Welcome to the day seven of PCMI summer school. Today we start a new series of lectures that will be about Riemen-Hilbert problems. The Riemen-Hilbert problems had tremendous success, while both in random matrices, improving various delicate asymptotic results and establishing universality theorems, but also very well beyond in different areas. And we are very lucky to have the world's leading specialists on Riemen-Hilbert problems first a dive from the Quarantine Institute in New York who will tell us some parts of the story. Welcome. Okay, first of all I want to thank the organizers for inviting me to participate in this wonderful, quite extraordinary event. Thank you. Okay, so the subject is Riemen-Hilbert problems, R.H.P., and Riemen-Hilbert problems mean different things to different communities, but I'm going to give one particular point of view on what they are. So my goal in these four lectures is to do the following. Is to say what a Riemen-Hilbert problem is, why we are interested in them, and lastly is how do we use them, how do we work with them, going on from that. Okay, these four lectures which I'm giving now are a condensation of a semester course which I gave it to NYU about two years ago. You can find it on AMS open notes. So it's a very nice thing that AMS have done. They ask different people just to put up their notes and you can find a much more extensive version of what I'm speaking about on the AMS open notes. Now there are many references which I've given. I'm not going to write them all down. They're references of two kinds. One's about Riemen-Hilbert problems specifically, and the other's about the general kind of mathematics, particularly from complex function theory that one needs to know to work effectively with Riemen-Hilbert problems. I'm not going to repeat it. You can find them all in the handouts. Now, I want to start off speaking about special functions. And what's important about them is that they give explicitly solvable models for a huge array of phenomena in mathematics and in physics and when I speak about special functions, I mean, for example, the Bessel functions, every function, and so on. Now, of course, let me just say if you haven't met up with these, there is no way that you're going to have any experience in mathematics without coming across them at some point. So a general reference, let me just mention one, is, okay, so this is a book by Abramovitz and Stegen. So it's a general reference for classical special functions. You can also find it on the NIST website in an updated free version which you can just download, so see NIST. So it's a go-to book for finding out anything you want to know about special functions. So how does it work? So let's write down the area equation. Looks like this y double prime of x equals x times y of x. And you look for a solution, so you seek the following, y of x equals an integral over some contour of e to the xs f of s ds. So you want to choose f of s in such a way that you solve this equation. And you begin y double prime of x is equal to s squared over c. And that you observe over here as the following form. If you alter x times y of x, this says x times e to the xs f ds of the contour. And this object here is equal to d by ds of e to the xs. And now you integrate by parts, assuming that you can drop off the boundary terms. And then you see, got a prime prime over here, of course. Then for these two things, for this thing over here and this thing over here to be equal, you see that you have to have that the f prime is minus s squared times f. So in other words, f must equal e to the minus one third of s cubed up to some constant. So what that means is that you can find a solution to the area equation in the following form, e to the xs minus s cubed over three ds over some suitable contour. Maybe with a constant. Okay, now why are you happy about this? Why is this good? Well, if you're an analyst, particularly, what's interesting about special function theory is you can evaluate the asymptotics. In other words, x going to plus or minus infinity. You're very interested in that. And what makes you so happy about this representation is there is a fundamental, all-important mathematical technique known as steepest descent. Descent, sometimes called stationary phase. And this technique applied to that integral allows you to compute with extraordinary precision what the asymptotic says for the solution. In fact, if you didn't have this representation, you would not, I think it's a fair statement to say, you would not ever be able to solve the asymptotic problem. So steepest descent, stationary phase, plays an absolutely central role in mathematical analysis of special functions. Now, if I take this contour, I take my constant c to be one over two pi i. And I take my contour c to be something like this. This goes off at an angle e to the i. And this is e to the minus two pi i over three. That's my contour. Then I introduce the function aix, which is one over two pi i. Integral over this contour e to the xs minus s cubed over three. Yes, and this is called the airy function. And plays a central role in many, many different problems. And you've seen it in earlier lectures, coming up in random matrix theory and different things like that. Now, by choosing the contour appropriately, you can get other solutions of the equation, like something called the bi solution.  