I'm Salvatore Bobonis, and this week's problem of the week is statelessness. The modern world is composed of countries. In fact, the division of the world into countries is a major distinguishing feature of modernity. And countries are governed by states. So what happens if a person somehow falls between the cracks of the world's countries? What happens if a person is not recognized as a citizen by any of the world's states? And what happens if a country just doesn't have a state to run it? All of these situations can result in statelessness. Statelessness is a serious social problem affecting around 10 million people scattered throughout the world. A state is a legal bureaucratic entity that governs a country and its population. For example, Germany is a country in Europe, but Germany has had many different states running it over the years. First Imperial Germany, then the Weimar Republic, then Nazi Germany, then West Germany, and now today the Federal Republic of Germany. We're all states that govern the territory of Germany in Europe. The Federal Republic of Germany has a government, just like all states do, that can change from year to year. Right now the Chancellor is Angela Merkel, but next year the Chancellor could be somebody else. The government changes, but the state continues. The state is a legal bureaucratic entity that collects taxes, that sends out social security checks, that enforces the law, and all of that goes on even when governments change year by year. A stateless person is a person who does not hold citizenship in any state. Most of us have citizenship granted by the state in which we live or the state in which we were born. Some people have citizenship in multiple states, but a small number of people are not eligible for citizenship in any state. This usually occurs when a state categorically excludes people from citizenship. Statelessness is a particular problem for the Palestinian people who are refugees from the 1948 creation of the State of Israel. Many Palestinian people live in states like Jordan and Lebanon and Syria on the borders of Israel. But those people are not necessarily citizens of Jordan, Lebanon, or Syria, yet they have no other state to be a citizen of. Even Palestinians living in the West Bank and Gaza are not citizens of any state because the West Bank and Gaza are territories they are not recognized as states in the interstate international system. A second group of stateless people are people of Russian nationality who found themselves living outside the borders of Russia when the Soviet Union was dissolved in 1991. These are mainly people who were citizens of the Soviet Union, of Russian language and Russian background, who lived in places like Latvia, Estonia, or in some cases Central Asia when the Soviet Union was dissolved. Mostly those in Latvia and Estonia wanted to stay on in those countries which eventually became members of the European Union, but Latvia and Estonia will only grant them citizenship rights if they learn the local language and pledge allegiance to the new countries of Latvia and Estonia. Many people of Russian descent are unable or unwilling to learn the new local languages of the countries in which they live. And thus have been denied statehood or denied citizenship in the countries in which they live. Yet they are not Russian citizens either. They are people of Russian background who live in other countries. Sometimes people become stateless due to contradictory citizenship laws. This often happens in cases of migration. Some countries grant citizenship on the basis of parents nationality. Other countries grant citizenship on the basis of birth. If you are born in a country that grants citizenship on the basis of parents nationality, but your parents are from another country, you may find that you don't qualify for citizenship where you were born, and you don't qualify for citizenship in the countries of your parents' birth either, and that can leave you as a stateless person. The United Nations has been able to document at least 3.5 million stateless people, but it estimates that there are up to 10 million. No one knows the exact number for sure. I would suggest that there are actually many more stateless people in the world if instead of taking a legal definition of statelessness, we take a social problems definition. When we move from the theoretical world of international law to the practical world of social problems, many people are effectively stateless even if they legally have states of citizenship. Take the difficult case of Syria in 2016. The Syrian state only controls about one-third of the populated area of Syria, the area marked in blue-green on this BBC map. The rest of Syria is controlled by rebel groups and other separatist factions. In international law, only the government of Syria can issue Syrian passports and confer Syrian citizenship. So what happens to the two-thirds of Syrians who live in places that are outside the jurisdiction of the government of Syria? In international law, they are not stateless, but in practice, they can't get passports and they have no government services. They pay no taxes to the government and they receive no benefits from the government. In addition, there are now millions of Syrians who live outside Syria as refugees. Many of them are also in effect stateless. So statelessness is much more of a practical problem or a much bigger practical problem than the theoretical status of statelessness in international law would imply. In fact, there are entire states that are clearly states from a practical social policy perspective that are not recognized as states in international law, thereby leaving their residents effectively stateless. For example, in the Caucasus, the country of Georgia in international law is recognized as having the boundaries marked here. But there are two territories of Georgia, Abkhazia and South Ossetia, that are effectively independent of Georgia and are not governed by the Georgian state. Both Abkhazia and South Ossetia have independent states that are recognized and supported by the Russian Federation. There are about 300,000 people in Abkhazia and another 50,000 people in South Ossetia. These people have passports issued by Abkhazia and South Ossetia, but these passports are only recognized in Russia and a small number of other countries. In effect, the entire populations of Abkhazia and South Ossetia are stateless from the perspective of the rest of the world. And if inside their own countries, they are members of their respective states. There are also large stateless populations in the making. One notorious example are the Rohingya people of western Myanmar. The Rohingya people are mainly Muslim people with close historical cultural ties to areas that are now inside the country of Bangladesh. Now, I should note that the name Myanmar is what the country calls itself, but the United States and many other countries do not accept the name Myanmar and still use the colonial name Burma for the country. Similarly, the Rohingya live in what is officially called Rakhine state by the Myanmar government, but many countries, including the United States, still use the old colonial name Arakhan state. In any case, the Rohingya live in this area in western Myanmar and also in cities in other areas around the country. There are around two million Rohingya people who are denied citizenship by the government of Myanmar and have been denied citizenship for some 35 years. They are stateless in the sense that they can't get passports and they are denied government services by their own government, yet they live in Myanmar. They have not left the country and become stateless persons in the rest of the world. The rest of the world considers the Rohingya people to belong to the Myanmar state and be citizens of Myanmar. Human rights activists regularly call on Myanmar to extend full citizenship to the Rohingya minority, but these calls don't really solve the problem. Since nobody is willing to force Myanmar to extend full citizenship rights to the Rohingya, in fact, what would it even mean to force Myanmar to extend full rights? No country is going to invade Myanmar in order to protect the Rohingya. No country is going to place extreme economic sanctions on Myanmar that might push Myanmar to extend citizenship rights to the Rohingya. And even if countries were willing to do that, we should question whether or not that would be correct. Would it make sense to punish the people of the entire country of Myanmar because the Myanmar state refuses to grant citizenship rights to two million of the residents of Myanmar? That's a difficult question. We could offer refugee placements as displaced persons to the people of Rohingya background in Myanmar, but no country wants to take in two million Rohingya and give them asylum. So what do we do? This is a very difficult question. In fact, even if Myanmar did give into international pressure and give formal citizenship rights to the Rohingya people, it's very unlikely that the Rohingya would be accepted by Myanmar society. There have been massacres of Rohingya in Myanmar over the last five years, and there's every reason to believe that massacres and severe discrimination would continue even if the Rohingya were granted citizenship. So if these are not ways that we can solve the Rohingya problem, what can we do? Well, I think that first we should ask, who are we? I'm delivering these lectures as an American university professor at the University of Sydney. I live in a very privileged place with a very privileged life. I am not willing personally to host two million Rohingya asylum seekers. I know that the countries of Australia and the United States, with which I'm connected, are not willing to take in two million people, and yet if we don't take in two million people, how can we expect Myanmar to adequately perform its responsibilities? After all, Myanmar has just come out of five decades of military rule. It's a post-colonial country that is barely held together as it is, fighting a major insurgency in the north of the country. Income per capita in Myanmar is just $1,500 per year, and the government itself, the state of Myanmar, collects only 4% of GDP in tax revenues. That's among the lowest tax takes in the world. To put that in perspective, the United States, which is a comparatively low tax country, takes about 35% of GDP in taxes. Most European countries take between 50% and 60% of GDP in taxes. The Myanmar state hardly has the capacity to solve the problems that exist within Myanmar, of which the Rohingya problem is only one of many. Three takeaways. First, statelessness is a serious and growing problem that results when states deny citizenship to some of their country's residents. Second, civil wars like that in Syria can make millions of people effectively stateless, even if under international law they theoretically have citizenship. And third, the Rohingya people of western Myanmar are a stateless people in the making that are clearly on the road to statelessness, unless something is done very soon, either to grant them citizenship rights within Myanmar or to accept them and give them asylum in other countries. Thank you for watching this podcast on statelessness. To subscribe to my newsletter, go to salvatorbebonus.com, where you will also find topical articles on current affairs posted.


