. So that's the definition of tight closure. I also need definition of test element. So c is a test element. If it works for all x and all i over here in this definition, it does not exist c, it's this c will always work. So it works for all x, all i. So this is the element you can always use to test the tight closure. That's why it's called test element. I will need the result of Hoxter and Heunicke, which give us existence of the test elements. If r is complete, well, for me it suffices complete and reduced, then test element exists. And I want to remind you one more thing which was already mentioned by Holger, well all those things more or less we've mentioned by Holger, is that if under these assumptions of the Watenabe you should have theorem, so r had unmixed, we have the tight connection between tight closure and Hilbert-Kunz multiplisit, then if i is contained in j and Hilbert-Kunz multiplisit of i is equals to Hilbert-Kunz of multiplisit of j, if and only if j is contained in tight closure of i. Okay, so I will need these four facts about tight closure. And I need also a couple of statements about it. So first I want a simple lemma, so if we have a test element, test element c, so i, any ideal, x is not contained in i, and I think, yes, that's all I need, x inside m, then the intersection of tight closures of i plus xnr star intersection of all m greater or equal than 1, greater or equal than 1 is going to be equal to the tight closure. So intersect tight closure by adding deeper and deeper powers of x, and it's still going to intersect just to the tight closure of i. So I'll leave this as an exercise on the definition of test elements, it's very simple, you really need to use that c is uniform for all those tight closures, and then the assertion will just follow. The second lemma that I will need is about filtration of ideals, lemma. So under the same assumptions, we have a local ring which is unmixed. So now we are going to use the connection with Hilbert-Kunz multiplicity, and suppose that, so we have local ring such that this completion is unmixed, and then le, so i is m primary, and le is a sequence of m primary ideals such that I have three conditions, maybe a. So this sequence contains bracket powers of i, this sequence behaves well with respect to bracket powers, and c, it converges to the Hilbert-Kunz multiplicity of i. So limit as e equals to infinity, the length of r mod le over p to the power ed is equal to Hilbert-Kunz multiplicity of i, then I want to say that my ideal le is contained in tight closure of bracket power for all e, so lemma, pause here for a second. So basically what I'm saying is that if we have Frobenius well behaved sequence of ideals which still converge to Hilbert-Kunz multiplicity of i, then all of them needs to be still within the tight closure, right, they cannot be too big. Is assertion clear? Okay, so let's prove it. So the proof actually is very easy, let's fix le, let's say, well let's just fix le, right, and what do we know about le? If I take e plus e prime, I'm going to have what, inside of it I'm going to, no, I want to say, so I want to compute Hilbert-Kunz multiplicity of le, so I need to take it to the bracket power, right, that's by definition how I compute Hilbert-Kunz multiplicity, and now I want to sandwich it between things and what I can use, I can use property a and say that this is going to be containing p to the power e plus e prime, right, and on the other side I can use property b and say that it's going to be contained in le plus e prime. So I sandwich the bracket power of le between those two things, and then I need to compute the limits, so if I take the column of those guys and divide by p to the power e prime d, right, so I divide it by p to the power e prime d because I want to compute Hilbert-Kunz multiplicity of this ideal, right, so e prime is available, so what I'm going to get by the lemma over there, here I'll get Hilbert-Kunz multiplicity of i pe, right, which is equal to, well pe something, pe d Hilbert-Kunz multiplicity of i, so this is the lemma, right, so this is the definition of Hilbert-Kunz multiplicity of pe i to the power pe and this is the lemma. Then what do I have on this side? By my assumption, my sequence still converges to Hilbert-Kunz multiplicity of i and I'm changing the index, so it is the same proof as what I have here, right, I changed index in this sequence, I got that the limit is multiplied by p to the power d, I change index in that sequence and I will get that the limit is going to be multiplied by p to the power e d and times the original limit, which was by assumption that I can get by Hilbert-Kunz multiplicity of i, right, so what happens? It follows then Hilbert-Kunz multiplicity of le is equal to Hilbert-Kunz multiplicity of i bracket pe and therefore I can use, well one of these properties, the last one, right, to say that le must be contained in the tight closure of p, yeah, here I used property c, does it make sense? Are there any questions? Okay, good, so as long as my sequence is respect in Frobenius, I can deduce statements about tight closure, not just from Hilbert-Kunz multiplicity of one ideal, but from the entire sequence. All right, so that was the tools from the tight closure theory that I will need in order to show, in order to derive the equimultiplisty machine, so let me start raising things and now we can talk a little bit about Hilbert-Kunz equimultiplisty, so our goal is to understand better what does it mean for Hilbert-Kunz multiplicity of localization prime to be same as Hilbert-Kunz multiplicity at the closed point, right, that's the maximal ideal. And the tool that we will use is the same tool that we used for the localization inequality, so let me remind you that we proved that if I take Hilbert-Kunz multiplicity of p plus x and r, so if my, so in this setup we had the dimension of r mod p was just equal to one, right, and maybe let's call them q. So we proved last time, right, that this sequence, Hilbert-Kunz multiplicity of my prime q, and then I add element not inside q, any element, so x inside m minus q, so it becomes q m prime ideal, x plus q, and then if I take limit of the sequence, it's going to be Hilbert-Kunz multiplicity of x r mod q times Hilbert-Kunz multiplicity of r localized, or this is a parameter ideal so I can write multiplicity, maybe I prefer to write multiplicity. So we had this lemma, and that's the lemma that connects m primary things to something q primary, right, that's the one that allows me to localize if you like. So I want to build more understanding from this lemma, and if you remember how did we then show the localization inequality, I bounded this Hilbert-Kunz multiplicity using the filtration lemma by Hilbert-Kunz multiplicity of m times the co-land, and it's also converged to multiplicity. So we want to build more understanding from this result, and I will do this by showing more about the sequence, so the sequence does not just converge, it's actually a monotone sequence. So the lemma, crucial for me, is that under this assumption, so dimension of r mod q is equal to 1, x is inside maximal ideal but outside of q, I can show that Hilbert-Kunz, I will show to you that Hilbert-Kunz multiplicity of x plus xn plus q over n is going to be greater equal than the same thing with xn plus 1. So it's a monotone sequence. Last time we just proved this convergence, but I actually explained better why does this sequence actually converge. And the important part for me, because I will try, I'm interested in equi-multiplicity, moreover, if equality holds over here, then we are going to get, well, rather technical look and condition on limits. So limit as, no, not limit, yeah, so limit as e approaches infinity, length of r mod, so let's see, so xp e, r plus r is equal to 1, xn minus p, no, not q bracket, p e colon xn, so this is my ideal, I take bracket power of p e of x, right, and then I take colon of bracket power of q, so this is different thing. So I take colon, ah, n should be p e, and then if I divide it by p to the power ed, this is going to be the Hilbert-Cons multiplicity, so this is going to be equal to Hilbert-Cons multiplicity, well, 1 over n Hilbert-Cons multiplicity of q plus