Thank you for joining. Lovely to have you on this summer evening. I know I can see a lot of people coming from around the country, so thank you so much. Oh wow, and we've got the Northern Lights even. So thank you. I'm just gonna wait a few minutes while people are joining and then ask that you keep muted just to give you a sense of the flow. I'm gonna start out by having a little conversation with John, our guest, and letting you get to know him through those questions. And then I'm very excited that today you'll get to meet Kale Holmes, who is the new coordinator of our China's Not Our Enemy campaign, and Kale will take over for me to ask the next round of a couple of questions and then you'll have a chance to ask questions also. So that's kind of the flow of our time together. So looks like we're getting some more folks in. Just give me a couple of minutes before I start. As people are entering, it takes a little while to let everybody in from the waiting room. And I just also want to thank Grace, who's here. She's one of the core bedrocks of Code Pink that makes everything happen.  So Grace, thanks for being with us while you're cooking dinner at home in Chicago. So also feel free to put in the chat where you're joining us from your name and where you're joining us from so folks can see who out there cares about peace and from where. It's always fun to know. All right, we've got a good group in. So I think I'll get started checking with Grace that we're good to go on. It's streaming. Yeah, it's being slow, but it'll start true. Okay, cool. All right. So welcome to Code Pink and another episode of China is Not Our Enemy. I'm Jody Evans, one of the co-founders of Code Pink. And I started this campaign about three and a half years ago when I saw the same playbook that took us to war in Iraq playing out towards China. And I couldn't believe that the US would think it was a good idea to go to war on China and nuclear power, especially since in this moment in history, we should be cooperating with China on very serious issues like climate change, AI, and the needs of the people globally. So you know, the campaign has evolved over time. And we try to focus on a few things. First of all, that from sanctions to military expansion, the US is already preparing and driving us to war with China. So we talk about those things. The campaign aims to stop this US war on China instead of pivot that energy to cooperation. So we focus on where should we be cooperating? Where's cooperating and happen? And how does that look? Which is in many ways, when it's happening, it looks awesome. And it's what should continue to happen and where the focus should be.  And you know, especially when you look at China, that's producing, I think somebody said 80% of the solar panels. And our trade with China is so extreme and needed as we've seen with Janet Yellen's concerns about what would it mean if we, the US decoupled from China. So, you know, paying attention to what those issues are. It already has casualties this drive to war on China and their Asian Americans. There are also indigenous peoples of the islands around China and the peoples of the Asia Pacific who are threatened by the war on China. And that's where we're going to have this conversation about today. It's like, we hear all this propaganda and we hear all these voices, you know, anything that goes wrong, it must be China's fault. And I'm really excited with our guests to be able to look from Asia back at the United States, which isn't a view we get to hear from often.  And we saw that just this week with the recent Pew poll that showed that 50% of the United States thinks the most dangerous thing to the US in this moment in history is China. And that was all created by propaganda.  So we're here to help unpack that, help give you talking points to have conversations with those around you because it's each one of us in conversation that can help debunk all these tools that are used to drive a war. So I'd like to now introduce our guest. I had the pleasure of being with John on on his conversation with his friends on Friday, and Kale will post that link in the chat. It was a really fun conversation. And so now we get to just learn about John and hear from him. He's been a policy and strategy advisor in government and business across East Asia for two decades. He has held senior fellowship at Columbia University, New York University Stern, and the Raja Atnam School of International Studies Singapore, where he helped start the Center for Multilateralism Studies. As director of a leading investment bank in Southeast Asia, he founded a research institute and later a council of business leaders to support regional economic integration. He is a former official in the Malaysian government. He was educated in the London School of Economics and Stanford University. He is interested in framing the political theology of international relations discourse, especially as it applies to China, East Asia, and the question of the whole world order. So welcome, John. Thank you for joining us today. Thank you very much. It's great to be here with you. Very impressive resume that you have, John.  Like, what have you seen from all those different vantage points that brings you to this concern about China not being our enemy? I have actually watched this escalation to this point over at least the last decade. It began with this pivot to Asia, which came across my desk or came to my attention, so to speak, as I was working on ASEAN. I was then running the ASEAN Research Institute, and I was very much involved in efforts at regional integration. That is that you have to know that there is an effort to build a peaceful economic region with free trade and investment and so forth. And of course, transportation links as well across Southeast Asia, but also, I think, at that time, there was also the idea with China, because in 2010, a China ASEAN free trade area came into effect, so very, very early. And so in the middle of this, and right after the financial crisis, we heard about this pivot to Asia business with an article by, it began with an article by Secretary of State and Hilary Clinton. I think it was called something like America's Pacific Century. And she called for a, well, it announced this sort of pivot and a large, and this really was a pivot in America's attention, strategic attention from the Middle East from, and we're still embroiled in the war in Afghanistan at that point, to Asia. And some of the, I was just looking at it just a moment ago, and some of the lines in it are really striking. So you have to understand that things date from there, but we can go into it later. I don't want to go into the weeds of that right now, but I'd like to later, if we have a chance, but I was already quite uncomfortable with it, because I didn't see China as a threat, and this was very clearly directed at a kind of, at that point, soft encirclement of China. So the TPP came about at that time as well, but in my own biography, I then had to come to the US quite suddenly in late 2016. And from there, it's been an absolutely kind of amazing, a tumultuous time. Things have changed, escalated, deteriorated to an extraordinary degree. Even knowing the trajectory, then, one sees the full, the thing in sort of at full pace right now. And I think the propaganda that we're all experiencing is a big part of it. The most disturbing thing is absolutely unhinged propaganda campaign, propaganda and misinformation campaign about China, but by extension about Asia. So one thing I want to talk about today, if we get a chance, is the extent to which things are quite linked there. And if you're attacking sort of the Chinese economy, you're also attacking the Asian economy and the Southeast Asian economy. So it's true that I became yet more engaged, but it just became absolutely nuts. I think the Hong Kong riots actually were a kind of turning point in my sort of decision to basically speak up. Yeah, we can talk about it more. Yeah, if you could describe that for those here, because you're closer to being able to understand it than people in the United States, because we're living in the stories we get told in the media, but you have a different understanding. So maybe if you could share what the shock was for you and how you saw it. The Hong Kong you have to realize is a kind of second place, a very, very familiar place to a lot of Asians, Southeast Asians, and particularly to the overseas Chinese community, of which I'm a member. There are about 30 million overseas Chinese in Southeast Asia. So I come from Malaysia where about a quarter of the population is Chinese. But whether you're Chinese or not, people are quite very, very used to going to Hong Kong. And many of us have family there. It's a bit like for me, it was like if you're from the West Coast, something like East Coast, and it's about that distance as a flight. Wait, how long is it? What was the flight time? It's less than that, right? It's about three hour flight from Palo Lumpur. I have family there. So I know the place and I know what it feels like. And these protests that cast the issue in that particular light, as if Hong Kong was this totalitarian, authoritarian place without what was being demanded, were absolutely ludicrous. I'm sure you've all heard it before and I don't want to go into every particular issue, but the place never had universal suffrage.  In fact, rather brutal repression of protests at certain times in the late 60s, for example. But right after 97, you have this, and there were elections. Hong Kong does have elections. Only you don't elect the leader of Hong Kong directly. Remember that Hong Kong is not a sovereignty, it's not a polity. It's like New York legally as far as China is concerned. And probably somewhat less sort of stroppy about its distinctness, in fact, than from the rest of the country, the New York City. Or just about as insistent on it. But here was this idea that you had to have direct elections for the chief executive of Hong Kong, or else it wasn't a democracy, but they did have wide consultation. They had a system in which you had different groups of parts of society represented, and also election for representatives. But the chief executive, the only requirement from the central government and from the system was that the candidates were approved or were not vetoed by Beijing. And so there you had it. We have elections in Hong Kong. It's not sort of direct elections. Neither do you have direct elections in the United States. Correct. We have elections but selection, the same as China. Yeah. Elections and selection. But you have an electoral college. This is not Switzerland. But the enormous hypocrisy of that, and then the protests were something else. They began as something and then developed into this, imagine a year-long January 6. And in fact, the relevant comparison is that, well, we had the capital sort of invaded here, and people call it an insurrection. You call these people terrorists and so on. You hunt them down. Well, Hong Kong had that. The legislature was broken into and defaced and sort of wrecked in a place that unlike the capital. And so all that was being excused away or rather portrayed, the students were, or not students, the protesters were portrayed as freedom fighters, democracy heroes. Let me get more direct and even more personal about it. I actually tried to teach a course on this as this thing was going on. You know, I was teaching a joint course with, and the plan was to have a joint program with Hong Kong University. That would have been amazing. So I was at my college. Actually, we shouldn't embarrass anybody here. So I would run the course with a bunch of students here. And the idea was to study the protests, to think about them as they were going on. Because of course there were issues, all kinds of issues we wanted to get into. And I wanted to get at the tremendous economic issues. Hong Kong is capitalism on, you know, on steroids. It is the most laissez-faire place in the world. Freedom House, the K2 Institute, they love Hong Kong. Every year it comes out number one in freedom. I kid you not.  