What's good Josh boros back again with another video? So we got to talk about some concerning issues today involving the rock Versus Roman at WrestleMania 40 is looking like that may be the main event Which we kind of got some indication of it last night on SmackDown but at the same time I was hoping and holding out hope that maybe Cody would be you know Challenging Roman for the title at the elimination chambers since he say it's not gonna happen at this This year's WrestleMania, but there are reports and rumors that are coming out that's saying that's possibly not gonna happen And it doesn't sound good Does not sound good in a sense of how they are booking this entire main event. It sounds very concerning just from the reports that are coming out today and It seems as if The online wrestling community aren't they're not liking what happened with the rock being involved I'm gonna show y'all some some Interesting stats on I think WWE's official YouTube page even though they've kind of taken away dislikes There's a way you can still check out the dislikes to like ratio and it's not Looking good for the that particular segment involving the rock and Roman Reigns So let me go and check out one of these articles with you guys And then we're gonna kind of check out also some tweets that have been sent to me Involving this issue, but not gonna lie to you. It's it's looking it's looking pretty Pretty bleak for Cody's story potentially facing Roman anytime Within the next for WrestleMania season for sure real reason for the rock versus Roman Reigns at WrestleMania 40 reveal The real reason why WWE change plans to the rock versus Roman Reigns for WrestleMania 40 main event has been revealed With Cody Rose winning the 2024 Rumble a Royal Rumble It appeared that the American nightmare would be getting another opportunity to finish the story in April Which a lot of people thought rose Interestingly interestingly announced that he won't be challenging Roman Reigns for the WWE undisputed Universal Championship During the February 2nd edition of SmackDown The following announcement the rock made a surprise return to confront the tribal chief Suggesting that the great one will be facing off against the rock Roman Reigns at WrestleMania 40 per Mike Johnson PW Insider numerous WWE sources have confirmed that the rock versus Roman Reigns is expected to be officially Announced during Thursday's February 8th WrestleMania kickoff event in Las Vegas The report noted that WWE decided to go with the rock versus Roman Reigns for WrestleMania 40 believing that the match would be a greater Attraction for the main for the mainstream and would help create positive momentum for the company Endeavor CEO aria Manuel WWE president Nick Khan and other reported for reportedly back this idea PW Insider was also told this change was not made to politic Cody out of the main event and Wasn't made out of malice the change was made because the belief that the rock would make the most money and To respect the rocks new position in WWE's parent company TKO group It was officially announced that the rock had joined TKO board of directors on January 23rd rock Cody Rhodes new WWE plans for WrestleMania 40 were also revealed Which you can read more about right here. So and We're gonna talk about his new plans, which makes no sense So basically what we've gotten from this article is the fact that They wanted to do this match to kind of put push the company in the right direction obviously with Vince McMahon some of the stuff that's happened with Vince McMahon and negative Look that is brought over WWE with the whole Case allegations and and the stuff that he was potentially doing to that young woman in the in the lawsuit And it just it didn't look too good and then Brock being involved in it John Laurinitis If it wasn't a good look Optically for WWE, but I do feel like they made the prop of the appropriate Decisions to remove Vince get them out of here the same thing with Brock So it looks like they're taking steps in the right direction And I think people the general consensus of people like, okay, we can work with this. Let's get into WrestleMania mode Here's the thing I'm all for the rock and Roman happening. That's why I was excited last night even if We go with what I was thinking of last night. All right, I guess the rock Really wants to do this match cool Cody didn't say he you know didn't want it You know still take the title for a moment. If there's some type of master plan between Cody and the rock. I'm all for it. Hell Let's have a match of elimination chamber. I know some people saying he needs to finish the story at at This year's WrestleMania, but I'm fine with it. I get it. It is what it is Take what you can give let's finish it our elimination chamber. Whatever. I'm sure the rocks gonna involve cool Well, if that's not the case and it doesn't seem like that is then Cody would per storyline wise He would have to be one of the dumbest individuals to win a royal rumble back-to-back years because you essentially said, you know what? Here you go rock You softened them up for me and then I'll finish them off at some point and Then you kind of book yourself into a corner Potentially with the rock and Roman because I just don't see the rock beating Roman For the title if it wasn't for the title. Yes But I just don't see the rock of all people beating Roman unless they're gonna pull one of the biggest swerves in WWE history and actually have the rock beat the Roman army beat Roman That's the only thing that would make sense because once again, you put you booked yourself into a corner now You booked yourself into a corner where now The rock Doesn't look like he's gonna win this no matter what he says. It just doesn't I just don't see Rock being the one to dethrone Roman because then it would be like damn well It just doesn't make sense because then at that point doesn't matter doesn't matter about Cody's story and finally overcoming Roman Reigns, you know I'm saying like it would now be Cody trying to overcome the rock I just it doesn't make sense. And if you have the rock lose, what was the point? If the rock loses to the wrong to Roman for the title How are we gonna believe anybody else is supposed to be him? At that point, I wouldn't even believe Cody's supposed to beat him Unless they do something else, which I'm really not hoping that they do but the reports of rumors are looking like They may be going another route with Cody, which may ultimately Make things worse, bro All right, let me show y'all some of these images that I was sent bro. This just just Shout out to the homie Cornelius on Instagram He's the one that's been keeping me up to date with a lot of the stuff that's been going on on social media and Like just the insider news and stuff like that So this is from rest office the current plan is for Cody Rose to face Seth Rollins at WrestleMania 40. No No That that that's and I hope that's not the case. We don't know but that makes absolute no sense, bro That makes no sense Because you literally spent time Bearing the World Heavyweight Championship Before Cody and Roman even came out there on SmackDown You made it abundantly clear that the title that Roman is holding is the it's the premier title and fans know that We love Seth Rollins, but we know that title is a secondary title. We know that to be true technically it was three titles at one point and then they merged the WWE and Universal Championship It's the secondary title Roman didn't even have to say anything you said in that promo on SmackDown. We know it's the secondary title. Okay, cool Then you You have Cody come out there and said even though Seth Rollins made a lot of great points That's the title I want to go for that Roman has that's the title that my father held But it was taken away. So you've already proven that Cody wants to go for that title So it makes no sense for him to have seat counsel to only give up his spot potentially and now go back to face Seth Rollins That makes no sense.  So I'm gonna definitely check that out But most like if they're having a face-off then there's a good chance that they're probably gonna announce it then But it we kind of already have an idea they're gonna main event WrestleMania this year. So that it's just I Just I'm just confused man And I don't know so we're gonna check out this another image that was sent to me This is also about wrestle ops as well those that have fightful select spoke to spoke to said that the Rock had not only pushed to work Work the match against Roman Reigns some thought he was even pushing to win the match Now here's the thing we just talked about that the Rock is winning this match Then Cody story doesn't even it doesn't matter no more Doesn't matter What's the point? What is the actual point at there? Like that doesn't matter. I Don't know. That's just It'd be weird because Now he he's the only guy that could stop Roman. Okay. He has the title Is he gonna be on the show every week every other week? He's he's most likely gonna have the same type of schedule that Roman had probably even less because of his other, you know job duties he has to do So that doesn't make sense. We're not even gonna have the the championship on the show So it's a lose-lose doesn't make sense the reason why Cody and Roman worked again It was because we can give the championship to Cody You know, you can involve the Rock and he had built up the feud with rock and Roman at next year's WrestleMania