Well, back with the breakfast and plus TV Africa set for a second discussion this morning and we have a guest already on standby to the justice to this issue of a head of farmer clashes. We'll introduce our guests in a second, but let's quickly give you a background to this discussion. And indeed, the Minister of Agriculture and Rural Development of Nigeria, Bahama Naboba Kar yesterday said that the incessant conflicts between farmers and headers that was threatening food security, not just food security, but also national security in Nigeria. He spoke in Abuja, the regional summit on human and climate security challenges and farmer header conflict resolution in the livestock sector. The theme of the summit was promoting peace and climate security in the crop and livestock farming sectors. The minister called and stakeholders to partner with the government to bring lasting solutions to farmers and headers conflicts in the region. He also said the summit was aimed at providing an opportunity for a dialogue and discourse between the sides and of course on the way forward to achieving peaceful coexistence between both parties that's farmers and headers. Now the minister said the actors, the farmers and headers were the best tool to bring about a solution, a lasting solution to the conflict. I'm glad to say we have joining us this morning to do justice to this particular issue of farmer header conflicts and the federal government's ideas as announced by the Minister of Agriculture and Rural Development and as to whether they can solve the problem. We have Shegun Shopiton, a principal partner, Woodridge and Scott Consulting Lakers. Shegun, good morning to you. Thank you very much for your time. Thanks for having me, Kofi. Good morning Nigerians. Alright, thank you very much for your time. Let's look at what the Minister of Agriculture is saying and as to whether you agree. He says that the farmers and the headers, indeed the actors in these conflicts, are the best tool to bring about a lasting solution to the conflict. Do you agree with him? No, I don't agree. I find that quite incredible, really, to hear such a highly placed government functionary applicator responsibility publicly on an issue that is this important on the national level. How can you in one breath say this issue has an impact on food security and has a heavy impact on national security and then in the same breath, you say the solution to the issue to that problem that is impacting food security and national security should be solved by the people that are involved in that issue? I mean, then why are you there? It's quite mind-boggling, really. The parties are in strife and in conflict for the very reason that they have been unable to solve this problem and it's an age-old problem. It's a problem that will not go away until somebody makes it go away. Somebody has to do something to make it go away.   I'm trying to be charitable with my choice of words because it makes no sense to me. The reason they are fighting and the reason this is going on is because they don't have a solution.  So how can the minister say this? It's weird. We also told that the federal government is soliciting for the support of the international community, development partners and then Nigeria's allies in addressing the farmer-header conflict also probably in a way also asking for international aid, international support to solve this problem. You think that is what Nigeria needs? I mean, look, if you live with issues, all issues to most government functionaries, they will take international aid. I'm sure that they will take international aid for helping Nigeria to breathe the air. Thank God that he means to everyone for free. It's really very, you know, I mean, I don't get it. Look, the problem, the problem and the problems have been well chronicled. They have been well analyzed, you know, taken to shreds and bits and pieces in the last, at least in the last 10 years, not to talk of the attention that this problem has received in the last seven years since the entrance of the Buhari administration because the issue escalated significantly in the early part of this administration. 2016, 2017, 2018, you know, really escalated. You know, so it has received a lot of attention both within government circles, you know, within the media space, civil society, there's been all sorts of interventions and analysis on this issue and I believe that the solutions are very, very clear. It's not to be asking for international aid, international aid to do what precisely? Well, they're asking for the international aid to, among other things, help, you know, recharge, recharge. This is a word to the minister now, to help recharge Lechad because I say Lechad is shrinking and that is a major source of this conflict because Lechad is drying up. They need it to be restored to its former glory. This is what he said, quote, our desire as a nation is for the restoration of the lake in the sub-region to its former glory by recharging it, by recharging it and also preventing further shrinkage. This is evident in our various communities, in our various appeals to the international community, development partners and other allies of Nigeria and Africa for assistance. It's monetary support to, you know, make sure Lechad comes back to what it was before. I mean, I don't think what we need is international aid in terms of funding. I think what we need is international collaboration between all of the countries that are affected by this issue, Lechad, public, Chad, I think Cameroon and Nigeria and then any other country that may have maybe the technical know-how to help with what needs to be done to achieve that objective. So, yes, that's a good objective, but I'm not sure that funding is the issue. I think that if you need it, they believe they need the funding to do this. It's so big, it's neither here nor there for me. I think that the solution, that definitely will be a part of the solution because we know that one of the things that has driven the escalation of this age-old problem has been desertification and just climate change and all of the issues around that. The fact that the Lechad has shrunk in volume by almost like 80%, obviously has reduced the available vegetation in that region for grazing and all of that. So, yes, one can accept that, but not international aid in terms of funding. I think what we need more than anything is leadership and a clear plan, a clear program to achieve that objective with miles, with clear milestones and timelines. So, you can say, oh, within the next 10, 15, 20 years, we would have achieved this volume of recharge of that body of water because, obviously, this is not something that is going to happen overnight. It's not something that can be done in one year, for example. So, where's the plan? Why don't you start talking about money? Anybody that has never gone to look for money from anybody, the first thing they ask is, how do you intend to use this money? Don't ask for a plan. So, where's the plan? Why isn't the minister talking about the plan for the recharging and he's talking about money, international aid? So, for me, the funding issue is not the problem. The real problem is the will and the know-how which regards to solving that problem. Yeah. This was sort of a talk shop, but also a way to see how they can resolve the conflicts. But, like you said, where's the plan? Because I'm wondering if the minister says, oh, we need international support to help recharge the chart and restore it to its former glory and know that this is a big source of the conflict. It's about increasing population, increasing livestock, human beings, diminishing arable and grazing lands in the northern part of the country, industrialization, so a negative, so politically influenced and all that. Will these issues solve themselves if we just say, so these are the problems, or will the international community, international aid, flow to Nigeria by just merely saying, oh, we need it? Don't they need to do something? I think that's what you're saying. They need to start working towards it. If it's desertification, what are they doing to fight desertification and all that? I think that's what you're saying. Absolutely. I read a book recently about some parts of China. You know, this desertification is not unique to Nigeria, to Africa. Other regions of the world have faced this, just now, but in the past, and you know, a province in China actually went about, there's something called the Green Wall. They went about, they went over a 30-year program to re-vegetate an entire province in China. I think between something like 1970, there about, you visit that same region today and you think that you are in a forest. And that place was a desert 30 years ago. There was a very, very clear plan that resulted in that. And the reason they did that was that as a wealth creation strategy, as a poverty alleviation and wealth creation strategy, they realized that a lot of the resources that the people in that region required was not available because of desertification and loss of vegetation. And then they went about a very careful program of re-vegetating and reforesting those places. And today, that plan has been implemented. So that's what we need to see from the Nigerian government, like where is the coherent, very well thought through, very well structured implementable plan to solve in the farmer product crisis. It's not just about talking. It's not about, you know, sound bites that we receive every now and then. It's really when there's a new incident somewhere, then somebody in government will come up and say a few nice sounding to them things. It's about sitting down and, you know, orchestrating a plan, a very well put together plan over an achievable timeline to solve this problem. This problem is not intractable. We just need somebody to sit down and put a plan together and implement it. All right. I mean, it seems to me the minister and his minister of agriculture and road development is just saying, these are the problems. These are the problems. We need to do this. We need to do that. But you are in government. So you are the one to do it. So why do you say we need to develop arable lands? We need to fight desertification. We need to reach out to the, when you are in government, it's your duty to solve these problems. Why are you telling us? That's the last question before you go. A lot of the farmers have been sacked from their farms. Those who have not been sacked are afraid to go to the farm because of these conflicts. In some cases, whole villages have been sacked. They've driven the villagers away and taken over the land. So those who are still there, they wake up in the morning and their crops have been eaten by cows. So what can be done in the short-term to medium-term to solve Nigeria's food insecurity, which is already staring us in the face because of this crisis, apart from even the floods that just recently ended? To be honest with you, we've had this conversation a number of times on different platforms and I tell you there are near short-term fixes for food insecurity because you don't manufacture these things. You don't manufacture rice. You don't manufacture yams. You don't manufacture tomatoes. You grow them and they have a gestational period that some of them, six months, some is one year. Some is an annual cycle. Some have a biannual cycle where you have to harvest in a year. So for some other types of crops, it's four cycles in a year. So these are not things that you can just solve if you have the food insecurity threat is looming. It's because things have happened last year that is reducing your harvest this year. So I'm not sure that there is a short-term to mention. I think what the government simply needs to do is to tackle this issue and solve it once and for all. And it still comes down to the will and the sincerity of purpose from the government. Nobody, nowhere in the developed world the places that we like to be like, do you have people carrying cows, cattle, through forests, looking for grazing pastures and then destroying and rampaging through people's property in the process. Nobody does that anymore. We're not in the stone age anymore. The government needs to come up with a proper ranching template. Thank you very much. Thank you very much. I was just prompted by producers that we have to go. So sorry to interject. I really appreciate your time and of course your expert analysis as always. Thank you, Barbara. All right. Thank you very much. And that has been Shagun Shepidong, principal partner of Woodbridge, Woodbridge, rather, and consulting leaders. And that's the size of our package. I hope you enjoyed the show. And please be reminded, you can follow us on social media, such as PlusTVAfrica, Facebook, Twitter, Instagram, and YouTube. We also have a second YouTube account, PlusTVAfrica, live star for all of us here at our studios in Victoria Island, Lagos. My name is Kofi Bartels. See you tomorrow.