xn. So we will see where this technical look and limit comes from. So the proof of the lemma is actually just by following the proof of this statement from the last time, but with paying attention to the details. So the key part from the last time was that if we had a one-dimensional, then we had exact sequence of, sorry, it was a, a mod xn, a, no, n plus 1, right, it surjects clearly on a mod xn, a, and we can compute the kernel as a mod x plus an annihilator of xn. So we have this exact sequence. Well, what I can get from this exact sequence? I am going to plug, well, I am going to plug into this exact sequence for a b-news powers, right? My a is going to be what? It's going to be r bracket q to the power pe, right? And my x will be appropriate powers of x, right? But maybe, let's see, yeah, let's maybe write carefully what do I get? What do I want to remind you? So I want to remind you that, so how did the proof go? So we have proven that length of a mod xn, right, a is equal to the length, also length xn minus 1 a plus this colon over there, so length of ax, ax minus 1 a plus this colon with xn minus 1, right? So this was the first step of utilizing this exact sequence and then we kept going, right? Now we can go from xn minus 1 to xn minus 2 and so on. So we would get what? We will get that this is equal to the sum of the length with different colon ideals, x a plus 0 colon xk, right, where k varies from 0 to n minus 1, right? It just utilizes the sequence over and over to decrease this power eventually just to power 1. And what else we observed in the just original proof? So I'm repeating the argument that we used over there. So we observed that this is going to be greater or equal, so each of these colon ideals is going to be less or equal than what I have here, right? So this is length of a modulo x a plus 0 colon xn, because my colon ideals, they increase, right, with them. So I have the containment 0 colon x i into 0 colon x i plus 1, right? The annihilators get bigger and bigger, so I get this inequality just because each of them individually is smaller exponent, right? Okay. So now I can look and apply my observations to what I had over there, right? So I can write to use at the length of, so I want to prove to use this inequality, right? So I need to get something with xn plus 1 and something with xn and I could multiply n plus 1 to that side, right? So the length of a modulo xn plus 1 is equal to the length of a modulo xn a. And then I have this colon piece, right? But I can, okay, let me write it. So I'm actually not worth to write it. So now I'm going to use this inequality to remove this colon ideal, right? So this is going to be less or equal than 1 over n length of what they have there, right? Length of, so what I have, so x, so the length of a modulo xn is greater or equal than n times this length of the colon ideals. So I replace this guy, right? By 1 over n length of just a modulo xn a, right? So I have the same thing here and the same thing there, so they add up and they'll give me this n plus 1 over n length of a modulo xn, makes sense? So if this was statement star, then here I use statement star together with this bound over there. So this is where this inequality comes. Into this equality I now replace, I give you a bound on this. Make sense? Take a look. Any questions? Okay, so now plug instead of a, r mod q to the bracket power. And the statement just follows, right? So take a to be, a to be what? a to be r modulo q to the bracket power pe. Then what do I get from this inequality? I get that the length of r modulo my q bracket power pe. And let's replace x to be xn to the power pe. What, so I get here x to the power n plus 1 pe is less or equal than n plus 1 over n, right? Length of r mod pe plus xn pe, right? So this is what I get by plugging a to be r modulo q bracket power. And then what do you see? You take the limit, right? And you precisely get the statement over here, right? I just left to take the limit to derive the first statement and the second statement just comes from looking at this defect, right? If you look at this inequality and I have the quality between this and that, then I should have the quality over here, right? Well, I'm taking limit, so I won't get exact equality, but I get equality in the limit, right? This column term over there, so this one over here, the ones that I replaced should converge in the limit to this additional term that I have here, right? Because this is the inequality that I used. So if the limits are equal, this thing and this thing should have the same limit. Does it make sense?  Any questions? All right. So that's a crucial level because what does it provide to us? It provides to us an interesting filtration inside my, I mean, it gives me something fitting into this level, right? Because I get now some filtration which has the same limit as Hilbert Kuhn's multiplicity, which has the limit equals to Hilbert Kuhn's multiplicity of some ideal. So from here, I can deduce something interest. So what I can actually deduce? So let me raise the proof. Let me leave the lemma. So same assumption. So let me just say dimension of r mod q is equal to 1, x not inside q. And suppose that Hilbert Kuhn's multiplicity of, Hilbert Kuhn's multiplicity of r localized at q is equal to Hilbert Kuhn's multiplicity of r. And then what I claim to you is that, well, let me just try that. If I take q to the power pe and I take type closure of them, then this is going to be a modically saturated, right? So this is going to be equals to itself. So the type closure in other ways because r mod q has dimension 1, m is the only potential associated prime. You can restate it as the type closures of Rabinu's powers are q primary. Equivalently. Equivalently, this type closures, yeah, maybe this is how I should reward, is q primary. So let's prove this. Well, I want to use the lemma. I have this family of ideals. So let's look at what I get. So if I take le to be q bracket pe colon xn pe plus xper. Then over there, I prove to you that equimultiplicity is going to force maybe add, let me add to you the actual proof, right? Let me actually remind what we deduced last time, right? So here we wrote this is less or equal than Hilbert Kuhn's multiplicity of r times the same multiplicity. This was how we proved the localization in equality, right? We filtered this thing and we got upper bound and this lemma that we had give us equality on the limit, right? And from here, we deduced that Hilbert Kuhn's multiplicity of r is greater equal than Hilbert Kuhn's multiplicity of r localized at q, right? So if I assume these two things are equal, right, then I am going to get equality over here, right? But then I have a descending sequence, right? So the equality must hold all the way through, right? From starting point q plus xn x, then going down and down, they all must be equal to this thing because I sandwiched it between two equal things, right? So I have a descending sequence which starts and adds at the same point, right? This is what happens. Okay, does it make sense? If Hilbert Kuhn's multiplicity of r is equal to Hilbert Kuhn's multiplicity of r localized at q, this monotonicity forces that Hilbert Kuhn's multiplicity of q plus xn, right? r is going to be equal to n times Hilbert Kuhn's multiplicity of r localized at q times this thing, right, e of xrk. In other words, the sequence over here will become a constant sequence. And this is why I can get this limit condition. Does it make sense? Okay. Good. So then I look at this sequence of ideals. It is really easy to see using the properties of colon ideals that the sequence satisfies the assumption of the lemma. So lemma, I don't know, I should give it a name. So lemma a. So by this lemma a, I will get that le star is going to be contained in what? In q bracket pe plus x bracket pe, right? Together tight close. I look at the definition and I see that this part is already contained in the right hand side. So from here, it follows that this saturation, this colon ideal and x and pe is contained in this tight close q pe plus x pe. This holds for all n, right? Because nothing depends on n on the right hand side. This is increasing chain. So eventually I'm going to