What does money play mean to you?  I'm playing again. I got a bro like dog.  Honestly mad streams have been good. I said since the beta man streams have been good I'm not mad about it. I like playing Madden. I had the streams have been good. We've got good viewership good interaction We're making good ad money things are good boys. I'm fine playing Madden Little little do you guys know I kind of enjoy this thing called Madden here, you know I wouldn't see about work on W. I wouldn't it Good pass rush from the boys right there. Good pass rush. Good job. I mean boys. We couldn't like The Eagles 14 and 2 14 and 3 like who really beats the Eagles this year the chiefs they play in Kansas City That could be a tough game Is it real dog like how are we getting shetted by three people like this?  Make things interesting here Shed I don't know how my running back in my in route. We're so close to each other right there though But that was a pick we could score get the ball a half things be looking up for boys. That was tough All we gotta do is go for a pick there. I think everybody I don't know what happened. Oh, I thought my right. I thought it was my running back. Damn. That was a big play, too I really thought that was my running back. It's that though. Hey, you see that Oh Baby good read dubby. God. That's a good read. That was a good read that guy's like never that guy's never the read So I mean did the same thing that time my running back if my running back in my damn in route there aren't right next to each other It's easy reads. I'm kind of glad he acrobatic because if you did like a mid zone knockout He might have knocked it out instead of trying to dive for that's why we are down 14 it's okay to go for two people go for two because I Mean, even if you don't get the two point conversion, which I didn't the first time you get a chance to do it again Guys playing so tough and like oh my god Ward just like jump from ten yards away Dog like how are you with routes beating us this bad?   Now he has all day. This is the best spinner pass protection ever Dog oh my god Just do Star to spin spin or spin one time Spinning that's what I love to see Of course this guy randomly is getting blocked the hell and then randomly just shows up Like he get he got knocked on the ground right there and then randomly got up and played Now Greg Olson said I should go for two now. I don't think so I don't think I go for two now because I wanted him to sweat I want him to sweat. I want him to sweat I feel like I have a better chance to get in the ball back if I if I'm down one store I have a better chance to get in the ball back. I don't want him to return this kick I could kick it out of bounds, but with mutt kickers. That's pretty much I'm gonna try to kick it as deep as I can. I got it. I got to kick it out of bounds here Give me a second time out really Now I'm gonna kick it deep. Hopefully out the back of the end zone But yeah, I'm not gonna be able to kick he's gonna run it back because they're in the chat listening Give me a thumb ball on this. Oh, he doesn't run it back. Okay more on so I get an extra time out. That's good Like this is real life that come on man, holy Let's go big sack Vic. Wow spinner spinning for once. Let's go boys Spinner is spinning for once Let's go baby. Those failed two pointers are hurting us. Okay before they go run through mean Joe green for me before That's what we love to see you do man See my you want to do something right there Bro these dudes are like come on with the shedding, dude No way we drop that you get me at the five right there man all together that's that's tough God, it might have been a dot everybody has 15 knockout. Are we not in? AJ you sold bro.  He held the ball. He said now. I'm good I hold the ball behind the line coach. I love the game, man


This is an MR of the brain and face in a one month old with a asymmetric growth on the left side of the face left cheek region. There's thought to be a mass, but if you look at it on this T two weighted image is relatively homogeneously hyper intense. It's hyper intense and T one weighted imaging suppresses on fat suppressed T one weighted imaging. And there's no suspicious enhancement within it. So this looks at first like a lipoma, which is a benign entity. Obviously there may be cosmetic implications, but it's a benign entity. There was more to it than that. So if you look at the T two weighted image, I look at the cerebral hemispheres, the right cerebral hemisphere, it protrudes a little bit over to the left and midline. So if you actually measure it, the right cerebral hemisphere is a little bit larger than the left. The right cerebral hemisphere look at the T two weighted image of the white matter. It's a little bit more hypo intense than the left. Additionally, it's a little bit more hyper intense and T one weighted imaging than the left cerebral hemisphere white matter. And it's noted that in a one month old, this T two hyper intense T one hyper intense appearance of the white matter is normal so while anytime you see an asymmetry it's hard to know what's abnormal. The left hemisphere seems to have a normal milanation pattern. Now, if I go out more superiorly, I'm seeing irregular sulcation pattern. So this patient has what looks like poly microgeria. And again, this hemisphere looks a tiny bit larger. And while there's a little bit more hypo intense appearance on T two and hyper intense appearance on T one weighted imaging of the white matter that can be seen with accelerated milanation. Well, accelerated milanation and asymmetrically enlarged hemisphere or portions of a hemisphere is a finding that can be seen with hemimegalonecephaly. Now hemimegalonecephaly does not even have to involve the whole hemisphere. It can be sub hemispheric hemimegalonecephaly. Then this patient has poly microgeria, which also can be associated with hemimegalonecephaly. So let's take a look again at the cheek mass. So a biopsy of this showed that there was a mutation in the pick three CA gene. What does that mean? Well, the pick three CA gene is noted to be associated with a rare congenital overgrowth syndrome, known as cloves syndrome CLO VES. That is an acronym for, you know, congenital lipomatous overgrowth. There's vascular malformations epidermal nevi and skeletal abnormalities. So this lipomatous overgrowth here of the cheek is actually related to clove syndrome with this pick three CA mutation. We just went through that acronym. And I don't see anything necessarily about the brain malformation, except remember one of them is overgrowth. And you could say that there's overgrowth of the brain, but it's noted that the pick three CA mutation is actually a different mutation in the pick three CA gene is associated with hemimegalonecephaly. So it's not unexpected that someone with clove syndrome may have hemimegalonecephaly. It just happens to be contralateral to the lipomatous overgrowth on the face. So this patient has a facial lipomatous overgrowth. Right sided hemimegalonecephaly with polymagogyria and accelerated myelination in the setting of clove syndrome.


What's going on guys? Welcome back to another video. So my baby here is actually feeling a lot better as you guys can see. Her voice is getting better. Yes, finally getting my voice back. I'm so happy. She still has little coughs throughout the night which you know startled me when I'm sleeping but you know it's getting better. We're getting through it and I'm really happy that she's actually feeling better. Guys today we're gonna be playing a game. We're gonna be taking turns. We have these upside down glasses. I'm gonna show you guys right now. It basically turns everything upside down when you put the glasses on. And we're gonna try a bunch of different tasks while wearing the glasses.  You think so? I was gonna ask you that. Like I feel like it's gonna like. Have you ever done like the drunk glasses? Yes, I hate that game. So I feel like it's gonna be like that but I feel like I don't know.  So instead of looking up you kinda gotta look down. It's gonna be weird. I don't know. I'm excited. Yeah, I'm excited too. We have a bunch of different tasks but let's get into it. Okay, so these are the glasses and so these are the challenges we're about to do. So first, we're gonna try to pour the Skittles that Isaiah ate by the way into a bowl. I have a sweet tooth, leave me alone. He loves Skittles so whatever. That's my best candy ever made. Then we're gonna try to write our name on my board. We have to pour the Skittles in the bowl but then we have to pick out a specific color. Oh yeah, I forgot to mention that. What color should we pick though? Let's do yellow. Yellow? Okay. So we gotta try to pick a yellow one out. So then we're gonna write our name on a white board and next is probably gonna be the hardest one in my opinion. Pour a bottle of water into the cup. I feel like that's gonna be really hard only because this cup is glass so it's see through. Yeah. So I feel like it's gonna be really hard to see but it should be fun. Another one is we're gonna try to throw a ball at each other and obviously like it's gonna be hard for the person who's throwing it and to catch it as well. And then for a little bonus, we're gonna walk the plank and try to walk in a straight line. I can't even walk in a straight line in general so. You would fail a sobriety test. I know. Like that's gonna be bad. The cup is gonna be like, yeah, you know what? Just put your hands behind your back. Yeah, I don't know bro. You might as well just do a cardboard. So to figure out, because we only have one pair of glasses, to figure out who's gonna wear the glasses first, we're gonna play rock, paper, scissors, shoot and whoever loses wears the glasses first. Okay, let's go. Ready? One time? Or best two out of three? One, one. One time? Yeah. I'm picking rock, I'm letting you know. I win every time. He always says he's picking something before we go. I'm picking rock. Rock, paper, scissors, shoot. I should have lied. See, this is what happens when you try to use reverse psychology on someone who studies psychology. She knows when I call BS and all that. But whatever, I'll wear the glasses first. Here we go. Let's get the glasses out of the box. What are these cards? Create your own challenge. Oh, they got little challenge cards in here. Man, our challenges are better. How do you take these out? They look like goggles. They do look like goggles. My grandfather saw them this morning and he was like, what are you gonna go swimming now? Bro, they're for a video. Like, let me be a YouTuber. Give me that. Okay, they go like this. Never put on goggles before? Janice thought, oh, sheesh. How is it? You're extra. No, that was a little extra. No, but it does look crazy in here. I got tight.  