But I want to give you a sense on what the standard is. When I say you can obtain precise information, I want to give you a sense exactly what one means by precision. And you find, again, you can find this in Abramovitz and Stagen or on the NIST website. If you introduce zeta equals two thirds x to the three upon two, then one has ai of x is equal to one over two root pi, x to the minus a quarter, e to the minus zeta. And this is asymptotic expansion. k running from zero to infinity, minus one to the k, ck zeta to the minus k. This is as x goes to plus infinity. And then you've got that ck is equal to the gamma function at three k plus a half upon 54k, k factorial, gamma of k plus a half. That's as x goes to plus infinity. And you also have ai at minus x, again, x going to plus infinity. So minus x goes to minus infinity, one over root pi. And you've got your x to the minus a quarter. And you've got the sine of zeta plus pi by four. Times the sum minus one to the k, zero to infinity. But c of two k, zeta to the minus two k plus cosine, minus cosine zeta plus pi by four, times the sum zero to infinity, minus one to the k, two k plus one zeta to the minus two k, minus one. Now, I'm writing this down because I want to fix the table. Now, this is what one wants and what one needs when one speaks about the pre-precision. You know every single number that you want to know about these functions. Now, what's particularly true is these formula and let me say again you obtain these formulae because you have that integral representation together with this all-powerful instrument called steepest descent. Now, these problems or these formulae solve the connection problem or sometimes it's called the scattering problem. And it says the following, that if you know the asymptotics of the solution as x goes to plus infinity, so you would know this form here, then you automatically can read off what the solution will look like at minus infinity. So it's a scattering problem because you think of x sitting over there, y double prime equals x. You think of that x as a potential, q of x times y of x. And you think you've got some wave coming in looking like the airy function and you want to know precisely what is coming up. And this solves that problem. Now, back to this, the erases are here. Now, what has emerged that was first submerged and it has re-emerged is what one calls modern special function theory. So we spoke a little bit about classical special function theory, Bessel functions, airy functions. But there's something which has emerged in the last 40, 50 years called modern special function. And at the core lie what are called the Pan-Leve functions or equations. Six of them. And just as classical special functions, airy and so on, we're extremely useful in solving the linear problems of the 19th century acoustics in electromagnetism. Now what has emerged is the modern special function theory gives you the language to describe and explain many of the modern phenomena which have arisen in non-linear science. So linear science. Mostly, that's a little bit of a simplification. And modern is non-linear. And as you've seen in the early election, many of the fundamental features of random matrix theory, for example, are expressed in terms of these Pan-Leve functions. Now, let me give an example of how they arise. Let's look at the modified quarterback, the Fritz equation. So he has a PDE, it arises in the theory of water waves, and it's played a very important role in modern non-linear science. He has the non-linearity in the equation. And then you find the following. Big pun. Okay. Find, we find as t goes to plus infinity in the region, in that region, that y of xt is equal to one over three t to the third p of x of three t to the third, plus order one over t to the two thirds. And p solves Pan-Leve two. As I said, there's six of them and I'll say more about them later. And what does it look like? p double prime x equals x times p of x plus pq. Usually there's a two in front there, right? Yeah. So it's a non-linear equation. And if you remember what the area function looks like, it's some kind of non-linearization of the area equation. So you just look at this self-similar solution. For MKDB in this particular region and you see what arises as this function. Now, such a point of view or such a computation would not be of any use according to the standards which we've written down a few minutes ago. What you want to know is as much as you know about the area function, you would now like to know about this Pan-Leve function. Can you, for example, describe the asymptotics as x goes to plus infinity and x goes to minus infinity? And can you solve the connection problem? Okay, so those are the issues. Let me give another example of how they arise. There's a problem which was mentioned. So you look at permutations, for example, two versus, for example, one. Okay, you look at the permutations. SN, permutations of N numbers. For example, if we take N equals six, and we look at the permutation, let's call it pi, is equal to four, one, three, two, six, five. Then these numbers here, one, three, six would be an increasing permutation of size three. So one, three, six is an increasing permutation or subsequence of size three. Another example would be one, three, five. That would be another example of an increasing subsequence of size three. And for a general permutation pi, you let ln pi be the length of the longest increasing subsequence. So in this particular example, L, N equals six for this pi is just three. And then you put uniform distribution on the permutations. There are n factorial of them. So each one has probability, one of n factorial. And you ask the question, what is the probability? That ln is less than or equal to n. And what does this look like as n and n go to infinity? And the answer is this. If you look at the probability that ln minus two root n over n to the sixth, this will converge as n goes to infinity. To e to the minus integral x to infinity t minus x squared, do I have this right? Of y or p of t dt, do I have it right? No, one of them just goes