get here the entire saturation. And x is a parameter, q has dimension one. So this is nothing else as just q bracket pe, saturated with respect to the maximal ideal. Because modulo q, x is parameter, right? It is n primary, right? Modulo q. All right. And then what happens then is that I have this containment, right? So what I have is that q bracket pe saturation is contained in q bracket. We have this thing. But this statement now holds for all x. In particular, I could take one element x and take its powers, right? I could take x and pe here, right? And greater or equal than one, right? Because on the left hand side, nothing depends on x. On the right hand side, I was working with arbitrary x. So I can take x to be anything in particular powers. And then I can use the tight closure lemma to say that this is going to be contained in actually tight closure of q pe star. So the saturation is contained in the tight closure, okay? Okay. And then an easy exercise. So I won't explain it. It actually forces our tight closure to be saturated. You just write down imagines that it's not saturated. There is an element sent by power of maximal ideal into the tight closure. And you apply this condition that the tight closure still converge to the same limit as the regular powers. And you are going to get that this condition implies that the tight closures are already saturated. So this is a tight closure. So you see, I mean, using all these properties of tight closure, we get at the end from this rather technical lemma over there, a rather pretty condition, right? We just get that the tight closures of Rabinius powers, they're going to be q primaries, they're not going to have m primary components. Okay, so let me then erase this lemma and write one immediate consequence of this corollary, corollary of a corollary. So if we know that an ideal is q primary, so the quotient by it, because it's one dimension that's going to be coin Macaulay, so we have the consequence between length and multiplicity. So under these assumptions, assumptions from here, what I'm going to get is that the multiplicity of x r mod q bracket p star is going to be equal to the length of r bracket q p plus x r, one dimensional coin Macaulay. So just the condition of x being a regular element in this quotient, this is all it is. All right, so I can erase now everything and I can finish the proof of the, what do I mean by the theorem? I have now everything that I need. So we do induction on d, d equals to zero, we have Hilbert-Kunz multiplicity of r is the same as the length of r. So being equal to one implies that r is a field and field is regular, so we are done. So if d is bigger than zero, then I have a prime q such that Hilbert-Kunz multiplicity of r q is equal to Hilbert-Kunz multiplicity of r, right, proper prime contained but not equal to n just by taking a chain of prime ideals. So this is equimultiplist condition and this being equals to one implies that Hilbert-Kunz multiplicity of r, so because this is equal to one and this is always greater or equal than one, so from this chain of inequalities right, the localization we proved last time, the equality must follow through, right? So we get that Hilbert-Kunz multiplicity of r q is equal to one and in particular is equal to Hilbert-Kunz multiplicity of r and by induction, we assume that r localized at q is written, what do we need to do? We need to construct the sequence satisfying the what an ideal satisfies the Watenabio-Schiddler conditions and I'm saying that now let's just look at ideals that we can construct over there. So I'll take q bracket P star. I take x inside m bracket P, right, without q. So I take this ideal. And I need to verify that it will satisfy the assumptions of the Vatanabian Schroeder theorem. So it is easy to see that if my E is large enough, this is going to be all contained in the bracket power of mP, right? So this condition is OK, right? So this IE, well, IE is bad. Let's call it LE. LE is contained in m bracket P for IE large. You can use that it's going to be, I mean, you can just use that the risk algebra of integral closures is finally generated. And this is contained in integral closure. So I need just to compute length and multiplicity, right? So the Hilbert-Kunz multiplicity of q, q bracket P, right, star plus xr, I want to compare it to actually to the length, right? But there, I mean, right, so I need to compute this length, right? But there, I can just use the multiplicity condition, right? And let me quickly speed it up. So what we are going to see over there is that, so what do we see? So we see that if I take, so basically what I see is that if I take, basically, look at this thing, right? So let me take P bracket U, right? So this is contained, this ideal over here, it is contained, of course, in tight closure of qx, right, together to the bracket PE, right, star. So this Hilbert-Kunz multiplicity is going to be equal to the Hilbert-Kunz multiplicity of that ideal, so it is Hilbert-Kunz multiplicity of qx together, bracket PE. So this is going to be, yeah, I should say, PE here. So this is just going to be equal to PE to the power d, right, and then Hilbert-Kunz multiplicity of qx, right? But then this is one of these things in the filtration that I used, right? So I know that this is equal to PE to the power d, Hilbert-Kunz multiplicity of xr mod q times Hilbert-Kunz multiplicity of rq. So I get this on one side. And then on the other side, I just use the consequence of this corollary, right, the length. So I could put P bracket E here. This is going to be E bracket here. So this is going to be PE. And then I use the associativity formula. This is multiplicity of xpe r bracket q. So PE are removed times length of rq, q bracket PE star. And because I assume that the localization is regular, this is just equal to PE d minus 1, right? So at the end, I get PE d times the multiplicity. And over here, I assume that, I mean, it is consequence that Hilbert-Kunz multiplicity of rq is equal to 1. So I see that those two things are equal, right? And from this, I can apply the lemma of Atanabe and Yashida. And it tells me that my ring is regular. OK. It's a place to stop. Thank you. Thank you, Greg.


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That's what I like. That's why I wanted to come down here. It's the first time we came out the studio, right? Right. We don't never come out the studio. We be in our place, in our zone. Right, right, right. We here. You're never here. I don't want to know what is the recipe for Atlanta, because a lot of times when we be talking on our show to different entertainers, they always say, Atlanta entertainers are so together. They do a lot. It's not like Texas where Houston over here and they rep Houston and this is Dallas and Dallas rep. Dallas and they don't really do that much stuff together. It's like, but Atlanta has this recipe where everybody is just doing stuff together. It looks like they respect each other on a whole level. But they just held her back for so long, man. I mean, you know, West Coast had their time but North had their time and they just never gave the South the respect, you know what I mean? They just never would get the South the respect. So as far as that, Atlanta just, you know, when we start doing music and people start respecting it, it's like, okay, well, we ain't gonna just let y'all respect it. We're gonna keep the dough down, you know?  They don't mess with certain people.  