Hey guys, and welcome back to another GCSE revision lesson. Now within this lesson I want to go over one really powerful structural technique that most students often overlook. In fact, they even find it really difficult to even spot it within language paper one inserts. This is for question number three and they also find it really difficult if they do spot it knowing how to actually talk about it when they're answering the Structure question now this technique actually cropped up to me when I was preparing for my Sunday GCSE masterclass Okay, I'm going to be going over with my group students the 2023 November Reset exam and as I was reading the insert and kind of looking through some of the really interesting techniques that this insert used One of the technique that really stood out to me and I thought this technique has come up a few times in past papers But a lot of students just don't really pick up on it It goes over their heads and even when they do they find it really hard to know. Okay, if I even spotted it What can I say and this technique is the use of time as a structural feature? Okay, this technique especially is a really powerful technique to mention in question number three Which is the structure question remember the great thing about this question is it's always the same You're told that you know this insert is other from the beginning middle or end of a novel and you're always asked to Talk about how the writer has structured the text to interest you as a reader now Of course some really obvious techniques that love students and to go for is talking about beginning versus end You know what's going on in the middle, etc Right, however, this use of time this reference to time has actually come up Not only in the November reset paper that students did in 2023 the students that didn't pass their exams But also another really great example of how this time as a structural feature came up isn't the 2017 November a QA past paper exam. This is the one on a girl called Alice who's like digging She's on this excavation mission and it Progresses through time. Okay, and on top of that towards the end of this insert There's also an element of flashback now What I'm going to begin by doing is firstly talking to you guys about how time as a structural feature is a really powerful Technique to firstly look for in extracts, but when you find them this is what you can talk about, okay? So firstly when it comes to time, right? And when you're looking at, you know, any language paper one insert What do you look for to then know that yes, okay in this extra that they're actually using time The author is using time as a really powerful structural technique. This is what to look for. Okay, so for example in this class I'm going to be having The insert that came up. This is the November 2023 exam. There was an actual clock referenced. Okay, it was 10 Then it was 10 30 it was 11 then it was lunchtime Okay, so when it comes to time being used as a structural feature You're literally bells should be going off in your head when you see any reference to time Especially from the beginning of the extract and any repeated reference back to time or even talking about any You know what the what time it is on the actual clock. Okay, so in terms of an actual feature to look for if the extract Mention's 10 a.m. 11 a.m. 12 a.m. 12 midnight 12 in the afternoon whatever it is that is time being used by the author Another aspect that could stand out to you and this is a definite reference to time is if the author refers to the morning Afternoon then evening or in whichever order right? However, if there's any kind of temporal reference to it's the evening It's the afternoon. It's midday. It doesn't even actually have to be like an actual time stamp that is still time That's being used as a structural feature equally. So for example going back to the example that I've mentioned This is an aqa past paper. This is an November 2017 exam where Alice reflects on in the days and weeks and months to come. Okay Time is being used in this particular insert as a structural feature equally for example if the Protagonist within the extract or the main character whoever Considered as a previous night or the previous day or the previous evening or even you know time in the future Right, so for example if you're thinking about some other extracts which talk about things that happening in the future That is still time that's being used as a structural feature by the author Okay, so make sure as you're reading your language paper on extract if some of these techniques Jump out at you. What that means is time is being used as a structural feature by the author now in terms of How it could appear in the paper and in the extract and this is now when it becomes powerful if you point it out as a structural technique Figure out whether the way it's been mentioned in the extract. Is it coming through chronologically? Is it for example in the November reset 10 a.m.. Then 11 a.m.. Then 11 30 then midday or for example Is it being used when the writer or the main character? Refers to the characters flashback or the flash forward. Okay, so again the use of flashback and flash forward Literally it goes hand-in-hand with time being used as a structural feature Okay, then if you spot it, right? So, you know you spot something here and something then you're like great I found time what how can I quote it right because obviously especially if it's running through the insert, right? You can't literally quote reams and reams of words In fact, that's the worst way to quote when you're thinking about you know, how is time used in the beginning? How's time used in the middle and how is time used at the end? This is the easiest way to quote the author's use of time. Okay, so pick something out Which is really really short really brief at the start even for example something as simple as quoting 10 a.m. Okay, then so that will be your first quotation pick out three Okay, then pick something from towards the middle and then something towards the end, right? So again, I'm gonna go back to the November reset paper 10 a.m. Is mentioned at the beginning then towards the middle It's 11 30 then towards the end. It's lunchtime. Okay, so literally picking out the quotation 10 a.m. 11 a.m. Lunch. There's three quotations That's what you would use to argue how time is being used in the beginning middle and end and in this case Not only are you talking about time being used as a structural feature but also you are literally killing like a million birds of the same stone because you're talking about what you think about the bullet points In the question the beginning that's bullet point number one And also how the writer changes the focus. That's bullet point number two in question number three now Finally when you are considering and analyzing, okay, how does this interest us as readers? Why do authors use time as a structural feature? Here are some effects that you can use when you're analyzing and expressing Why this part of the passage or even the entire passage is used by the author in a way that Interests and intrigues us as readers. These are some of the effects of time being used number one It creates a really overwhelming sense of mystery again I'm going to go back to the November 2017 paper on Alice right time was being used then especially this flashbacks Right that she had when all rather flash forward when she thinks about the days and weeks and months to come Right what this does before we even discover what her this mystery item She spots is when she's on this archaeological dig This time the reference to time and the days and weeks and months to come ahead Creates mystery and intrigue for us as readers were then really curious as we read on we think oh my gosh What is this thing this momentous thing that she's about to discover? However, that's not the only effect of time being used as a structural feature another effect that you can talk about is Okay, time being used. Does it increase tension? Does it increase our sense of anticipation? Does it increase our feeling of suspense? Okay, again? You can justify why time is such an interesting aspect that captivates us as readers in question number three another thing you can talk about in terms of effects of time being used is It can time can be used to either speed up or slow down the pace of the text Okay, that's another really powerful effect and finally when we are reading something and then time is shifting through time Right, so for example, you know, it's 10 a.m. Then 11 then 12 then 1 2 3 4 sometimes what that does is we're reading through the passages readers is we feel powerless Right, we're kind of like on this train this steam train when we're reading it and we hurtle forward Right, we know maybe perhaps something terrible is going to happen, but we don't know how to stop it Okay, so also another really powerful effect is you can state and just And justify I'm getting too excited about this but you can say and justify how we feel powerless as the text Hurtles to the end. Okay, so guys as I said Literally, I think time being used as a structural feature is such a powerful technique to look out for and of course if you can even tie it to Flashback and flash forward. That's literally a double whammy for your examiners and your teachers when you're answering question number three of language paper one Okay, so really try your best especially in the coming months and of course if you're part of my group classes I'm going to be going over that this Sunday from 5 p.m But try now when you're reading different inserts and different extracts, right try and see if you can spot Instances of this happening in the text and then comment about it in this way when you're analyzing its effects So thanks guys for your attention and I hope you've learned something new Also, don't forget guys that from Sunday at 5 p.m. This week all the way until the final GCSE exams in May I'll be running weekly English language report on a paper to master classes to make sure you sign up