But at least we'll have the championship on the show weekly God So it's a lose-lose you have them win I'm sure there'll be some people that will be shocked everybody would most likely be shocked and you know fans there will probably be shot But in the long run it messes up things Cody technically would have never finished his story We don't know what implication that means and where they go with that and then on the other side of things if you're gonna have Cody face Seth Rollins Seth Rollins is losing the match. He's not winning though That makes no sense. He's not winning that match So Seth Rollins will essentially lose to Cody again and then what? We'll literally end up with one of the most predictable WrestleMania's because I still think the Rock is gonna lose to Roman because he has the title and Seth is gonna lose to To Cody I thought stuff was gonna lose the title at WrestleMania. Anyway, cuz he's injured So we he's definitely gonna lose to Cody if they do that match. So ah This is very It's very confusing brother. None of this makes sense Now we got show I gotta show y'all the stats on for really the backlash from The Rock returning The rock and roam range segment from last night SmackDown now has surpassed 300,000 dislikes in under 15 hours extending its record as the most dislike WWE YouTube video of all time 2.5 million views so far 77,000 likes 310k dislikes Now once again WWE I Don't think they're really too worried about that Only because I mean one I think the tickets are already sold out for WrestleMania So even even if you want to push the narrative they want to make more money Well, I think the show is damn. They're already sold out Anyway, how much more money could you make if anything you're probably trying to make more hype? Because the Rock is coming back to wrestle. That's the only thing I can see them ever saying they're trying to make more hype Trying to probably get more sponsors the Rock is coming back get more eyes on it That's about it, but outside of that the event the venue is already done there showed out for both nights So that can't be it. It has to be other external factors and We all know the internet wrestling community is much different than the ones that actually go to the shows depending on what city I also want to bring this up That it's crazy how things have changed within just a few days Remember there was a lot of people talking about how predictable Cody winning the Royal Rumble was and how some people felt Disappointing they didn't want to see Roman versus Cody again, and you know people were definitely hating on Cody winning. There was a lot of people down again and Now a lot of those people are now In favor of Cody getting some justice and and feel like he's being you know mistreated here is crazy The wrestling community can be some of the most interesting individuals not granted I understand why people would be complaining about this because it just doesn't look good Even no matter how old they try to spin it optically. It does not look good that the Rock comes back and now he's He's essentially Forcing Cody to finish his story with Seth even though that was never his story. I Was under the impression that once again Cody was going to finish the story I guess at elimination chamber, but that may not be the case man. So I don't know this is just This is one of those type of things where I don't know. I don't know what you do here This is this is very weird And I think we're gonna check out one more tweet and once again, nothing has been official yet So I'm not gonna say that this is true But this doesn't look good if it does become official the current plan for Cody rose to face Seth Rollins at WrestleMania 40 Which it's a bad idea while finishing the story was primed to climax at WrestleMania 40 They were they there were already some in WWE openly talking about the idea of Cody winning the World Heavyweight Championship And then challenging the winner of Roman vs. Reigns Roman Roman Reigns vs. The Rock For SummerSlam in a title unification bout so that Cody could finally fit that. Oh my god And that's why I don't want to believe this to be true because that That sounds even worse. We literally would be doing this all over again No, I don't think Seth should be faith facing Cody at WrestleMania No, just for him to drop it to Cody. No, I don't think it makes any sense for Whoever wins out of Roman in the Rock to have a unification match for SummerSlam. No We don't need to be unifying nothing else Because we'll literally be putting ourselves right back in the same situation That's the only thing we will literally be putting ourselves right back in the same situation That we were a few years ago when they unified the titles So I don't know I Just I don't think that that that's not a good idea for So what Cody's gonna have both of them and he's gonna drop one of them Or is he gonna just unify all the time the title the world heavyweight championship The new one doesn't even have any lineage. So what's the point of unifying it? There's no lineage outside of Seth Rollins, and then it would be Cody. That's it. It's the only lineage it has There's no point in doing that. I hope that's not the case. This is just all very concerning. I Still have a little bit of hope but That hope may be running out very quickly It depends on what happens this Thursday with their whole WrestleMania Media press that they got going on this Thursday in Las Vegas. So it depends on that. It also depends on What happens on SmackDown Also depends on what happens on Monday night raw what Seth Rollins is gonna say What he what is he feeling like what are they gonna do to the side? It's really confusing. It got it's very confusing And I know some people are saying what things got into a disarray with CM Punk being injured Or what not and you can say that but it's a simple out if they if If the rumors are there to be true that CM Punk was supposed to win and they pulled an odd call in audible Me and Matt because CM Punk was hurt Those rumors are true Then you still it's easy you it's it's really the easiest way to book this you still have Cody versus Roman Reigns WrestleMania 40 have the Rock in a fear to help out Cody so he doesn't get screwed over again and then then you could build towards Roman and the Rock WrestleMania 40 and Then you can either have whoever wins the elimination chamber whether it's Drew or whoever you can have them Beat Seth Rollins finally at this year's upcoming WrestleMania WrestleMania 40 and then you could even did a cash-in on Drew which would further the story that drew can never Truly finish his story and have a cash-in where you can have Damian Priest cash-in and win and beat Drew McIntyre and become the new champion himself. You could you could do so many things like that probably would have made a lot more sense, but pushing the narrative that oh we're trying to You know further the company from the the negativity that it's recently gotten bro I don't believe that only because people are gonna be excited for WrestleMania regardless You you trying to push that narrative? I think it more so it's it's coming down to money And maybe getting other sponsors and more people to watch only because the Rock is such a big superstar That's really it, but I think Cody may have any against Roman Reigns would have been just fine That's just my personal opinion. I don't know It's good very concerning. Like I said last night. I was very optimistic My maybe they're gonna do something at the elimination chamber. They I cool I know that's not the ideal situation Rock versus Roman at WrestleMania But as long as Cody gets the championship before then I whatever now It's not looking like that's the case and it's very confusing. We don't know what's going on still So I'm not gonna trash it yet, but if these reports are true Yeah, bro, you can just go ahead and close close the book on Cody story and me personally I'll probably stop caring myself now because then it'll be like what's the point? What is the point now? So I hope this is not the case. We will see comment down below Let me know. Do you guys believe these rumors that have been circulating? Do you guys believe that? That Cody instead will be facing Seth Rollins for the championship at WrestleMania 40 and then potentially Facing Roman Reigns at this year's Summer Slam. Also, do y'all feel like because I do believe The rock and Roman that's probably gonna be that's most likely locked in do y'all feel That if that does main event WrestleMania that the rock will actually win the match Or do y'all feel like it's gonna be super predictable and the rock is going to most likely lose Let me know how y'all feel about all of these these recent story updates and whether you believe them or not It's just chaos unnecessary chaos. I don't know man But I appreciate all of the sport wrote on 50k and I'm still getting speedy you to rest in the world Appreciate our game with me. See you next week


could learn from India, certainly in the West. I mean, this is a young, vibrant, exciting economy. And coming back here after three years of COVID, it's great to see people back in the office collaborating and learning. It's a very young and diverse economy. It's embraced technology more than most countries. And I've seen a massive shift there since I was here last time, the explosion of digital payments, the digital infrastructure that the country are building. And enabling a massive growth in the economy.