You see, that part. And Dallas don't do that. He, Texas period don't do that. Watch your mouth. Watch your mouth. You know, don't get down here and get beside yourself. Watch my mouth. But okay, can you tell me when Texas did that? We've had issues, you know? But at the end of the day, a good family gonna fight. Right, right, right, right. You know what I mean? Like I said, we do have our problem and we do have our situation. We just had a situation on the news. They had like a thousand people in the park a lot. Yesterday, somebody just got killed. You know what I mean? It was just yesterday. So don't get me wrong. I ain't just praising us. We do have our ups and we have our downs, you know what I mean? But as far as the music comes and how the music going, that's just what happened in the hoods. As far as the music, man, Atlanta come together in a minute and just go crazy. You know what I mean? We've been here up back for so long, man. Like they wouldn't never, they still don't want to get a respect. They say, Migo, Mamba, Rappers. Migo, Biggs, I'm round them on my show. They're the biggest group out here right now. Bro, I got on them on my home. I don't play that, bro. I don't play that. He's not to talk about nobody from the South, period. But I'm not the one. I'm not playing that game. But you feel what I'm saying? I know what they say. They still won't get them, man, you know what I mean? They still won't get them. They flower. They still won't get them. That's it. So let's back up a little bit. I want to know. Hold on, hold on.  I know what you're trying to do. Say, man, we want to know who is the DJ Ace. Who is he? How did he start? What's up with? Before the music, before all of that, like the young DJ Ace, before he was DJ Ace. Before I was DJ Ace, man, I was I was a star football player in high school. I played back when Quincy Carter played. Wow. Quincy Carter was my he was my neighbor across the street. Played for the Cowboy. Yeah, played for the Cowboy, man. The Cowboy was my weed, though.  I wanted to see the grow. We went to Southwest to Cal. And he was supposed to go to Cedar Grove and be a quarterback. OK. But he brought a BB gun to school in the in like middle school, elementary school. And my daddy, he lived with his mom. OK. He was the head of their mom. So my dad, you know, went to court with him and basically acted as a lawyer for him or whatever. So I think in the end, he just couldn't go to his home school. He ended up going to Southwest to Cal. His home school was Cedar Grove. It was a blessing for me because I was able to go to Cedar Grove and start as a ninth grader. You used to run that ball, didn't you? Yeah, I already know. I was a quarterback. I was a quarterback. Yeah, but I was ranked. I was ranked number one in number three in the county five in the state. But I was ranked in Russian and passing yard. You must have been fast. Yeah, but he built up like a running back. So he can do both. Yeah, man. That's dope. I started playing football, man. But at the same time with that, we all played Gresham Park. Everybody played at Gresham Park. Me, Quincy, Felix Alden from Southwest to Cal. At the same time, I was racing dirt bikes. OK. Yeah, my dad had been big in racing dirt bikes. Very active. Yeah, we had sponsors, WD-40, Troy Hellman. WD-40, good. We had different sponsors. We was racing all up in, like, Florida, California, Tennessee, and all the big AMAs, like they do in the stadiums now. So anything you touched turned to go. You did it very well. I didn't want to say that, but my daddy kept us active.  How many of y'all were there? There's three. I got a little sister, too, and she was even racing dirt bikes. Wow, wow. That's dope. I know you like that. I love it. So was your mom in your life? Yeah, my mom, yeah, my mom lived with us all together. My mom and my daddy had their own band, though. They had a live band. My daddy was the drummer. But that's where the music came from. My daddy was the drummer. My mama was the lead singer. When I was about 10, A-Town Players came out. Yeah, yeah. A-Town, dropping all that kids around. My brother was one of the dancers. OK. He was doing all the cranking and stuff. So as I'm about 10 left, I think I was like, 12 years old, man. I woke up one morning and one of the dancers couldn't go on tour with A-Town Players. So you had to do it. My dad, my brother asked my dad, my dad, it's a hell no. Boy, I was like, 12 years old, even though I don't know a road to a job. So you're the youngest? No, I got a little sister, too, in the middle. So I'm like, 12. They asked me to go and the show was with 95 South. Wow. Tag team. Whoa. All of them had one of these. You hit them. You hit them juggler bikes. It was all up. Yeah, yeah. It was at the Miami Hurricane Stadium there, you know, in Miami. So my dad said, yeah, he let me do that. That's don't let nothing happen to him. Did you freeze? Oh, no, I was ready for it. I was ready. Shit. I was ready. I couldn't wait to do this, man. I was waiting to put me on a plane. We flew down there. And that's crazy, because I was young. This at the time, we didn't have to have no ID. So I flew on his name. Yeah, I remember those. Yeah, I remember his name. That's the way it used to be. I was 11 years old. But all of you remember the days when kids was half price? Yup. I remember that when I was a child. Man, we get on the plane. I'm riding limos and all that. That's why I first learned how to smoke weed. Shot the bonnet keys in and play a punch up. 12 years old. Yeah, I used to steal my daddy's weed. That got me in Miami. Yeah, you're early on. Yeah, yeah, man. So when you went on that stage and that feeling that you got, is that a time when you're like, man, this is what I want to do? That was what I wanted to do. But I wanted to rap. I wanted to do, like, it would. I saw thousands and at least 20,000-30,000 people out here. Mind you, Woop There It Is was the biggest song. Yeah, it was. All three of the artists with Woop There It Is is on this show, along with other people, like Woop and other folk. And it's in the Miami Hurricanes Stadium. And I'm like, man. So I'm dancing though. I'm cranking it. Oh, go on all that. Yeah, yeah, yeah, yeah, you rock out. But as I came back to, you know, back to Atlanta, and I'm watching kids rock, DJ. I'm watching Raheem Adrien. I'm doing shows. I'm like, man, I want to rap. I like how one person is controlling thousands of people. They can say, put your hands up and a thousand hands up.  And everybody be quiet. Everybody get your phones out. I was like, damn. But I didn't know how to rock. So I put it into a DJ's perspective. I started DJing, like, after the football games, I would DJ the basketball games at school. And I started doing house parties on the East Side. Did you buy your own equipment? No, my dad had his own band. When they wasn't doing nothing, if I wasn't running this time, I was just taking their speakers. I was doing the basketball game for, like, 50 Lottles a game.  He got three life plus 25. He's gonna be my little host. So we used to go to different little, little bowling at little clubs. We would charge him, like, 50, 75 Lottles. He the host on the DJ. I don't know how to talk on the mic. He talk on the mic, our host.  But the house party started to get to the point where they started getting shined up back in like 95.  So I moved to Clayton County out there with my mom in 96. And then when I met the neighborhoods of Ellenwood and John Lake, met everybody from like Rex Roll, Mount Sin, like people like Granddaddy Southside, Tricky Dollar was one of the first. How old were you at this time? Shit, I'm about 18, about 16, 17. I was a 20 break. I'm 12 to 18. Yeah, I'm about 17 right now. And was your cousin with you even at that time? In and out of prison, well, in and out of jail. He been in and out of jail since seventh grade. He talked about school in seventh grade. It's your first cousin? Yeah, they're my first. They're my dad's brother. So me and my daddy took him in like, I even moved in the house with them to help him stay out of trouble. You know what I mean? I'll try it. Be that positive influence in his life. Yeah, yeah. And I think when I left, when I left and went to Clayton County, I left him out there by itself in jail where Haywire. Yeah, yeah, yeah. Because you say that he was- He never killed nobody. He got three life plus 25 for kicking in those. That don't make sense, man. He never shot nobody and never got killed. But he beat up people. He never beat nobody. No, he's just kicking in doors. That's it.  That's an evasion. It's not- Well, they charge you for everybody in the house, too. Yeah, yeah. But it's not a big deal. But he was, I guess they gave, what they say, the three strikes, a habitual offense or whatever. But they gave him through like, he never killed nobody, never shot nobody.  