Well, that's the neoliberal notion of freedom. It's very easy to start a company and do business and so on. But especially after 97, it became more and more the province of the, it was always controlled by the economy was always dominated by tycoons. Well, the word tycoon comes from Cantonese, right? But by these big bosses. And the real estate sector is very powerful. And rents there are sky high. People have a very, very difficult time. So you have what felt to me like a huge bunch of disaffected youth, but there were all kinds of reasons for them to be unhappy. But, and then one began to see clear signs of unmistakable signs of instigation. And so actually for me, it was seeing it, you know, almost embarrassed to say it's like, this is when it happens to you, to your own society, you know, color revolutions. So it's one thing. And when they happen in Egypt and so on, you know, I could stand, you know, I could be quite uncritically, sort of think, wow, this is a great thing or cheer them on when it happens to your own society.  It's really quite an experience. I'm not the only one. Hong Kong was a turning point for a bunch of guys like me.  Okay, I worked in I worked for an investment bank for heaven's sakes. You know, I was a Davos guy. Right? But once you've seen it, you can't unsee it. You cannot unsee people being fed certain lines and the media just lying 180 degrees day by day for a year about what was going on. So it was way too much for a whole bunch of people.  Once you have seen that, you'll see, wait a second, it isn't just accidental. It isn't just these media people carried away by their own sort of their own beliefs. No, there was clear suppression of what was going on. Those kids, these protesters were, there was a very, very strong right wing and racist element, believe it or not. And they were literally no clubbing people on the head, right? Hitting people with bricks. They set a man on fire. They were stabbing policemen. Not a single protester was killed. If you had tried any of this in New York, you know, or in LA, right? Yeah, you know, you'd have been shot for sure. And the Hong Kong police managed that for a year. And Beijing, right, despite all the blood thirsty, you could see the press wanting to see a Tiananmen incident in Hong Kong. And of course, they were too smart not, you know, to do that. So even the PLA, which has a barracks in Hong Kong, I mean, they provoked them, they provoked the embassy, or the, or the, or the, not the embassy, but the Chinese government presence there tried to set it on fire. But they didn't resist. So it was a, you know, it was a tremendous restraint. And the city went through hell. My aunt was there, again, very personal. You know, she couldn't come downstairs. She was afraid. She's in her 80s.  Ordinary people of Hong Kong who want to get on with their lives being terrorized. So no, that, that was, that was something. So one of those things, theoretically, but to, to see it in action, you know, brings it home. So that was your turning point. I mean, mine was noticing the propaganda and saying, oh my god, this is how the United States always goes to war with lies and propaganda. Absolutely. Absolutely. I share that with you. Yeah. And so you're seeing the same kind of lies and distortion, but you're seeing it much more personally in relationship to your experience of what's happening. And then that's right. That's right. And really the, the worrying thing, and this, of course, you know, you, you remind us of all the time, the really scary thing is to see the, the progression, the playbook, first the propaganda, then the demonization, and then stuff happens.  It's a playbook that works. And again, we saw it happen with Ukraine. I'm very familiar with the issue from, from 30, 14 onwards. But I didn't realize it would, you know, be allowed to get to this point. But then you see the demonization, but the demonization of China, this Hong Kong, and the, and what's been happening over, over Taiwan, the crossing of very, very clear red lines. Those all lead up to something. And then it's, it's really worrying what it leads up to. Yeah. So, so the, the propaganda is not incidental. It's not accidental. It accelerates. You can observe its progress. And it doesn't lead to a good place. We have seen time and again. Correct. And, and the distortion confuses everyone. Because if you're not on the ground, if you're not from there, if you don't understand, but every day for, like you said, a year, you're getting propaganda. It's very hard to have a true relationship with what's happening. Because you're having, indeed, it is hard for us. So I'm early, I think I've seen how it works. You know, it's like, it's really like stigmatization, right?  So it, it works on this sort of social dynamics. It's, it's not based on, on, on, on reason. It becomes discrediting. It becomes sort of beyond the pale to discuss certain things. Right. And I, you know, by talking about these things, I, I'm beyond the pale in this society, at least. Exactly. What I'm giving, what I'm trying to say is a lot of this is basic common sense out in Asia. One thing this does is set the Western population so far from what is common sense. And what, what I would maintain is most of the world, but especially in Asia, you guys have to have it, you, it is sense it, it's really quite terrifying. It's, it really, really alienates the, the kind of elite class, the funded class of the West from, from the common sense of Asian people. This, this experience of Hong Kong, for example, a very well known, very respected statesman, a friend of mine, as it happens, George Yeo, former foreign minister of Singapore. If you look up some of his talks on YouTube, you know, a guy who had been foreign minister for many years, regular general in the, in the, in the Singapore armed forces. This is not a guy who's a radical in any way or, you know, someone very comfortable with US power in East Asia. Yeah, that was too much for him. The Hong Kong thing. There is no way to talk about it nicely or to talk about it honestly while remaining on basically remaining polite with what the West has done to it and how it is talking about Hong Kong. Right. The great news is it's now under control. It, you know, they, they implemented a national security law such as you find in every country. That was just the one gap that Hong Kong had. Yeah. So I, I, I don't want to make this a seminar about Hong Kong, but anybody curious about it, I can go on about it. I thought I taught an entire course in it.  So let's talk about that because there's Hong Kong or there's, it's like even Kayla and I were talking about the way we see the world because we've been through China to China, but that we can't even talk about with anyone else because it makes us feel crazy. Absolutely. Absolutely. I think that's the part that you're talking about. It's like, so do you experience that?  Let's just say I have lost my positions and opportunities over my speaking out. Yeah, it hasn't been, it hasn't been free. Yeah, it hasn't been free. So yes, I have. I've just been willing to do it. Wow, I have more. I just couldn't keep quiet about it. Sorry. So, so I, yeah, I have lost those positions. I'm no longer at these places, nor do they want to be associated with me because decent people don't talk like me. So now, I think one thing is this. I mentioned political theology, sort of, you know, in my bio, but one might also talk about political anthropology. That is that when you engage in these disputes with people, you're not, you're naive if you think that you're in the space of reasons. You're naive if it's about, if it's, if you think it's epistemology, right? This is what liberals like to pretend. It's all just, you know, the space of reason, right? No, it's the, a clearer frame for understanding this stigmatization, for example, is the religious one, or in terms of religious anthropology, this is pollution, stigma indeed, right? Pollution, it's between the, the, you know, this, this is a phenomenon in religion.  So it's, they're working with, with that. They make entire topics. They make China, anything around China becomes that. And if you are associated with that, you are also the impure. Now these, these phenomena are, are quite deadly. So from a certain perspective, the US continues to be, it's sort of like a village, you know, Salem, circa 1800s, or was it 1700s? The Salem witchcraft trials. So the, the, the phenomena of the, the witch hunt, I'm not just talking metaphorically. I'm not just talking about being, colorful here. There is other dynamics that are mobilized, right? But except by the massive apparatus of, of state propaganda, state and state affiliated media. And, and one discovers an entire media class of people who are prepared to play this game. They either get something out, they, some satisfaction out of it. Or again, another thing I've seen is how they are rewarded for it. But, you know, from my perspective, the US looks like, you know, it's like looking at a village of really superstitious people. You know, it's as small, it's, it's like a village of, of what it is, semi, semi-literate, sort of witchcraft believers, but witchcraft phenomena are real in the anthropological sense. You can do this to people. And another age, so if I may, a kind of Southeast Asian perspective, I just tweeted about it yesterday, is the understanding that the, of the relationship between this and mass murder, because it has happened time and again in Southeast Asia, quite often to the Chinese community, but not just to them. So the Indonesian massacre of 1965, for example, that it's just forgotten, maybe 800,000 people or a million people were, were killed by hand. Okay. Shot, you know, bludgeon over their head, stabbed, strangled until the rivers ran red, literally. How did this happen? And quite recently, these documents were released about US and UK involvement in this. British are very, very good at this. They had an entire unit for spreading black propaganda. And the black propaganda included stories such as, you know, these communists. So this was the mass slaughter, just to recount the broad outline of the largest communist party in the world outside of China. It was peaceful. It was unarmed, which is perhaps their, their, their, you know, fatal for them. So they were, they were demonized. It was an argument. It was portraying them as like demons, as murderers. And then there were these atrocity stories, you know, they would do these horrible things to people, et cetera. And this came out of a newsletter, run out of Singapore, laundered through several countries and purporting to be Indonesian, in Indonesian.  