I'm looking down and I'm getting really unbalanced. Oh God, I'm scared now. Now I'm not being extra. That's actually very trippy. Oh man. Go ahead and adjust my goggles. Yeah, adjust all goggles. All right, I think I'm good. You're ready? How do I look? How do I know if I'm looking at you right?  I can see you, but again, everything's upside down. So it's like, I don't know if I'm really looking at you like level. Like, is this level?  It's my head up or down. I'm serious. Is it up or down? I'm not being extra, I'm being serious. It's my head up or down.  What about here? Yes. This is level? Yes. Bro, I'm looking at your feet. Oh, this is crazy. This is about to be wild. Try to write your name. Yo, what the, I can't. Okay, hold on. Yo, guys, I recommend, this is not a sponsor.  This is actually very crazy. He said this is not a sponsor. No, for real though, because I don't want them to think like, oh yeah, we're just promoting a toy. Like, nah, bro, this is actually really fun. Like, imagine doing this drunk. No, I can't imagine that. That's fun. All right, hold on. All right, okay, I think we're good. Ready? Yeah. Seriously? Can I take the glasses off and look? Yes. That was so easy. That's an N. That is an H. Yeah, but look, I wrote it like that. This is how I would really write it. That's way different. I feel like it. I'm gonna do it again, hold on. I wanna do it again. I can't have terrible handwriting, so it looks bad both. All right, all right. No, chill out, chicken scratch. All right, good. All right.  Yo, it's actually, see, it's like a fancy. Yeah, but it's at a slam.  It's actually not that easy. It kind of like- I'm not even talking trash. I'm saying that looking at it now, it looks like you just try to write it in cursive. Yeah, but I'm not trying to do that. It's literally just going in a slant. I'm gonna try to write it in cursive now. Let me see. Oh my gosh. I just messed up my hairline, didn't I? Oh my god. All right, let me, see what's hard is actually trying to locate the whiteboard. You're gonna see what I mean when you wear these. Like, you look down and it's not really down.  That's not that bad. I thought it was gonna be way worse. That's not that bad. Wait, that is atrocious. I'm gonna say Dorea. Dorea. You're gonna see how hard it is when you have the glasses on, all right? All right, so pass it over. I'm gonna go ahead and make mine how I would regularly use. Geez. Don't come at me, all right? I know a lot of you guys are probably like Gen Z, so you guys probably didn't even practice cursive in school. I had to practice that because I'm 35 years old. Everybody's gonna believe you now. I'm not 35, I'm 25. All right guys, so she's about to put on the glasses. Go ahead. Oh, I don't like this. It's crazy. Pretend like you're looking down. Tell me that's not weird.  Oh, I don't like this. All right, now look at me straight in the face. You see guys how she's angled up? It's not, I'm telling you, this is crazy. Can you see your eyes?   Okay, get the camera out, I'm scared. You look like you're in a fishbowl. No, I just feel like, I don't know. Like, I've had nightmares like this. All right, go ahead. Grab the marker and we'll go ahead and write your name. Oh no, I hate this. I told you it's not easy.  Okay, are you ready? You gotta go ahead. Oh, I told you. Wait, wait, I can't see.  I'm left handed, so I feel like it's backwards. Everything is backwards. Oh. Babe, you only got a J, come on. What the heck is that? John, Johnny, Janio, babe. Take your glasses off and look at that. Are you kidding me? What is that? You did worse than me and you were talking all that kaka. No, I was saying yours looks good, like you did it easy. All right, but you're trying to say I was trying to write it fancy and all that, like as if I meant, look at, what is that? This is really hard, like I'm not even exaggerating. I told you. Wait, is it because I'm left handed? No, wait, guys, every time something happens, she blames it on her being left handed. All right, I'm not even gonna look. It's probably, it might be better that way if you don't look. Oh, that's actually not that bad. That's not that bad. You were trying to decurse him, right? Yeah. All right, that wasn't that bad.  It's because I didn't look. All right, try one more time. I would have to start here then. Why? Because. Why are you starting, you're going backwards. No, I'm not.  Look. I'm not. Oh my gosh. What are you doing?  I'm trying to cause this rain. I'm trying to cause this rain, shoes. Babe, what is that? God, yeah, take it off. Period. It's not backwards? Not through here? No, yeah, not through here. That's insane. This was hard. All right, babe, your next challenge is the Agua. You want me to pour the. All right, you need to start. Ready? Here we go. The glass is on. All right, I'm gonna go over here. Beesmote activated. Let's see. Okay, all right, hold on. We're off to a best. I'm nervous for you. I'm nervous for myself. Where's all the ball? I got it. Let me get that. Here, why do you need it? You're not doing that one right now. I'm trying to move everything out of my way. Okay. All right, here we go. Here we go. See, I'm gonna zoom in. Nope, wrong way. Ooh. Ooh. Wrong. No, wait. Oh my God. Hold up. Hold up, I think I got this. Am I doing it? Oh. Am I doing it? Oh. Am I doing it? You're laughing. Am I doing it? All right, you know what I'm stopping. Oh, I'm over here thinking I'm putting it in the glass. You just let me pour it all over the plate. What am I doing with this? I didn't see nothing going in. Yeah, at first you thought I was, I thought I was doing it the whole time. Bruh. How did the captor do it? You keep laughing and all that. I wanna see when you try. I have a tactic. What's your tactic? I don't know, but I'm gonna figure it out and I'm gonna pour it, watch. I'm gonna do better. You know what?  I wanna try it now. So, yeah, go ahead and put the camera down, get your guess out, because this is gonna be crazy. Guys, watch, I'm gonna do better. Oh no, it's on the chair. God. Not the Persian leather. Oh, I'm dead. If I went ahead and I capped the bottle because she has to go through everything that I went through. Go ahead, miss, I can do it. I know I can. That's the spirit. Let's see. Go ahead, it's tough, isn't it? All right, I'm not gonna lie. The fact that you're actually doing it is actually getting me really upset. Told you I could do better than you. It's actually getting me really upset. Mm-hmm.  Oh, yeah. That's it. Whole bottle. Bro, how? Period. How? Which is mad, is you serious?  We just lost a couple of subscribers. Yo, how'd you do that, bro? Cheers. I don't even know where the camera at. You think you're better than me? So next one is the Skittles. You ready? Skittles? Yup. I think this one's gonna be pretty easy. All right, let's see. Pour them all in. Bro, I hear it falling in the plate. I can see it. It's not falling in the plate, it's everywhere. You can see it. Oh my God. Oh, oh my goodness. All right, and a yellow one? Mm-hmm. Hold up. I think if I get closer to it, it'll be easier. OK, look at my neck like that. Shit, that's about a full. OK, hurry up. I'm trying here, hold on. Boy, it is only one. Ha, why is it wet? Why is it wet? I don't know. Is the bowl wet? Probably. Look, they're all like changing colors. They're all right now, and now you're doing the most. No, seriously, look inside. They're changing.  Yeah, because there's probably water in there. From when you pour the water everywhere. That was good. Yeah, trash. Do you see the mess you've created? The fact that you let me. I told you to stop. I didn't stop because I heard him falling in the thing, so I'm like, yo, I'm doing it. Why are you looking at me stop? You're looking on the floor, and then it's about to have a freaking heyday. He's going to have a whole, like, sugar rush. He's over here looking at his lips already, right in it? Right? Guys, that was such a fail. It wasn't, though. Mm-hmm. Oh, OK. All right, Miss Skittle, let's see you do it. The intensity. Miss Skittle, come on. Why are you calling me a Skittle? You think you're good? You think you're better than everyone? Bro, how? How? Pick the yellow one. How many? All right, all right, all right. No one likes to show off. No one likes to show off. No one likes to show off. I'm not eating them, though. You want one? Maybe? Give me that. Ew, ew. Yellow's the best flavor next to green. This is so easy. All right, you know what? Cut it out. Cut it out. No one likes to show off. This makes me dizzy. No one likes to show off. Wait, do the dance. Ew. He has the glasses on. And then now we're going to do the catching. So you ready, babe? You have to catch the ball. I think so. I really don't talk it to Nene. All right, hold on. Where are my hands? All right. Where you want them to be? Go, go. Illuminati. Wait, are we too close? Are we too close? No. All right, go ahead, throw it. Ready? Throw it.  