That don't make sense. Because sometimes if you have a really good lawyer, I hear you can hear him. He didn't have no lawyer back then. That's why. That's it, right there. Now he say he got like 900,000 in the account that he's sitting in prison. He been in prison since he about 30 now. He probably been in there, basically. He was 17, man. But he- Can he still appeal it now? Or is it not? No, it's too late now. Yeah, yeah. So, okay, you said that he was your voice and because you didn't like to talk. Yeah, he was on the mic and we just spent a month. But since he's gone, you had to speak. Yeah, so that's where it came out. I used to, like I say, I used to watch, I DJ T.I. When T.I. first came out, remember when he came out with, I'm serious. Yeah, yeah, yeah. I DJ, my dad ran the sound. That's how I got that show. So, you know what I was saying? If you know somebody, you can get in the game. My dad was a sound man down in Athens, Georgia. This club called the Gator mouth or something like that. Down with George Bulldog. Yeah, yeah, yeah, yeah. Yeah. What's the white boy? The fact, the fact white boy used to be out. I don't forget, man.  Oh, yeah, yeah. I know the fact of the white boy you're talking about. The fact of the white boy. The country white boy. He was with, who was he with? Bubba Sparke. Bubba Sparke. That's him. Bubba Sparke. He just came out. Yeah, I was a young nigga man at T.I. Conrad Parke. Well, that's who Bubba was. He was there with his release party, but it was T.I. singing release party. And I just happened to, since my dad ran the sound, I was the DJ for it. Okay. You know what I mean? Definitely not my hand Clayton County. Now I'm not getting big show, but my first, that one of my biggest shows. Like, I'm like, man, I'm out here with. They feeling you? Yeah. So then all the way down to, well, I started doing high school, high school parties and house parties in Clayton County. Wow. They started getting too big. Like the houses wasn't big enough. Yeah. So kids of rock was getting skating rings, man. He started getting skating rings and he would get like, yin-yang twins with his folks. Smurfs for all them with his personal folks. Sammy Sam and I was the DJ for that. Wow. But mind you, it was my daddy's sound system. I was the DJ. It was my flyers. I would wake up, get somebody to make the flyers, go to the rent office where my mama live at Clayton County, run all the flyers off in the rent office. We would go to the schools, pass all the flyers out in all the schools. I ain't be like 17, 18. I'm out here riding around, patting flyers out and everything. Wow.  So I sat back with my partner one day. I was like, bro, I'm getting $150 and I'm doing all the work. It's my daddy's speakers. I'm the DJ. I'm pressing up the flyers. I'm paying for, now he paid for the flyer. He paid for the paper from Walmart. But we ran them off and then we go to the schools and we put these flyers out and all the money went to go. And all the money go to them and they break us out. Wow. I said, I ain't going back. I ain't doing it no more. You done? I said, I didn't. Did you tell him or you ain't tell him? I ain't tell him. You done with it? I'm done. I said, bro, let go find our own. So we went riding around one day and we found this one in Skate Ring. And the Skate Ring say, we went to Old National. They say, well, we don't do parties over here, but we know somebody who will. Send us over to Far Park. We were like cool. We went over to Far Park, got Far Park Skate Ring and the man was like, You tell my son for the kids. Wow. I would love to do that. So he gave us an opportunity, man. And the first show I ever did was Thug Nation. Okay. Saying that Thug life. Thug life. Yeah. But I didn't know how to book shows. So when I did the Thug life, I just put them on the flyer. Yeah. Put them on the flyer. They called me like, bro, you put us on this flyer. We're going to get paid. I'm like, we're going to get paid by who? He was like, you're going to pay us. Y'all put us on that flyer. We're going to get paid. And I'm like, bro, I ain't know nothing about that. I didn't thought you put us on the flyer and get paid. Yeah. So he said, I'll tell you what, man.  Just make sure we get paid. The show went so big. I ended up giving them that money and paying them that night for a second show. Wow. That was my first two shows that I ever did. My third show with Patrick Troy, it was Christmas. It was Christmas. I'll never forget. It was Christmas, man. It was December the 20th. Some crew Mazeve. It was iced up. Patrick Troy was huge. Tom might not be. Yeah, I know. No more playing G8. The only song he had the vice of, not vice versa, Deronda Hill. Yeah, yeah, yeah. He called it crazy, man. So I wanted to book Patrick Troy. I'm a young nigga, man. I don't know how I'm going to do this. I just went through it with the nation. How about to ask you that. So I just took a chance. I just took a chance and caught the number, man. And somebody was talking to me real fast. I had a feeling it was Troy, but I ain't know. But to this day, I know it was him. I know how to talk. You know what I mean? So we set it up, man. He charged me $2,500 back then. And I was scared of it. And I was like, man, what if I'm gonna make it? That's it. I'm looking for it. It was iced up. The streets was iced. The schools closed because the streets was iced. Man, Patrick Troy came through and everything performed like a whole album, everything for them high school. Man, that might have set me off for life. Hang on. He did that dog. Like the whole Clayton County looked at me as like, that's our DJ. I'm doing all the house parties. I'm with Ella Wood and Jutley. I'm with Mount Sin. I'm with Rex Roll and all of them coming to everything I do. So as that, now people starting to rap. God, coming out to East Side. No Gucci. Got the black team. That's what I'm about to ask you. Like how did, how did, I know you saying people starting to rap, but there was a relationship between you and Gucci and Walker and them like- Right. Well, how did it mean Gucci? I can't know Walker. Okay, so when you and, how did you end up linking up with Gucci? I've been doing Gucci since like third, fourth grade. Oh, so y'all, it's- Yeah, Gucci from the East Side. Even like Trigga Doll. I know him. I know Trigga from the East Side. I know Gucci since third, fourth grade. Gucci know the fur girl I've had. And you know, I'm somebody younger than him. So was it like the first- To my virginity. There you go. There you go.  I seen Gucci after some years, after I'm out here in Clayton County. They had a club called Club 112. Okay. I read that.  Club called Club 112, man. Gucci, at the time, Gucci had black teeth. Yeah, yeah. My daddy was the sound man once again. Your daddy only. You gotta be plugging in all the time. My dad was running the sound for the DJ. He would, mind you, the club got their own sound system. So they don't need my dad, but my dad is just so respected out here from sound system. Every club. Is he still doing it now? Yes, still doing it now. Church pay him 1500 a Sunday for running the sound. How old is your daddy? My dad, like 65. He's young. He's still young. He rocking. Yeah, man. I gotta call him. His birthday is July 11, mine is July 12. Oh, y'all, y'all something else, man. Y'all Kansas. Yeah, yeah. Y'all something else, man. So we in 112, man, and Gucci come up to me. Gucci said, Corey Cran. Yo, your whole name though. I said, what? Boy, what's up with that? You doing this? He said, what? What you doing here? I said, you know what I'm DJing, that my dad has a system. What you doing here? He said, nigga, I rock. Black team, my song.   So I'm not talking. I'm like, Gucci been rapping though. He had different songs. Yeah. Like, Gucci got song before the end with saying himself that we did, but I didn't know he was rapping, rapping. Yeah. Everybody can rap. Yeah, yeah. Okay. But rapping for real. I can't rap. I'm just saying. It's a known thing when a person, everybody wanna be a rapper too. Yeah, everybody. But you don't know. But black team was actually buzzing. No, it was. Black team was buzzing. Look, man, I'm gonna prove you. He didn't have a release at this time. No. They were the original black team. Yeah. But they'll never get in niggas over there. I don't got them Gresham Roll.  