Okay. This is completely in, now it's in public domain. When you see what these witchcraft sacrifice mob violence things do, and I was very aware of this in Hong Kong. Okay. Uh, you take it a lot more seriously. This isn't just about, you know, it's unpleasant for me as a Chinese person. No, because I know the intimate relationship between these processes of victimization. Right. And mob sacrifice, because in Hong Kong, again, you saw the, the crowd, the mob and mob behavior. A mob is something else.  Um, so they play with these phenomena and you are seeing this also being played with on a mass scale in, in, in the US. This is just a perspective on this. So these things, this black propaganda has huge effects on people in Southeast Asia. It's not, you know, not just you get beaten up in the subway. Okay. There's a mass murder. One of my earliest memories was, was of one of these incidents. So, I mean, you're talking about what happened in Rwanda. You're talking about what happened, but really this is what happened in Germany. I mean, because that fascism was a mob behavior where the mob was, you know, riled up around the same thing with Jews by the same stories. Well, they knew how to invoke this. Yes. Yes. Yes. And the people who invoke it very, very well. Uh, you know, people on this side, actually, if you look at the largest propaganda apparatus in the world and what it is doing. So it's quite a shock. You know, look at me educated in the UK and so on to, to realize, wait a second, these people are doing this scientifically, right? Deliberately. And well, they've done it to all kinds of people. And now that they're back at it, they did it in, in, in Indonesia. Uh, they used it in Malaysia. The Cold War was fought also in Malaya and in Indonesia. It's just people forget it. All the stuff you hear about Vietnam, strategic Hamlets. In other words, mass interning people, Agent Orange, all these were pioneered by the British in Malaya. They, you know, they consulted and, and, and taught the Americans in, in Vietnam. So there is a history to these, to these things.  There are people, very, very kind of well behaved, straight down the line people, Nuri Vitachi, for example, this extraordinary, really, really fun guy, right? This, this extraordinary journalist, I've been reading him since I was a kid. And that's a long time ago, based in Hong Kong. He too, he was a supporter. He, he started out supporting those protests, which began long ago by the way, 2014 umbrella protests and so on. And he saw with his own eyes in this recent set of protests, US officials handing out the lines, teaching them to ask for, you know, to be saved by Donald Trump. So, so you see this, this, this manipulation, and I have an absolute horror of this, this kind of manipulation. It's, you know, there's a line there. I think that's, that's the same with, you know, what we do with food pink, it's that we see the smoke. And when you see the smoke, you're supposed to put out the fire, not flow, you know, blow more oxygen on it. So it turns into a full blown fire and does destroy people. And I so appreciate you are grounding us in these are lives. This is, this is murderous. This ends up really, really ugly. And yes, these are people who are living in peace with each other. Yeah. So it shouldn't, we need to take this seriously. It's not light. And the, the fact that this Pew poll just came out and said that, you know, when Americans are asked what is the greatest threat to the United States, they say China. When China's done nothing that could be a threat to the United States, and where they're suffering floods and, you know, fires and, you know, homelessness in their cities, but the greatest threat is China, that distortion of like, we can't, we're not getting anything else taken care of. If everything can be blamed on China, then, and we can go to war with China, it's probably better when you're talking about that's a fantasy on steroids, because no, that will just make everything worse. That is a real it. Yeah. Right. Right. So there is the, the conceptual part. If you ask somebody on the street, well, what's the greatest threat? And then if he or she says back, oh, well, it's, it's, it's China. On one level, you know, and we went over this in, in the space, you might, it may not be that deep. It may just be, well, this person realizes that's the right answer. They hear it every night, right? On every mainstream channel. But it doesn't, it doesn't stop there. If it was only that, China is too far away for people to bother with going to war with. The propaganda doesn't stop there. It's not at the level of argument. So if you see the coverage, it isn't just actual argument about China doing this, China doing that. It's China bad in every reference possible. Every reference, every photograph, every photograph that comes out is a security camera, a guard. They literally fill, you know, put on a, a dark grim filter, a cloudy day.  You know, so every single image is a negative image. So they're playing on the, this, this phenomena. They're othering it. They are quite honestly, they're scapegoating and, and this scapegoating phenomena is, is kind of, it is also politically the diversion. Scapegoating is, is, is political diversion. Right. That's another reason why it's so strong here. Because we need a lot of diversions. Right, right. And so one worries that as it gets, things get more and more out of control back here for reasons internal to this place, that there's more of this scapegoating because that's the one thing that people can agree on. And that's the other point. The agreement, even though the agreement is the cost of their, their lives. Yes. So, you know, I just would like to go back because you started that you had just read, you know, we were talking about the pivot to Asia, or that's where you started. And you said, I was just looking back and reading some things from back then. I think you said from Hillary Clinton or something. Can you, what was it that you saw them that you found so interesting? Well, she had some statements, right? Like, she had to make this argument for turning to Asia after the administration had been focused on the war on terror and the Middle East. And we're failing at that. So they needed a diversion. That's right. So they had to say, well, we have to come here and the words were harness Asia's growth and dynamism. This is central to our strategic interests and a key priority for President Obama. Harness. Harness. Yes. Harness. Asia's growth and dynamism. Yeah. Yeah. Right. So, and the U.S. portrays itself as maintaining peace and security across the Pacific as so there's this whole Pax Americana idea. So another, you know, a great paragraph from her is just as Asia is critical to America's future and engaged America is vital to Asia's future. The region is eager for our leadership and our business, perhaps more so than at any time in modern history. We are the only power with a network of strong alliances in the region, no territorial ambitions and the long record of providing for the common good. This is, you know, it's hilarious actually in retrospect reading it at the time I wouldn't have been able to. I wasn't going to wouldn't have laughed as I do now. Right. This is a country that has, I don't know, three, four hundred bases in Asia and no territorial ambitions while you maintain these bases in South Korea, Japan, you know, and all the islands around. Yeah. And bases in other countries as well, small bases and large. But the issue that they used back then was this freedom of navigation and it puzzled me at the time because wait, all those sea lanes, they all go to China. If you're worried, I mean, it's not that China is going to blockade itself. Who is threatening freedom of navigation? So what they do is they come up with a concept. And, you know, I was at the a think tank strategy and strategic and international studies type of think tank and very, which would look at things from a military and strategic perspective. So all of a sudden when they bring this concept out, I think what a lot of us would have thought is wait, there's something I don't know here.  They seem to use this vocabulary. And there are concepts in there that I know, maybe there are there are things happening that I don't know about. Actually, there's nothing behind it. This is like rules based order.  There must be something, you know, something sophisticated that I don't understand. Well, actually, it's simple. It's as simple as my rules. You take the orders. It's a way of not talking about international law. It's a totally empty concept. So you have these totally empty concepts being put out there. And then I saw diplomats from, you know, from Japan and then from the US as well. And one voice after another echoing this. It's amazing. They all have the same vocabulary all of a sudden this new vocabulary comes out and they're all parroted. It's something to watch. So I saw that kind of build up. I didn't realize he would build up to this. Well, I'm thankful that you like talked about what how you read Hillary the first time and how you read it now and how we're not even aware of how the information that we get distorts our thinking and allows us to accept things with an imperialist mindset, even as we're peace activists or even as we care for the planet, or we're not even aware of the contortion of our own thinking and where we are in our lives. Right. Right.  Um, and so before we move to Kail, to let Kail ask him questions, you know, what in you encouraged you to tell the truth, even though you knew you were going to pay prices? And then what has happened since you've paid those prices? Have you become more silent?  Like, if you could unpack that a little bit, I think it was in the first place, an isolating experience, which is how it's meant to work on you. You lose friends. You lose, you lose being an acceptable member of a certain circle, certain class. And you realize that they, they, they, they surround themselves with a, with, with a certain worldview. And within that worldview, there are these assumptions that you don't question. And you then realize that one of those assumptions is American empire.  You know, it's nice to have the quiet part spoken out loud. And it is, it is also white supremacy. If behind it all there is, when I, when I talked about the stigmatization, there is racial stigmatization going on. It's an essential, essential to this. You might wonder, well, these people don't need to do this. They're too smart. Well, we're behind that. We're talk, we don't need to talk about, you know, bringing civilization to people, right, or Christianity or whatnot. We have democracy now and justice. No, it's not enough to do that. You do have to racialize the chinks. You do have to associate them with certain images and you see that happening in the media. Your images of disease, for example, a COVID, what proportion of the US is Asian America is Asian. And yet the predominant image is of some yellow face, some Asian person. Even in Germany, it was really, it's hilarious to go back over these things. So then you have the tagging that the association with disease. This is all old stuff. We know this from what was done to the Jews. We know this from what was done to the Chinese way back, the association with disease, for example, right? These people coming across these Coolies, they were the bearers of disease. Therefore, they had to be expelled. So the racial thing is very strong. Now, I'm not someone, as I said, who, you know, for whom speaking about that was part of the way I operated. Remember, I was in polite circles.  