Oh, righty, welcome to the day and age when a theme park can't announce a 300 foot tall steel structure with amazing elements and have excitement. So obviously Orion was announced yesterday at Kings Island at 10 p.m. And boy, have I seen some of the dumbest comments online about this coaster. Everyone is, and I'm sorry, I shouldn't say everyone. A lot of people are focusing on the negatives versus the positives. People are trying to find every little detail about this coaster and completely shit on it and it's getting really annoying. I'm seeing posts about like temperature change, decreasing the height of the coaster. Get over yourselves. It's a 301 foot, from what I understand, drop. It's 300.9 foot drop. It's amazing. It's something Kings Island needed. It's something that Kings Island fans have wanted for ages and let them have it. It's an amazing coaster. It looks slightly better than Leviathan and Leviathan is my favorite out at Canada's Wonderland which tells me it's going to be an amazing coaster. If you can't hear it in my voice I'm really triggered right now. I'm really triggered. I went through this with Yukon Striker last season, okay? I went through it. People were completely crapping on Yukon Striker. Oh, it's just a dive coaster. The vests ruined the dive coaster, blah, blah, blah. And here we are again. And we're sitting here wondering why parks don't invite enthusiasts onto the media list for parks and are starting to exclude me, sorry, enthusiasts from media events. There's a reason for it.  Now that that's done, now that I've vented let's go over Orion. So Orion is a giga coaster that was announced for Kings Island for the 2020 season and it's exactly what Kings Island needed. It looks amazing. It's got elements that I wish Leviathan had. It's got a taller speed hill which looks absolutely amazing. It's got like this Amberson element that doesn't fully look like an Amberson that's that one element that I really wish Leviathan had as a turnaround. Leviathan has that typical kind of like hammerhead turnaround and I wish it had the Amberson element. And correct me down below if I'm mispronouncing everything. Again, everyone who watches my channel knows I am slightly more GP than every coaster YouTuber out there and fully aware of it. But nonetheless, it's a 300 and one foot drop. It's 287 feet tall and know the argument of is it a hyper or is it a giga isn't valid. It has a giga drop. BNM doesn't even classify giga coasters. So regardless, it's a hyper coaster that is a giga coaster according to enthusiasts. I don't think there's a valid argument to declare it's not a giga coaster. And for those of you literally looking to find any negative detail about this coaster, just stop. Just let Kings Island fans and all the rest of us enjoy this amazing steel coaster. This is like seven and a half hours away from me. I will definitely be there next year riding this and I'm definitely gonna like it more than Leviathan and it's definitely gonna probably be my favorite ride at the park. And it just looks all together amazing and good job, Kings Island for finally getting the giga coaster since the giga right in the stove a couple of years back. I remember that. It's just super exciting. Congratulations to all you Kings Island fans for finally getting the giga coaster. And it honestly looks amazing. Guess the brake runs long but that's because it doesn't have mid-course brake run. And guess what? I mean, fingers crossed. It doesn't have trims by the looks of it. This looks amazing. So all together an amazing attraction. I know this was a quick analysis. I hope you really enjoyed it. I just wanted to get out my event. Exactly everything that I've been thinking. Don't forget to hit that like button, subscribe if you haven't, and share this video for others to enjoy. Have a good one guys. Bye.


Yes, the ghetto prince has just performed with his Javan Javan Si javan, si javan Sorry, it's Monday and it's January It's a dangerous combination Yes, my name is Valentine Or at Color Me Val on everything And you are watching Man Crush Manituna Rap I Monday Vizuri I told you we run from 7 10 in the morning Again 7 to 10 AM is the freshness that is Why in the Morning only at Y254 channel You can find me at Color Me Val Or real quick because we put up a poll By the way, because the discussion is Are women important in a man's life? Do you need a woman Dare king Me si juriyu W2M At Y254 on Facebook At Y254 channel on Twitter Hashtag is why in the morning We put on that poll To say 100% that women are optional Now na nivako kiasi But you can tell me if it's true Or not Now we had the first Think with Joy and at Hilda And then after that we had the interview Of course the ghetto prince and Javan with Joy And then youth in politics by the way Was lovely to see good job Two queens you did amazing And Auntie Hilda took it home At Color Me Val Are you ready to meet my panellist now Are we ready? Almost at Y254 on Facebook At Y254 channel on Twitter Hashtag is why in the morning We put on that poll Talk to me Talk to me is very important So that we can communicate How are you? Hi I have scared you These ones are used to me You look amazing What is your name? My name is Kavata Masti Grace Nice to meet you You want a repeat of the name Rewind please Kavata Masti Grace What do you do Kavata? I am a student I am also a small to medium university Of Kenya Where? I am taking journalism actually He is also a journalist That is why he is very happy He is a nursing professional Where can we find you on social media? On Instagram Kavata underscore On Facebook Kavata Masti Grace I know Uli kuna plan kwongia vibhaya But if they look nice like this What is introduced? Introduced today Sayze wa danganya I am a musician So Call me the only general Follow him on Twitter, Facebook, Instagram And if you go to poetry I will tell you I will tell you If you go to And if you go to Weta And after 2022 But if you go to Weta In 2022 Dropsmike Sorry Sorry Audience Thanks Hi Afu lota jamu Ata una kapua Iskwe una kapua Introduced today My name is Isaac I am a print journalist So I think that is enough for today So you can find me on Twitter And Instagram at So I wanted to say We made a trend in Kenya So musicians when they come please They start with Kenyan music I was told that because I didn't hear Kenyan music So the first thing you play Kenyan music Instead of singing Hordari You sing Miacheni There's something like that Lambalolo by But it's Kenyan No We are going to celebrate our Kenyan artist That is all of them So we are going to start Today We are okay Alright So we prepared a couple of sides With a couple of quotes Of how women are important to men I wish We are going to put them up And then I am going to shoot them shots At But in the meantime Do you think women are necessary In a man's life Very Because I normally say that If you look at how men Were created At some point I feel that They were created As people who are Somehow lazy And that you confirm when you get Into a house of a man who is single Is disorganized But once A woman comes into your life You start seeing some organization of things Some of us wouldn't be Looking like this But because of those people I know We are like this So they are very important actually So I can see the woman behind you You can see this is a woman behind She's doing a good job I follow you have something to say If you I will take you to my place Okay We are a generation What now We can't make money If we want to make money We have to make money If we want to make money But I don't want to make money You want to make money I want to make money I want to make money I want to make money But I want to make money Wow Do you agree with the sentiments? No, I think you're wrong An upstreet woman Will help you manage your financial Where are they? Brokers No, they are all over No, they are all over You only need an upstreet woman Not a girl Then give me one Did you hear You need a woman, not a girl Why do you say that?  