All right, I'm going to throw it. OK. Ew. All right, the throw is that, Nene, where are you at? Don't make me, Nene, I'll chase you with these on. Give me that, give me that. Oh, he's out. He's out. Wait, where? What is it? Nab it. Give me that. By the way, this is his toy.  All right, let's try this one more time. The throw wasn't that bad. I just want to try catching it again. OK. The throw wasn't that bad. Who are you starting to? Nene, give me the ball. Give me the ball. Give me the ball. OK. All right, you got it. Take that. Ready? We're going to try catching it. You have to catch it. Yeah. One, two, three. Where's the ball? Oh, shoot. Wait, go try to catch it again. This is my last time trying to catch it. OK, ready?  All right, you try it. OK.  I'm scared. Because I feel like this was the toughest one. OK. Ready? And boom. Exactly. Exactly. What do you have to say for yourself? Nene, no, give me. He's playing soccer. Give me the ball. Give me the ball. I'll just go stand here. All right, let's try this again. Here we go. One, two, three. No, I told you. Nene, give me the ball. Give me the ball. You know what? I don't even care. I got the yellow one. Ha, ha.  They're upside down. That's insane. Ew. All right, last time. Ready? Wait, go. Here we go. Three, two, one. You hit my shoulder. Nene. All right, hold on. I want to try one more time. You just collected them over here in the corner? Three, two, one. Time you, man. It's not that easy. Yeah, no, this is hard. I failed. Now for the bonus round. This is a straight line separating our kitchen from our living room. And Isaiah here has to walk the plank. Bro, this is going to be easy.  I had to do this one time. Whoa. I got pulled over. Really? Yeah. All right, we'll get on that line. No, it was a lie. I never had to do this. Let's say we all had this conversation later because I never heard of this. No, I never had to do this. All right, ready? I don't get caught when I do stuff. All right, let's go. Ready? Mm-hmm. OK. Mm, mm, mm, mm. Chill. Don't make sound effects, because then I'm going to freaking lose it. All right. Let's go. Try again. Mm. I'm doing it. Mm. I'm doing it. I'm doing it. Nanny, the sound effects is not needed. Here we go. Oh, oh, he said you don't know how to walk the plank. You almost knocked me over. Nanny said you don't know how to walk the plank. All right, here we go. Oh, teach me how to doggie.  Teach me how to doggie.  I have to pee. I got this, man. I know I can do it. Oh, my god. It'd be a nice move. All right, one more time. This is my last show.   Give me complete silence. I know I could do this. OK.  I'm just like, you hear it. Put the goggles on. Put the thing on, yo. All right, let's see you do it. Let's see you freaking walk the straight line. Yeah. Yeah, yeah, yeah, exactly. Look at you. Exactly. I told you. I told you I can't walk in a straight line no matter what. That's why everybody's talking. Yo, Google Yard and stuff. Look, you're not even stepping on the line. Yes, I am. You see this foot? Yeah, it's on the carpet. I'm not even on the line.  No, man, you wanted to have sound effects and commentary with my story. Now it's, look at you. What the heck is that? Just stop. Just quit.  I'm feeling better than you. No, you're not. I think I did way better. All right, man, you need to see. Yeah, huh? Look at you. What are you, a crane? You're still unbalanced. What are you doing?  No, I didn't. Yes, you did.  This is bad. Look at you. What's wrong with you? Babe, you're mad crooked. What are you doing? I'm a ballerina. Oh my god. This is horrible. No, I'm done. All right, that's it. That's it. That's it, that's it. I did better than you. No, I don't think so. Yeah, I think so. Guys, comment down below who did better with this test.  I think I got the line walk. Everything else you got. Well, no, actually, I got the drawing, the name part too. I'm good on that. No, you were sitting here dougie, he said. All right, well, I added a little pizzazz, all right? All right guys, so that is it for today's video. If you guys liked today's challenge, that was honestly way harder than I thought. I thought it was gonna be hard, but that was actually really hard for me. Yeah, for me it was hard too. I got, I think, two out of the five. How many challenges do we have? I don't even remember. I think we had like five challenges. I think I did two pretty good. However, you got a majority of them. I give it to you. I don't know how you do it, but whatever, bro. What can I say? We can all be queens. So like I said, guys, if you guys enjoyed today's video, make sure you guys smash that thumbs up button. Comment down below what your favorite part of the video was. And if you guys wanna see any other challenges like this or games, comment down below as well. Let us know and what all that being said. We'll see you guys in the next video.


Hey traders, this is Tosh. I go by T Bradley 90 in the My Investing Club Chat, a general reminder for those who do not know, MIC is having a one year anniversary event where BOW is going to be trading live in front of our members. It's coming up August 17th, mark your calendars. As an added benefit for our members, the event is 100% and exclusively free for annual and lifetime members. While lifetime on top of that, get extra coaching before the event and guaranteed front row seating. While most charged for these events, we show our support by making it again free for annual and lifetime members. If you are interested in signing up for this event, DM T Bradley 90 in MIC Slack Chat and or email myself at Tosh at myinvestingclub.com. Now, today we have a very special video for you guys as Joe Kelly, one of our head moderators, does his Trading Basics Weekly Sunday video series and today he signs up for episode 34, in which case he talks about trade journaling and tagging in specifically the platform of Evernote. And while today is just a preview of the full length video, if you wanna watch the full length or any of our exclusive content, then become a member of MIC. What's up guys? I wanna do a video for you about trade journaling. As a new member or as a new trader, you're most of the time gonna end up with this fire hydrant of information coming at you. And you're not quite sure what you want to do with it, how you wanna process it, how you wanna apply some of it to your trading, whatever it may be. So I wanna give you guys a little idea here on how to kind of catalog it, keep track of it and kind of filter through these things. So with Evernote, that is what this program is that you're seeing in front of you right now. Evernote is a free trade, or is a free journaling or note-taking software. You can just go to evernote.com and download the software and sign up for a free little log in. I already have a notebook over here that I've taken a lot of other notes for myself in, but one that I wanted to point out was I wanted to create this trade journal and show you guys how I journal and I use that in this other section, but this is just one of the simple ways that I do it. And the way I break it down is in two different parts in the beginning. So the first part is my watch list. And I do this before I'm ready to trade, okay? And then after I finish trading, I go back and I look at my notes prior to the trade and then I look at my notes after the trade and you can start to judge whether in the moment you decided to change your plan because maybe you were emotional about the trade. And for this particular example, missed trades and shorting the death line is the topics of today, basically. But now you've got this run up that's happening on SU&W and you've got to assume that they're gonna try to use some of that ATM to be able to raise some money there. And so I always link that in my watch list that way that I can look at this stuff. And it highlights it right there. And then there's the filing. So it's an at the market offering be Riley up to 17.7 million shares. And for MCP, one of the key things here was that there was a line 85.1 and 110. I wanted to short into the 85 line if it did not gap down. Ideally, I wanted to gap down, but here's the thing. Now I go down and I save the line chart, okay? After the day is done. And this is what I wanna point out. I call this a missed trade. So I always have two categories. I have missed trades and actual trades. My missed trades, I always wanna visit those and my actual trades, I wanna visit those as well. But I also want to consider, do my actual trades cost me missed opportunities in other places because I'm too focused on other things? So a missed trade for me was on MCEP and it was perfect to my plan. You know, two lines, 78 and 84 risk being 85 since it was a slight gap up and it started spiking into the prior days of resistance. You know, this is the first resistance short and I failed to take this trade because I was focusing really heavy on RHE and I again missed a super easy opportunity. Hey traders, this is Tosh. I go by T Bradley 90 in the My Investing Club chat. Just wanted to reach out and say if you have any questions about MIC, joining MIC, maybe you're a member already. You have three ways to contact myself personally and through MIC, you can hit our social media. You can hit me through PMs in chat or you can contact us through my email at Tosh at myinvestingclub.com. That's T-O-S-H at myinvestingclub.com. I will get back to you in a timely manner and I'm saying this because I'm here to help and I don't want anybody to be afraid to reach out and ask any question that they have. We are here for you guys. All right, see you guys.