Yet these are essential to understanding what's going on. So this is a very interesting moment. This is when these old things come out and they just come out and say it. In that way, it's interesting and it's worth talking about because I think China has caused a kind of derangement. It is causing a panic. And I sometimes, I often say this, look, the US goes picking on one, creating one enemy after another. But this time you have picked on the largest and longest lasting. There isn't going to be one after this. So there better be some way of de-escalating from it because they ain't going to be, this is not Iraq. You can't even fail at this.  This is going to be really, really bad if it gets to blows. Well, short of that, this demonization was going on. I think to answer your question, one of the reasons, one of the things that made me speak up was these attacks on people during COVID, my own safety. I live in a pretty sort of nice place. But even around here, occasionally, you sometimes you get accosted, right? And certain racial remarks are made. So the Asian community here has had quite a time of it. And nobody wants to know about it. Because this is the permissible racism of the moment. There was Black Lives Matter, there was BLM and so on. But suddenly you have this and this is very inconvenient. And so it's, don't talk about this. But yet they're doing classic techniques of racialization. So then one has to think further back and you realize that racialization, the introduction or the invention of race and its introduction as a concept for dividing and ruling people and for creating a certain hierarchy, race as a political, as a power construct, is very much part of how Asia is thought about. So well, yeah, I don't know if I've answered your question, but I couldn't keep quiet and be a human being. I couldn't, there's absolutely no way, you know, okay, personal again, but what could I do? What job, how could I function and keep quiet about it? You know, when I came to the U.S., a lot of the work, whatever, what expertise or networks or knowledge I had was to do with Asia. But if you have this totally arranged, deluded idea of China, you also have a deluded idea about the rest of Asia. Please, it's even worse. They know nothing and they care nothing about Southeast Asia, right? So it's, no one wants to know, no one wants the truth. There have been times when I was a consultant working on things in which, you know, you help people understand a sort of business environment, an investment environment. Well, the whole thing is politicized and militarized now. There's no room for that, that kind of thing. Still, yeah, I mean, basically, you know, what we've been talking about is, is the distortion of reality in the United States has almost made brittle. The people of the United States, when the truth hits, it's kind of like, you know, a parched soil. Yes, yes. Find a way in and even I think the water hits, it must really sting. Yes. Yes. So that's a, that's a lot. And I feel like everyone's taken in a lot today that you have been so generous. And I, John, I just want to say to you, like, I know the courage it takes for you to be who you are, for you to give up a life that you've built and positions that you've built and, you know, your capacity to be someone in the world to instead, to instead be what we should all be, which is human beings in relationship with each other. And they have is that and I, I think that's my experience of Asian values that I think might be a little painful for people that on the West that have those values of humanity kind of stripped from them as part of being in a white supremacist, you know, you know, the roots of United States are based in, in humanity. And so, you know, slavery and genocide of the indigenous peoples that we're still trying to heal from and change from. But humanity and being human is really at this moment in history, the most important thing. So I just, well, that's what you taught us myself and the co-host, right? I want to honor who you are as a human. And then I know we've like on way over time. But, Hale, I wanted to bring you in and ask you to ask John some questions. Absolutely. Yeah, I just want to say it's a pleasure to speak with you, John. And thanks, Jody. Thanks, everyone. You know, I really thought it was interesting how you were talking about, you know, the link. Well, I mean, this is not what you explicitly said, but you know, I've been thinking about the link between kind of white supremacy and this notion of rules-based order and how it's been propagated by, you know, western government. And I think a lot about how that relates, especially to all the tensions in the South China Sea, where you have, you know, China, for example, has been pushing for much more regional dialogue and solutions to resolve different territorial disputes in the South China Sea.   This wasn't an issue that the United States was so obsessed about 10, oh, you know, maybe 15 or 20 years ago or 30 years ago, but it became such an obsession in, you know, within the last 10 years. So how do you think, why do you think that is and how do you think it relates to this notion of a rules-based order that's deliberate? Yeah, that's why I started with this pivot to Asia business. There was a status quo with the U.S., the top dog in Asia. And at a certain point, it became not acceptable. And, of course, it had a lot to do with the rise of China. It's not accidental, I think, that this happened after the global financial crisis, in which actually the capitalism, global capitalism, western capitalism, was saved by China, ironically. But it's around that time, 2010 and so on, that the Chinese economy started to, well, it exceeded Japan's and then it started to be a threat to the U.S. economy in terms of, you know, which one was larger. And they had to be put down. It's really as simple as that. It does not tolerate a rival. U.S. empire does not even a rival in that sense.  If you know, in the late 80s, they basically kneecapped the Japanese economy. Of course, it was possible to kneecap Japan. You have bases there, you know, you could bring them to heel. They are trying the same thing with China through these sanctions and it's not going to work. So what next? So, you know, on one level, it is just, it is that no one should, the U.S. cannot, if you hear these people talk, it's this bizarre language. I think the scientists did it the other day too. Are they becoming larger than us and therefore this is a mortal threat?  So it's that kind of thing. At one level, it is that. And that's how a lot of Asians see it. What they don't see is this embeddedness in racism, in settler colonialism, etc. That they don't see, that they're less aware of, that I saw as an Asian person living here and understanding, wait a second, to understand this, the full depth of this. You need that, you need this perspective. I became a James Baldwin, Malcolm X guy here. I was reading him and said, this is really, you know, the 60s guys, the Black Power guys, they understood things. There was an identification with decolonization, a solidarity with the Third World that was then killed. And we have the Third World rising again now. Yeah, I feel like, you know, I was living in China for three and a half years. I was in China during the, I was living in Beijing during the tail end of the unrest in Hong Kong. And, you know, some people were framing the situation as a project, a decolonization project. And, you know, I guess like, what do you say to people who, I guess, regardless of whether or not, you know, whatever is happening, whatever decolonization efforts are going on in Asia, how sincere they are and whether or not they are not sincere. Why do you think the U.S., like, what do you say to people who think the U.S. should be involved either way? Because it seems like the U.S. getting involved. So they see, you're talking about Hong Kong as the protest movement is decolonization? No, no, no. Rather what the, what people in the mainland, officials in the Chinese mainland were trying to do for, but that was what my colleague, while I was working in Chinese news, was telling me, but what do you tell people who, regardless of whether a decolonization effort is sincere or not, why the U.S. should be involved?  And so how do you converse with people? The U.S. should get out of the business of suppressing decolonization, which is what the Cold War was about. Yeah. Hong Kong is, your colleague is right, is a case of an still ongoing decolonization. I come from Malaysia, which obtained its sort of independence in 1957. One part of it did anyway. It's not a complete process. As you can see in Africa, and particularly in West Africa right now, it's not a complete process. You know, I think we're going through a second and perhaps final wave of decolonization going on now, a decolonization of world order. But Hong Kong, you expect that a place that was colonized was an utter colony for so long in 1997, has the process complete? No. You had people who were very, really colonized in their thinking, for example. You had the attempt to preserve a colonial political economy in Hong Kong, which is what it was, this extremely exploitative economy, as far as the working class were concerned, it's inherited from the colonial era. If you know, if you ask me, Beijing should have intervened earlier to not let it get to that stage. Hong Kong should have had some of the social equality that people in Guangzhou had, rather than become a kind of extremely unequal hellhole for people at the lower end, while being a kind of capitalist paradise, a real estate and finance paradise. So there is a decolonization that Hong Kong has to go through and it's none of the US business. What I mistook you for saying earlier was there are people on the left here who like to use that language and talk about the protesters as decolonizing. I hate the way words like, that's why I don't use them normally, decolonize, even settle a colonialism and so on. They're bastardized later and virtualized by pseudo academic use. There's a kind of left here that wants to be disconnected from or with no connection with actual attempts at attaining sovereignty in the rest of the world. 