Yes I want to make money with a woman How will you know? Because I want to make money Always enjoy by the looks I want to make money with a woman Yes I want to make money I want to make money on Facebook I want to make money on Twitter Hashtag is what in the morning I promise to slides The first one Tada He who finds He who finds The wife must submit He who finds a wife What is good and receives Favour from the Lord Proverbs 18 verse 22 Afulu Mekubaliyo story He who finds a wife finds a good thing Una jwa shida izi watuwa na indika izi Okay, wa indishi Zuni parables Zuni butu zunina hawa malizi Wa sasa wewe Isaac, kwa kwa kwa kwa kwa kwa In fact, when your pastor Let me now preach the gospel to this woman Amen It's good you've taken it from the Bible But I would want to Just mention a quote from One of the Greek philosophers He's called Plato He said that By all means, I mean a man shall marry If you find a good wife You'll be happy If you find a bad one You'll become a philosopher So how do you become a philosopher You'll be like Afulu now You're telling all negative things About women So I think the one you find wasn't a good one But I would like to confirm that Women are different There are good women out there There are bad ones It depends on which one do you land on So as far as I'm concerned I think I have the capacity to say Women Are important because the one I have is important We can see the suit Yes So you know When you see poor women How do you know if a woman is good Or not Remember when I was a baby Straight from a woman How as a man How as a man Very good question This is how Even when we were born Some of us couldn't speak English But we went to school and land There's a school for women I'm just saying that is how We got to where we are now Even when you're getting Into a relationship You have to study You have to study the person You're in a relationship You do some kind of research That our people have today Is that you don't research About somebody You want to be in a relationship So they end up Having wrong people in their life So you can only Find or realize A good woman through study You date each other For some time You study what this one likes What she doesn't You weigh positive And negative If positive surpasses the negative That's a good one Let us be practical I like being practical So positive So there's a good woman And there's a bad woman And now we are studying So the positives Let's say she's understanding She's patient And all these things And let's say maybe negative So she became matumbu And she says that she is in a relationship So what happens Is that negative over weju? What is it going to be? It is it going to starve? Is that a negative That overpasses a positive Or how do you play this game? In that case I would say Like matumbu It's food And then there are some people So if your bae doesn't like it Because of one or two reasons You buy what she can cook And she cooks it for you What is matumbu? It's food It's food Now see There's a problem here Yes Why do you have a problem? Okay You started inium You started inium The problem is With what you had You had a problem People didn't understand That what's going on The problem is What to say You had a problem And things have changed Now you have a problem Mom and Dad pass away You can't change People don't understand This is understandable 2. 2. 3 2. 4. 5. 6. 7. 8. 9. 10. 11. In 14. 15. 17. 18. 19. 20. 19. 20. Wale, Y music is 19. 20. 20. 21. Wale is 21. How do you feel about that? Receiving that as a lady? Well, I think he's just negative about women. I'm not negative. I'm just saying the truth. Sayi ziti mena kukati uta hiki ya boxi yungu. Uta nga liya nini dressing code kitu ya kwanza. Na kia tu. Bua yu sayi kia tu sayi kablatwendele. Azi kwa? One thousand five hundred. Azi kwa sawa? Nini loan. Sayi niki kwa mbi asina pesa. Uta nuni fikiri ya azi? Ha, ok, well. Kama hauna pesa. If I'm in love with you, I'll be there to help you build. Ndaku wa poj sayi dianit pateyo pesa pamoja. Like we grow together. But where's the love coming from if he's broke? See, it has to take time for you to love him. No, like you don't love a man because of what he has. Like love is just something that cannot be explained. It's just a feeling, you know. Ya, so if he's broke and I'm in love, I'll just work things out with him, grow together. Ya. Kusuna wa tu apateya kwa. Kusuna sayi generationia sayi ya kuna dema posingo. Oh. Ume uleza. Siyeti uleza kwa usimifanya risachi angu. Nimi katini. Maidata. Nani amiyangchi. Sensas. Alright. As we get to Afulu's problem place out there, if you have just a feeling about how nice Afulu looks, slide into our DMO. Wait for it on Facebook, at 254chano on Twitter. Hashtag is my Indian morning. Next slide. A man with dreams needs a woman with a vision. A man with dreams needs a woman with vision. Chinak bali Afulu. Ya na kata. Aji saa saa. A man with dreams needs a woman with the vision. Sikua datta manome tu anizu vision bada konazo tu. Manome tu kaziya tu niku dandi amat. Hazak, help me here. Afulu is becoming a comedian. Mazenali aso kusimaisi comedian tu kiaza shu. No, I'm curious. Kwa na takalili? Okay. The point is well put. I agree with it. So in that, there are two different things I want to talk about. Number one we have dreams. Number two we have vision. If you have a wife who has a vision and you also have a dream probably the two of you are good to go. So the wrong one comes when you have a dream she doesn't have that vision. You cannot go anywhere. So when it comes to the point I think I'm totally in agreement. But I also have to say something about Afulu has talked about money and in those other properties some things she was in whatever. Women sometimes tend to focus on what somebody has. But you've just heard her saying it's not about what a man has. No, because you know Afulu has told us that he has done a research. Okay. I've also had some experience from friends and older. But what I would want to say is that love should be beyond what I have. It should be real. So that if you love someone she'll just say that she can contribute to the success of that person. I don't have to have something for you to come into my life. You can as well come when I have nothing. We make it together. That would also be nice. So if every woman can have that mentality we are going to get rid of being single being whatever. I applaud your train of thought but kuna waschanu kunjonezakata. Have you ever seen a scenario in which una, let's just speak to the queen for example you two are together, okay? Mkae mseme, okay we're going to work this out we're going to do this together we're going to grow.   Maas! Mepia na! All right Yeah, white faithful of Facebook at White faithful channel on Twitter Just as Kenya got independence, women Also need independence from women We are tired of kunyo nyuwa And freedom is coming tomorrow Aluta, continue your brothers Buyu wa fulu wa na seima taki ma dem na meshinda, my inbox He he Akin ni katia Akin ni ya mbe ni kikubaliata ni unliya gari Amma ni tumes screenshot Mami ya tume Bebi, unne choma Oni blogas Unne choma Unne choma Mm, mm I thought I didn't need a woman in my life until I saw that queen you have there on set Haia Kindly ask her to send her contacts again Uno na no to mi mani No na ni kiyoa 2020 Mano tu wa miwa sa utapatitu Weyem wanyu na tumiwa screenshot apa sayi Mano tu wa kwa miwa sa utapiyambu Satsakia Namuza hopu, umbonu na rukes tuwaji Fulu ya screenshot Please, please, please Ja na Kun namstia na ali kuna vision Akadetum dosi wa Amazon Sayi ni bilion Nia hi vision Inafat chunguze sana Mato from Thika Eh, tuna wa oni Oni lumenat Aje, sasa Uskwa evo Then we have Talia, Owizop, of course Oh, so the question is Are women necessary or are they optional? La nukenda Facebook na Twitter We have a poll So umtama sama, of course Banat To continue with the life cycle Nia ni wascana tuniwa kuprocreate Kupop babies The eyes are cute We are coming, we are coming back Cynthia Morgan, I see you locked in from Kamarok Kariuki wa gatanga una fukpe wa kitu nawe tufe You're very active, I like it Tyler Owizop again watching from Bamburi, Mombas Tabelwa On Twitter Ibuned sets We are just necessary for progression That's a bad way of thinking Afolo na kaziye tuna kuza Wani mulu kwa mako yoni ni ni nia Ami nuku tumbuizu wa gu Oh Uto ngei vo ya ni kika ko Memba utataba mendsiti sa Ok. Ya. Os sila zimishi. Nitres. Nikitu mungo no apati ya pende. Ya. Ya. Oh. You wanna say something? I think that's a very ugly way of taking women. But. Ya. Ok. Tu wa fichu tuwambia kwa maskio. No. No. No. No. No. No. No. No. No. No. No. So w金ia tzeo mmingi bibili ya manze? Nyeha. It is not good for the man to be alone. I will make him help need for him. So apu wigni mn nye baki mma .. On the last ama I say ma .. And here we go here we go. Are you ready? Are you ready? represented. Is not good for a human being? Is not good for a human being.oqu Eric, Ahe and the Lord God Said. Nya lotu m increased vanilla manze. It is not good for the person to put his head in Altiaje. Man батy ajie. Yes. And he gave .. And the Lord God said. It's not good for a human being alone. Hey, we need help out here, is this a crisis? I'm there, help, a fullo, brush up on our Ciri, this is Genesis No, I'm not going to mind someone's mistake So, no matter what, it's up to me. It's all right Help him I'm God when He says help Oh, thank you Nani, Is this a helping? Um, woman said, okay, so I'm not just going to say this Because he never asked anyone for help Ouch, ouch, ouch, ouch So can I trust you? I personally think like women We come into a house and build a home in it, you know. Like sabili sama, ukingia nyumba bachela, like it's all messy, but ukingia nyumba nyikona a woman in it, like you will feel that umf of a home, you know. It's even more homey. And kwa nyumba, monoma is the head and the woman is the heart. Thank you. Una kubali sayi. Monoma niki. Kichua. Next slide please. Strong nanavision.   