So he was like, yeah, man. He was like, man, let's do some shows. Boy, I can't wait to do some shows. But that's what, I'm just popping myself off. So big. So it was a blessing to me because everything keep falling in place.  They definitely had the white team. Throwback boy had the up and my throwbacks. Yeah, yeah. They CEO is my partner. He paid me 10,000. Shout out to what I can't tell you, man. He paid me 10,000 to promote the throwback boy. Wow. You know what I'm saying? Like, hey, I need you to promote this song.  So I promoted that. I had the white team from franchise boy could probably end up my partners. Yeah, probably. And then Gucci, I went to school with them.  Man, this whole deal was jumping off back then too. The guy called Chevy Ali came up with a yep in my something I forgot. So I had him at it on. So now I got this whole campaign going. I'm taking there. Well, we take it over national. I hooked up with right here in the dream. He got shows over there doing shot a low first. Yeah, yeah. I'm about to bring him into it because you can't get that laughing taff and all that stuff was going on during the time you're talking about. Shout out to low. And Jack came out, man. I'm taking these shows everywhere. So I was DJing a little spot on Terry Boulevard in Clayton County. It was called J-Pause. And this at the time with the red, the shine was. Man, you messed me up with that one earlier when you said that off line. Now he had another name. Man, he had five different names. Five different names. It takes whatever you're taking it off. Man, we don't want to do so much, but everybody wanted to rap. Okay. So I ended up finding this spot. My daddy was running sound over on 20 grand. I was DJing in the club called J-Pause doing hardest there, but I wanted a bigger spot. Yeah. I'm taking this white teeth thing, black teeth thing to different spots. And I wanted to make some money. So my daddy got 20 grand on Old National. It was a two side club. It was a concert hall side and it was a club side. And I came up with a plan to do Gucci, Pastor Troy, Kaia all on one show. They ain't nobody ever seen Kaia was huge, too. Yeah, I remember her, too. Kaia was huge. Yeah, yeah. Pastor Troy was huge. Gucci was huge. And nobody ever seen that before having on one show. You didn't see all this stuff even coming together like this before that when he had brought Pastor Troy for that first time. You know, I like doing stuff that nobody's ever seen.   My dad's the sound man. It's on. So all the security is my own security from the club I was DJing in that over on Terra Boulevard. So I didn't brought my whole campaign. I did the promotion myself. And I had one investor shot in my boy, Ricky D. He gave me the money for that. We did that like small. We did that like $5,000 total, maybe seven, maybe like 20. So I wanted to test the waters. Now I just did a big spot. I did the high school for the skating rings. I done did all that. I did the 20 grand with the black team, Gucci, with the, with the Pastor Troy Kaia. I wanted to test the waters out. Gucci come to me one day and Gucci say, bro, you but don't know about my new music. I said, what? What new music? He make it so much. He fast with it, man. He can go. He go so fast. He hard work. That nigga work hard, bro. Now you know, he had already been working this in the midst of I'm still promoting black tea. And white tea. And white tea and I'm promoting to jump in my throwback with throwback bars for Kentay. He already got this emotion. He come to me one day and say, bro, you don't know nothing about my new music, do you? Wow. I said, by what new music? He said, my song with Jesus. I don't know who it is. I said, with Jesus. He said, bro, don't worry about it. He said, come to my show Tuesday night.  Yeah, yeah. Come to my show. I think it was that it was across from vision to maybe in the velvet room downtown. Yeah. I go to this show man, everybody in all white. Everybody. Trina there. She in all white. Jesus there. He in all white. BML there. They in all white. All white. Gucci, we pull up. Gucci in all white. Gucci a whole clique in all white. We all in all white. And I'm tripping. I'm like, damn. Okay. Now there's another party. Gucci said, why there? So they don't know that now we party. We chilling, popping bottles. That song. So I said, come on. The whole club went absolutely crazy. Everybody. BML throwing ball to everybody. I mean throwing money. They popping bottles. Wow. You got Gucci rapping. Everybody. Jesus. They having a good time together. It's the first time you ever see Jesus and Gucci on stage together. Wow. First time. This will be the first and only time you see Gucci and Jesus on stage together. And you was there. And I was there. So I got in my mind. I went back to my, my investor. I said, bro, I got, I think I got Jesus and Gucci together. I got a hot song that I know we can make a killing off of. All I did. God, Jesus spoke to have a hot name. If we can get him, I got Gucci. We can do that on one show. And we'll be, we'll make a killing. He said, Jesus. He said, I messed with those guys. It's kind of fine. Him and Coach K. Potters. Wow. Yeah. Coach K. was managing back then. Riga D. Him and Coach K. Potters. I'm Gucci's DJ and road manager. Big Cat and Jacob, they doing the managing. I'm doing the road. I do all the bookings. Gucci told Big Cat and him if Ace don't sign my contract for doing my paid show, I ain't doing the show. Wow. They did the radio bookings. I did the paid bookings. I did all the features and all that. So cool. I said bet. So I went ahead and set it up with Gucci. And I said, Rick, if you can get Jesus on this show. I went through Gucci first and let Gucci do it. But I didn't know Rick was like this with Coach. It just made everything fall in place. So I got the only show in history until they do this big stage together. Yeah, yeah. With Gucci and Gigi on stage together. They got it on video and everything. I threw it in the 20 grand concert hall we had about. Wow. Bro, it had to be about 10,000 people in there. Wow. It was wall to wall. And then in the end, there was already back and forth. It wasn't no beef at that time. Yeah. But all G's in them car got broken too. When they got there, you know, they in the hood. Okay.  Wow. Group city. So they on, yeah. Man, they went and went through photo with through all the cars or something, photo went through.  So I guess they thought we had something to do with it. Mind you, I'm driving Gucci's van. I'm driving the van and everything. Oh, you giving up detail cause I never heard this story. I'm going to nobody to know. Jesus and I'm surrounded to be man, Jesus, all the security and everything. My daddy in the club with a third-eighth special. That third-eighth. Revolver. Yeah. Old school. That's old school. They surround me and I don't know what they surround me for.  And I'm like, what? And nobody else's cars, but just theirs. They parked in the back. Yeah. I mean, they're running the show. And this before any other, any, all other stuff happened just before everything ever. Just think this was like the beginning of the this was like the kickoff. Okay. Because Jesus and them felt like Jesus and their Gucci and them set them up. Wow. When that wasn't the case. Yeah. You knew me or Gucci, nobody knew nothing about that. Yeah. You know what I mean? It just fell that way. It just fell where the people who the people who work the parking lot, they work for the club. They parked them in the back. Wow.  