Thank you, thank you. It's been fantastic week and I'm really happy I got a chance to be here and listen to all those really inspiring talks that really synthesize all of the wonderful things Maxim has been teaching us throughout the years. So I gotta say an anecdote too, right? I mean everybody is telling one of those so I met Maxime z nami, da je tudi svoj tudi 20 let. In tudi sem tudi, da se počekajte o formacijenih kvantizacijovih K3 servici. In ne bilo vštih, da se ovo pričeš, da se nekaj se nekaj nekošli. In se da se počekajte, da se nekaj nekošli, da se nekaj nekošli, da se nekaj nekošli, da se nekaj nekošli, da se nekaj nekošli, da se nekaj nekošli, zato, da se je več vsema, da je boš češtje, tako to je pravdje, da je vsema, z kateriji, zači je. In nisam, da ne bilim, ali, da sem vsema, in, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, da je, Nekaj. Zanimlj wasn't there, but then you gave a talk in horror. This was the first thing you said. He was really excited about that billboard and he really wanted to talk about that. Zato, da je tudi začusten, da je to. Tako, tako. To je taj pa. Zato, kaj je taj stor, je tudi o zvršenih folijacijov v drevjih geometriji in zvršenih folijacijov v drevjih geometriji. Zato, različno je, je, da je, In zelo izotropika in lagranja infuljace v števnoj zimplektivne geometriju zelo začeličnico s tem zelo potenšeljem. So, še je to pa vse, ki smo otekli, bari je matematik, začeljamo v matematiku, vzene, ki je, da modulno je vse zelo of geometric objects or a vacu or for whatever the physicists are interested in, in physics are always given in some global way as the critical loci of potentials, whereas for us there are some intrinsic objects that have nothing to do with any ambient spaces, any actions or anything like that, and in fact very often the spaces we describe may not even be describable as critical loci of potentials, and so in that sense they're not physical, and so there is this conceptual problem of trying to understand which moduli problems arise as critical loci of potentials, and this story with the fluctuations actually comes as a mechanism for providing an answer to that problem, especially isotropic fluctuations. And so, yeah, so I'll talk about these live spaces of fluctuations and their relationships to the derbut theorems in derived geometry, and the most interesting part of the talk will be the examples and two general constructions for producing these fluctuations and potentials, which are, I think, quite intriguing. So I got to apologize for about 20 minutes, it's going to be kind of dry because I need to set up the language and explain the concepts that we're going to be working with, but once we have that under our belt, we'll start actually seeing some interesting geometry, so bear with me for a while, don't fall asleep. So, OK, so here is the setup. I'm going to talk about fluctuations first in the affine setting, so suppose that we have non-positively graded, commutative differential graded algebra over the complex numbers, the same way it appeared in Bertrand's talk, and we're looking at the derived scheme, which is the spectrum of that. And so the most economic way to define a fluctuation, which is not the way you really think about them and work with them, but the logical reason is best to think about it this way. It's a mixed graded, commutative differential graded algebra, such that its weight zero piece is isomorphic to our algebra functions on the derived scheme, and there are two conditions, the weight one piece is a perfect module, so it's like a vector bundle on our derived scheme, and ignoring the mixed structure, ignoring the second differential, our this algebra is free, freely generated by its weight one piece. And since it's going to be relevant, let me just recall what the mixed graded, commutative differential graded algebra is. So it's a bi complex, it's a bi graded vector space, which is equipped with a graded product, which is associative, which is graded commutative with respect to either of the two gradings. So one of the gradings is written as a superscript, that's the homological grading, and one is written in parenthesis, it's called the weight grading. And it's equipped also with two derivations for the product, one is of homological degree one and weight degree zero, and the other is of homological degree minus one in weight degree one. And those anti commutes, so they give you a bi complex, so it's a bi complex, which has a homological differential and a homological differential, but also has an algebra structure. So that's what the mixed graded, commutative differential graded algebra is, and oh, that's the problem. Okay, thank you. So this is really what the affiliation is, but let me try to explain that and reformulate it in a way that's more familiar and makes it easier to work with. So since as an algebra, differential graded algebra with a homological differential but ignoring the mixed structure, the other differential, it's freely generated by its weight one piece, I can actually describe it in terms of that perfect complex, which is the weight one piece, but before I do that, let me just give you the two standard examples, which are really the model examples of what's going on. One is the trivial affiliation, which is given by the weight zero piece is our algebra that was part of the definition and there is no weight one piece. The weight one piece is zero. And then there is the tautological affiliation, which is given by the derang complex. So you have the cotangent complex, which is the complex of forms on our derived scheme and it has a homological differential because it's a complex and it also has a mixed structure, which is the derang differential. And so the only non-familiar thing here may be the fact that I've chosen a weird grading. I've shifted the form degrees so that all my forms sit in negative degrees and that's so that we have compatibility with cyclic homologes and functions on the whoopspace. But it's not really essential. I mean it's just a convention. Okay, so these are the two standard examples of foliations and they really model what's going on. So you can say what the foliation is in this language in terms of the derang complex. So you can think about it as a triple. L is a perfect module over our derived scheme. We have an anchor map from the cotangent complex to that perfect module and we have a mixed structure on the free algebra generated by that perfect module shifted by one so that the algebra map induced by the anchor map is a map compatible with the mixed structure. So intertwine the derang differential on the derang algebra with the one on the foliation. So why is it called foliation? I'm explaining. It's coming. So there is a dual notion of that which is... So if you dualize this perfect complex to the dual perfect complex then the mixed structure dualizes differential graded Lie algebra structure. You still have the anchor map and again the condition is that it gives morphism of shifted Poisson commutative differential graded algebras. So this is more familiar. This is similar to the classical notion of a foliation when you talk about an integrable distribution in the tangent sheave. The only difference with the classical differential in the symmetric notion is that there is no injectivity condition because we are in the derived world. So any morphism works. So in the previous one, on the previous slide we had it as quotients of the derang algebra. Here we have it as Poisson sub-algebras in the algebra vector fields of our polyvector fields. And they are not really quotients or subs. They are just things to which the vector fields. That's the only difference that's specific to the derived setting. So these are all equivalent data. The data of the mixed CGGA or the one coming from the cotangent complex is actually better than the one coming from the tangent complex when you start doing descent. So the ones that's written in terms of forms it's much better adapted to writing gluing conditions. To was also foliation simple example of le algebra. So the previous slide, the thing that we have is really a le algebra in the derived setting. But le algebra can be understood again in some DGM manifolds, which can be contained. In le algebra give a special example that is a particular case of foliation in this sense, but may not be a foliation in the ordinary sense, depending on the behavior of the anchor map. OK. So this is what happens on affine guys. So this is what happens on affine guys. OK. So this is what happens on affine guys and then you can map foliations to each other by saying that you have maps between these vector bundles that generate the foliations and they intertwine the anchor maps and the mixed structures. So this is what happens on a given affine guy. And now the interesting thing is that if you have a morphism between affine derived schemes which comes from a morphism of CDGAs, you can ask how to base change and you base change the same way you base change le algebraids. So you pull back so there is this notion of a base change of foliation which is not the pullback of the vector bundle that generates the foliation but it's a pull push construction. So you pull it back so you base change by tensuring with algebra prime and then you take the push out under the co differential which is the map on the cotangent complexes and that's the base change of the foliation bundle. And once you define it that way then the mixed structure descents along the right morphism and that gives you a notion of a foliation. The anchor map is the one just thought logically defined by this diagram. So that gives you a notion of a base change of foliations and again let's look at some examples if you take the trivial foliation then when you base change it by a morphism you get the foliation which is tangent along the fibers of the morphism. And I'll talk about it, I haven't defined it I'll define it a couple of slides later but it should be obvious in the ordinary differential geometric setting what that one is just vector fields tangent along the fibers if you base change the tautological foliation you always get the tautological foliation. So there are complexes that are funktorial. And here is an amusing example if you take a point a foliation on the point in this derived setting is just a differential graded le algebra and the base change along the morphism is a split foliation it's the foliation that's this differential graded le algebra extended by linearity on your space plus the vector fields with the standard track. So ok, so hopefully this gives you some sense of what these guys are and the good thing about this base change is that it allows you to descend and you can define now foliations for derived spaces and derived stacks so you can look at the assignment that goes from derived affine schemes to the space, the mapping, the classifying space, the groupoid of foliations on the affine scheme and this is a stack in the tautopology with this base change notion and then you can define a global foliation as an element in the mapping stack if you have any stack derived stack in the tautopology on the stack affine schemes you can take the map from that to foliations and that's a pattern derived stack geometry the stackiness is always a problem because a lot of notions that we want to work with like forms and vector fields and differential operators they have bad descent properties in respect to smooth morphisms and you have to stackify every time you try to globalize and they make perfect sense on affine locals but once you start to globalize you need to do something quite homological descent on hypercovers and that's what this thing actually achieves so there is a I don't want to spend time, there is a way to actually write that in terms of local data on affine derived schemes that probe your stack but I don't want to go into that so I'm going to skip that part Excuse me, is it groupoid or high groupoid? It's groupoid means an infinity groupoid for me there are no trankated things there are no trankated things in this talk everything is infinity so the tangential that I promised suppose you have a morphism of derived stacks a local affine presentation the tangential is given so I didn't give you the description in terms of local data but it is vertical tangent complex the cotangent complex along the fibers of the morphism if you want to write it in