Kizungu vene mechapa vizuri afu lu ta kachan. Kujia kwa ba usiku. Una jadu wa kinga na protecti wa. Una ngeze wa pombe una kujia zia kila kitu. Una lala bibi amenda mwingine. We know you. Oh no. Isaac, please help me. Okay. I don't agree with you. Afu lu is a psycho fan. He's crazy. He's not crazy, he's mad. But let me say this. We are told, it's from the Bible, that God gave us women to help us. So we should really know how are they supposed to help us. Number one, the man will not have everything all the time. But the woman will have something at some point. So you cheap in. That is one of the help. When it comes to procreation, people want children and women help when it comes to giving birth. So that is important. So when I hear people like Afu lu speaking the way they speak, they tend to think they can also give birth to children. But it's not easy. Okay. We are going to summarize, give me your last thoughts. Afu lu anza? Okay. Ladies, please. So it's time you sort yourself out. ... ... That's why I wanted him to start. Kuna kwa ente tu wa pohen. Okay well, I think it's high time for you to find real women. Be the one, what would change me? I knew this was going good. We'll talk about that after this show. So you have to find yourself a real woman. Okay, for me, I just want to say that respect is important. And ladies please if you can manage to be independent. Be independent so that men don't disturb you around. If you're independent, you can argue something out. If you're not, if you're dependent, Afulu is coming for you. There's a saying that you should be a woman that a man needs. Not a woman that needs a man. Yes, if you're independent, it will be true. And my friend is 30 years old. I'm a buyer. Afulu mute. Afulu mute. This is so musinatembera. Yes, yes, yes. Hey, hey. If you're not, if you can manage to be independent, you can argue something out. Be independent so that men don't disturb you around. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute. Afulu mute.


Okay, I think the mic is on now. All right, well, let me begin by thanking the organizers for the invitation to come to this beautiful place. I've been really enjoying all the talks so far. And I would like to talk about boundary and boundary and playing the fact criticality in the 3DON model. So I have to apologize from the very beginning that there will not be very much quantum in my talk, but there will be criticality. So let me begin by explaining what do I mean by boundary criticality. So imagine you have some bulk system that is tuned to the bulk critical point. And for definiteness, let's assume that is described by conformal field theory. And suppose I want to study this system in the presence of a boundary. For instance, I might be interested in correlation functions of operators on the boundary or mixed correlation functions involving operators on the boundary and in the bulk. So that's the problem. And there are a few general things that can be said right away. The first is that in general, the operator spectrum on the boundary is distinct from that in the bulk. So operators on the boundary have scaling dimensions delta hat, which are distinct from the scaling dimensions in the bulk and the fusion rules are also distinct and so forth. So that's the first comment. Second comment is that given a bulk universality class, the boundary universality class is not unique. They can be distinct boundary universality classes corresponding to the same bulk universality class. And you can tune between those boundary universality classes by changing the details of the Hamiltonian near the surface. And we will see some examples very shortly. Now, you know, this problem of boundary criticality is very old. It goes at least to the 70s and 80s, where it was considered in the context of classical stat mac. But there's been renewed interest in this problem coming mainly from two directions. The first is just improved understanding of conformal field theories coming in part from the numerical conformal bootstrap program. The other direction is from topological phases. So we know that the topological phases are gap in the bulk. They have a finite correlation length and they often host some kind of protected boundary state.  For a very long time, it was thought that the protection of the boundary state relies crucially on the bulk being gap. But later it was understood that there are some cases where actually the boundary mode survives in some form even when the bulk gap closes. And this goes under the name of gapless topological phases. And such gapless topological phases are often quite difficult to quite challenging to understand. You know, they lie squarely in the domain of this boundary criticality. So my interest in the subject came from the direction of this gapless topological phases and of course, quantum states of matter. But today I'll be mostly talking about just classical step-map model where I realized that something has been, some important qualitative aspects have been missed in the literature. And in fact, I'll be talking about the simplest classical step-map model there is which is the classical ON model, right? So I will be mostly considering bulk dimension which is three and so this is a cubic lattice. And there are classical spins that is length one classical vectors sitting on the sides of this lattice. They have n components and they're coupled with nearest neighbor ferromagnetic interaction. And I want to consider two geometries. A semi-infinite geometry where there is a boundary and I will allow the coupling on the boundary to be distinct from the coupling in the bulk. And the second geometry is this plane defect geometry where instead of a boundary I have a defect plane and again I allow the exchange coupling between spins on the plane to be distinct from the coupling in the bulk. So I'd like to understand the phase diagram of this system. Let's begin with this case of a semi-infinite geometry. Well, if the bulk dimension D is greater than three then the phase diagram is essentially understood. So first of all, what is the phase diagram in the bulk? There is a paramagnetic phase of high temperature. There is a paramagnetic ordered phase at low temperature and there is a critical temperature, Tc, here. Now let's ask what happens on the boundary. Well, if the surface coupling K1, if the surface exchange coupling is not too large then the boundary will order at the same temperature as the bulk. And this is known as the ordinary boundary universality class. However, if you make the surface coupling large enough then the surface can order at a higher temperature than the bulk. So as we load the temperature, first we go into a phase where the surface is already ordered and the bulk is still disordered. And then subsequently, once we reach the bulk critical temperature, the bulk orders in the presence of an already ordered surface. So this is known as the extraordinary boundary universality class. And finally, there is this multi-critical point known as the special boundary universality class. Each of these classes is a distinct boundary universality class corresponds to a distinct boundary conformal field theory. All the exponents are different for them and so forth. All right, so this is the situation in dimension greater than three and it's largely understood, yes? Is it a very, very suffocated one? Where? Is it a very suffocated one? I believe it's actually here, but it's not very important. This critical value, of course, will depend on dimensionality and it's order one. Yeah. And the extraordinary case is going to be seen larger than the three to two times three to two times three. Well, sorry, what? Oh, so there was a very critical thing. Well, maybe here, very good. Yeah, so I think the question was what is, whether the critical temperature in the extraordinary regime is larger than the bulk critical temperature. So there are two critical temperatures here, right? There is a temperature at which the surface orders and it is higher. Oh, okay, let's try that. Yes, and then there is a temperature at which the bulk orders, right? So these two temperatures are different. No, I mean the temperature I think is five. No, it's the same temperature, right? Because this is some bulk property. You can think about order parameter very, very far away from the boundary and when that order parameter acquires an expectation value, this is the bulk phase transition, it doesn't really care about what happens on the bone. Boundary, like the fact that the external, because the boundary already ordered. In the thermodynamic limit, no. In finite size system, yes. All right, so this is what happens in three dimensions. There is one more interesting point, which is that so far I've considered the situation when there is no symmetry breaking. Either on the boundary or in the bulk. Now, let's imagine that you actually break the symmetry on the boundary by applying a magnetic field on the boundary. Well, then it's believed that you have just one boundary universality class for any value of the boundary exchange coupling. And this is the so-called normal universality class. Don't ask me. Well, actually these names have a history going back to criticality and fluids, but so this is the nomenclature. And it turns out that if the bulk dimension D is greater than three, then the extraordinary universality class here without the symmetry breaking field is essentially the same as the normal universality