wrong. Sure, where am I up to over here? And again, p is exactly the same function which arises there. On the understanding, so p solves panel of A2 with the boundary condition that p of x looks like the airy function as x goes to infinity. So you see, you begin to get a sense in which the panel of A functions, which are non-linear functions, enable you to express the solution of a problem which arises. In common combinatorics, yeah. This is a very special function. It's the distribution function for Tracy Whitham, which gives you the distribution function for the largest eigenvalue of GUE matrix and that you have seen earlier on. Now, there are many problems in common combinatorics which are expressible in terms of these random matrix theory ideas, but I just want to get the idea across here that these panel of A functions are things which you want to understand. If you want to know now about this probability distribution, for example, when x goes to plus infinity, it's clear that the right-hand side is going to go to one. On the other hand, what does the distribution look like is x goes to minus infinity. Then you're going to have to know a great deal about this function, p, p of t. Okay, so now, as I say, question is this, what do I do with this here? Can we solve a connection problem? So that's the basic issue. If we know the behavior at plus infinity, can we immediately conclude and know what the asymptotic behavior at x goes to minus infinity and vice versa? Now, the difficulty one faces here is that if we knew that there was an integral representation for the pan-panel of A2 function which is similar to the integral representation for the ARI function, we would be in good business because then we can just use a classical STC PIS descent method. But there is no known, and this is where Riemann-Hilbert problems come in. Riemann-Hilbert problems gives you a way of representing these functions which is amenable to as detailed analysis as you could perform on the ARI function using its integral representation. But we do have, and this is one of the many reasons why one is interested in Riemann-Hilbert problems. And there is a non-linear steepest descent method for RHPs. So if there's nothing that you take away from these lectures, except the following, you will have gained something. That when you find that you have a representation for one of these functions, in terms of a Riemann-Hilbert problem, there is a technology there which will enable you to evaluate that problem of any precision that you need. And the non-linear steepest descent method, which is the non-linear analog, was introduced by Zinjo and myself in 1993. So we get to what is a Riemann-Hilbert problem. It involves two objects, a contour, a choir, a contour, which we'll call sigma, which is oriented. So each of the arcs of the contour, which can have points of self-intersection, has a direction associated with it. And by convention, the plus side is always on the left as you travel along the contour. So you have such an oriented contour, and you also have a function V, which is called the jump function. And V goes from the contour to the al-infinity functions. Al-infinity functions on the contour, such that V and V inverse belong to al-infinity. They are the invertible, let me put it this way, GL or KR. So you have a function defined there, a K by K matrix function, and it's in al-infinity and it's in inverse. These two, yeah, big pun, at this stage, any union of arcs, any union of arcs, finite unit of arcs, but I'll say more about that later. We say that the n bar K matrix function, m of z, solves, or is a solution, let me put, is a solution of the Riemann-Hilbert problem, sigma V.


The state PDP governorship primary election may have come and gone, but the controversies remain mercy, indeed both parties and both sides of the same party are still in difficulties and of course the controversial issues, especially coming from Shigoni who is the leading contender who didn't win but also came out and lost the primary election and he's been singing and shouting and saying a lot of things regarding that convention. Well the AKG State primaries may have come and gone, but the controversial issues remain that defeated aspirant Chief Shigoni and the former state governor, Chief Shigoni has accused the former governor, another former governor of AKG State, Ayodhya Lefayeshia of selling out the party's candidates to the all-progressive Congress. Oniya has also accused the PDP national working committee led by Ayodhya Ayu of hurriedly ratifying the outcome of the governorship primary election which he alleged was conducted in a shoddy and abysmal manner. In his words, basically the APC's candidates duplicate copy. So he's calling the winner of that PDP primary who was his opponent in the primary. The APC candidates duplicate copy. However, Ayodhya's media aide Larry Olaenka has dismissed the allegations saying Shigoni is basically on his own as far as the PDP is concerned. We'd like to find out what the future holds for the People's Democratic Party in AKG State. That's what we're out here for to find out what the future holds for the People's Democratic Party in AKG. So we have joining us Yamiya Olaenka who is the chief candidate of the People's Democratic Party in that state. Mr. Olaenka, good morning to you and thanks for joining us. Good morning. Good morning. Thank you, Nigera. Thank you for having me. Is Shigoni on his own as far as the PDP in AKG State is concerned as said by the spokesman for Bicicolaole? Yeah. Well, Larry is free to say whatever he likes. In the free world, there is no limitation to anybody to say whatever he likes. But whether or not time will tell, I mean, you know that in the state today everybody knows and