terms of an anchor map and mixed structure you have to take the big cotangent complex on the big et al side because the RAM differential doesn't exist on the quasi coherent cotangent complex globally and the anchor map is just the restriction from global forms to vertical forms and so this is the relative cotangent complex you have the restriction map from global forms to vertical forms that of course if you take the quasi coherator acting on the big cotangent complex you get the quasi coherent cotangent complex and this gives you the restriction map and the only thing that doesn't exist on the quasi coherent version is the RAM differential which you have to keep there so that's the tangential foliation this is an important remark even though it's not gonna well it's gonna appear in one of the examples but it's not gonna appear essentially in this talk but it's really important so let me make it you can define the tangential for morphisms which are not morphisms of algebraic derived stocks and are not locally defined presentations and there are many important examples where you really need to do that so they make sense when the target is a formal derived stock and again this is slightly delicate so I'm gonna skip the technical definition locally defined presentation the formal derived stocks do not even need to be locally defined presentation they can be almost locally defined presentation here in kukumologi but maybe unbounded tor amplitude and and they can also be informal derived stocks almost a finite presentation locally and this actually have been studied extensively by Nick Rosenblum and there are many important examples coming from representation theory which are exactly of that type so I said in this case will be kukumologi in unbounded tor amplitude and let me just give you some examples of these guys to convince you that they are important geometrically they arise really naturally one example is a formal stock that Bertrand discuss last in his lecture is the drum stock which will reappear very soon in play a very prominent role in our discussion so it's a formal derived stock of locally defined presentation but it's not algebraic the derived Hilbert and Quartz hems of Chukan, Fontanine and Kapranov they are almost locally defined presentation and run spaces are informal and almost locally defined presentation so those are important and you would like to work with them and they do appear when you start dealing with geometric settings or the place ok, let me just since I'm talking about tangential fuljations let me just mention two examples that the trivial and the tautological fuljations are tangential the trivial fuljation is just a tangential and the structural morphism to a point gives you the tautological fuljation so those are particular examples of tangential fuljations and in fact with the exception of one construction in this stock all the fuljations will be dealing with will be tangential ok, now the one thing that we really want to extract from this formalism is leaf spaces so we want to be able to take a derived guy and quotient it by a fuljation and as in usual geometry the output of that process is not going to be a space but it's going to be or a stock and it's going to be a formal stock and so you have to actually depending on the generality of formal geometry you want to allow yourself you have to work a little bit for that so here is a definition which is actually a theorem so this is what Bertrand mentioned so these quotients are defined by universal property and they exist so if you have a derived stock luckily a finite presentation and a fuljation on the derived stock in the strict sense so given by a perfect guy then there exists a formal derived stock which is the leaf space of that fuljation and a quotient map and it's uniquely characterized by universal property universal property is that if you map x to any other formal derived stock so that the tangential fuljation to the map to the test stock maps to the given fuljation then that map on fuljations induces a unique morphism on the from the quotient to the test map and this is unique so that's the universal property and you can construct these leaf spaces which are formal stocks and we'll be using them very soon so again the reason maybe just let me just say a little bit about quotients they behave exactly as you expect them to behave first of all these quotients are really sensitive to neopotents or to derived structures I mean if you reduce everything so if you truncate to something which is non derived and pass to reductions the quotient by fuljation gives you an isomorphism as a higher under derived stock so the quotient by the trivial fuljation doesn't do anything, just gives you x the quotient by the tautological fuljation gives you exactly the deramstak which Bertrand defined it you attach to a commutative differential graded algebra the points of x or the reduction of that is first you kill all the derived pieces and then you reduce by neopotents and this is carvers definition of the deramstak and when you work out this universal property this is exactly what you get for the quotient by the tautological fuljation if you take the cotangent complex for the leaf space it is exactly what you expect it to be it's the cone of the map from the cotangent complexes from x to the fuljation bundle you can in fact ignore the neopotents in x you need to keep the derived structure but you can ignore the neopotents so you can kill the derived structure kill the neopotents take the reduced underived space sitting inside as a closed sub-scheme in your derived stock you can base change the fuljation now this is not going to be fuljation in the strong size it's not going to be perfect but it will be in locally almost a finite presentation and then the map on quotient is an isomorphism so we can't prove it in this generality we can only prove it for the strong fuljation for the perfect ones so this thing exists in this particular case in general we don't know how to prove it for general fuljations which are almost locally finite presentations ok now if you have a reduced algebra finite type nothing derived non non-dg and you have a fuljation derived fuljation on it then the algebra functions on that leaf space is exactly what you expected it is the total complex the negative cyclic complex of the completed symmetric algebra fuljation shifted by minus 1 so you just you have this mixed complex and you take it as total complex so again if you understand formal spectra properly mrtran was discussing in his lecture in the affine case the quotient by the fuljation is just the formal spectrum of this total complex so here is probably the most useful example if you have a morphism of derived stacks locally finite presentation and you look at the tangential fuljation then the quotient is the relative formal completion along the fibers of f so what you have to do is the derived stack whose value on committive differential graded algebra is the fiber product of the points of it's the fiber product of the points of the target over a with the reduced points of x over the reduced points of the target so if the target was a point roughly the deram stack so this is like the family of deram stacks along the fibers and there is a reason why we call it a formal completion because if the morphism is smooth morphism of schemes then you really get the relative deram stack along the fibers but if it's a closed immersion you get the formal neighborhood you get the functions on the formal neighborhood of x inside y formal completion of y along x so there is a slight caveat in this isomorphism but it's technical I'm not gonna discuss it right now but they are isomorphic if you interpret the isomorphic what isomorphic means correctly I mean there are extra structures which not quite matched but as algebras they are isomorphic ok so we have these very nice properties of quotients and we have this relative completion which is a quotient by tangential foliation and now I wanna bring the symplectic geometry into this game and see what can we say if we have not just foliations but we are Lagrangian or isotropic so if you have say a fine derived scheme and an n shifted to form which doesn't have to be symplectic just closed n shifted to form so in in algebraic language it's just a morphism from this mixed graded commutative differential graded algebra generated by a piece in one homogical degree to minus n and one degree to to the derame algebra and so that's what a n shifted closed to form is and an isotropic structure on such foliation is just a homotopy between the induced morphism to the foliation from the symplectic form with the anchor map and the zero map so that choice of a homotopy is a structure you need to keep track of it but that's what it means for the foliation to be isotropic and you can also define a Lagrangian foliation I actually wrote down here explicitly how you write isotropic structures in this derived sense you can write close to forms as infinite sequence in terms sitting in terms of the cotangent complex with the corresponding degree which are annihilated, which are co-cycles with respect to the total differential in the double complex and then h is just a co-chain that bounds that form in the double complex corresponding to the foliation so in the affine case it's something very explicit I mean it has a large amount of homological data but it's something completely explicit it becomes complicated when you start gluing things and then you can play that game with gluing again you can define a morphism of isotropic foliations, you can define a base change of isotropic foliations this is where you need the form not to be not degenerate because when you start pulling back non-degenerate forms can become degenerate but we don't care I mean the notion of being isotropic doesn't care about non-degeneracy so you can define a base change of isotropic foliations and again the same trick works the assignment that sends shifted symplectic or affine scheme with a shifted close to form to the group point of isotropic foliations is a stack in data topology and you can define a global isotropic foliation as an element in the map stack then you can put a non-degeneracy condition on the isotropic foliation once you have one for non-degenerate to form then the non-degeneracy condition is a purely algebraic condition is just the condition that says that the foliation is isomorphic as a perfect complex to the comormal bundle of the map so you just write down the composition with the symplectic form to the quotient by the foliation and you want this to be a quasi-isomorphism so it's exactly, I mean it's a complicated formula but it just the most nifty thing you can do it's the standard notion in think of granshin so the reason we care about these guys is as I said because so this is our granshin when it's a quasi-isomorphism and the reason we care about them is because we want to talk about potentials and this is related to the derbutiura so in classical symplectic geometry the local structure the symplectic manifold is given by the derbutiura which says that say locally in the c-infinity setting or formally in the algebraic setting the symplectic manifold is isomorphic to the standard symplectic structure on a cotangent bundle and you would like to have something like that in this derived symplectic geometry the problem is that you have more cotangent bundles more than one cotangent bundle more potential local models than just a cotangent bundle so the most main thing you can do is what Bertrand described in his talk is the shifted cotangent bundle so you just take the tangent bundle shifted by minus n, take the symmetric algebra and take the spectrum of that that carries a natural exact shifted symplectic form so that's a perfectly nice linear shifted symplectic manifold differential graded manifold or a stack the problem is that not every shifted symplectic derived stack is isomorphic locally to this so there are deformations of these guys which are not locally isomorphic to them so the derived critical locus of a function is equipped with n-shifted symplectic form and in general is not locally isomorphic to a shifted cotangent bundle so if you have a function mapping you to the n-post first shifted line so you can think about this as a degree n-post kuhomologi class with coefficients in the structure shift of n this it has a well defined