class. That is, it doesn't matter whether you break the symmetry on the boundary explicitly or spontaneously, once you have a boundary order parameter, you essentially have the same universality class of the transition. So this is essentially understood. Now, the interesting thing is what happens if the bulk is three-dimensional. So this will be the subject of my talk. And well, if you have ising spins, then essentially the same story goes through. You have a same phase diagram. You have this surface phase transition where the two-dimensional surface undergoes an ising, two-dimensional ising transition. Everything essentially the same. Now, if you have x-wise spins, that is n equal to two, the situation is already more interesting because you know that in two-dimensions, you cannot have a true long range order. You can only have quasi-long range order. So this phase here at large surface exchange is a quasi-long range ordered phase. And this green line is a two-dimensional costal stylist transition. So now you ask the question, okay, what happens when the bulk orders out of this surface phase with quasi-long range order? And turns out, yes, Liang? Well, yeah, the question from Liang is when I say extraordinary transition, whether I am referring to transition on the boundary or transition in the bulk. And well, this extraordinary transition is exactly when the bulk is tuned to the bulk critical point. So the bulk has an infinite correlation length here. And I'm interested in calculating correlators on the boundary or involving both the boundary and the bulk when the bulk is already critical. It's a boundary in the gapless system. Yeah, the bulk, definitely. If the symmetry is broken in the bulk spontaneously, then of course you also have an order parameter on the boundary, but the scaling of that order parameter, you can ask if you go a little bit below TC here, how does the boundary magnetization scale in T minus TC or TC minus T? And it will be a different exponent depending whether you are here or here or here. Even, well, once T is smaller than TC, bulk magnetization induces a surface magnetization, of course, because it's proximity, proximity effect, if you wish. Yeah, are there questions? Okay, so let's continue. So the question is what happens along this orange line and in the vicinity of this orange line in this case? And this question actually has not been answered in the literature. There have been some discussions and actually some suggestion that perhaps along this orange line, even though you don't have a long range order in the bulk, maybe the bulk fluctuations induce a true long range order on the surface. No theorem against that, as far as we know, it would have been kind of an interesting way to bypass Merman Wagner. Well, of course, Merman Wagner does not strictly apply here, but it turns out what I showed is that doesn't quite happen, although the system gets close to a long range order along this orange line, but the spin-spin correlation function on the boundary doesn't quite go to a constant. Instead of the case very, very slowly as a power of logarithm of the separation along the boundary and this power is universal. So I'll explain where this result comes from. It's a consequence of a renormalization group analysis. So this is already kind of interesting, but let's continue. Yeah, and I call this extraordinary log universality class in order to distinguish it from the conventional extraordinary class where the correlator on the boundary goes to a constant at large separation. Okay, now let's discuss what happens when N is greater than two. So here, you think maybe N equal to Heisenberg spins, right? So here we know that when the temperature is above the bulk critical temperature, the boundary, the two-dimensional boundary will have a finite correlation length. You can have neither quasi-long range nor a long range work. So it's completely consistent that the phase diagram could look like this. They're just a single boundary universality class, the ordinary universality class for any surface exchange K1. However, it's also not ruled out that you could have two distinct stable boundary universality classes and the special transition between them, even though all of this would connect to the same phases above and below the bulk critical temperature. So which of these two scenarios is real life? And if you look at the literature, I think people assume that this minimal scenario has to be real life. Well, that turns out to be wrong. Turns out that the answer depends on the value of N. If N is large, but finite, indeed this minimal scenario is realized. However, let's be serious and let's treat N as a continuous parameter. Then it turns out that when N is slightly above two, you can show convincingly that the second scenario here is realized and you have the extraordinary log universality class where again the spin-spin correlation function on the boundary decays in this logarithmic manner. You might say, oh, what is this limit? N is really an integer. Well, from numerics, it seems pretty convincing that N equal three is actually in this regime and I'll discuss that shortly. Yeah. So let's discuss where all of these results come from and they come from the following renormalization group analysis. So what you would like to understand is what happens in the regime when the surface coupling K1 is large, that is there is a possibility of some kind of extraordinary phase. And well, in this regime, there is a very strong tendency in the surface layer towards local, at least local magnetic order. So let's describe the surface layer by the following nonlinear sigma model, two-dimensional nonlinear sigma model and the coupling G will be small when K1 is large. And before we, of course, the interesting question is what happens when this two-dimensional surface layer is coupled to the bulk fluctuations? But before we answer that question, let's remind ourselves, if we just had a purely two-dimensional layer, what would happen? What is the IR fate of this theory? And we know very well, Polikov has told us that this coupling constant G, even if it starts out small, in the infrared it runs to infinity and this signals the appearance of a finite correlation length in accordance with Merman-Wagner theorem. Okay, so how is, now the real question is how is this RG flow modified when we couple the surface layer to the rest of the system? So let's try to answer that question. So this is the action for the surface layer. Then for the rest of the system, the rest of the system is going to be described just by the bulk or three model with the ordinary fixed point, boundary fixed point. And finally, there will be some coupling between the order parameter N in the top layer and the boundary field of the remaining system. So that's this coupling. And well, let's work around the fixed point with G equal to zero, so it'll be coupling. And let's actually begin by just freezing the fluctuations of this surface order parameter. So G strictly zero, then this surface order parameter of course acts just as a symmetry breaking field for the rest of the system, boundary symmetry breaking field. And as I told you, the system will flow to what I call the normal boundary fixed point. Right, remember, normal boundary fixed point is one where I apply a symmetry, explicit symmetry breaking field on the boundary. And interestingly, a lot is actually known about this normal boundary fixed point. In particular, we know leading operators appearing in the operator product expansion of the bulk or the parameter, right? So imagine I take a bulk or the parameter and I take it close to the boundary, I should be able to expand it in terms of boundary operators. And this is this bulk to boundary operator product expansion. And I have to distinguish between components of the bulk field parallel and perpendicular to the symmetry breaking field on the surface. So I take the symmetry breaking field on the surface to be along the Nth direction. So then the component phi N, well, it should acquire some profile, right? Some expectation value away from the boundary and it's a power law profile just given by the bulk exponent of phi. And so the identity operator appears here in the operator product expansion of phi N. And the next operator is believed to be so-called displacement operator, which has a protected dimension of exactly three. It doesn't get renormalized. And for the transverse components of the order parameter, the leading operator here, again turns out to be a protected operator, which has a scaling dimension of exactly two. This protected operator is an N minus or N minus one vector. And we call it the tilt operator. All right, so these are known facts. Now these coefficients A, B and B actually are universal once you normalize your bulk and boundary operators. Appropriately, we don't know this coefficients exactly, but we have some knowledge about them from large N expansion, from Monte Carlo and from numerical conformal bootstrap that I'll describe later. Okay, so this is the normal fixed point, right? So this is what happens when they just freeze when they just freeze the fluctuations of this field N. Now I'd like to make the coupling constant G of the nonlinear sigma model finite, small but finite, and allow for fluctuations of N. Well, so there are these fluctuations pi of N. And well, naturally, these