they're aware that Shigoni is a candidate to beat. I can say that Shigoni is on his own. Okay, let's wait and see. Time will tell. But I can assure you by the time they get the results, they will know the scores. What do you mean, sir? What I mean is that, well, the other plans on the ground, as I'm talking to you, there's so many plans going on within the camp and I believe so strongly that by time we come up with our plans and what we tend to do, let us see whether or whether it is possible for them to see Shigoni is on his own. But I can assure you that everything is on course. I mean, the primaries have held the People's Democratic Party, national leadership has ratified the outcome of that primary. You know, every party has its internal rules and processes and once the party ratifies it, that's done. So I mean, isn't Shigoni already fighting a loss-battle-loss cause? Let me say this, let me be clear to Nigerians. Unfortunately, we have laid a democracy setting on a bad footing in our country and I'm afraid that the younger ones will not meet this absurdity, this theater of absurdity that happens everywhere when it comes to primary and when it comes to election in Nigeria. It was a plan when the question created rigging that took place in equity on the 26th of January at the primary where plan supported by the national, it's unfortunate, we find ourselves in this situation, it's unfortunate that Yosha is that will believe and do the right thing is saying that that primary was okay. It's unfortunate, but I'll tell you, they are all acting as cheap that I've been reading, is cheap to redeem in favor of the candidate of the APC. How is this a script written in favor of the candidate of the APC? You have the entire, are you saying the entire people, okay, yes, go on please. Let me say something to you, there was a celebration at that night because Shigoni lost, that was a party that the government has in the state, I don't want anybody to prove it wrong, they jubilated at the APC camp, they had a party, they drank, they almost finished all the beers and all the beer pallows in that night, that yes we are happy that Shigoni lost, the only person they know that they want to beat and that is there that people love, the artisan, the civil servant, the teachers, everybody loves Shigoni and they wanted him back and we told them, don't throw away PDP, don't let this election go away, I think you should have more people that will be governor of PDP than that can help you and that's exactly what we told them, but they refused, so they planned it, if you look at what happened at the primary, you will be shocked, I'm sure you must have seen some of the footages and all that, you know, I mean how can they be voting, they will be showing to a particular candidate and they will vote and let them show it to another candidate before they move and the chairman of the electoral committee was there looking at everybody and if anybody says anything he will fight you, he will ask the police to remove you from the hall, so that's why I said it was a well-planned orchestrated move by the APC, by the PDP to favour the APC and that night, apart from the fact that at the Turei party, Ayodele Faoshi was at the state house, was with Fahemi, they were there together that night drinking, that yes we won the battle, we finished Shigoni, but let us see who the people want, you know, it's just a matter of time. So another issue that was raised is the issue of results she's giving to electoral officers, you know, the night before the primary elections, can you, you know, help us describe and tell us how that happened? That was in the PDP, that is the issue of the APC, that they are the one that has the issue of the distribution of electoral material the night before, as you know, I mean, we didn't have the kind of primary they had, they had the direct primary at the APC, we had an indirect primary, I mean, it's a delegate election, so and we were all there, so it wasn't us that complained of that, you know, it was the APC and I cannot speak for the APC, I can only talk about the PDP. So but another issue again is the fact that Governor Faoshi has been accused of betrayal, betraying, you know, the People's Democratic Party, can you, can you also tell us what that means or what kind of betrayal we're looking at now? I can tell my jury, I would say Faoshi is a traitor, he can't trade anybody off, as long as money comes, that's the kind of person he is. He doesn't care, he doesn't care, he told me, I mean, if someone told me that they actually mentioned to me like, it's not as much as you know that Shagun is the best candidate, why not to allow your candidate to support Shagun so that he can win the election?  Okay, I mean, I'm still trying to understand how this emergence can be a script being played out in support of the APC in Hikiti state, it's quite well documented, the rivalry between, sorry, I mean, you're like, the rivalry between Fahimi and Faeshe is well documented, you know, there's no love lost between There's no rivalry between them lately, you can see the two of them jolly, you see them in the photograph together, even on the night of the primary, at the government house, and you see the kind of gritting the way they embrace there's no rivalry at all, but sir, I'm looking at a copy of that photograph, politicians can meet anywhere, even though so have the fiercest rivalry, in the public, they can just keep a sort of a formal and official pose. Faeshe didn't go to see Fahimi alone, he went there in the company of Badaru and Imanu Odomimano, governor of Aqaibum state, who was a returning officer for the PDP at that state governorship primary, and yes, so they just basically had enough evidence, and enough evidence to show