critical locus which is equipped with a symplectic structure which is shifted by n so there is a dropping shift by one because this is a Lagrangian intersection picture so if you have a shifted function n-post one shifted function is derived critical locus is equipped with an n-shifted symplectic form if that function is constant then you get a shifted cotangent bundle or locally constant then you get a shifted cotangent bundle but if it's not constant then the derived critical locus is not necessarily isomorphic to a shifted cotangent bundle and that's very easy to see in examples so you have a choice here whether you think about these guys as your local models or these guys and since I said these are more general they don't specialize to this even locally it's better to use those as your local models and so if you have a hope for a derbut jurem you want to say that a shifted symplectic manifold is locally isomorphic to derive critical locus of a shifted function and so that's what we want to do and this leads to this remarkable derbut jurem that Dominic Joyce and his group proved if you have a derived Dylene-Mannford stack with an n-shifted symplectic structure where the shift is non-positive then at all locally it's isomorphic to the derived critical locus of a shifted function so this is Dominic Joyce and his postdocs graduate students and in fact in all schemes it's a risky locally so it's a very strong statement and now the problem we were trying to solve where these relations were needed was to try to understand what's the ambiguity in this the choice of these local structures and when can we hope for them to be global so this tells you that locally you always have a potential but maybe sometimes you have globally a potential so when can you hope for the potentials to exist globally and so this is what the fluctuations help you answer so the point is that potentials always exist if we have anisotropic foliation so here is the theorem suppose that you have a derived stack locally finite presentation and an n-shifted symplectic form on it and assume it's exact of course if you want to have a potential it better be exact the ones that are shifted symplectic forms on derived critical loci are always exact and suppose that it's equipped with an foliation foliation with anisotropic structure H then the claim is that on the leaf space of that foliation there is a shifted function m plus 1 shifted function and a map from x to the leaf space factors through the derived critical locus of that function and in fact not only factors but it's symplectic it pulls back the shifted symplectic form on the derived critical locus to the original shifted symplectic form and that's completely global if the foliation exists globally then on the leaf space you get this function and you can identify the whole space as a derived critical locus if in addition the the foliation is Lagrangian then that map to the derived critical locus is also et al it's kind of it's subsuscable super meaningful in that is it's it's a very natural statement and it's actually not very hard to prove once the technologies I mean where is the function coming from it's coming from the fact that the form omega is zero on the leafs of the foliation for two reasons it's zero because it's exact and it's zero because the foliation is isotropic so you can find a homotopy between these two zeros and that's the function so it's just as simple as that and it really connects with the result of Joyce and Company where there was no exactness condition but there was the condition that we were local with non-positive shift and the point is that if you work out through the Hoch theory it turns out that if you have a close p-form which is n-shifted with a negative shift it's always exact so that's something very peculiar for forms with negative shifts and this is not a tautology, I mean it's a statement with content because the corresponding derangue homology is not zero so this is really a property of this mixed complex of forms ok so let me show you examples and I want to really show you two constructions of these global potentials that come from these foliations which are cool so of course the basic example is a derived critical locus if you have a smooth scheme and a regular function so this is just an underived ordinary scheme then you can take the derived scheme x to be the critical derived critical locus of W it has a minus one shifted symplectic structure now this better be coming from a potential we know it's coming from potential but in fact this potential is coming from a foliation what's the foliation you have the map from this derived scheme to Z and you can look at the tangential foliation for this map the map, the inclusion map from the derived scheme to Z and it has a Lagrangian structure which you can write explicitly in terms of the function W and the quotient is exactly the formal completion of Z along the underived critical locus and the potential is just the restriction of the function to that formal completion and the map is just the map from the derived critical locus to the formal completion and the pullback of the symplectic forms is the fact that the pullback of the function is the pullback of the function so this is a tautology but it should be there as a check that what we are doing is correct and you can do this with shifts so this was for an unshifted function you can do it for a shifted function and again you get the same foliation gives you a shifted function and again you get the potential is a pullback formal completion another example if you take a cotangent bundle so you take a smooth manifold it's cotangent bundle with the standard symplectic structure then you have a projection from the cotangent bundle to M with Lagrangian fibers the tangential foliation is Lagrangian the quotient by the tangential foliation is of course as a underived space as the space underlying a stack is just the total space of the cotangent bundle but the fibers are completed in the deram sense so it's the deram stacks of the fibers the function is just zero but viewed as a one shifted function and the derived critical locus is the shifting of the one shifted cotangent bundle which is just the cotangent bundle so again in this case you get exactly what you expect more interestingly you can do twisted cotangent bundles so suppose that you have a smooth manifold and you have a symplectic twisted cotangent bundle so those are classified by elements in the hypercuchomology of the stupidly deram complex in degree one so they are affine bundles over the cotangent bundle equipped with a symplectic form corresponding to that class the tangential foliation mapping to the base is still a grandian the problem is that the symplectic form is not necessarily exact anymore twisted cotangent bundles are not always exact depending on the twisting if the symplectic form happens to be exact then you should be able to find a twisted function one shifted function on the deram on the deram completion of the fibers and it's actually not hard to identify if you see where this function should live it should live in the degree one homology of m with coefficients in the structure shift and it is just the function that bounds the class 8 so it turns out that 8 will give you an exact twisted cotangent bundle exactly when it's in the image of the deram differential with respect to the hotch filtration and whatever bounds it is exactly the function so and then you get identification of this with the derive critical locus and let me just point out that this is of course interesting on m's which are not compact because this function f it's not gonna be unique, it's gonna be unique only up to a function which is locally constant only up to something that's coming from h1 with coefficients in c and of course if we had something locally constant then there is no shift because dff is 0 so what you really get is a shifted cotangent bundle again or the original shifted twisted, unshifted twisted cotangent bundle so you cannot have m to be something for which the hotch theorem holds if you wanna get interesting examples but for affine m's you'll get interesting examples ok, one purely derive example and then I'll give you the how am I doing with time, 10 minutes ok, great so purely derive example which is neat so suppose that you have a symplectic manifold which is a point zero symplectic structure but you view it as a one shifted symplectic structure the zero symplectic structure you can put in any shift so on the point you can talk about shifted symplectic structures of any shift so we can actually describe Lagrangian foliations if we have a finite dimensional vector space and you look at the map from the point to the classifying stack of that space so the stack classifying affine space is modeled on that vector space differential foliation is given just by the dual space with the zero anchor map and the zero mixed structure anisotropic structure is a self-homotopy in this negative cyclic complex that has a zero differential so it's actually an element in the second wedge power of the dual space and it's Lagrangian if and only if this element is non degenerate so if and only if V with this two form is a symplectic vector space so Lagrangian foliation for this so a situation in which this map from the point to the classifying stack of a vector space is a Lagrangian foliation it's a it's just a choice of a symplectic structure on the vector space now the quotient by this Lagrangian foliation is just the classifying stack of the formal group which is the completion of V at zero and by the theorem there should be a two-shifted function from that formal group from that classifying stack to a1 two-shifted function so that the point with the zero-shifted symplectic structure is the derived critical locus and so in order to find that function you need to compute the second cohomology of bV hat c in o and you can actually do that because we have the Brin calculation which in characteristic zero was redone by Carlos and it says that if you have a finite dimensional vector space and you look at the Albert McLean stack kVn then the height cohomology of kVn with coefficient c in o is either an exterior algebra or a symmetric algebra depending on the parity event or it's zero if the degree over the over the homotopical degree is not an integer so in particular in this case when we are doing something two-shifted the answer is exactly wedge to a Vdual and the function is just h so so it's it's a complete circle okay so I have another example about integrable systems but I'm going to skip that even though it's interesting I want to show you two constructions of isotropic foliation and one of our grandchef foliation which are interesting and give you new new realizations of modular spaces of critical loss of potentials so suppose that we have oriented c infinity manifold of odd dimension choose a more smell function so it's a self indexed more function where the critical values are the indices and choose a regular value between the two middle critical values so now if you take the half of the manifold that corresponds to everything smaller than that regular value you get a sub manifold with boundary which when you include it in M you get a homotop equivalence on the k-dimensional skeleton in fact any such guy will do this is a way to construct it now if you have a complex reductive group and you look at the derived stack of local systems m so these are maps from m to bg as a derived module i then this guy carries a 2-d shifted symplectic structure as Bertrand explained by this ak-zik formalism and if k is greater than or equal to 1 this 2-d shifted symplectic structure is negatively shifted so by this theorem that I mentioned about the how it's exact so you have the derived stack of local systems on an all-dimensional compact-oriented manifold as soon as the dimension is bigger than 1 it is an exact shifted symplectic manifold or shifted symplectic stack and the claim is that tangential variation for the restriction map from local systems to local systems on this half of it given by the Morse function has a nitroisotropic structure depends only on the orientation data in the shifted symplectic form and so you can find a shifted function 2-2k shifted function on the quotient by that foliation which is the relative derived stack and the module of local systems with its shifted symplectic