Parking out here. It was a big, you know, the Walmart and all that was the club. So they basically, that was the club was they where we don't know, you know, but those guys to park them in the back like they could have been the one. That's what I'm saying. But it left me vulnerable because in the end over everything, everything was me. Right. Yeah. I'm driving the Gucci van. They know I'm Gucci DJ. You know what I'm saying? He calls back on you regardless. No matter what. Yeah. So, you know, in the end. So when they surrounded you, how did you get out of there? Man, I sat back and I think when my dad came over there, I think that kind of did kind of sell. Cool. But I had my security too. Mm-hmm. My security work for me came in and they was like trying to see what was going on. And they never touched me or nothing. Jesus in them said they were just a big circle. And I'm in the middle like this microphone. I'm standing there watching all this security around me and everything. And I mean, I know they got something on them because niggas holding their passes. Yeah. But in the end, you know, everything got squashed. But like I said, I think that was the beginning of a long journey right there. Yeah, yeah. You know what I mean? Yeah. Man, we used to go on a roll with AI-15s in the bags. Yeah. We're going to shows and we're taking six, it's me, Gucci, and two security guards. We got six guns. Wow. You know, when you got a license, you can take up the three guns on the plane. Yes, sir. Yes, sir. Yes, sir. All right. So it's... Where you got, hold on. When you have a license, you can do what? You can take up the three guns. Three or four guns on the plane. Oh, I didn't know that. With a gun license. OK, I got that. Man, we all strapped. She said, I got it. I got it. That's all I need to know. It had to be, though, because this was a hard time. Yeah, it was serious, dude. We're talking this serious, bro. Yeah, man. It was to the point where we had Gucci doing shows and Bulletproof vices. Wow. Let me bring you up to like today's sound. How do you feel about where the music is today in Atlanta, like versus back then? Because you've seen it all. Oh, I'm talking about all since my daddy and them were doing live band stuff. I mean, I feel good about it, man. You do.  OK. I never forget Bigger Rankin' to tell you. Shout out to Bigger Rankin'. When OJ the Juice first came out, I drove. We didn't have no internet. Wow. We didn't have no e-mailing. So I had to drive that arm kit in my hand. Yeah, yeah, yeah, yeah, yeah. I drove it. I drove the CD down to Bigger Rankin's in the snow, in the snow, October, Halloween, man. Bigger Rankin' to tell you, 10 people all the time. Wow. And I drove it down. Now I went down there. Hey, Bigger, man, I got this new artist, OJ the Juice.   He wasn't even, man. He love him a damn now.   It's OJ the Juice. He was Gucci. He don't even know. He was Gucci. He was like, man, I got you just hold on. So I held on for a while. You know, Bigger did me like anybody else. He helped me. He made me wait by the hour. I'm feeling like, I didn't drove six hours, dropped it, man. You feel what I'm saying? But he not respecting it, you know, getting in, could that what we would have did up here? Yeah. He ain't going to get what you want with you on the win, our mix right now. Oh, really? Yeah, yeah. He end up playing later on, man. I'd be damned if a couple months later, we up in the lounge. I'm over there, up house. Somebody come knock on the door. I don't know. He's going to open it up for me. I'm going to open the door. Hit Bigger Rankin'. Bigger, what's up? Bigger, what's up? You got me all over. Get what you were coming up to. I ought to talk about. Oh, J.D.J. Oh, J.D.J. I was very sad. So like I say, man, back then, man, it wasn't on internet. Now you ain't got to drive six hours. Yeah. You drive six hours to go network. Wow. Now you can just press a button. Exactly. Now you can go do your video and you can upload it on YouTube, man. You can go do a video right now in the parking lot and you can upload it on YouTube. You know what I'm saying? Yeah. What? Go ahead. I'm about to ask. I got to get a question out.  Right. All of them at the top of their game have all their business together. Who makes the most money? Kind of who makes the best deal. No, no, no. I'm just saying. If all of them at the top of their game, all the top of their game, all of them have their business, their lawyers, their contract, everything set. What category can make the most money? If the artist don't get messed over, the artist and the CEO should make the most money. But it ended up happening. Game crazy, ain't it? Yeah, but the game is so crazy that your management has set it up to where they're making a bigger percentage than what they're supposed to be making. And that's why you get artists to sit back and they change their management and all that years down the line. I've never signed a contract with nobody I've been with. Wow. Nobody. Nowakha, OJ, the juice. No, the only contracts I've signed and when people finna pay me five and 10,000 for promo, them the contracts I signed. But as far as the artists, I've never signed a contract.   Because I could be getting way more money and all that. And I just feel like, you know, when it's time for me and the real artist to sit down and sign a contract, we get to that then cool. But in the end, it's like the artist is the CEO. If the artist stop rapping, the whole project is over with. That's why I love the role with Gucci because he kept getting locked up.  It's coming to you anyway. Yeah, I see, you know, I always say that, man. I always say that I don't look for nothing like a shop. I didn't ask a shop for not $1. But pay me $2,500 for that first mixtape. I ain't asking for a dollar. I just say let do it. Then you can't, hey, boy, I got a show to do. I need you to play three songs. Then you turn around and gave me a stack. I'm like, man, I ain't asking for this. You know what I'm saying? You just keep coming to me. But, you know, the artist, the artist and the CEO is supposed to be the top of that dollar, man. But you got these managers out here. You got these cricket accountants, you know, doing their thing to where they're making more money than the artist making or just as much money as the artist making. Push show, man. So give me top three artists of all time. We do the same. Dead or Alive. Dead or Alive, top three. Any genre. Michael Jackson. Michael Jackson. We can do the future. Future. And Gucci. And Gucci. Quick. That's what I'm saying. I think you people already know. You are the quickest on the job. They never do that, man. Everybody be kidding. Man, that is the future. You and everybody. It ain't that. It'd be, uh, yeah, you did that. Hey, man. So what do you think? So when it comes to why Mike, why number one? Man, Mike did everything, man. Mike did the dancing. Mike did the singing. Mike did the concerts. Mike did the sold out concerts. Mike set the stages for Jay-Z. When they say, oh, Jay-Z, the legend and all that, man. Mike set that off, man. Wow. All this dancing, everything. They dancing. They doing the dancing that Mike did. Wow. The Mike and such, somebody and they faint. Huh? Yes. Mike put his hand out the window. For real, man. You don't have, has anybody in rap ever had that impact? No, not yet. No, but future, if I ain't gonna lie, if it wasn't on Mike, future would be, man. He'd be the one. He'd be the one. Future, future going crazy. Now, Lil Baby, Lil Baby making the money. Lil Baby, I hear about all the time. That's the reason we have number ones a lot. Oh. Yeah, Lil Baby number one, because he hot right now. That's it. I'm out all around. See, people ain't giving them respect to who already been out. You know what I'm saying? With Gucci, Gucci really came from them trenches. Yeah. Gucci really came from selling dope and going robbing niggas. I'm talking about niggas. But Gucci done robbed somebody and sitting in Blaineville. And reinvented himself and said, so. And rapping about it. And ain't scared to go on the street and say, hey, how you doing? Yeah, I robbed you like, man. I'm trying to tell you. So we're winding down now. So where can people get a hold of you? How can people find? 447236449 or the real DJ Ace, man. I don't care how much money I make, man. I don't care everything in the real way to go the way. I got an assistant and all that, man. But I'm straight about to come talk to me personally. I like that. You can talk to me about being an assistant and a publicist. They really can't get to the bottom of it.  If I need to sing it, I'll sing it up. But far as me, you go straight with me, man. My Instagram, the real, the common country. So they say, I'm saying the real. Yeah. But it's T-H-E-R-E-A-L-D-J-A-C-E, man. All right, man. Thank you so much, man. We love you, brother. And, hey, man, this been another great segment of Boss Talk 101. Boss is on it.


Stare. Yep. Not a cult BTW.  Any gifters wide hard do. Any gifters wide hard do. Stare.