Yeah, so as I said in the first lecture, I'm roughly dividing this course into three parts. The first two parts are rather short. They are on SON1 and SP2N. And then I'll move to the third part, which is PGLN. And we were in the middle of the discussion of Siegel modular forms. And yeah, so what I would like to discuss briefly at this point is HECA theory for Siegel modular forms, of course, only in the un-rammified case, the rammified case. I don't know if this has ever been worked out, but it's certainly very complicated. So gamma is the group SP2NZ, so the analog of the full modular group. And HECA operators are parametrized by double cosets of the form.   And we can order them such that a1 is greater than 0 and so on. And it's in increasing order up to an. And then it continues to increase. So an is bounded by r over 2. And r is some integer. So r is basically the degree of the HECA operator. In particular, if r is 1, then there is only one such HECA operator. That's simply Tp. And by slight upuse of notation, I just write the double coset. That's just 1, 1, 1, 1, 1, and then P, P, P, P. There are several HECA operators of degree 2. Ti of P squared is of the following form. I have a couple of ones, i of them. And then I have a couple of P's, n minus i of them. And then again, a couple of P's, n minus i and P squared. In particular, so this is for 0 less than i, less than n, with possible equality. In particular, if i is 0, then this is just P, P, P, P, P, P. So this is the identity. So T0 of P squared is the identity. And it turns out that Tp and then TiP for 1 less than i, less than n minus 1, generate the P part of the HECA algebra. So every HECA operator in P is a polynomial in these operators. They have some nice properties. There are Hermitian with respect to the inner product that we defined there commutative. And of course, by the Chinese remainder theorem, everything is multiplicative. So if I take two different primes, then everything is nicely multiplicative. But if I stay with one prime, then the HECA relations become very complicated. HECA relations are very complicated. This is a very, very complicated combinatorial problem to write down a linear. So if you multiply two HECA operators, you can write them as a linear combination of other HECA operators. But the linear combination is very complicated. And I don't think, so to my knowledge in general, there is no closed formula or not even an easy algorithm to compute what the product of two HECA operators is. Here is a simple example, T p squared. We would like to write this as a linear combination of degree two HECA operators.  But this is the simplest of all non-trivial HECA relations. And they become completely crazy if you want to write down linear combinations for products of HECA operators. What am I missing? You don't write a double costed for T i of square. Oh, yeah, yeah, yeah, yeah, OK. OK, for holomorphic Ziegler modular forms, the Ramanujan conjecture is known, just as in the case of genus 1. Yes, yes, genus 2, Ramanujan conjecture, is known. This is work of Weissauer. But as I said, there is no really clear connection between the Satake parameters and the Fourier coefficients. And so what does this mean? It means that the Satake parameters have absolute value 1 unless the form f is a lift. And I will explain what a lift is in a moment. All right, L functions. I'm not going to go in any detail. I will just mention there are two types of L functions. There is the so-called standard L function, which is an L function of degree 2n plus 1. And here, the analytic continuation and functional equation are known. And there is the spinor L function of degree 2 to the power n. And here, the analytic and functional equation is known in the case n equals 2, but not in general. My impression is nevertheless that the spinor L function is used more often than the standard L function, in any case. I'm not going to go into more definitions. But certainly, in the case n equals 2, there is a degree 4 and a degree 5 L function. OK, finally, lifts, because they produce some arithmetically interesting objects. The most famous lift is in the case in n equals 2, the cytokoro cover lift. This is the case. n equals 2. And this has been generalized to arbitrary, I think, even n or so that I will discuss this later. So the idea is the following. We take a classical holomorphic cusp form of genus 1 and weight 2k minus 2. So this is the space of holomorphic cusp forms on the upper half plane, the usual upper half plane, of weight 2k minus 2. And by the theory of half integral of modular forms, as developed basically by Shimura, you can associate to this half integral weight modular form with the following Fourier expansion.  So the exponent is k over 2 minus 3 over 4 e of mz. And this is a half integral weight form of weight k minus 1 half of level 4. And it is in Conan's plus space, which means that m is congruent to either 0 or minus 1 mod 4. So only half of the coefficients occur. And then, Wald's Po-Jay's theorem tells us that these coefficients are central twisted L values of the original function f. So this is up to normalization. I mean, g is only defined up to a scalar multiple. But I can choose a normalization such that the coefficient is the central L value, chi d, at least for d, a fundamental discriminant. Yes. Yeah, for non-fundamental discriminants, there is also a formula, but that's a bit more complicated. And then I can attach to g, or these coefficients, a Ziegler modular form as follows. So I proceed on this blackboard. To this, I can attach a Ziegler modular form capital F of z. It has a Fourier expansion sum over matrices t, a t, e of trace tz. And that's a Ziegler modular form of weight k for sp4z. And the at's are given explicitly. And in certain cases, they can be described quite easily. It's determinant of 2t to the k over 2 minus 3 over 4 times c where c is this Fourier coefficient determinant of 2t. And this holds at least if minus 1 to the power k minus 1 times dit 2t is a fundamental discriminant. And if not, then there is a slightly more complicated formula that describes these Fourier coefficients. Yeah. So the Fourier coefficients are up to normalization. Well, they're basically the Fourier coefficients of this half integral weight modular form. So capital F is the so-called cytokuro cover lift of either f or g. This is also sometimes called the mass special char, because Hans Maas investigated this a lot, and he called it special char. So special whatever, I guess it's untranslatable. But if you find this phrase special char, then it refers to. Or sometimes it's also called the mass space. So the subspace of capital F of this form inside the whole space of Ziegler model.  But this is sometimes called the mass space inside the space of all Ziegler modular forms. OK, so these lifts are quite interesting. Let me mention two results. There is Ichino's period formula. So what you can always do, this has nothing to do with lifts, what you can always do if you have a Ziegler modular form, you can restrict it to the diagonal. And by this I mean, if you have a point Zx plus Iy in the Ziegler upper half space of genus 2, then you can write this as x1, x2, x2, x3 plus Iy1, y2, y2, y3. And you can project this onto the diagonal x1, x3 plus Iy1, y3. And then this lives on two copies of the usual upper half plane. There is a complex number x1 plus Iy1, and then there's a complex number x3 plus Iy3. So the restriction to the diagonal restricts to two copies of the upper half plane. So you get a function that lives on two congruence quotients, and what you can do now is you can take the L2 norm of the, so both of these are, of course, equipped with an inner product, and you can take the L2 norm of the restriction relative to the L2 norm of the original function. And if you equip everything with probability measures, then it turns out that this ratio is given as follows. It's pi squared over 15 L3 half f. So now f is a lift.   There is a unique way of doing this, putting the first Fourier coefficient to be 1. 1 sims square f times 12 over k minus 1, and then a sum over an orthonormal basis. So this is an orthonormal basis of sk. So notice that f has weight 2k minus 2, but here we are summing over forms of weight k. 1 half sims square phi times f. So this makes good sense. I mean, this sum has size k, and on Lindelof, all of these are essentially bounded. So you divide by k, and all of this is also bounded. So roughly speaking, the mass is rather evenly concentrated on the diagonal. But it's a very beautiful formula. It compares the mass on the diagonal with the complete mass, and it's given as a mean value of certain degree 6 L functions. OK, so that's one thing. And the other thing is that the L function, so the spinor L function, L spin of this lift f agrees with the original L function of the cusp form little f up to some simple factors. zeta of s minus k plus 1 times zeta of s minus k plus 2 times L fs. OK, and this cytokoro cover lift has been generalized to arbitrary values of n. Well, it was conjectured, I think, by Duke and Imamoglu, and it was then proved by Ikeda. So this is called the Ikeda lift, generalization to arbitrary n. This is the Ikeda lift, which has similar features. But it's more complicated, for instance, in the sense that for cytokoro cover, one can give the Fourier coefficients exactly, even for non-fundamental discriminants. This is a complete disaster in general. There are formulas, but they are not manageable. OK, so finally, a bit of literature for further reading. A very good book, and I think one of the standard references, is Freitag's book, Siegelsche Modul Formen, which unfortunately is in German. Nevertheless, I think it's one of the standard references. There is a shorter book that basically contains a subset of Freitag's book by Klingen. This is in English, introductory lectures to Siegel Modul Forms, or something like this. There's a very old book by Siegel, which is called Symplectic Geometry. And it was, in fact, a research paper that appeared in the American Journal of Mathematics. But it's like 100 pages long, and then they decided to make a book out of it. So it's the exact copy of the original paper. This Siegel's book contains much of the underlying geometry. OK, any questions? Is the analytic continuation and functional equation known for the spin or L functions in general? No, no. I think for N equals 2. And I'm not sure what the state of the art is with N equals 3. Perhaps there is some partial, I don't know, but certainly not in general. OK, any other questions? It was a lot of works of Conan and Zagir about Schumann relief from the congruence subgroup. And we