fluctuations will have to couple to the operators of the normal boundary fixed point that I introduced here. And in fact, the only coupling that you can write down is this coupling pi dot T, where remember T appears in the operator product expansion of the transverse component of bulk or the parameter. Okay, so this is actually the action I'll consider. Now you might say there's something very strange here. You start with an O-N invariant action and then you work around a fixed point where N, which breaks the O-N symmetry to O-N minus one. So you don't have explicit O-N symmetry anymore. You only have explicit O-N minus one symmetry. So how to restore the O-N symmetry where is the O-N symmetry hiding? And turns out that the O-N symmetry actually fixes the value of this parameter S to be expressed in terms of the universal constants in the appearing in the O-P. So S is not a pre-parameter, but is rather fixed like this. And there is a rather simple argument for this, which is again, imagine you freeze the fluctuations of N and take N to point along the north pole, well, then the bulk or the parameter, the expression value of the bulk or the parameter will also point along the north pole. Now what happens if you rotate the surface field a little bit, the bulk field should also rotate just by O-N symmetry, but so it should acquire a profile like this. Okay, but you should also be able, if it's a small rotation, you should be able to do perturbation theory in pi to obtain the bulk or the parameter profile. So it reduces to this correlator. This correlator turns out to be completely fixed by conformal symmetry up to the O-P coefficient B-T. And then doing this integral here, you get the relation that S is expressed in terms of A-sigma B. So this is the action I'll be considering then. And now we are in business and you see there's only one tunable parameter in this action which is the coupling constant G of the non-linear sigma model. So all that remains is just to compute the better function of this parameter G. And while there is a contribution to the better function just from the non-linear sigma model that we discussed a little earlier, Polikov's contribution, and it's right here, this N minus two G squared, but there is a new contribution coming from the coupling to the bulk. And it comes simply from this very simple diagram for the two-point function of N. Why? Yeah, so I'm working usual perturbation theory where I expand N around the north pole and this is the, yeah, good question. Right, so this diagram is very easy to compute and what it does, it gives you a new contribution to the coefficient of the better function of G squared term, which is related to this coupling S. So now, oh, and one more comment, the anomalous dimension of the field N actually remains the same as it was in the stricter 2D non-linear sigma model. Doesn't get affected by this coupling to the bulk to this order, yes? You just expand. You use this expression for N and you expand the D mu N squared, right? So N has length one, so that's why it's non-linear. And that's why when you expand in pi, you get this extra, you get this extra here. All right, so now we are in business. We just need to analyze the consequences of this randomization group flow and the consequences just depend on the sine of alpha, namely if alpha is positive, then G will run to zero logarithmically in the infrared. This is like, you know, pi to the fourth theory in four dimensions and integrating this RG flow together with this anomalous dimension for N, which is order G, you exactly recover this correlation function on the surface that decays as a power of logarithm and the power Q is given in terms of alpha like this. All right, so this is my advertised extraordinary log fixed point. This is how to understand. On the other hand, if alpha is less than zero, then we're kind of back to the situation similar to one we had exactly in two dimension where the G equals zero fixed point is unstable. Where does it flow to? Well, we will discuss further. All right, so the main question now becomes whether alpha is positive or negative. And for general values of N, I can't give you an exact answer, but there are some limits that I understand. First, if N is equal to two, then the only contribution to alpha comes from this coupling to the bulk. And this contribution is manifestly positive. So for N equal to two, we definitely have the extraordinary log phase being realized. That's good because for N equal to two, remember the topology of the phase diagram, the KT transition required a separate extraordinary phase. And here we learned that this phase must be of the extraordinary log character. On the other hand, when N goes to infinity, we definitely alpha becomes negative. We can come, there are one, yes. So for N going to infinity, I can compute this A sigma and BT, this universal constants in a one over N expansion. And then alpha is given by this expression, so it's negative. So alpha has to change sign as N increases from two to infinity. And the minimal assumption, which actually seems to be supported also by numerical conformal bootstrap that I'll show is that alpha changes sign just once at some value N equal to Nc. So then for N smaller than Nc, the extraordinary log phase is realized for N greater than Nc, we don't quite know what happens. All right, yes. So now this is all theory, but can we check this numerically? And actually shortly after my, and of course, the most interesting question is, what is the value of Nc? And in particular, is N equal to three above Nc or below? Because for N equal to two, we know that we have to have the extraordinary log phase for N equal to three, we don't quite know. So shortly after my paper came out, there was a detailed study of the problem for N equal to three for the Heidenberg model by Francesca Paris and Tolden. And he actually found a special transition on the boundary by looking at the Binder ratio and extracted boundary exponents at the special transition. And he also studied the regime of large surface coupling. And in this regime, he found that his numerics was consistent with the extraordinary log universality class. He saw a stiffness that diverges logarithmically, which is exactly what one would expect for the extraordinary log class. And he also saw a two point function that roughly decays as a power of logarithm. And he actually extracted this power. And from this power, he extracted alpha. And this is the value of alpha that he got for N equal to three. And then this group, Hu, Dang and Ut have repeated also the calculation for N equal to two for the X, Y model. And again, they found that for the large surface exchange, the results were consistent with the extraordinary log universality class. And they extracted this universal constant alpha and it's given here 0.27. Okay, so this is kind of nice. So in particular, it means that Nc is greater than three. This extraordinary phase for N equal to three. Now, as you remember, a prediction of my theory was that this number alpha should be given in terms of this universal quantities, A sigma and Bt for the normal boundary universality class. That is the universality class in a symmetry breaking field. So I convinced Francesco to also do the simulations with the explicit symmetry breaking field on the boundary and extract this universal coefficients. And after he did that, and took the ratio, this is what he obtained. So it's actually the agreement is quite good. Specifically, especially given the fact that it's very hard to fit things to this power of log. So it's quite surprising that the agreement is so good. And then together with J. Padajasi, Abhijit Krishnan, Elia Gruzburg and Marco Mineri, they also studied the normal boundary universality class using numerical conformal bootstrap. And they also obtained estimates for this universal constants, A sigma and Bt. And they're given here. So it's actually, this is not a super accurate method. It's not like the bootstrap one has in the bulk with the pop point function. But again, the agreement is actually not bad. And we expect the agreement to get better actually as n increases. So from these calculations, while here it looks like nc, we can put in any value of n. So it looks like here nc is of order is something like five. Actually from monomerics, we believe it's probably somewhere between four and five. I think there is a question in the chat from Andrei. Oh, I can also open it up actually here from the question from the, on the, on the slide. On the slide, on the nc alpha square, why on the same slide? Yeah. So let me repeat the question. So Andrei is asking about this alpha is given here, but also for n to infinity, I write it like this. So this result here comes from computing this a sigma nbt in the large n limit, which can be done by studying the ON model with a symmetry breaking field on the boundary in the large n limit. And this is the result to first sub leading order in one over n. There is, there are also order, there are also even more sub leading terms that I haven't included here. So this is only true for n going to infinity. Yeah. I hope that that clears things up. So yeah, just to mention this bootstrap work here was done with, was done with my wonderful collaborators who taught me all about numerical conformal bootstrap, J. Padayazi, who is a graduate student of Ilya Gruzburg