80% of the world was under and the land mass and the population of the earth was under western domination was colonized. And that 80% of the world, it's not completed, it's path to freedom. Let's talk freedom, but in that sense. Well, and I think when we talk about freedom, we forget that that's freedom for everyone and so many times we love freedom with sovereignty. Right, we look through a class lens instead of understanding there's a whole class that isn't free. That is what isn't happening. You tend to rely in western media, it relies on a class of people on the other side that they have cultivated. These particular voices, all of whom were educated at certain places or they are being funded by certain organizations. And that's their job. Their job is to reflect those western values back. But if you actually live there and have any concern at all for people there, you would actually be looking more broadly and asking how are people doing. And I think that's the way to do it. One doesn't have to be an expert on Asia or on any particular part of this vast continent. But wherever you go, actually go, actually see people, actually observe their lives. Are they well? Are they not? As Jody likes to say, relate to them as human beings. Thank you, John. I know we've taken up over an hour of your time and so grateful. This has been so interesting. And I really wanted you here so that people could witness and hold space for a voice from Asia. Because we listen to people that have never been to Asia and talk about Asia like they know what's happening. So just to hear your thinking and your voice has been refreshing. Thank you, Kale and Grace for holding us all together. And we've gone over the hour. I just want to thank everyone for being here and to say next week our guest is Kale. So Kale has just joined the team. He's now the coordinator of this campaign. China is not our enemy. But Kale lived for three and a half years in China during COVID. And I think it's going to be fun to hear from him of what that was like. Another voice from, let's hear from the voices from Asia because we don't realize how manipulated our brains have been by the propaganda, the stories and the lies.  Our brains need a little bit of flossing so that we can also see and be clear and be humans together. Just in our holding space for each other and listening. So John, thank you for your courage. Thank you for your commitment. And thank you for being in conversation with us today. Oh, you just- Thank you. Thank you all. Thank you all. And thanks for- Yeah. Thank you. Thank you. Good night. All right, everyone. Good night. We'll see you next week, I hope. Bye.


Thanks for giving me this opportunity to say a few words about Basterdicks Holm, who very sadly passed away in January and it came as a great shock to the whole of mathematical community and to everyone who knew him. So I was one of his first students and I would like to say a few words about his work in general, but in particular his work related to the topic of Harry's talk, namely the Androids Conjecture. So Basterdicks worked in many, many subjects, number theory and algebraic geometry on modular curves, modular forms, also some algorithmic problems, and the Androids Conjecture. In fact, he did some seminal work on the problem and his ideas certainly contributed to the eventual resolution of the problem. Buzz was in fact the first person, so the conjecture was formulated first by Yvandre in the late 80s and then by Fransort in greater generality in the mid 90s and Buzz was the first person to come up with a strategy, a general strategy to approach the problem in full generality and in fact his ideas and what his work led to the resolution of this problem under GRH. Well, the eventual resolution is, follows the approach by Pilar and Zanya. However, the ideas of Buzz, for example, the use of monotony and the properties of hypercorrespondences are still crucial elements of the proof. So most importantly, Buzz was the person who isolated the crucial ingredients which is bounding below the degrees of special points and this will be the topic of Harry's talk. And he was actually published this as an open problem and pointed out the connection with Colmey's formula, Conjecture, which for the Foutings height of Cme billion varieties and this is what, this is also the crucial ingredient in the proof. So the proof of the final ingredient and of what you might call Buzz's Conjecture was announced in September and I'm sure he was very pleased to learn it. So yes, I would say that Buzz is passing away, it is a great loss for the community and mathematically, of course, he's family and friends and he'll be a certainly remembered. Well, this is what I wanted to say now over to Harry. All right, thank you, Andre. Yeah, thank you for saying a couple of words. I personally didn't know him that well, but I met him once at the Fields Institute and I was a young student, younger than now. And he was always very friendly and open and open to discussions. So, okay, thank you to everyone who showed up to this talk. I will try to give a brief overview of the history of the Underwater Conjecture and its eventual resolution last year. I mean, I will give my perspective, obviously, which is influenced by my taste. And I would say that the problem or the eventual resolution of the problem had, of course, many ingredients and parts of it come from model theory slash transcendence theory, I would say, and this is more my turf. So I will concentrate on this part of the proof and all the people who contributed to this part. Of course, I will try to mention everyone who made a contribution, but please correct me in the chat or whatever, if I missed something or if I forgot something. As I said, this presentation is heavily influenced by my own tastes, obviously. Yeah, I guess it can't be helped. So I will start with an introduction basically to everyone who maybe has not even heard of the Underwater Conjecture. I mean, I guess there's still a lot of people like that, even some who showed up or maybe students. And then I will explain what the Pila Wilkie counting theorem is. This is perhaps even interesting to people who are not interested in the Underwater Conjecture. We explained the Pila Zania strategy, which applies in many, many situations. And then some ingredients that go into the Pila Zania strategy. And well, particularly, so the sort of the new ingredients come in section six, which I doubt more counting. And at the end, if there's still time, I will talk about recent work of that was that goes perhaps a little bit beyond Andre Ortt towards the pink conjecture or silver pink conjecture and mentioned work of other mathematicians as well. In particular, there are many young mathematicians who work on these kind of problems. Okay, so what is the Underwater Conjecture about? So we start with the lattice in C. So that is its free being group generated by two elements in C that are linearly independent. So one can really imagine this as some sort of lattice in R2. But we think of it as being in the complex numbers. And then given such a lattice, we can sort of study its symmetries, I would call it, or the formal name for it is endomorphisms. And these are all complex numbers that if you multiply the lattice by the complex number, you stay in the lattice. So multiplying by a complex number is really you scale the lattice by a certain number, then you you rotate it a bit. And most of the time, so like in my second example here, if we take generators of the lattice as being one, and i times pi, say, the only endomorphisms that preserve the lattice are the integers. Okay, so you kind of can only multiply, for example, that's by two, and you will still stay in the lattice. But there are there are exceptions. So for example, if you take the square lattice, so generate by one and i, that are sort of perpendicular to each other, then you can also rotate by 90 degrees. So if you multiply by i, and you will still stay in the lattice, I hope that's kind of visual enough. And we say that if this happens, if this endomorphism ring, so this animal is a former ring, is bigger than the integers, then we say that the lattice has complex multiplication. So this is really also where the name comes from, which is a bit weird, why complex multiplication. It's because we can multiply the lattice by something that's not real, not the integers by some complex number, and we still stay in the lattice. Okay. And I think this observation probably goes back to, yeah, the 19th century, I would say, at least. Okay, so what does it have to do with number theory or, I mean, we just looked at lattice or algebraic, sorry, algebraic geometry. So to each lattice, we can attach an elliptic curve. Okay, a curve of genus one with some specified point at infinity. So I've written down sort of a universal family, elliptic curves, the Legendre family here, and which is parameterized by all lambda that sort of by the f i line minus zero and one. Okay. And okay, so each such elliptic curve is isomorphic to see modulo elettis. The isomorphism can be written down explicitly. It's actually given by Weierstrass p functions. So these elliptic functions that were constructed by Weierstrass also very classical subjects. And what what what what comes up, if we look at this particular family of Legendre curve, curves is this particular group gamma two. And I will just explain a second why these are sort of elements in SL2Z. So integer matrices with determinant one. And this particular subject was given by all the matrices that are congruent to the identity model of two. Okay. And these elements, these matrices, they act on the upper half plane by Möbius transformations. So in particular, because they are defined over R, they preserve the imaginary part being positive. So they really act on the upper half plane. And there is a covering map, this lambda function, I think is as it's known, it goes from the upper half plane. So or one could say is a complex analytically the disk to stay without zero one. Okay. And this is kind of, yeah, we'll see this kind of structure a lot in the store. And this lambda function has the property that it is invariant by the action of this group gamma two. And so in particular if you quotient out H by this gamma group, then we get C without zero one. So topology. So really C without zero one is isomorphic to H modulo this arithmetic subgroup of the group of symmetries of H. So all symmetries are given by SL2R. And particularly arithmetic subgroup gives us this curve. Okay. And what's also important is that this function lambda, it in particular if we translate tall by tall plus two, then we get lambda back. So this function lambda has a Fourier expansion. Yeah. And this fully expansion I've written down some, some terms is defined over the integers. So it has some arithmetic nature to it. It actually appears also now in other interesting conjectures, some of them by a Ramanujan, for example. And it is basically given by, this Fourier expansion is defined as basically given by a series in Q and converges on the upper half plane. And this will be important for us later, this particular form of lambda that we can write this lambda function down like this, a sort of an analytic function of an exponential function, but more about that later. Yeah. Okay. So I've written it down. So yeah, as I said, this lambda, it induce an isomorphism H modulo this arithmetic subgroup to, we call it Y2. Y2 is just a projective line minus three points. So let's just, as an aside, this function lambda is also important, for example, to showing like these, I think it's called little Picard's theorem, every entire function that emits at least two values as constant. Okay. And here now we can, the