start not the grammar reforms or model groups, but congruence subgroups. And then leave them for half waveforms. And then I wrote us here. Yes, yes, sure. So I mean, I'm not going to go into the greatest, most greatest detail. So certainly you can do this for congruence subgroups as well. But I mean, this nice formula of Conan and Zagir, to my knowledge, exists for the full modular group. Although, of course, the general framework holds in generality. In any case, this certainly is possible for congruence subgroups. There is nothing special about the modular group, except that everything is simpler. For these two NL functions, I mean, how should one think about the fact that it's two different ones, that the answer reflects the underlying aspects of the form, or if you think about it? Well, combinatorially, it's a different combination of the Satake parameters. I mean, they are, of course, defined by Euler products. And the Euler factor is a certain combination of the Satake parameters. And you can do this in different ways. Well, at least for SP4, it's also there's two fundamental representation of SP4. And these are the Langlund's NL functions, but actually, it's two fundamental representations. So I'll prove it, they'd be quite independent. OK, well, then this ends my short discussion of Siegel modular forms. And so I'm now going to move on to PGLN. OK, so here's the setup. Our group G is PGLN of R. I won't mention Adelts. In this lecture, everything is either over R or over QP, but no Adelts. OK, it has an Iwazawa decomposition, NAK. N are the unipotent matrices. K is PON. Gamma, for us, is just SLNZ. Again, you can talk about congruent sub-cruise, but I'm not going to do this. H, this is now a third H. It's not the Siegel upper half plane. It's not a hyperbolic upper half space, but it's a model for G mod K. The dimension of H is N minus 1 times N plus 2 over 2. And we choose the following coordinates. We choose the Iwazawa coordinates coming from A and K. So a point z, little z, perhaps, is x times y. And x is 1, 1, 1, 1, 1, something. And y is given by 1, y1, and so on up to y, N minus 1, y1. OK, and double use the vial group. OK, so for N greater than 2, strictly bigger than 2, there are no holomorphic forms. So everything is a mass form. And so we really think of these forms as mass forms. And so we talk about differential operators. D is the algebra of G invariant differential operators on H, and that's the center of the universal enveloping algebra. And this turns out to be a polynomial ring in N minus 1 variables. And this can be viewed as polynomial functions on the dual of the Lie algebra of A. So A is the group. German A is the Lie algebra. This is the dual vector space. And I take all symmetric powers. So I can think of this as polynomial functions. And they should be invariant under the vial group. This is the so-called Haas-Chandra isomorphism going from here to here. So A is the Lie algebra. And it's isomorphic to R to the N minus 1. But we view it as a hyperplane in Rn. I mean, this is a reflection of the fact that we are working with the projective group. So we are working with a trace 0 hyperplane. Trace 0 hyperplane. So a typical element in A has n components, and they add up to 0. Trace 0 hyperplane in Rn. And this isomorphism here sends a differential operator to, well, a map lambda d that goes from A star to C. And for instance, the Laplacian goes to the map that sends mu, which is mu 1 up to mu n. So this is now an arbitrary element in A star to n cubed minus n over 24 plus sum of the squares. To each operator in script D, there is attached a polynomial. And this polynomial tells you that if you have an eigenform, an automorphic form with these spectral parameters, then the eigenvalue under the corresponding operator is this polynomial. OK, so for me, always mu is the notation for an element, well, and potentially the complexification of the dual of the Lie algebra, say, modulo of the vial group. These are the spectral parameters, or Langland's parameters, of an automorphic form. So each automorphic form comes with such an n tuple of spectral parameters. And if you want to know what is the eigenvalue of this automorphic form with these spectral parameters, then you just plug the values into the respective polynomial under this isomorphism. OK, so for me, everything is normalized such that the Ramanujan conjecture says that the muses are real. Other people normalize differently. For instance, in Goldfeld's book, the unitary axis is 1 over n plus i a star. And some other people, other authors, say that the unitary axis is i a star. This is a matter of taste. For me, the unitary axis is a star. OK, as you know, the Ramanujan conjecture is not known, not even for n equals 2. And the best general bounds are imaginary part of mu j is bounded by 1 over 2 plus 1 half minus 1 over n square plus 1. And for n equals 2, better bounds are known. So are for n equals 3 and 4. But in general, these are the best bounds. And this is due to Luol Rodnik and Sarnak. OK, so how many mass forms are there? How dense are they, in some sense? And this is measured by the Harris-Chandra C function. There is a general definition for the Harris-Chandra C function for any Lie group in terms of root systems. I'm not going to go into detail here. Let me just say that in our case of the group Pgln, the Harris-Chandra C function is given by a constant times the product 1 less or equal than j, less than k, less or equal than n, g of lambda j minus lambda k, where lambda is lambda 1 up to lambda n in A star, perhaps star c. Well, let's define it only on A star. Well, yes, that's right, except that lambda, for me, is an integration variable. Later, I integrate over lambda, and I keep mu fixed for my favorite automorphic form. But yes, they play the same role. And g is a quotient of gamma functions that you can simplify, and it just looks like x times tangent hyperbolic of pi x. So the tangent hyperbolic, of course, only plays a role if x is very small. Otherwise, this is essentially 1. So g of x, for practical purposes, g of x is x. Well, in fact, it's absolute value of x, because if x is negative, then also the tangent hyperbolic is negative. So this is bounded by product of 1 plus lambda j minus lambda k. OK, so unless there is some conspiracy between the components of lambda, if you choose a generic lambda such that all these differences are roughly of the same size, then this is the norm of lambda to the power n choose 2. If you're at the walls of the vial chamber, when some of these are perhaps identical or very close to each other, then, of course, the spectral measure is a bit smaller. So this drops at the walls of the vial chamber, of the vial chambers. So the density of mass forms is a bit less at the walls of the vial chamber. And there is a vial law, and this was proved by Müller and Lapid, 2009, that this spectral density really measures the density of mass forms. So the number of cusp forms with spectral parameter lambda plus o of 1, so you take a ball of size 1 about a given parameter lambda is of size c lambda. So what I wrote down here. So I mean, the precise statement is a little different. So the ball has to be sufficiently large in order to get a lower bound. And then if you expand the region, then they actually get an asymptotic formula with a power saving error term. So this counts the number of mass forms. For instance, in the case n equals 2, you get the usual vial law and this then holds in general. OK, so I mentioned earlier, so I'm using these blackboards rather randomly. So I mentioned earlier, for n greater than 2, there is no discrete series. We only have mass forms. However, we do have lifts from holomorphic forms for n equals 2. We do have lifts from holomorphic forms on GL2. So you can take a holomorphic form on GL2 and, for instance, take the symmetric square and then you get a mass form on GL3. OK, any questions? OK, then next thing I want to discuss are Whitaker functions. Whitaker functions. OK, Whitaker functions have two arguments. Well, they have an index and an argument. And the index lives on AC star modulo the vial group. And the argument lives on H, this H here. And the value is a complex number. OK, and they are defined as follows. We take an x in A and I write down the first off diagonal as x1 up to xn minus 1, and I don't care about the rest. And then I can define a character. Theta of x is just E of sum xj. This is a character on n. Character on n. And then a Whitaker function satisfies the following properties. w mu of xz is theta of x times w mu of z. So it transforms by multiplication from the left with respect to this character for all z in H, x in n. And it satisfies differential equation. If I take a differential operator d in script d, then this is lambda d of mu. So lambda d is this map that I defined up there, times w mu of z for all d in d. OK, so this is what I want to call a Whitaker functions, by no means clear that such objects exist and so on. But they do exist. And you can actually explicitly construct them as follows. So in particular, these are all eigenfunctions of this algebra script d. Construction is as follows. You integrate over n a function i that I'm going to define in a moment, i mu.  And i mu of z depends, in fact, only on y. It's independent of x. It's a product. It's basically a power function. j from 1 to n minus 1, yj to some power lj of mu, where these are linear forms in the mu that I'm not going to write down. So lj is a suitable linear polynomial. Basically the idea is, so you choose lj in such a way that this power function, i mu, satisfies exactly this differential equation. And then the Whitaker function inherits the differential equation from the differential equation of i. You don't have to take the long vile element. You can also take other vile elements here. And then you get degenerate Whitaker functions that come up in the constant terms of the Fourier expansion of Eisenstein series. So yeah, if you take other vile elements and the long vile element, you get degenerate Whitaker functions. Degenerate Whitaker functions for other vile elements. For other vile elements, will the integral be convergent? Sorry, what's that? For other vile elements, other than the long element, the integral will be convergent? The what? Ah, for GL2, there are two. Well, yes.  