that it's a straight-up plan, so it is, what is the PDP, former governor, meaning the government house at the night of a primary, what is the chairman of an electoral committee, yes, the chairman being that a governor of another state, I mean maybe a same-place country with the governor of the whole state, that is understandable, but for all of them to throw a party to drink together, the only picture you saw was the picture that was shown outside, it did allow people inside, there was a party inside the government house, then you asked a question earlier, how would you say that okay, that something was so constituted to favour the APC, the moment you carry a candidate that is not acceptable to the general of the PDP, definitely you are saying APC should win, mind you, currently the governor of Aqaibum state is from APC, the national that controls every apparatus of government is APC, beat such a government in any state, you need a candidate that is well acceptable by everybody, it's as good as gone, okay we'll come to that, but are you saying that Don Mimano, governor of Aqaibum state is also working for the APC? They work in consonants with an orchestrated plan to ensure that they carry a lesser candidate, that's the candidate of Ayodele Pauche, a candidate that is not well or generally acceptable to the general of Aqaibum, that's exactly what we're saying, or all to make sure that the APC wins? That's all, that's not a thing, that's the script, that's all, when you carry a lesser candidate, definitely APC will have an upper hand, they are the one controlling the state, but from what I can see, if you know where you have the likes of Aqaibum state before, and where not by the people you can find out by yourself, or ask your correspondent to find out who the Aqaibum state is, who is generally acceptable to the people of Aqaibum state, they will tell you, give us Shaguni, everybody start shouting, give us Shaguni, give us Shaguni, and so we don't want Shaguni. So let's come to the matter of the popularity of B.C. Kolaulay and Shaguni, of course you had the likes of the female senator who also pulled out and Rujimi and others, some would argue that, and I'm sure you've said the same thing, that popularity is not by mouth, it's not by what people say on the streets, you have to win the delegates over, and if the delegates are not on your side and don't vote to you, even if you're popular outside, you cannot win, those are the rules, and you play by the rules, so what do you say to that, because you're saying that Oni is on the mouths or lips of a lot of people in Aqaibum state, they love him, they want him, he's popular, fine, that could be the case, but did the delegates vote him? Well, let's talk about the delegates, unfortunately before Oni returned to the PDP, the delegates are there, the executives have been selected by Ayodele Faoshi, so the answer to Ayodele Faoshi, there's no doubt in that fact, if you remember Senator Olujimi that you just mentioned is in court regarding the executive that voted at the primary, they are still in court, and the woman said, she withdrew at the last minute, and said that the primary election is illegal, that the people voting at that primary election is illegal, in fact it's not a contention, by the time you get to court, I mean you are just working straight to the answer for the APC, if eventually Senator Olujimi led a group wins at the court, that means whoever wins the election under the PDP is a non-advised thing, that means that the APC will just walk into the government and be there, and Olujimi has not withdrawn the case in the court, even though the party has instructed that to withdraw the cases in the court, they are sitting in the court, if they eventually wins in the court, that means whoever becomes the gunner of the case is under PDP, it's a non-advised thing. Well that's the probability, it could also turn out that they could also lose, but before Messi comes in, so you said, you're giving us a history, Mr. Yeme Yolanko, you were saying that Shigoni has been criss-crossing carpets, crossing carpets PDP to APC, APC to PDP, and so he left the party, and by the time he came back, the delegates were loyal to Ayodele Faioche, but some would argue that's politics for you, politics for you, maybe he should have gone to Faioche to say, Faioche, I come in peace, let's have a pact, let's have an agreement, I will work with you, let's work together, you know, it is the way it is, and in some record Faioche I said, you can't eat where you didn't sow, that's what he said, you cannot eat where you did not sow, so it's sort of a proverb to say, well, you'll come back, but we've been planting, we've been working here, we've been trying to hold the party down, Faioche has been holding PDP down, even in Nigeria, when he was governor, we see what he did to Buhari, and after he left and all that, so I mean, is anything wrong if he's been able to take hold of the structures, that's politics, that's what everyone wants to do, I'm sure if Shigoni has this way, he would be in Faioche's position to control the structures of the party, so what do you say to that? If he has allowed a free and fair primary, without intimidation, without cohesion, then maybe we'll have seen a different ball game, if this part of father is the one that put the executive there, and the judge of delegates in this table, but you still find out that Shigoni is loved by everybody, even those that voted, apart from the indigestment, I may not want to go into that here on national air, apart from the indigestment, the kind of indigestment that went on on that day, which is absurd, which is evil, which is wrong, which should not be acceptable to the generalty of Nigeria, and I think the youths