first time this word appears, we can say that this curve Y of two is a Shimura variety, but I will talk about it a bit later. Okay. So because I think this E lambda is isomorphic to C modulo the lattice, each endomorphism of the lattice gives us an endomorphism actually of the elliptic curve. So algebraic endomorphism. And we say that an elliptic curve has complex multiplication. Now, if it's lattice has complex multiplication, and we can write down a specific condition for the lattice for this to hold, namely, if we write the lattice as z plus z tau, which we can always do after scaling, then the lattice or the elliptic curve has complex multiplication, if there is a non-trivial element of SL2Z that fixes tau. Okay. And if you write down an equation for this, then you find quickly that tau has to be an algebraic number in fact. So yeah, algebraic number and is projectic imaginary. Okay. So now, actually, these are the only numbers that are algebraic and whose value by lambda is also an algebraic number. This is a theorem by Schneider. And we already see kind of the connection to transcendence theory, but of course, Schneider was a transcendental number theorist. Okay. Some questions in the chat? All right. So far so good. Now, we come to the first theorem, namely for André, who was mentioned before by André. Okay. So we have, namely, we have these modular polynomials. These are polynomials defined over the integers and two variables. And they have the property that if I have two lambdas that vanish, then the attached elliptic curves to lambda one, lambda two, are isogenes, we say, and they're connected by an isochini whose kernel has cardinality n, say, or even we can even say its kernel is a cyclic group of cardinality n. And, okay, I think at the end of the 90s, at least was published then, André, so Eva André, proved that if you take a curve in the affine plane, and you intersect it with all the invariance lambda one, lambda two, that correspond to CML elliptic curves, and you find infinitely many of those, okay, then your curve has to be special, namely, it has to be a modular curve. So either one coordinate is constant and is equal to a CM, corresponds to a CM elliptic curve, or it defines a modular curve. So actually each point on the curve corresponds to elliptic curve being isogenes. So, so how did he achieve this feat? He used transcendence theory, in fact. So he used very innovatively the theorem of linear forms, logarithms, and he combined it with class field theory. It's a very interesting development. I think it was a bit, well, I probably claimed too much here, but I think it was quite surprising to the community back then that this works. And however, the problem with the proof is, even though people tried, I know some of them, in fact, I haven't tried myself, it doesn't seem to extend to higher dimensions. So it is really restricted to curves. Okay, so this is the first instance I would say of the Andree-Aud conjecture, okay, which I will formulate a bit later. But if some of you are familiar with Man and Mumford, this is really a direct analog of this. The Man and Mumford conjecture says that the sadistic closure of torsion points is a subgroup, is contained a finite union of subgroups, say in the multiplicative group. And this is a very similar statement for CM points, special points. Ari, there's a question in the chat regarding Picard's theorem, a little Picard's theorem. Yeah. Yeah, okay, the question was why it was a little Picard's, yeah, maybe I overdid it a bit with a connection, but if you want to prove a little Picard, one way to prove it is to use the lambda functions that I just introduced, because it gives a, so if you remove from C to points, the covering map is, yeah, is a disk, which is, yeah, compact, which can be put into a compact, or is rather bounded, bounded domain. Okay, great. All right, so now we go to higher dimensions. So we take a product of Y2 now, Y to the n, and we can also define a special point. So here's special point is each coordinate corresponds to a CM elliptic curve. So now we're moving sort of from 2 to n dimensions. Okay. And there's this famous theorem of Pilar, who proved, actually proved a more general statement, but this is kind of what his theorem is known for. He proved that if you take any collection of special points, so that each coordinate corresponds to a CM elliptic curve, you take the Zariski closure, then the Zariski closure is the finite union of special subvarieties. Special subvarieties are just products of special points and modular curves. Okay, maybe I should say what a Zariski closure is. So it basically means that if you take any algebraic variety in Y to the n, and you intersect it with a set of special points, then the intersection can be completely described by special subvarieties. So for example, it could be a finite union of modular curves. Okay. Or it's a finite union of products of modular curves. Okay. Now, what did Pilar use? I mean, this was a real breakthrough because for years, there was only Andres's theorem. People tried to generalize it, and as I will say later, and Andrei mentioned, there were also other approaches, but what Pilar did was he used his counting theorem with Wilkie. So it is stated here. So there are some words that come up that I will explain. So the counting theorem is a very, very general theorem. It says that if you take any what is called definable set, so definable means definable in some fixed or minimal structure in the real numbers, and you count the rational points on this x, then you can bound its number sub-colynomially. So that means if you fix the height, say it here, if you take a rational point on your x, it's just some subset in the real numbers, you take a rational point, you bound its height, which I denoted here, which is the maximum of the numerator and denominator by some t, then you get a bound that is sub-colynomous. You can beat any power of t. What's important here, though, is that you have to remove some set of x. So you have to remove what is called x-alc, and x-alc is sort of the algebraic part of x. So it's kind of surprising we want to do algebraic geometry, but this theorem is important, and you have to sort of throw out all of the algebraic parts. The algebraic part is really everything that is positive dimensional and can be described by algebraic qualities, or inequalities also. So what I would also say, the proof also allows to, here we focus on q where you have the height. You can also put in some fixed number field, and what we'll see later, we can also count algebraic points of bounded degree, and of course you have then to extend the height from q to the algebraic numbers in sort of the usual way, which I hope is familiar to most of you. Now, okay, so more to the pillar, we'll give the counting theorem a bit to its history. It's inspired by a theorem of Pompierian Pila, I think at the end of the 80s, beginning of the 90s, where they proved exactly this theorem, but only for transcendental curves. Transcendental curves are curves in R2 that are not zero sets of some polynomial and two variants. Okay, and I think the idea, I think I heard the idea to get these sub-pollinomial bounds is due to Pompier. But also intermediate results, so from curves to this very general theorem, were previously obtained by Pila, for example, surfaces, they were used by Masa and Zanier to obtain some of their theorems for relative manamumfolk. But I think perhaps one of the great innovations of the theorem was that they introduced this very general theory of hominimality, which comes from logic, into this kind of counting theory. And as I said, I don't know much about this because I'm not a logician, but it was developed more or less, I think, by one of these Pilae, and of course, there are other names like Gabrielov and, as we say later, Wilkie McIntyre, who played a pivotal role in this. Okay, so I will very, very quickly explain how the proof goes. So you have this x, and I'll give some example later, which you can think of sitting in Rn, some, some, some, let's say, analytic set. The first thing that you do is you cover it by smooth charts. So you don't assume axis is definable in hominimist structure. It doesn't mean that it's smooth, but it's sort of piecewise smooth. And you can control the degree of smoothness depending on how many charts you put. So after you sort of parameterize your set, this is the first very difficult step. And I think the first work towards this also goes back to Gromov. Then comes sort of an arithmetic part where you use the determinant method of Pilae that Pilae introduced for the counting. Or, yeah, as I mentioned below later, because it's important later, you can also use Siegel's Lemma to show that all these points of bounded height are contained in an algebraic variety. And then you intersect this algebraic variety with your x. And this is, in fact, where the assumption comes in that you have to put, that you have to take out the algebraic part. Namely, if your x doesn't have any algebraic part, then this intersection will have lower dimension than x. If your x is not completely algebraic, you will cut down the dimension and then you repeat all of the arguments again. So this is roughly the idea. Okay. So now, oh, yeah, I have messed up the pauses here. Okay, then in order to prove a theorem, Pilae used the so-called Pilae-Sanje strategy. So the Pilae-Sanje strategy was developed by both of them to give a new proof, in fact, of the Mandemann-Foth conjecture for a billion varieties. Okay, so what's the idea? The idea is you take a fundamental domain F for lambda as I said, you have the upper half plane. It's not, yeah, it's, and you, but you have sort of many, yeah, lambda is highly non-injective on it. It takes the same value quite often, for example, at tau and tau plus two, the same value. So you have to take a fundamental domain for lambda on H, and it has to be a suitable fundamental domain. This is, you can't take any fundamental domain, but sort of the first one that comes to mind works. And then you can show that for every quadratic imaginary tau, there is some tau in the fundamental domain, such that its height is bounded. Okay. And here M is some number that doesn't really depend on anything. Okay. So this was shown by Pilae in this case. Then there is a theorem of Siegel that says that the number field generated by lambda of tau for a quadratic imaginary is bounded from below by a power of the discriminant. Okay. Now we look at sort of the uniformization map of this product of modular curves by the upper half plane to the end. And this we do is given by each coordinate is just the lambda function. Okay. And then we look at the inverse of an algebraic variety in y to the n, in the upper half plane by pi, and intersect it with the fundamental domain. Okay. So I denote this set by xv. So it's all the toss in the fundamental domain that map into our variety. Okay. What's important here is that because this whole hominimality theory is a real theory, we always sort of identify Sie with the real numbers in the obvious way. Okay. But it's kind of a step that I will skip. So this set xv is very important for the proof. Okay. So first, xv is definable in the structure R1xp. So we have this xv. It's defined by this sort of complicated formula. So you have any algebraic variety. You take sort of all the toss that map into v. And what I'm saying is that even though it's complicated, there is a mathematical formalism that captures it. And it's actually the structure called R1xp. What is R1xp?  