And for GL2, there is no other vile element. But I think if you take a non-trivial vile element, then it converges. OK, so you can write this down. In principle, it's completely explicit. It's an integral over the unipotent group. But these Whitaker functions, we have to admit, they are very poorly understood. OK, as an example, the case n equals 2, well, then we can write down explicitly the Whitaker function. So the Whitaker function has an argument here, which is a pair of two numbers that add up to 0. So it's mu minus mu. And then traditionally, it's just mu. There is no extra information. But nevertheless, z is up to scalar multiplication, square root of y, e of x, k i mu of 2 pi y. And then it's a matter of taste, whether you further normalize this or not. I like to normalize it by multiplying by cosine hyperbolic pi mu over 2. But again, that's a matter of taste if you want to do this or not. The Bessel-K function decays exponentially in mu, so you can compensate for this by multiplying with the cosine hyperbolic. Or you don't have to do this. And OK, so Bessel functions are fairly well understood. So this is a Whitaker function that we can handle. But in general, for n greater than 2, it's very poorly understood. So if you take the construction you gave for n equals 2, do you get this cosine hyperbolic? You just literally take the sitting line. I forget. So the cosine hyperbolic, if you include it or not, is a matter of whether you take the so-called completed Whitaker function or not. I have to look it up. I forget whether this integral produces the completed Whitaker function or not. But we do have some partial knowledge on general Whitaker functions. And what we know is the following. So you can recursively get a degree n Whitaker function by integrating a degree n minus 1 Whitaker function. Then if you repeat this, you can get down to degree 2 Whitaker functions, which are Bessel functions. So general Whitaker functions are integrals over Bessel functions. So it can be expressed as iterated integrals over Bessel functions over k Bessel functions. But of course, if n gets big, then you get a whole bunch of integrals, and things become very complicated. But in principle, there is such a formula, and that's eurostat, eric state. I would believe in the spirit of Emanuel's talk that this is a reflection of the fact that the GLN closed-term insum attached to the long vial element, at least in certain cases, can be written as a product of GL2 closed-term insums if the moduli are pairwise coprime. And I would assume that this is some weak form of reflection of this fact that in certain cases you can reduce the GLN case to products of GL2. For n equals 3, a bit more is known. So for n equals 3, we have a fairly explicit. The iteration of the communicative function? I'm not sure. I have to look it up. I think it's more complicated. You get arguments u. Well, perhaps you get u and 1 over u. Well, I don't know exactly. I think it's not just a multiplicative convolution. It's a bit more complicated than that. But you can look it up in state's paper. We know the double-mellon transform of, so if we keep x fixed, then in the variable y, I have two entries, y1 and y2. So the double-mellon transform in y, y1 to the power s1, y2 to the power s2, dy1 dy2 over y1 y2, is known. And it's, in fact, what you, well, perhaps I don't know if you would expect this, but certainly it's a ratio of gamma factors. So that's fairly simple. And then we have a very important formula. That's a very strong tool. And it's called state's formula. This is the Archimedean rank in Selberg theory. It's the product of two Whitaker functions. If you take w alpha of y and w beta of y bar, determinant of y to the power s, and then the correct measure on the group A. So in the classical case, this is a product of two Bessel functions, but now you take a product of two general Whitaker functions. And this is the sort of rank in Selberg ratio of gamma factors. So it is what you would expect. So gamma, OK, gamma r is the usual thing. I'll define it in a second. It's s plus i alpha, I hope I get the signs right, alpha j minus beta bar k. I hope that's correct, where j and k run from one to two. And so basically you take the Langland's parameters and combine them each with each. Divided by whatever you expect from rank in Selberg theory, gamma r of ns, so that's kind of zeta of 2 in the classical case.  So I don't know if this is readable or not. Hopefully it's not readable because it's perhaps slightly wrong. And perhaps there is a constant involved. So if you want to get the constants right, that's also a complete nightmare because everybody normalizes slightly differently. And you can be sure in the end you will be off by a power 2 pi. OK, so what is gamma r? Gamma r is the usual thing. Gamma r of s is pi to the minus s over 2 times gamma of s over 2. OK, let me just write down one more formula to wrap this up. And then I'm done for today. In GL2 there is the so-called Contorovich-Lebedev transform. If you integrate the Bessel-K function against a test function and then integrate it back, but this time over the index, then you get the original function back. And this holds in general. And this was recently proved by Goldfeld and Contorovich.  So if you integrate f hat of mu against the Whittaker function and now you integrate with respect to mu d mu over the spectral measure, OK, I said that lambda would be my integration variable. Now it's mu, whatever. Over the A star, then you get f back. So this is the Whittaker functional theorem, right? Yes, yes, yes. I'm just, isn't that was proved to be by Wallach? OK, that's true. That's true, but yes. OK, yeah. Goldfeld and Contorovich give a very explicit formulation of this. But certainly you find an abstract version of this in Wallach's book and in Wallach's work. Is this really Wallach? Yes, OK. OK, fair enough. Didn't you say yesterday I'm going to conclude the session? No. OK, anyway. So that's it. Are there any questions? OK, well, that's it for today. Does the speaker really ask for questions? But if you just want to take questions only from the organizers, then ask the questions now. Yeah.  How many percent, what is the percentage you can get in the leaps from which you can get from a lower order? In general, you mean? In a special case, for instance. Well, I mean, if you look at Weil's law, so for GL3, in if you take, so here you're sitting in A star. And in a ball of radius 1 of size t, you have roughly t to the three guys of mass forms. And on the diagonal, so the Gehlberg-Jacke lifts by Weil's law for GL2, they are of size t. So you have t lifts sitting exactly on the diagonal, but in the whole square of size 1. So this is t, t plus 1, t, t plus 1. So in this ball of size 1, you have all together t to the three mass forms. So the lifts are, in some sense, negligible.


Thank you so much for joining us here at Stagwell Sport Beach on the beautiful Mediterranean Sea. What does this mean for you as part of the Stagwell family to be part of this? The thing that unifies humanity is sport. And now we have a place where we talk about sport, but we play sport. There's fitness, there's workout, there's basketball being played just over there right now. There was football played right here yesterday. It showed like the greatness of the sport itself. Like it is fun to play, it is fun to watch, it is about creativity, it is inclusive. Pickleball was being played. So it just shows how it unifies and unites a community and for it to happen. Can is important because can is a place of creativity and it just so happens that sport is a truly creative endeavor. It's exciting to bring that to this place. Really kind of just jump head first into this intersection of sports, branding, marketing, advertising. It's been an eye-opening. I kind of feel like I'm peeking back behind the curtain of how the world works a little bit. Best of the best people are here. So to be able to connect with them and to talk about what I love, which is sports, it is one of the best things. So what have you been doing here at Sport Beach? Any of the sports you've been trying out? Obviously I play football and all football players can't wait to do something else and swear they're the best at it. So I've done some golf, I've done some basketball, we've hit around tennis balls. So it's been really, really fun to act like I'm a pro in something else and then see these other pro athletes in that sport just laugh at me. Whenever there's a sporting event like this, I actually shy away because I should be good at it. And then when I'm not, the whole world is onto my secret. I got a putting lesson from Monica Sorenstam that is definitely going to shave two strokes off my handicap. How do you choose some of the brands that you want to work with? For me, it's got to be something that I'm really attached to. The money doesn't really matter to me. So for when I'm picking a brand, it's got to be something I use. Casio is one of them. You've been wearing a Casio watch for all ten seasons. Yeah, so every year I've been in the league. I don't wear this one. I wear a black version of it, but I only wear the F91W model. I've worn every single game. I have every single color combination of this model. That's an example of like, I would work with Casio. Casio, if you're listening, this is my pitch right now. I'm your number one supporter in the National Football League. The first thing we think of is whether there's alignment in our mission and our values. I think that's really, you know, at the core values of what we're trying to build for Bay FC. We have massive opportunities with just those big brands that are born there. We're bred there and then go on to do bigger things in the world from there. So there's a lot of value that I think we can offer each other in that partnership. This is one of the most undervalued properties in the world when we talk about women's soccer. And it's just a massive opportunity for these brands to understand and now to lean into. And it checks a lot of boxes, quite honestly.


cheering. This presentation is going to focus on the theories, method and techniques of teaching and we're going to start with a quote. This is an interesting quotation because it contains a philosophical argument and it's a philosophical argument in which we learn. This one is saying that the intelligence of their own children process natural. So, yma could be said to be due to nature. This is exactly the opposite of this one, which is saying that they're teaching the environment that we create creates that intelligence. So, this one can be said to be due to nurture. And this argument, nature versus nurture, has been going on for thousands of years. These two viewpoints are two ends of a scale or a continuum, if you like. And every teaching methodology that's ever been created has its starting point somewhere on this scale. For example, if a particular methodology has its starting point here, then that would be 50% due to nature and 50% is due to nurture.