should come out to say no to such a thing, but that was exactly what happened, people were induced greatly, a lot of gratification went on, just part of father Faioche knew that okay, this executive have put them there, if he didn't do what he did, I'm telling you, we'll beat him hands down, because people love Shigoni, that is the truth. And when Shigoni came back to the party, when he came back to the party, it's not because he wants to face cross or whatever, if it's people are on his neck, when you don't answer to the call of your people, it falls back on you, people are on his neck, we love you, you have done well with us when you were here, we want you back. And unfortunately, at APC, it was rejected, and that was planned by the current governor in APC, that's what I mean, Shigoni should be expelled from his word, Shigoni is not the kind of a man that gets involved in all these dirty things, bribe people, give people money for, no, he's not that kind of person, he's a distant person, he's a classy person, a well behaved person, well nurtured, well tutored, classy. Okay, so let's also talk about the fact that some persons are disgruntled in the party, the likes of Fermi Bamishile, who vows to challenge, you know, the equity governorship primary elections in court, what does this leave you ahead of the elections proper, especially when you have the opposition? The Fermi Bamishile is in APC, and the APC are not happy with what happened in their phone, we have a lot of very, very prominent people that contested that they are on primary too, many of them are saying they're going to court, if you see the MOB that's Michael Oppo, who is a senator, with the chair of the committee on judiciary, he has vowed to challenge the primary at the court, and Bamishile has promised that, that is the affair of the APC, what they're going to court, they want to go to court, I mean it's not dependent on what the court is going to say. So but looking at all of the issues that's going on now, where does this leave the People's Democratic Party with the elections come? So there's no tendency that the internal mechanisms of the party can actually help in resolving the issues before the elections? And the public can come behind me and say that and pet me, let's say Yuribah did that, don't you take me back, that's Yuribah did that, he can't disgrace me in the public and come behind me and say oh and pet me, no it doesn't work like that, it doesn't, it doesn't, it can work, it is my own work, and I can assure you it won't work, and that's why I said okay a lot of clients are going on the ground and by time when what is going to happen in the next few days, we know that we mean business, we want to change the narrative, we want to tell people that you, I or the people cannot constitute themselves as God of policy in the United States, but we cannot constitute themselves as God of policy in the United States, if the people are ready for liberation and we would liberate them, and that's exactly what's going to happen, just wait in another few days, don't follow that plans. Mr. Lank, between Chief Shegouni and Ayodele Faeshe, who is more popular in the United States, since you've been giving us a bit of popularity, there's no basis of comparison between Shegouni and Ayodele, popularity, popularity now, that's what I'm talking about, that's what I'm saying, there's no basis of comparison, that's the truth, from the look up, you have your correspondence in the United States, ask them questions, I'm not just making them out, but the truth is Shegouni is far, far above them, there's a culture, there's a tradition that he's not in Ayodele Faeshe, he's not in him, and whatever you don't have, you can be. He's won election twice in the United States? Yes, he has. You don't win elections two times if you're not popular. I'm not saying no to that. He has won election twice in the United States because he has the opportunity, good enough, but I'm telling you categorically, Shegouni is more popular, and that's why both APC and PDP are saying, please, we don't allow this man to win, and sure that he doesn't win, because they know it's a problem. For you to see Shegouni's name, everybody find out, the civil servants are calling for him, the artisans are calling for him, the market women are calling for him, give us Shegouni, why? He's a gentleman to the court, he has the culture, what we call it, if it's a culture in him. So, I mean, if that's the case, we're just having, you know, a logical conversation now, if he has such popularity, would he be okay if he's dissatisfied with what's going on in his party, and he decides to come to another party and then contest the elections? Do you see him, you know, making any kind of progress? Don't let the cat out of the bag yet, I've just told you, there's a lot of plans going on, just a few days, and you see exactly what the plan is going to be like, just a few days, and then you see, we unfold our plans to you. So you're saying that there's a possibility that he might just come to another party? That's nothing wrong, what's wrong in that? We want to library people, it's a possibility. Isn't that the problem right there, if only he had stayed where he was before? The chances, or had stayed with the PDP, the chances are that... Just maybe he would have his structures of the party having stayed there all these years for now, you know, by now, like Fahime who's been this way for forever, and Fahime who's been the other way forever, being a one-time governor, one-time governor Shigoni, if he probably had stayed in one party, he maybe would have had a greater influence, you'd say. Is it advisable, a good strategy to still keep Chris crossing, you know, from party A to party B? I was good with