Hello everybody, I am Seha Krishnam from LAFSTD. Our project is Learning Aid for Education is first key influence. We are working on this project, Learning Aid for Education. It's basically in consonance with the basic permission of NSID, which is working to get the gap between the facilities that are available to the students of government schools and not up to date. They lag behind in laboratory facilities and in fact in quality teaching. And by this methodologies, we are just trying to give them an opportunity so that they can avail those situations and can come up with a better so that they can have better learning environment. Here we can see the students from the government schools don't have adequate access to resources like quality teaching as I mentioned. So we are providing them with simulations and applets, very interactive applets so that they can practice and have their illustrations properly. Now I am going to introduce my group members. She is Dhaval, she is Piyush, she is Navi, she is Shritya and Vaisal, this is Seha. The objective is Mathematics, you can guess Physics and then Chemistry. Mathematics. The project objective is to develop Java applets. I am working on developing Java applets. We are having applets working on concepts like how to teach, countings, basically we have started from class 1 and we are going to come to class 10. It's our basic motto right now. So the first is to develop Java applets. We have worked on counting, addition and subtraction. Simulating simple concepts using graphics and animations available in various Indian languages. We have made them available in at least 8 languages including English, Hindi, Bengali, Marathi, Telugu, Malayalam etc. Now various practice exercises to test their understandings. While the person is working on an applet, using an applet for illustration and editing the corresponding exercise is attached to those applets so that the student can have access to those exercises and can test his understanding skills. Now I will be showing you some demonstrations. This is an applet for addition of numbers ranging from 10 to 99 so that is something like 99. We have different categories of additions like 0 to 9 and 11 to 99. This is how we have designed this applet. It has to be very interactive in order to just maintain the interest of students while they are learning. We have used various images, various nice images like apples, mangoes, even pencils and whatever the kids like. We have used images of those. This is from Marathi. We are defining this category by this alphabet. Sir, this is addition of numbers less than 9. We just kept the thing in mind that the images have to be very interactive, very... Very understandable. Now I will be showing it in Marathi. What keyboard have you used to enter the numbers in the respective languages? Sir, I have passed the unique or parametric to S. Oh, unique or parametric, yes. Sir, depending upon the language setting it will display... Yes sir, we planned to upload it on Aksaksha portal. But somehow some circumstances are... Sir, we couldn't... I am showing it... Ideally on the Aksaksha portal, the student will select his language. So, all the tools that are available will come in that language. So, it will be the same thing. It will go to the database and find out what is the symbol for one. Well, we use minimum text in this. So, it is the same for... It will go to the database and find out what is the... The whole base is not different from anything else. No. We have introduced two controls here. Refresh means the whole after you will be running again. And I have exercised this exercise and click the phone. It will give you a corresponding exercise to this. Exercises like this. This is a subtraction exercise. Now, there are... There are seven mangoes here. Minus two. This should be five at all. Then the student takes some five. Then it appears like this. So, minimum text has been added. So, we use the image for tick marks and nurse. If the answer is wrong, this appears like this. So, the same thing. Appearance in maths and Marathi and Indian. So, there is another exercise. This is in Hindi. We have planned to change this into Hindi, the text part. This is four and five. The student has to count the concept of tens and ones. Counting from ten to ninety-nine. So, the bundle has ten states and these are individual states. This one is two tens and seven ones. The total number of states is twenty-seven. The student has to enter it like this. Two and seven. So, because we just wanted to make it very friendly for the user. So, there is an exercise on counting again. The student has to match the two columns. Count and match. So, he chooses the first column and then it comes. After modifying this, but this is the basic thing. We call for teaching tens and ones. So, we are having images, randomly generated images for these. Instead of for bananas, there can be bundle of states. Petals, jars, all that kind of thing. If it has been refreshed, a new image can happen. So, now pass this to Shruti for selects. I will be talking about the physics module and the project. The objective of this module was to develop Java applets using EJS. EJS is easy Java simulations. It is a tool used for creating scientific simulations. We will come to that later. But right now we will focus on CDSE textbooks of classes seven to 10 standard. Phenomena like reflection of light, refraction of light, and electricity, magnetism, such activities have been described within simulations. Now, I would like to tell you something about EJS. EJS is easy Java simulations. It is a free tool which is used for creating scientific simulations in Java. It is for teaching purposes and it is part of the open source physics project. Now the EJS window has got three panels. First I will be telling you about the view panel. This is where you actually design the view of your simulation. And then how your simulation will look. So, you can have various objects like whatever you want. Lines, rectangles, images, everything is available. 2D, 3D objects, all that is available. You just have to drag and drop them onto the page over there. And your tool will be created. It will be shown in the preview also. Then you have the model panel. Here is where you model the simulation. I mean you have to decide what variables you have to use. And you will get a table like this. And also this is where the coding is done in the model panel. Then you have the description panel. This is where you can add text which will appear when your applet is run. But we have not done that because we want to minimize the use of text in any particular language. So, now I will be showing some simulations which we have developed. Where the angle of incidence can be improved. So, and when you click on play the simulation will be played. The slider above will match as an alternative for the angle of incidence. The corresponding angle will be shown in the field there. When you play again. Also similar to reflection. But something which can be done here is you can input the refractive index. What? Now change the 1.0 to 0.6. This is a simulation which demonstrates the ohms law. Here you can input the voltage in that field. And like the ohms law says that voltage and current are directly proportional. So, when you input voltage here correspondingly the bulb will light up. And when you increase the amount of voltage the current will also increase. And the intensity of the bulb will change accordingly. You can also change the voltage from the slider. From the experiments we have also done some activities that are given by textbooks. So, the students can understand better. This is one of the simulations there is Newton's third law. It states that every action has input and opposite action. So, this is the activity which shows from that the chemical effect of current. It shows the slow movement of as mentioned earlier by Shreya. In rural areas the students cannot do experiments as they want. So, we have tried to make a virtual lab. So, just create a base where the students can do their experiments. Let us see how it works. So, we have shown a demonstration mode. As the experiments will be performed as per the general. Can you go ahead? And it has options like drag and drop. So, the students can do their experiments on their own. Move the instruments, the patterns accordingly. Divide the play, pause mode. So, the students can see what has happened again and again. So, if they have any doubts, they can be cleared. And according to it, the students can do their assessment. So, we will show you the demonstration of how it works. As we can see the activation of the building job. We have five major packages. The executive package or the executive program. These will be what we see here. These are all the objects designed by these two guys. And I was the one who worked on the executive program. Which could actually elevate all these objects and have. And get a sense of real experimentation. This is the experiment shown here. It is in the demonstration mode. So, what we have to do is just express a whole solution. And I can go through this order. We have to make a, the variety of the solution is 0.1 both. And experiment says that we have to make it 2.0. So, actually there is supposed to be a white board. This is not all. What I have to say is that they should be an experiment. Plus an explanation. So, that did not come with this. That can come as HTML. So, that I can do it in all languages. So, that was one thing. So, the experiment from is prepare a solution of 0.01 molarity. Yes. Could come actually there as a demonstration. So, with next explanation for each. And that can be done because he has a journal. Journal in and journal out. So, what we are showing a demonstration mode. The input is actions. And the actions have take this equipment. Put it on table. Take this equipment 4. I will show the XML. This is the XML input. Experiment actually happens. First take the empty vehicle. 4 ML of explosive core unit. Take a model in 4. 4 ML of explosive core unit. Keep the model aside. Take some water. At 36. So, that 36 plus 4 plus 40 and the polarities. This is the demonstration mode. The feature here is the CPAP. So, that the student can go back to previous stage. What was the scenario at that time. Actually, we need to have a property span here. So, that the student can click over here. And the corresponding properties including polarity. They have just done the framework. Similarly, 5 days from this. Same thing happens. Actually, we had a tough time depending this sigma. Since it utilizes each and every object in the file. And upon assuming the object that is read from the file. And the experimentation goes on. It's actually serialization of the objects. We are saving every coordinate that is happening. Every feature. I think it's moving from here to here. So, we are saving that part as a temporary one. In that part, when the C bar gets reduced. The number gets reduced. And at the same time, the same serial number file gets accessed. And it gets there. This was the demonstration mode. This is the activity mode. So, we can form activity. Like, I told you earlier. Challenge here. Actually, in practical, I suppose, a challenge is never going to get solved. But for sake of, I want to go over a amount of 20. And then from a challenge, it gets solved. If I want to read a solution. These are here. Read the language of the readings. Or you say, readings. We get read. Chemistry mode. Chemistry mode. Chemistry mode. And the things that are happening here. Sample Maximus is an experiment. The experiment which I first showed. This one. It is actually taking from this. Each and every step is mentioned in the Activity Tag. Action type move. Move the corresponding apparatus. That is the ID. Here, that is required. The ID, we did it. It identifies a particular object uniquely. Move ID. To do this. It actually moves the object to the corresponding location. Similarly, 4. 4 is for pouring the content from one given manner. And similarly, we have a heat. Heat of the content. I want to say amount. Yeah, amount is understood in the context of a normal moment. I'm going to end this. Chemical equations, chemical theories. I'm going to end this. This is the Sample Maximus. This is one. Experimentation mode. After this, glassware. Non-glasswares are there. So non-glassware, particular burners are there. In glassware, then sub-tag is there. We have glasswares. We can have ground-bottom glass for the unit of the bit. So we have type and sub-tag as well. Responding attributes are mentioned.