But you also joined sort of a finite number of analytic functions that are defined on some compact on R. Okay. So power series in several variables that are defined on some compact and the exponential function that's in fact unbounded. Okay. Now, if you look at lambda tau, this expansion, you see it's actually an analytic function of q. Okay. You have some, if you think of q as some variable, then it's an analytic function of q and q itself. Well, it's, if you restrict it to a fundamental domain, it sort of consists of the exponential function over the reals and extended a bit. Okay. So in fact, it's not hard to believe that this lambda is in fact in this structure. Okay. But of course, yeah, I mean, I skipped a lot. So if we don't move to the fundamental, if you don't restrict to the fundamental domain, this is not no longer true. It's not definable in this O minimal structure. But yeah, what is an O minimal structure? Indeed. Yeah. So I won't explain it in detail because it can take takes a while, but I will tell you how I think about it. So an O minimal structure is kind of a general, you can think of it as a bit of a generalization of an algebraic variety. So most of what you're looking at are sort of equalities and inequalities of polynomials in analytic functions, at least in practice. Of course, the theory itself, if you want to develop it, is much more complicated. So you allow, for example, to take any zero sets, then project it, and so forth. And you have to, in order to tame it, you have to do a lot of work, which was luckily done by Wilkie. And for this particular thing, the extension of R and X done by van den Driesen, Mechendier and Marker. And as soon as we have their work, we don't have to worry about anything. But to give you some intuition, I will give you sort of two examples of sets that can be defined in an O minimal structure and or not. So the first set X1 is one that you might know from school. It's the graph of the exponential function on the positive reads, or actually, no, on all the reels. So I have not put the empty set here. So I just put an inequality to show that it doesn't really add any magic. So here the graph of the exponential function is definable in O minimal structure, but it's of course a highly transcendental thing. So it's not, it's not given by an algebraic function. But if you take, for example, X minus sine X to the graph of sine X on the positives, this is not defined by an O minimal structure. So why is this if you, for example, fix X1 to be say one half, you get an infinite discrete countable set. Okay. And as soon as you have this, you have sort of a form of defining the integers. And if you can define the integers, then there's really no hope of any tameness. You can think of this, this, this at least is how I think about it. Okay. All right. So there are no questions. Okay. So, so this, this, this was sort of our short primer, our short introduction to O minimal structures. Then how, how do we proceed? Okay. So what I will explain now works is again, as I said, is the structure is, is the strategy of pila insanya. And it was first employed to give sort of alternative proof of money month for really the money month for, for example, proof by the new. Okay. So you take a special point on your variety V in the product of modular curves. Then the first thing that I said was you can then find in the inverse on the in the fundamental domain of the upper half plane, you can find a quadratic imaginary or a tuple of quadratic imaginaries whose height is bounded by the discriminants of these points to some power in. Okay. Never mind that we have a tuple here. It's kind of, it's exactly the same, same principle. And we fix the number few K has been Q adjoined by this toe one up to two N, which is just a number of feet. Okay. Now, if we want to, we can now apply the pilawilki theorem to the inverse of V in this fundamental domain. Okay. So we count the, because we have this height bound here bound by discriminant, we can count these points and we get some sub polynomial bound on the number of points in the inverse. Okay. Bound by the discriminant. So here we can take any epsilon that we want. Right. So we can beat any power of delta. All right. So that's the first part. All right. Then the second one is okay by what I said before, we have a Galois lower bound, a polynomial Galois lower bound for the image of this point in the upper half plane by lambda. So, or you can say for the special point, we have a Galois low bound in terms of the discriminant. Here I've taken one fifth. I could take one over 100. It doesn't really matter. All that matters is that we have some positive power of the discriminant. Okay. Now imagine that your V is defined over Q, some fix now if it doesn't really matter. Each of you can now apply the Galois group, the absolute Galois group over Q on V, and it will permute the special point P. Okay. And fix V as not commute, send P to another special point, but fix V. So that means that for each given special point of some given complexity given by the discriminant, you can find a positive power of the discriminant, many more special points on your variety V. Okay. But this is in contrast to the bound that Pila-Wilke gives you, namely that you have this sub polynomial bound here. Okay. So if we compare the two, the upper bound given by Pila-Wilke and the lower bound given by the Galois bound, so you have just put an M because we have some tuple. Okay. And then if we choose epsilon small enough, we can get a bound for the discriminant delta. All right. And here delta as we have a tuple can be set over the maximum of the discriminants of tau 1 up to N. Okay. But as soon as we bound the discriminant, we are finished. We have only finitely many special points in V. So in particular, its risky closure is of special points is finite, contained in V, excuse me, is finite. Sorry, the intersection of V with the special points is finite. So that finishes the proof. But well, but that can't be the story. That can't be true. Why? Because for example, if V is a product of modular curves, there are infinitely many special points in it. As I explained before, if you have a modular curve, then the coordinates will be isogenist with others. So if one coordinate has complex multiplication, the other coordinate will have complex multiplication as well. Okay. So I've omitted a certain step, and this will be, comes next, is a functional transcendence. Okay. So how do we know that this set that I define the inverse of V intersected with fundamental domain is not completely algebraic. It could be an algebraic variety, a real algebraic variety. Okay. And this is, well, I would, yeah, most say this is probably one of the really significant innovations that in that paper of Pila where he proved the underwater conjecture for products of modular curves is that he showed that if you take some algebraic set in the upper half plane, and you apply the uniformization map, you take the ceristic closure, it will be a product of points and modular curves. So he described sort of the sets that are algebraic on the cover, and whose image is algebraic. Okay. So I think Ulmo, who I've heard many, many fantastic talks on this about, called this bi-algebraic, although I'm not sure who exactly coined this term bi-algebraic. Okay. So in some sense, for the experts, it means that bi-algebraic varieties, the ones that are algebraic on the cover and in the image are weekly special, what it's called. In this context, weekly special means a product of points and modular curves. Okay. So this is what Pila proved. How did he do this? So I think this, this is one of the, one of the, yeah, I heard this back as a student and I was really struck by this proof. So what he did is he, he used the Pila-Wilke counting theorem again to prove this transcendence theorem. And just to make some, some comment on the proof, one of the difficulties of his proof is to show that if you have some algebraic variety that intersects the upper half plane, that intersects many, many fundamental domains in the upper half plane. It's kind of an interesting part of the proof. And it's actually one of the difficulties in where, when the proof of Pila was attempted to be generalized, yeah, which I will talk about later. Okay. So now Pila has, now Pila has obtained, after Pila has obtained the underwater question, why, why two to the end question is, okay, how do we proceed? So the underwater conjecture itself is about Chimura varieties, which the product of modular curves is one of those. But of course, there are much, there are many more.  I would just say that they are in general given by some Hermitian, Hermitian, sorry, yeah, I think it's Hermitian symmetric domain rather H. And we quotient out by an arithmetic subgroup of its symmetries. And they have the properties, these, these, these objects, they satisfy certain axioms that were rigorously specified by the linear. And these axioms, they ensure that actually this quotient is an algebraic variety, which was actually proven by Bailey Borrell, and yeah, just as an example, above we had the upper half plane is our Hermitian symmetric domain, and the arithmetic subgroup was gamma two. So these are the subgroup, as you said, yeah, and I would just want to say, even, even to show that, that these varieties, firstly, are right varieties, it's kind of very well, and that they have a model of a number fields. I mean, there's lots of work who goes in there by Borrell Boy, for example, and so forth. Okay. All right. But what we always have on S is that we have special points that these are kind of analogs of CM points, points with a lot of symmetry. And they have some attached complexity, like the discriminant of the the endomorphism ring of an elliptic curve. And we have higher dimensional special sub varieties. And these are kind of Shimura varieties, or sub Shimura variety in the fixed Shimura varieties, like for in the example, Y2 to the end, these were modular curves or products of modular curves contained in Y2. And of course, a famous example of a Shimura variety is the modular space of a billion varieties. This is probably the most the best study studied Shimura variety. And of course, there we have the seagull upper half plane and and and it's the theory and seagull seagull already worked. Okay, so one of the I think why people got initially interested in this is also the Torelli locals. So here I just wrote it sort of MG sort of, you look at a modular space or curves of genus G, you can attach its Jacobian to it. And this gives you a point on a G so you can embed sort of the modular space of curves of genus G into a G. This is called the Torelli locals. And one can show that if G is at least four, then MG is not a special sub variety. It's actually not everything after G is equal four. And I think I'm not sure about this. So correct me if I'm wrong if someone knows I think odd especially was especially interested in this kind of questions connected to the Torelli