you to submit, I was good with you to submit, but there's so many issues that arose to the movement that happened. It didn't just happen suddenly, that there are so many factors that are responsible for the movement we were talking about. But nonetheless, the most important thing in this wise is the equity people, it's the delivery of governance, good governance for equity people, and that's exactly what we're looking at. Whether you're doing it in APC or in PDP, or in ACC or DDD, the most important thing is that what does equity people want at this time, and who do they want? And the answer is Shigoni in the list of everybody, and that's exactly what's going to happen. All right, all right, we would like to pull the plugs at this time, Yemi Olayankar, is of a chieftain of the People's Democratic Party in AQT State. We've been X-raying the issues around the rejection of PDP governorship primary results by leading contender in that primary, one-time governor of AQT State, Chief Shigoni. Ms. Amy Olayankar, thank you very much for your time, and we will be surely getting back to you as the events unfold.  Maybe you should start a church or a ministry, but thank you very much for your time. Thank you, thank you for having me, thank you Nigerians, God bless you all. Well that's it on the AQT PDP crisis, and what have you. What fingers are crossed? We'll see how the event of things actually the issue of internal democracy and politics in political parties would always be a major concern where you constantly have strong men who dictate who become what and get what at what point.  I mean, you know, sometimes I ask myself when people complain about politics being played in political parties, I say, but that's politics. It is politics. That's why it's called politics. So we shouldn't be complaining about politics. No, when you're in politics, you play politics. If I'm in a political party, I will want to control the party. So when you talk about politics, you know, because the issue of politics, like what we say is for me, politics is interest. And for every time you have your interest overriding another interest, that's politics for me.  So can we have a time where politics and democracy would be in sync? They're probably not just aligned, but just for the purpose, because democracy would say, let's have a fair playing ground. Let's give people the opportunity to run.  But we need to move over. You know what I think? I think you should climb a campaign stage and do the talking. All right, we will be back and then we'll talk about the joint admission matriculation sport, introducing new subjects into the curriculum up next on the breakfast.


The United States has the tools and capabilities to physically eliminate Russian President Vladimir Putin in case he decides to use tactical nuclear weapons in the war against Ukraine. Ukrainian diplomat Vladimir Yelchenko told his press-TV channel on Thursday. Yelchenko, who was Ukraine's ambassador to the United States in 2020 and 2021, as well as the country's former permanent representative to the UN, stressed that Americans have already explained this scenario to Putin very simply and clearly. Perhaps they took a piece of paper and drew what would happen to the Russian Federation if they used tactical nuclear weapons. Firstly, there will be a physical destruction of Putin. The United States has the tools and capabilities for this. Secondly, within 20 to 30 minutes, the destruction of the Black Sea fleet of Russia will happen. All military groups located near the border of Ukraine will be destroyed. And the next step will be the strikes on all military bases and strategic facilities on the Russian territory, including Moscow and the Kremlin, the diplomat explained. In Yelchenko's words, only conventional weapons will be used. This is not about nuclear weapons, but about conventional ones. Because unlike the Russian Kinzhal cruise missiles that fall on us, American Tomahawk cruise missiles and other weapons are more accurate. They hit the target with an accuracy of 50 to 20 centimeters. All this information has been presented to Russia. After that, talks about nuclear weapons by the leadership of the Russian Federation has stopped. The diplomat stressed.


Welcome to ToffeeTV, it's a deeeeeeealy extra. Look at this. We are. Excellent. Going behind the stories. That's what happens every daily extra. You mentioned yesterday on the news daily for all 13 seconds. Players that are out of contact at the end of the season. This is always the time I think around now where people start getting a little bit worried or cautious about players. Now we're not in a too bad a position. I think the club have started to realise or say for the last 2 or 3 years have started to handle it a little bit better. Make sure that anyone who is out of contact is sorted in plenty of time to be honest. Not only a couple of years now. The one Ross Barclay was the one really where it really stung us. It doesn't really happen too much that way. When we saw Romer and Le Carr could get a year left they made sure that situation didn't get anywhere. Coming up to next summer I think it's Leighton Baines, Phil Jaggelke and one more. Sorry Ashley Williams. Ty's Browning. That's why I completely forgot him. Ty's Browning. So I suppose Baines and Jaggelke signed one year deals didn't they? So they're on basically one year deals anyway. So they're almost out of contact now. Do you think it's too early to discuss their futures? Because obviously coming back last summer. Baines signed 2 years. There was a lot of talk in the summer about Leighton Baines going to America. I mean I think it was more just people putting two and two together because we'd signed a left back and he just happened to be in America. He seems to really enjoy LA. He really enjoys Santa Monica. People put two and two together. It doesn't actually work like that either. You can't just decide where you want to play. So I mean Phil Jaggelke let's just start with him. What would you think it would take for him to get a new contact? It's a good thing because like I said yesterday on the daily.  