at Ohio State, Mark Aminari, who was a postdoc at Lausanne and now has moved to postdoc position in Geneva and Abi Krishnan is my career student at MIT. All right. So this is about values of NC. Now we can ask what happens as we cross NC? What happens as we get into this regime where alpha is negative? And well, here the physics will be in the vicinity of NC, the physics will be controlled by the next term and the beta function for G, right? Because the first term vanishes at n equal to NC. And the physics will depend on the sign of the subleading term. So on the sign of B. And well, there are two scenarios. If the sign is positive, then what happens is we find an infrared unstable fixed point for n just below NC at weak coupling. And we expect that this fixed point just corresponds to the special transition between the extraordinary log phase and the ordinary phase that we know exists for n equal to two. And then we expect that it just continues, moves to weaker and weaker coupling until at n equal NC it collides with the extraordinary log fixed point and annihilates. So that for n greater than NC, we only have the ordinary fixed point left. So this is the simplest scenario. If this coefficient B is negative, the situation is more complicated. Namely, this extraordinary fixed point moves away from G equal to zero for n slightly above NC. And then presumably it would have again to annihilate with a special fixed point at some yet larger value of n. Because at n equal infinity, we know that only the ordinary fixed point is left. Nevertheless, at this point, we cannot compute B for arbitrary value of n. So in principle, this scenario could be allowed. Now what we, so what we want to know is B at n equal NC. And that's hard, but what we, yeah, so this is again the picture for the two scenarios. Now in the n, and this is the K1 over K plane, the red line is the special transition. Yeah, so we don't know the value of B at n equal to NC but actually recently we were able to calculate it together with ABI in the n to infinity limit and you see it's positive. So it's actually pointing towards this simple scenario. In fact, if you look just at a two-dimensional non-linear sigma model, it's given by this expression. So including the coupling to the bulk only makes it more positive. You see it's four thirds instead of one. So yeah, so this scenario is favored and it also seems to be favored by the numerics, although probably more study is necessary. How am I doing on time? Yeah, so in the remaining five minutes, let me very quickly talk about the other problem, the other geometry that of a defect plane. So, all right, so same problem, but actually the phenomenology is a little bit different here. So here, on this defect plane, I have this coupling K1 and there is one point where we know exactly what happens, which is when K1 is equal to K, right? That's the situation with no defect. And that situation just corresponds to a bulk ON model and perturbing away from K1 equal to K just corresponds to inducing the five squared operator or the thermal operator on this plane. And this is a relevant perturbation. So it's going to drive you away from this K1 equal to K fixed point, but it's the only relevant perturbation at that point. So this is actually the special fixed point in this case is K1 equal to K. So if you have the special fixed point, it's natural to assume that different signs of perturbation away from it will lead to different phases, which I think was not appreciated in the literature. Somehow people may be thought that you have ordinary phase on both sides for N greater than two. But so actually this is the natural phase diagram with the extraordinary phase being realized for any value of N. There is no, we don't expect a critical N in this case. And indeed that will be confirmed by RG analysis. So what are these fixed points for the plane defect case? Well, the ordinary fixed point is quite simple. This defect plane just cuts the system into two halves and each of the exposed boundaries now has an ordinary universality class and the coupling between them turns out to be irrelevant. Same with the normal fixed point. If I apply a symmetry breaking field on this plane, it just cuts the system into two normal boundaries. And again, the coupling between these two boundaries is irrelevant. Now what about, yeah, so for the Ising case, then the extraordinary fixed point will be just the same as this norm. Now what about for N greater equal than two, right? So we have to write a theory which is along the same lines as I wrote for a semi-infinite system. But now the order parameter on this plane defect can couple to the tilt operators from both sides of the interface. And because of that, there is this extra factor of two in the better function here. And it turns out that even when N goes to infinity, alpha remains positive. So alpha is expected to be positive here for any value of N and the extraordinary log phase will be realized for any N greater equal than two. All right, so the phase diagram is, as I said here. Now something actually very interesting happens when N is equal to infinity in this model in this plane defect, which is that this entire line becomes a line of fixed points. There is a exactly marginal boundary coupling at N equal to infinity. And the exponents on the boundary change as you change this boundary coupling, which I parameterized by mu here running from zero to one. And then at one end of this line, you have the ordinary at the other one, you have, well, extraordinary or normal. And then at mu equal one-half, you have the special. And then the scaling dimensions on the boundary change as you change mu. But this is only the case, you know, this is kind of special case N equal to infinity. Once you make N large, but finite, you can calculate the flow of mu, the better function for mu. Actually you can calculate it to order one over N exactly. And we did this with Abbe, kind of nice exercise. And it turns out that this line of fixed points is lifted to just ordinary, special and well normal. And then the approach to this normal is exactly this quadratic one that we expected from the other RG approach. So this is very non-trivial check of the RG that I described that works for any N and this large N calculation that only works for N large. All right, let's see. So I guess I'm running out of time. There is this, yeah, so for these problems with the boundary, there is an analog in two, we know that for two-dimensional CFT, there is the central charge and the central charge decreases monotonously under renormalization group flow. So for this problems with the boundary, there is some similar boundary central charge that increases monotonously under boundary RG flow. And for this line of fixed points, we were able to calculate these charges. But maybe I'll skip this part. So let me conclude by saying that, well, the simplest classical static model, the OIN model, actually the story of boundary criticality was not fully understood. I think in the classical model, numerics, analytics and conformal bootstrap are now converging, but there are still things to understand, namely precise value of NC and yeah, and well, which of these two scenarios is realized. So more Monte Carlo and bootstrap I think will be helpful. But there are also quantum analogs of this boundary story that there is a lot of Monte Carlo on, but which are not fully understood analytically. So that would be a separate story that unfortunately I do not have time for. Thank you. So I noticed that when you're talking about the boundary, you're only considering homogeneous transitions in the ising nematic iron-based superconductors. There are these persistent claims that there's actually a surface smectic at temperatures about the ising nematic transition. That would be like an n equal one because it's fixed by ising. And could there be actually finite momentum transitions which would go above? Finite momentum, so density wave transitions. That's what they keep on claiming happens and it's not understood by. In principle, in a general microscopic model, yes, but in this particular simple model, no. Well, this is the same type of problem. This is the boundary conformal field theory except in two dimensions, well, in one plus one dimension, we know much more because of verisorosymmetry and because, yeah, there are minimal models and we'll see equal one theory is essentially understood in higher dimensions, it's much harder, right? So this is kind of, even in the simplest stat-max model in three dimensions, already it's much harder to even nail down the phase diagram. So this is kind of an attempt. Yeah. Why is it plus minus and minus? There is some integral that needs to be done and this is the precision to which I was able to make the, to do the integral. Now I suspect that it's actually a four thirds. I wasn't able to do the integral analytically. Now in this plain defect problem, you can also ask what is the G cubed term and there we do know it analytically and it turns out to be five thirds. So I have a very strong suspicion that for this semi-infinite geometry, it is exactly four thirds, yeah. Any other question? Okay. If not, let's sign it again. Hi. I guess there is a question in the chat. What do you want from this? One thing more. Yeah, I don't know. Do I? Again, I can maybe answer during the Q and A session.