Now the need to create awareness and the dangers of substance abuse and the impact on young people has been re-echoed. Now these form the main thrust of a health seminar organized by the Cres hospital ministry in Nigeria to commemorate its 22nd annual conference. The hospital ministry says it is worried about the dimension substance abuse is taken on Nigerian youth, hence the focus on prevention. Recently the National Drug Law Enforcement Agency, NDLEA reported that 14.3 million Nigerians between the ages of 15 and 64 are involved in drug abuse. While fielding questions from newsmen, president of the CHM Nigeria, Reverend Samuel Ajibola, lamented the devastating effect of the menace on the family and the society. Guest speaker at the seminar Dr. Olajumor Kekoejo called for collaborative efforts to tackle substance abuse in the board while also tasking government on better policies. The way of escape or to overcome of drug abuse, the most important thing is the awareness whereby both adults and young and the community will be aware of the danger of the drug abuse. And also in order to prevent it of growing among the young people, especially with the exposure that is happening on the social media now. Today we believe by bringing the children from different schools and now bring the S parties that can educate us about drug abuse that will help us in order for us to prevent it. Government policies and implementation of these policies is extremely important. Let me give you an example. Now, when you go to legal state parks, they don't sell substance there anymore. So it is not at least accessible to them. Before now they would display it glaringly. So if they tax it to the high heavens and it's not easily accessible to people, it's not affordable to them. These are policies that will help in reducing it. And I talked about the school prevention. It's very important. Life skill training for our school. There won't be appreciable improvements if the Ministry of Education is not part of this. We're joking. So these are things that, at effectiveness training, the life skills of our children are built. It gives them leverage, it helps them in saying no to these substances and to hold on to it. Even in their decision making skills, this would really help our children. Now Chairperson of the Ministry in Nigeria, Joyce Akionla, informed that the theme of the seminar was born out of the need to catch them young as the trend has eaten deeply into the fabric of the society. She spoke alongside a participant. As much as we try to avoid talking about it. And right before our eyes is spreading. So the church is a shiny way from talking about this. And I'm afraid to say, even when we're talking about AIDS and HIV, whatever you want to call it, the churches were shining away from this. There are some things we can't shine away from. It's a problem in the society. And the churches, the mosques must be able to face. If they address it in the mosques, in the churches, it will help us. Because the younger ones tend to believe more in the clergymen, in the imams. They tend to believe what they say to them. But we're judging if we're not even talking about this in the churches. And we believe that it's a sin to even talk about it. At first, she told us on how to work circle-active substances. And circle-active substances are like drugs that alter the brain relaxation. And when the hijack the brain from relaxing. So examples of circle-active substances are marijuana, cocaine, cannabis, and so on. For example, if the government could establish a prevention against drug abuse, drug abuse came, a prevention. And also if schools could be more effective in the social life of students. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


For sailors currently serving maybe a second class or a lieutenant, what changes could they expect to see during their career? And they're going to see big changes over the course of their career. They'll be able to go to the reserve component for a while if they'd like, perhaps to continue their schooling, to raise their family, to pursue a civilian career, and then come back into the active component. They'll have a chance to get that graduate school. They'll have a chance to take time out to care for an ailing family member, or to raise their children, or for whatever reason they would like to do. They'll have a chance, they don't have to wait in line just based on their kind of year for a promotion, but instead it's based on what competencies you've acquired. They'll have a chance to have a career path that is individually tailored for them, that recognizes the unique talents each of us have, and doesn't try to fit you into a one-size-fits-all personnel system. So we hope there'll be big changes in the future for both the enlisted and the officer side.


There's the close and then there's the closer and without one of them being present The deal doesn't work, and I've never taught this Okay, listen a closer get somebody to move in the direction that they want them to move am I right? Okay, what could happen right now if you guys?  Do you guys want that? There's two things There's two things you have to learn and I'm just gonna do like lay this out And I've never taught this before the first one is the ability to master a stranger Okay, I've never taught this before in my life, but I'm gonna tell you this This is the fastest way to because a lot of people they say Andy look dude. I'm doing the training a You want to go to point a to point B am I right? You're like I want to go to a to b I want to go. I went to the class. I'm doing the training. I'm watching the videos And you know what I mean like some stuff's changing right like I mean clearly getting a little more results than I used to But I'm not getting the big results.   It can happen you're tricking yourself right now if you don't change nothing changes Listen to me some of you right now the number one problem is you don't want to change you want to get more information You don't need more information Okay, now you do need closes that is information. You do need to know the words You do need to get put where your backs against the wall know what to say know how to close a deal Know how to wrap a customer and how to set up a close. I'm gonna teach you today how to set up closes But you're the close Okay, listen, what is a closer think about this is this you is this you or is this you okay? Guys a lot of people train with me because I'm real I say terms like dead bob. Okay, nobody has deep conversations with dead bob You get me. Hey guys, what's up? It's Andy Elliott. I just released my social media total domination playbook Now I want to ask you a question right does everybody know who you are what you do how great you are what you do and where you're at If not, I'm gonna show you how to make that happen.  I'm gonna give this to you for free I currently train over 300,000 salespeople and have over 4,000 dealers on my training platform. There's another level I'm gonna take you there guys click the link below. I'm gonna give you this for free. Let's kick Let's destroy your competition. Okay, you know a guy that knows how to master a stranger He has deep conversations with his customers and he hasn't fast When people are with them, you know what they're doing.  It's probably 1% of this room This is the hardest thing to master why because you have to initiate Okay, you have to initiate. What does that mean? That means I look at Eric Eric's not smiling You say Eric. What's going on, buddy? How you doing, man? That's my guy. God. You're looking good, man Tanned up looking nice. Did you get a new haircut? Listen, I want to make him hold on but you look better. How you getting older and looking younger I want to know the secret Watch us. He's gonna start talking.   Go ahead and keep doing transactional your managers and GM's I'm sorry to say this. They don't know how to master the stranger They don't talk to anybody but Their team that's a problem.   Listen to me. I'm gonna tell you the secret. Okay. Listen. We're at a dealership, right me and him together and We're walking in and we're training a sales team Okay, a lady and a husband pull up up front, right in the salesman walks out there shakes the hand It's going normal and I could tell that this blah blah blah Person conversation is clearly being had and guess what I said me come on man Let's go take care of this how you guys doing welcome to the store. Who's this? Is that your daughter? Oh, it's your wife Oh my god, what do we got going on here? What's your name? Is that Tom? Remember the guys like you can call me Tom call me whatever I just want to get a good deal That's why I'm here. I might do listen welcome to the brotherhood welcome to our store Welcome to our family It means everything that you guys drove how far 30 minutes one hour How far did you guys drive to get here about 45 minutes well means everything does that you drew 45 minutes come here Thank you. Give me a hug. I'm not a hugger. I don't care. I'll hug your wife Guess what? He said don't he said he said don't hug me. I see we said yeah, we're gonna hug you We're gonna hug you and he goes don't I kind of like that I'm not sure he's like I don't normally like guys hug me I said I know but this isn't a normal deal. Well, guess what happened We have a lot of training that we have to do so we go back inside and I walk up to the manager and I said hey There's still right here. It's just a lay down. It's easy. Just go land them on a car. Ride it up I Come back and the customer and the salesman and the manager and three other people are all bickering because They they don't know how to open people up Listen to me. Do you guys do you guys understand this? Listen, I swear to God on my life if you want everything in this world that you really truly want and more There's the close and then there's the closer and without one of them being present The deal doesn't work And I've never taught this Nobody's ever heard this on any training video or anything before because I don't usually talk about mastering the stranger because it's a little bit advanced selling When I go into talking about like you and me having an intimate relationship like one of the things this kid right here Makes 25 grand a month. He lives up in Canada, right? But they like he's 21 You know I'm saying but guess what one of the things Happy birthday, baby. Come on. Hey guys. Let's sing this. Let's sing him. Happy birthday real quick guys. Come on. Come on Do you follow Bradley guys? It's Andy Elliott right here my conference room in Scottsdale, Arizona We are putting on the event of the year June 4th entrepreneurs salespeople Closers business owners you want to build a sales team to learn how to close anybody anytime any place anywhere This is gonna be the event by the way Bradley isn't gonna be here like a speaker at most speaking events He's personally gonna be training from 9 a.m. To 4 p.m. Everything you need to know to triple your income this year and by the way This is an event that ain't gonna happen again if you want to be the best if you want to be so great at what you do You make your competition look like freaking amateurs. This is the place you want to be we only got 350 seats so the spots are going to go out fast.  Let's go