This is the 11th year. And he knows Aberton and he was there. And the team spirit that Moise created and he had a grand and with Osmond and Aberton all the time and all that. And he's part of the family isn't he? And I think he's a good pro. Jags, I think he's a good defender but I think he's a good pro. But he's 36 and we've got four centre backs at the club now. With Jags shows five with Jags. We've got Michael Keane who's 24, 25. Keatruma and now he's only on loan but he's 23. Yerri Mina who's 23. Mason Holgate who's 20 or 21. And then you've got 36 year old Jags. Now it's easy to go. There's another contract. There's another year but we're in October. Come towards the end of October. Can you see him getting back in Everton's side if the other... Not so much Holgate but if Mina, Zuma and Keane fit. No, but I don't think that matters. I think they'll offer him a new contract if he'll get another year. I think they'll offer him one and it'll be up to whether he wants it or not. Whether he wants to play on somewhere else. The reality is that Jagiel has been a Premier League player for 12 years now. They went down and we got him. So I think he's been a Premier League player for 11 or 12 years. Depends on how many years we've shifted tonight in the Premier League. 11 or 12, whatever. Definitely in 11, so it's 12. So I would think he's pretty conditioned to life in the Premier League now. And it's whether you can take that step and whether you want to take that step. Now we've seen John Terry last season take that step to Villa. And I think Villa would have had a look at Phil Jagiel because they wanted him. They wanted him on by. And now it's that challenge of could he go down. And help bring the team up as he got what is needed. The flip side of that is actually Williams. He hasn't been great at Stoke. And you think, has he got that in him? Or would he be happy enough to go? You know what, to stay at Everton. Another year. I might play, I might play. Training every day. I'm having a laugh with the lads, which let's be honest, is probably what. That's what you get most out of it. As you come into the end. That void of not having gone in somewhere every day and having a laugh with your mates. And younger players and players around. The game almost becomes incidental sometimes. Exactly. But also he's got a lot of knowledge and maybe does he want to go into coaching. Now, if you've got ones to go into coaching, where would be the best place for him to be? It would be at Everton. It would be somewhere where, let's be honest, we always have, we've looked after our own. Some people like that, some people don't like that. So, I think he's got his plot what he wants to do now. And I think he'll get a contract no matter what. I can't see Everton saying anything to the club captain. No, no, thank you. I just can't see, that's just not the kind of club we are.


In the far north-west of Kenya, on a spear of land between the Megila Mountains, bordering South Sudan, Ethiopia and Uganda, is Takana County, home to the second-largest pastoralist community in Kenya after the Maasai. In the 1990s, Takana was the site of one of Kenya and the world's last-known outbreaks of the deadly Rindapest virus, a disease that affects cattle, yaks and buffalo. Although the 90s outbreak was a milder version of the deadly virus, older herders still remember the devastation caused by earlier outbreaks in the mid-1900s. Emoria Aropacol Paracol is one of them. With a mortality rate of up to 95%, Rindapest was the most destructive livestock disease ever known, before it was confirmed globally eradicated in 2011. While there's no more threat of Rindapest in the wild, it's still stored in certain laboratories around the world, and risk exists around the potential for an escape of the virus, whether accidental or deliberate. What would happen if Rindapest re-emerged? There would be very traumatic deaths of livestock because of no immunity and this would kill up to 95% of the livestock, and this would impact food security of the communities. This would impact on their earnings because they would be trade bonds, so they would not be able to sell their livestock. And therefore, it would also affect the economies of the country, and it would require a lot of resources to control and prevent, and, eventually, get the disease. One of the challenges of recognising Rindapest if it re-emerges is the similarities between the clinical signs of Rindapest and those of certain other diseases, including foot and mouth disease or FMD. Kenya's Nekuru County is currently experiencing an outbreak of FMD.  In Rindapest, you don't see foot rations, but you see tear links and also nose discharges. You also get diarrhea in Rindapest and mortality rate is higher. If a livestock owner suspects an animal may have either of these diseases, the veterinary services should be called as they can then institute immediate quarantine so that the disease is prevented from spreading and healthy livestock can be vaccinated. It's important that local communities understand that regulations are in place to protect not only the animals, but also farmers' livelihoods. And in countries like Kenya, where 40% of people are employed in livestock farming, it's critical to the nation's economy. By working together, animal health professionals and livestock owners can help ensure that if Rindapest ever returns, they are prepared.