form is the critical locus of that so for three manifolds this just gives you an incarnation of the transimons function if you choose a Higgs splitting and this gives you a generalization of the transimons function to higher dimensions but unfortunately the off-shell space has no natural interpretation of a space of connections it's really very derived so that's one construction the other has to do with the non-o-bilian hotch theory so it's very similar maybe I didn't say that so you can prove that this structure is isotropic unfortunately we cannot prove its Lagrangian I believe it's Lagrangian so that this map is really a towel and in fact when any simply connected we can prove its Lagrangian when in any case under simple logical conditions we can prove its Lagrangian but we cannot prove it in general and I think it's just stupidity but it's certainly isotropic so it is really a pullback of a derived critical locus symplectic form of a derived critical locus is there a shift of vanishing set both you mean for shifted functions? you can define shifts of vanishing cycles for shifted functions but because these are formal stacks you really have to be very careful with your you know the boundaries properties of your complexes so we can formally define it I'm not sure that it actually exists because the cons may not be well defined in complex so we haven't tried really you can try to mimic the standard definition but maybe if you don't have bounded below bounded above complexes maybe you're not going to be able to do it so okay but let me do this example so suppose that we have a smooth projective variety of dimension D and a modular stack of rank and local systems again as a derived stack so this is now equipped with 2-2D shifted symplectic structure and as Bertrand pointed out this stack X it has a tangent complex and the tangent complex has a natural hot filtration from non-nuclear hot theory coming from the modular space of lambda connections so if you look at the relative modular of lambda connections in fact the shifted symplectic structure exists relatively in the twister space and this the C star action on the modular of lambda connection gives you the hot filtration on TX and the map given by the construction with the symplectic form actually is a filtered quasi isomorphism for the hot filtration and as a consequence if you look at the middle degree the middle step of the hot filtration middle then the degree step of the hot filtration when D is odd dimensional again this middle step of the hot filtration has a canonical Lagrange infoliation structure for the shifted symplectic form it also works on the Higgs module I but here it's more interesting because on the Higgs module I it's everything is split and so you can you can take this fuliation quotient by it and get the potential so you can write the module I of local systems on an odd dimensional projective manifold as critical locals of a potential and in fact this fuliation given by the middle step of the hot filtration is again a tangential fuliation so you have the local systems the derived stack of local systems and you can look at the derived stack of modules so this is like the DG modules over the full derang complex of M which as all modules are of rank N but you can look at DG modules over the truncated derang complex in the middle step of the hot filtration and you have a restriction map from those and the middle step of the hot filtration is just a tangential fuliation for that so if K0 if we are doing one curve then this is just the ordinary map from the module I of local systems to the stack of bundles but the moment we go in dimension bigger than one this map actually on truncations so this is just the truncation but this map on truncations is an isomorphism so you don't get a new space but you get a new derived structure and the full truncated stack is recovered as a critical locus of a shifted function on the relative derang stack and you can actually identify that function explicitly there in terms of the symplectic structure and I think I'll stop here in this case thank you very much


Hey, what's up? We're good by June and this is her to hear. Yeah, right now. We're listening to Leon Russell God rest his soul. Yeah, Russell. Dr. Dre Chronic record For real a pink Floyd dark side of the moon for real. I've made love and contemplated life to that record The person that changed our life the most was Tyler's brother Shane He passed away in 2005 after Shane passed away. I decided to basically to live with his parents and Tyler for about a month after he passed it was Kind of like a light switch and it changed my life trajectory Like I was supposed to be a preacher. He's supposed to be a music minister or whatever So-and-so forth. I had dreams of being an engineer Prior to that or you know like I don't know do something Normal I guess obviously it brought us all together. We wrote a lot of music after that It was a huge part of the healing process when we were able to realize that us three could create music They're not only like killed what we were going through at the time, but we were like, hey, this is something that we could actually You know gravitate towards forever I want to do this for the rest of my life because it because it's so short and we don't know What we got next we kind of grew up in a real strict environment a Christian church Pentecostal Church And a lot of great people, but I mean it was a very one-set one-track mentality this way or the highway as we've traveled You know touring and everything's like that. We've actually been able to meet a lot of people That most of the people like that we grew up around would never be able to come in contact with so we we realized that There's a lot of great people out there if there's one thing I think that we could promote and without sounding too cheesy would be you know just love each other a lot of times you just get wrapped up in your own ideals and You just guys see other people's point of view sometimes. Yeah


This 1999 Pontiac Firebird Trans Am is stock number 11682ZA. We are here at Summit Automotive in Fond du Lac, Wisconsin, you're new and use sports car headquarters. This 1999 Firebird has the 5.7 liter V8 motor which pumps out 305 horsepower. This car has been fully safety and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off and this car is 100% ready to go. Pewter Metallic is the color we shoot all of our videos in 1080p 60 frames per second so if you have HD capabilities on your computer tablet smartphone or television turn them on right now because it is definitely your best way to check out the quality and condition of the car before seeing it in person and if you like the video and want to subscribe to our YouTube channel in the lower right hand part of the screen is a subscribe button. Click that and then click the bell notifications to get updates every time we do a video here at Summit of one of our amazing pieces of inventory. This one comes with the chromed alloy rims these are 17 inch rims in the front. In the front here you can see it has the drilled and slotted rotors and these rims are in excellent shape just very nice no corrosion no scuffs no scrapes and it has hand-cooked Ventus 245 45 ZR17 tires on here. These tires are really new I would say probably 70 to 80% of the tread left on them maybe even a little bit more. Pewter Metallic's got a lot of metal flake in it you can see that shine right there looks really good in the sun. Has the pop-up headlights factory fog lights front bumper is in excellent shape I didn't see any scuffs scrapes or cracks and the hood is in very nice condition as well no dents or dings on there. Passenger side front fender looks really good too and the passenger side rim no scuffs or scrapes on there. As you go down this side of the car take note of how clean the body is how reflective and mirror like that paint is. You take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the car you can see the car hear the car and of confidence in the vehicle that you're looking at before you even get here so when you do get here there's absolutely no surprises and you can make a smart buying decision from the comfort of your own home. So I wanted to stop here and take a look at these teatops they look like they're in really nice shape the outside weather stripping looks like it's in nice condition and down this side the car is exceptionally clean this whole car is in really really nice shape you have the drilled and slotted rotors in back as well and this back rim no scuffs or scrapes back tires have just as much tread as the front tires and as we come around to the back of the vehicle rear bumper is in great shape you get the dual rear exhaust now that is an SLP exhaust on there sounds really good you get the deck lid spoiler and the trunk lid is in nice shape too tail lights look like they're in nice shape and down the driver's side just as clean as that passenger's side no major dents or dings and for full disclosure this back rim is in excellent shape as well driver's side door looks really good inside the trans-am package gives you the gray cloth interior there are no rips there are no tears on the seats you get a power driver's seat with lumbar factory floor mats you get the back bucket seats and those are in really nice condition as well power windows power locks and power mirrors and we'll take a quick look in the trunk here as long as we're standing up back trunk area is very clean you get storage for those t-tops this one does have a 12 disc cd changer back here it's like a factory one and that's where your t-tops go when they're in storage really nice system actually that shuts nice and solidly we'll hop inside take a look at the miles and then we'll start it up check out that SLP exhaust and then we will take a look under the hood this one has 67,248 miles instrument cluster is very nice and clean comes with the leather wrapped steering wheel volume controls and radio controls on the left volume controls on the right does have that CD player in that 12 disc cd changer in back AM FM radio the monsoon radio automatic transmission traction control system passenger side format and seat are in excellent condition no rips or tears on there and then you get those t-tops up there they look really good no rips sorry about that flip her back around no rips or tears in that headliner looks really good and we'll start it up and take a look under the hood check out that exhaust no check engine lights or anything like that sounds really good take a look under the hood I would personally like to thank you for checking out the video today and hopefully from this HD video you'll been able to tell just how clean this car is all the way around those pop-up headlights work really good under the hood we have the 5.7 liter v8 motor engine base very clean runs very smooth once again this car has been fully safe and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off shocks are doing a nice job holding that up and this car is 100% ready to go I do just want to show you that those pop-up lights work flawlessly so turn them off here turn them on you have to turn the car off so they work nicely now I would personally like to thank you for checking out the video and I highly recommend this car from a quality and condition standpoint and to see more pictures of this car one of our other 450 new and used cars trucks SUVs mini vans wranglers sports cars Pontiacs Mustangs Camaros Corvettes you name it we got to go to that website right there www.SummitAuto.com full pictures and descriptions of every single vehicle from two locations all at SummitAuto.com and if you'd like to check out more HD videos you can go to youtube.com slash SummitAuto remember to like subscribe and share on this video and all the videos that you see there click those bell notifications to get updates of the cool inventory we do videos of each and every day and in fact in second you'll see a link to subscribe to our YouTube channel in the upper left to link to more Trans Am videos like this one in the upper right a link to this vehicle on our website in the lower left and a link to one of our latest YouTube videos in the lower right click those check us out and we're super excited to help you with this ultra clean 1999 Pontiac Firebird Trans Am in pewter metallic thanks again and remember to like subscribe share and click those bell notifications