Ancient building techniques are an excellent subject to explore if one wishes to understand just how advanced our hidden ancestors were. Additionally, it allows one to get a true insight into the contradictions currently upheld by academic institutes the world over. There still exists an extraordinarily diverse array of building techniques. Some, interestingly, appear to overlap even older advanced methods. For example, a stone-boring technology, seemingly used upon many ancient monuments, in many cases it appears to have been deliberately used to alter, and in many cases slightly damage these ancient stones, leaving them etched with uncanny marks, possibly in an attempt to also leave their mark to prove their past existence, later to be realized by us now laying within their very distant future. We feel that these marks, along with many other aspects of these ancient sites, indicates that many ancient civilizations have been and gone here upon our Earth. Ancient metal clamps used to seat enormous stones, precision machine-cut blocks, some left with inquiries, clearly indicating machine manipulation, impossible block building, effortlessly fitting random-sized blocks perfectly together. Yet the most enigmatic of these ancient building features, which many suspect was indeed somehow connected to the construction of said sites, has to be the protuberances. Rarely mentioned within history books, yet these protuberances are present on many of the most ancient of block structures, which can be found all over the world. No one seems to know what these protuberance were placed upon these structures for. The biggest of these, undoubtedly carved into the still in situ Igaliths at Yangshankori, a feature we have previously noted and pondered over. Not only do these enigmatic notches suggest a past, world-going, highly advanced civilization, having once prospered here upon our planet, but a feature known as the boss mark, found deep within the Great Pyramid of Khufu, may link for the first time the builders of the Great Pyramids to a number of ancient structures found elsewhere on Earth. We now feel that it is highly likely, regardless of past cataclysm, that the human species has successfully survived long enough to have actually outlived our own most ancient ruins. Furthermore, the methods used by the pyramid builders are, interestingly, the same method used by builders of the other sites containing protuberances. This strategic building method, meaning that their ruins have outlived, we feel, many other ancient civilizations now lost to history. Their capability to move such mind-bogglingly huge stone blocks, and their ability to create such erosion-resistant structures, indicate to us that the builders of these sites may have lived an unimaginably long time ago. And probably chose to create such Earth-shifting structures in a bid to indeed survive the eons. Were they doing so in an attempt to leave their legacy on our planet? Or maybe they were and are still trying to tell us something. Only time will tell. We've covered many strange and unexplained things which can be found within Egypt. Home to undoubtedly one of the most perplexing structures on the face of the planet, is a place which also displays erosion from an as-yet-untold history, evidence of a far greater antiquity, and obviously its many unexplainable creations. Yet there are still many amazing areas of this once-fluorishing civilization's home which are yet to be told. One such site which is currently being unraveled is the once-lost, submerged city of Heraklion. Also known as Thonus, it was a place long thought to have been mythical, a city of extraordinary wealth, mentioned by Herodotus, visited by Helen of Troy, and Paris, her lover. But according to legend mysteriously buried under the sea, recent discoveries have in fact confirmed that Heraklion was true. Not only that it existed, actually know where it is. Successfully uncovering many of its treasures, archaeologists have been able to produce a picture of what life was like in this city in the era of its existence. Although it was long attested as mythical, upon its amazing discovery, the same academia immediately put forward a dating for its apparent submersion, stating beyond doubt that the city disappeared beneath the Mediterranean waves around 1200 years ago. So far they have discovered the remains of more than 64 ships, lots of gold coins, giant 16-foot statues uncovered and brought to the surface, with hundreds of smaller statues of minor gods being found on the sea floor. Dozens of stone inscribed in ancient Egyptian have also been brought to the surface. Dozens of small limestone sarcophagi were also recently uncovered by divers, and are believed to have once contained mummified animals put there to appease the gods. Dr. Damien Robinson, director of the Oxford Center for Maritime Archaeology at the University of Oxford, who is part of the team working on the site, said quote, it is a major city we are excavating. The site has amazing preservation. We are now starting to look at some of the more interesting areas within it to try to understand life there. We are getting a rich picture of things like the trade that was going on there, and the nature of the maritime economy in the Egyptian late period. There were things coming in from Greece and the Phoenicians, end quote. Another string to a once amazing civilization's bow, we will keep you posted regarding any perplexing finds. Thanks for watching guys, and until next time, take care.


The annual GemTech Awards are an important way in which ITU and UN Women recognize the tremendous power of ICTs to transform the lives of girls and women everywhere. I congratulate not just this year's winners and the finalists, but all the amazing projects that were submitted a truly inspiring global effort. I'm co-founder and executive chairwoman of the Mozilla Foundation. I'm proud to support the GemTech Awards and the recognition of outstanding work and the promotion of gender equality with technology. Technology plays a critical role in the empowerment of every woman and girl in providing access to education and economic opportunities to enabling personal and professional growth. Switzerland cares about digital equality, empowering women and girls through ICTs. We proudly support the GemTech Awards and extend our warm congratulations to the winners. For their accomplishments in utilizing ICTs to reduce the gender digital divide and mainstream the inclusion of women, girls in the use of ICTs, here are the winners of the 2015 GemTech Awards. Applying technology for women's empowerment. The Research Centre of Communication and Development Knowledge Management, Thailand. Since 2006, CCTKM has set up itself with the mission of ICT for the marginalized empowerment. And then women and girls are one among them also include with others disability group and others. So with the decade of development that we have done with a lot of partners in using ICT to empowering all the marginalized people more than 300,000 people are trained with ICT. We are very proud but anyhow still a challenge in ICT for gender empowerment in Thailand. This is our mission to prolong. So we hope that all the partners can still working with CCTKM to achieve our gender and ICT empowerment. Promoting Women in a Technology Sector. Technovation Challenge. So we should start with the problem. In our school we have 67 cases of COVID-19 because of the water. 18% of women engaged in self-harm and 6% of men said the same. Drunk driving has plagued real problems such as women's safety, waste removal and childhood obesity. I see a lot of problems in our town. We don't have boxes for garbage. Who knows better the problems in the community than the people? A business in technology competition, you have the ability to practice your English, learn some new things. My computer science teacher sent out this huge email to all the students about Technovation. Welcome to the Technovation Pearl Kitchen competition. You need to find the girls to do it. Most of the girls were like no, computer science is for boys. Only 7% of tech startups are led by women. And I feel like I look everywhere and like that's a problem and then this app could solve it. This is the next social media button. We are sophomores and we're all 15 years old. Elclina, Rina, I'm Sefa and by the way... You want to make it perfect. An actual problem and finding a way to solve it like that is a really good feeling. Developing gender responsive ICT, governance policy and access. The Ministry of Posts and Telecommunications, Senegal. The reinforcement of the role of the responsibility and the participation of women in the development of all sectors is a priority for the government of Senegal. The new technology of information and communication. Our ambition in any case is to promote female entrepreneurship through the team. Women's entrepreneurship. But also to take care of gender problems in the different public policies. Our ambition is to set up a place where we can support innovation. Where we can support women and girls in the tech sector. And we wish that there will be a global alliance for women's entrepreneurship through the new technology of information and communication. And I think it's possible. Global achievers. The opportunity costs for non-inclusion of women in national mainstream is immense. I strongly believe that women empowerment using ICTs is a key driver for transformation to knowledge society. In my own capacity we focus our work on the most disadvantaged of our women and young girls and to provide them the opportunities that they well and truly deserve. We are taking whatever measures that are required to empower women and young girls of my country through the use of ICTs. We've come up with a new cross-cutting initiative focused on protecting and empowering women and girls and it's called The Future She Deserves. We've been bringing together key diplomats, agency heads, industry experts and business leaders around the same table really forcing each other to think outside the box. These are powerful decision makers. We believe that by working together across sectors, men and women that we can drive toward innovative solutions and really have a profound impact. I'm Nancy Hafkin. I'm greatly honored to have been chosen by ITU and UN Women to be a recipient of the 2015 GEM Tech Award in recognition of the work that I have done for over 25 years to promote gender equality and information technology. This is an area that I think is of tremendous importance for girls and women all over the world.


This study examined the experience of treating wounded soldiers with gunshot injuries to the abdomen. It found that multiple and combined fragmentation wounds were most common, and these were associated with increased risk of large bowel damage and higher morbidity rates. This suggests that a differentiated approach to treating such cases may be necessary to reduce the length of hospital stays and prevent complications. This article was authored by A. Louren, K. V. Geminiuk, O. B. Timchuk and others.


We're back! The Fusik Manifektorum. I'm checking in from Lothlorien with a kettlebell session. A quick and easy one, so I will just guide you through my movements here. So now I am simply warming up. You can do this as your main exercise as well, but I usually do this as a warm-up. So just swinging it, swinging the body into action, and I'm using a 32 kilo, that is roughly 70 pound kettlebell. So now I'm doing my first real set here, so you see that I am switching hand, and I'm trying to get a nice deep range of motion, a full range of motion, so I'm trying to activate my legs as well. So I do try to make it into a full body exercise. Now of course this does not, it can never replace the gym, it can never replace the heavy compound movements in the gym, but as an exercise you can do like this on a nice summer's day. If you don't have access to a gym it's a very good piece of equipment, the kettlebell, so I use it as an accessory.   So now you see it from the back there, you can see that I'm engaging my legs as much as possible, and I do this by taking the kettlebell as close to the ground as possible, so I'm really activating my legs and hip there as well. I'm pushing through, pushing forward with my hip, and then of course you can see I'm trying to have a nice back position there as well. Boom, absolutely aesthetic, look at that, aesthetic physique if I may be so bold. So now we're doing it from the front to show a different angle, so you can see there it's good for the forearms as well. I'm gripping it, gripping the kettlebell tightly, so of course I have a good control of it, and perhaps you can see from this angle as well that I am training my legs of course not in the same way as a good old squat would do, but still you get some nice leg training and you get to train your hip drive there as well, which is good for all manner of things. So that is at least what I'm doing usually with my kettlebell when I'm not training in the gym, so good stuff, good stuff. Then lastly of course you might wonder what sort of garments I wear in this fine video, new releases from Legi Gloria, you can see they're absolutely aesthetic as well, the Oracle Guard sleeveless hoodie and the Salmoxis gym shorts, so two great new garments made of cotton made in Poland, proudly made in Poland, so check it out, first link in the description box below. Now thank you for your support and thank you for watching XXO, BOOM!


Hello everyone, this is financial author Amit Dan of amitdan.com. On this channel, you'll find financial travel and more videos just like the one you're watching right now. If you like what you see, please give me the thumbs up and consider subscribing. MasterCard will eliminate signature requirements. Hello everyone, this is financial author Amit Dan of amitdan.com. Today I'll talk about MasterCard eliminating signature requirements for USA and Canada. I'm expecting this video about 3-4 minutes long. It is estimated that only 20% transactions in North America require signature for MasterCard customers. From my own experience, I can tell you that whenever I go to stores or anywhere to buy something, usually I never ask for any signatures. Very rarely, as to sign for a purchase if the machine had a problem or there's something else. So this is the common case in Canada that usually we do not have to deal with any signatures or anything. So MasterCard recently announced that starting 2018 April, they will be eliminating signature requirements totally or 100% for Canadian and American consumers. So what it means is that you will not be asked to sign anywhere in the USA and Canada and this is a total elimination and this is what MasterCard is working on right now. I think this is a step towards the right direction because even if we are asked to sign for any particular transaction, usually most people just sign which is not a real signature. We just like you know put a dot or just trying to circle something make it look like a signature but most of consumers do not bother to sign the full signature or the real signature. So eliminating signature totally will not make that much difference and this is going to make everyone's lives a lot easier because in USA and Canada you will not be asked to sign for anything starting next year. So that's all for now if you like what you see please give it a thumbs up and consider subscribing and on this channel you will find a variety of videos and there will be more videos coming up. Thank you for watching and I will see you shortly.


CNN reporter Donio Sullivan attended a Trump rally. Yes, you heard that correctly. I said a Trump rally They're still taking place in 2021 believe it or not but anyways, he spoke with Trump supporters as he usually does at these types of events and The rhetoric that they used was I mean, it was predictably deluded and silly But you're gonna see that there is this growing sentiment within, you know Trump communities and Q communities where they are more open about Their predisposition towards authoritarianism. They genuinely believe that Donald Trump won and as Time goes on they believe that that makes it more justifiable that the military steps in and Actually re-installs Donald Trump is president He didn't lose I know he didn't lose your shirt here says Trump won Yes, he did. Is this about 2016? It's about all of them and 2020 and the next one. But he lost in 2020, right? No No, do you think what happened on the 6th of January was a sort of stain on his presidency? This is all staged I Truly believe that conspiracy theories about the election and the insurrection are par for the course at Trump rallies But now another false notion is circulating among some Trump supporters that Trump could be reinstated as president Later this summer. What are you hoping to hear from Trump today? I hope to hear he's coming back Coming back in 2024 sooner. He's coming back soon and you guys are going down Trump has been falsely suggesting that the sham Republican audit in Arizona could lead to the election being overturned Stay tuned for Arizona. We need two states. It's gonna be a very interesting time. How do you govern when you lost? How do you govern when you lost? You think the election is gonna be overturned in some way. Oh, absolutely. There's no The military already knows it was a fraud. He won by over 80 percent Run you genuinely believe that he's gonna he's coming back that he could come back as soon as before before the middle August And what if that doesn't happen? Huh? What if that doesn't happen? We're gonna be in a civil war because the militia will be taken over among Trump supporters at his rally in Ohio Saturday Do you have a second to chat to us? We always want to talk to a proud boy A man wearing a proud boys t-shirt and a self-described member of the three percenters militia group Some people believed to be associated with the group were charged for their alleged involvement in the insurrection Do you think though what happened on the 6th of January was a bit of a stain on his all the violence a bit of a stain on his presidency or No, I don't I don't think so. I was I was there. Were you up at the Capitol? Yeah, we was there Yeah, didn't go in didn't do none of that stuff.  Yes Some of your guys have been caught up in a conspiracy, right? Charged by the FBI bars. I know there's some of them are being held and a lot of them are just being questioned Do you think your guys who went inside shouldn't have gone inside or what? Yeah, I don't think anybody should have went inside, but you know when you're worked up in that moment and You know the adrenaline's pumping. I mean it just just happens Are you worried that we could see more violence? Yeah, I Honestly believe it's coming Okay, I Don't like a lot of CNN reporters. I think that they're hacks, but what CNN does to Donnie O'Sullivan is so unfair I mean, maybe he likes this in some way, but I think that if he were to apply for disability Sighting brain damage is the reason why he's unable to work The government would be obligated to grant him that request because I mean the people who he talks to I mean This is demoralizing at this point I think I've probably covered every single one of the rallies that Donnie O'Sullivan has went to and he he doesn't Necessarily insert his own like opinion he fact checks people But he just kind of gets them to say what they want to say and it's just it's deeply depressing to see so many people say things that are Laughably wrong and I mean everyone who we talked to believe that Donald Trump won so at that point That's not even controversial within Trump circles and Q circles But now they're taking it a step further and they're explicitly calling for authoritarianism for military coup and violence And that's really really bad. I Shouldn't have to explain why this is bad So that last guy there the three percenter when asked if he thinks there's gonna be more violence he said Yeah, I honestly believe it's coming Okay Why do you believe it's coming? Who is going to carry out said violence? Are we going to see more insurrection style events? Do we? Have to expect like a military coup of some sorts like why do you say that? Why do Trump supporters who believe the election was stolen from him think that there's gonna be violence? Like do you understand why what he's saying there is so worrisome on top of that? There is the other guy who said that he thinks the election is going to be overturned saying the military already knows it was a fraud Trump won by over 80 percent And if Trump doesn't come back before the middle of August that we're gonna be in a civil war because the militia will be Taking over now the subtext there is that that individual Wants there to be a civil war if this means that Trump would be installed as president now am I absolutely But heard about the loss of Bernie Sanders in 2020 Absolutely still bugs me to this day. I donated so much money tried to do everything in my power to elect Bernie Sanders But we lost What I feel better if the military decided you know what Bernie Sanders is the rightful president. Let's install him No, because democracies don't work that way sometimes you win sometimes you lose and as a result of their loss that they refuse to accept now they are actually yearning for and calling for a military coup and That just really speaks to How extreme the modern GOP is and it's not like the base is Only full of crazies. I mean at the highest levels of government in Congress We have individuals who are part of these communities part of QAnon Who tweeted out the location of Nancy Pelosi during the insurrection? We can only guess why Lauren Bobra did this We have individuals like Marjorie Green Also perpetuating the sly about the 2020 election and calling for her political opponents to be imprisoned Simply because they're her political opponents and she disagrees with them I mean people have to understand that this isn't just a small issue with a bunch of kooks at a rally saying really silly things This kind of sentiment is wide spread and far reaching. He's coming back soon and you guys are going down I mean, what does that mean when people are so deluded that they think that a military coup would be a good thing and Implied that it's gonna happen and would be good. I mean, what does that mean?  Does that mean that your ratings are gonna tank or does that mean? You know since I already support a military coup. I also support Donald Trump shutting down the media it's just At this point, how do we bring these people back to reality? I genuinely don't know I mean if you remove Trump from the situation and he says look I'm out of politics forever I'm never running again it's not like all these people suddenly are going to become de-radicalized like that because a Vacuum will be created and some other kooky person perhaps worse than Donald Trump is going to fill that void So the question is is it possible to put the cat back in the bag? Is it possible to believe in democracy again? After they've become so radicalized after they have absolutely no faith in American electoral institutions And there are reasons why people should be disappointed in our institutions and our electoral institutions I think that they are absolutely biased in favor of the two-party duopoly. I want to see electoral reform So we can get multiple parties in power. I mean, there are a number of reasons to be dissatisfied with our System, I mean the electoral college is one of them But that doesn't mean that you check out and you say now I support a coup You always fight to further consolidate democracy fight to make the system even more fair, but that's not what these people are doing and so this culture of You know pro-democracy and support for democracy and supporting the outcome of elections Even if the person who you want to win loses That's going away quickly in the span of a year. It's diminished something that America has taken centuries To cultivate so How do we move forward? That's a genuine question that I don't have the answer to but right now just seeing this it's It's soul crushing