locals. Okay, so what does the underwater conjecture state in general? It states if you take the characteristic closure as any set of special points is a finite union of special sub varieties. Okay, this is a very simple, very elegant conjecture. One consequence is okay, if you should know, if we know in addition that for example, the Torelli locals doesn't contain any special sub varieties, which is not always true. But if say for some G, it is true, then you should have shown that for this G, there is no smooth curve, whose Jacobian has complex multiplication, sorry, there are only finitely many smooth curves, whose Jacobian has complex multiplication. Okay, so there are that sort of direct applications to a right geometry. Okay, so to apply the pilasania strategy in general to so we want to prove now on God conjecture, we need three roughly three ingredients. Okay, the first I would say, yeah, well, no, I wouldn't say anything is polynomial lower bounds for Galois orbits. This was open the longest. The second functional transcendence this I have talked about in length before. And the third is what we had before that you have to show that each special point has a an image in a suitable fundamental domain, a preimage, sorry, whose height is bounded. Okay, so the second part function transcendence was often called functional X Lindemann. I'm sorry if I made it someone here. But I think the first is for for a G, this functional transcendence statement that is needed is was proven by Pilar Zimmermann and then later in India for for for all she move over ties by Klingler, or more in your five using also Pilar strategy. And okay, and right, the problem three, so the height bound for the pre images was completely solved by Donor. Now I should also say before we go further, that actually a proof of complete proof of the underwater conjecture, however, assuming the general Riemann hypothesis was given by Klingler and Yafayev using equity distribution techniques. And as Andre mentioned, there was important input by edexhoven. However, I don't know the history of this exactly, but I think also important input by Ulmo. But as I said, I'm not I'm not an expert on this part. Sorry, we're pushing the chat regarding the complexity. Yeah, it's always defined. Yes, that's a fantastic question. So if you have a CMAB and variety attached to it, then yes, it's sort of, you can think about it as the scrimmage of the endomorphism rings. In general, yeah, I'm not sure that you can actually attach some objects with endomorphisms to it. But yeah, maybe there's some yeah, maybe Andre can answer this. Ah, great, one one one person said one half is possible and thank you others. Yeah, that's true. Okay, I knew I messed up. Okay. All right, so is this okay? Is the so in a G the answer is yes, to the to the last question. Okay, so now we come to yeah, I put a timestamp on it this time because yeah, it's already well seven years almost. So we have a Zimmerman proved the third part. So as I said, we had the second and third part were already done. Now the first part remained for a G and Zimmerman proved it. And yeah, I wrote written down the statement like this. So you have this complexity, which is given as as was mentioned in the case of CMOS is the discriminant, more or less of the endomorphism ring of the, the a beam variety with complex multiplication. And all right, so how does this proof works work. There's two crucial ingredients. One, which I would say is average columnist conjecture, which I explain a second and the second are the social estimates for a beam varieties. Okay, so what what both have in common is that they are completely restricted to a beam varieties. Okay, so you can't go from a G using these two ingredients, you can't go from a G to other she more varieties. Okay, so I would just say the average comments conjecture as Andre, I think Andre mentioned it, it connects the logarithm derivative of some RTL function. So like analytic objects attached, attached to the endomorphism ring of the beam variety to the faulting side of the beam variety. And when it has complex multiplication. And so columnist conjecture is I think is stronger than the average columnist conjecture, but the average columnist conjecture is sort of enough for the application and it was proven by Yuan and Zhang and independently also by Henrietta, Golden Howard and Hera. And I think also the methods of both proofs were really distinct. So they came up with two independent proofs. Okay, so this is number one. And second, isogenous is of course, people are not familiar. This is part of transcendental number three. And for example, I think they were more or less created an attempt to to make parts of the desk conjecture effective. Okay, all right. So as a consequence of the average columnist conjecture, we get a height bound on a special point. So here H stands for some logarithmic while height on a G. So it really a height in the traditional sense, let's say. And it gives you a bound that is subpolynomial and discriminant. Now we want to generalize these two ingredients. Now, so we have the average columnist conjecture with strict AB and varieties, and we have the isosceles estimates that are restricted to AB and varieties. So how do we overcome these restrictions? And the answer for the isosceles estimates is, well, we just do more counting. Now I just want to sidetrack is the Pila-Wilke theorem holds for any o-minimum structure, but Wilke already shortly after they proved it or maybe even before forming a disconjecture that in this particular structure are X. So if you only enjoy the exponential function, a polylock bound should hold. So you should get actually instead of t to the epsilon for the number of rational points, you should get a polynomial in the logarithm of the height. So the observation, so there were some proofs of some special cases by Gerbys Jones, Margaret Thomas, Binyamini, Pila, and but they also, they were mostly concerned with Q or when you attached the number field, the dependence on the number field was actually exponential. And my observation was back then that each time you can sort of prove this, you can prove a polylock bound that is, yeah, that is polynomial in the degree of the number field that you put in. Okay, this comes sort of from how it's proven, running a bit late. So I will do this a bit faster. Just say that it's part two where you intersect your X with an algebraic variety. If you have some control on the intersection, then you can improve on the Pila-Wilke bound. And this is how most of the proofs go. And I should say, excuse me, I have forgotten to say that actually a proof of this was put on the archive by Binyamini, Novikov, and Zak, I think this week. So it's quite, yeah. So you need some end. In fact, what you can do, you can also instead of count points in a fixed number field, you can count algebraic points of a fixed degree over Q, and you still get sort of a polynomial bound. So what's the idea? So the first observation, which when, when, when I saw this, I was quite struck by it, which is if we know on a Shimura variety, this is, we know that given some special point, we can find polynomially many in the discriminant other special points defined over a number field that has the same degree as the number field that is generated by my point. Okay, it's a bit of a complicated statement, but sort of given one point, we can find many. Okay, so this is always true in the case of modular curves. This is already enough to get to get a Galois bound, but in the general case, it's not. And the idea is now to look at the graph of the uniformization map. Okay, so we know that the height of the pre-image is bounded by the theorem of Do and all. And if we knew that the height on the image is also so bounded sub-pollinomially in the discriminant, then we can use, we can use the upper bound coming from the counting traded off with the lower bound coming from this observation to get a lower bound on the degree of the number field generated by P by the special point that is polynomial in the discriminant. Okay, but what we need is we need this log t, this pesky log t needs to be bounded. Okay, so what Binyamini said in the FI we've shown is that we've shown that if you have a special point, then you get a polynomial lower bound for the degree of the number field generated by P if you have a bound on the height. So this replaces the isogenic estimates of Massa and Wüstholz and gives a new proof, in fact, of Andrea Ortt already gave a new proof of Andrea Ortt for AG. But of course, to have the full Andrea Ortt conjecture, you also need a height bound. And this was shortly after then put on archive by Pila Schanker-Zimmern is known in Gröhlich. And they proved the necessary height bound. So you can hear for the HM, you can plug in something that is subpolynomial in the discriminant. So you can bound this, you can beat this M by far, and then divide and you get a polynomial lower bound for your for your field. And yeah, this completes the proof of the Underworld Conjecture. Yeah. So hooray. Okay, I'm not sure, Philip, how much time do I have left? Oh, maybe a few more minutes. Okay. Yeah. All right. So maybe just to finish up. If nobody has a question, what else is there to do for Andrea Ortt? So if you want to go to mixed Shimura varieties, as well, bad news, if you want to do something new, because Gao has shown that this the Underworld Conject for mixed Shimura varieties holds also, but he has kind of reduced it to the Underworld for Piusz Shimura varieties back in the day. So I think five years ago, six years ago. But a big open question is whether we can actually find an effective proof. I want to advertise a bit for that. So can we actually find, given an algebraic variety, find all the special points in special subvarieties contained in that variety. And there is some, there's some progress has been made by many people, but mostly for the case Y2 to the N. And yeah, we just, yeah. And now it's maybe a theorem that they will come out soon where we reduce the effectiveness of the Underworld Conjecture for product of Legendre curves to effectiveness for a product of modular curves. Here we use the awesome theory of Paphion functions and some work of Gareth Jones and myself and I. Okay. And maybe just to finish up, I want to say that there's Pink's Conjecture, which is a mixed Shimura, it's a vast generalization basically, yeah, includes almost all known conjectures in diaphragm geometry, like Modell Conjecture, Manning-Mamford Conjecture. There are similar conjectures by Bombieri, Mars and Zanier, like they were formulated in parallel and also by Zilber. What I want to say is also that Zilber was inspired by model theoretic questions, which I think is quite interesting in itself. And he was interested in a model theoretic approach to Shanwes Conjecture. So there are very interesting connections here. Here's a sort of a formulation of Pink. If you just read it through, you will see that if you replace special sub varieties of codemesh, at least in V plus one, by special points, you get exactly the Underworld Conjecture. And okay. And yeah, I just want to say that there are some cases that were proved, for example, by Baruero, Mars Zanier, Habegar, Pila, who proved certain cases of, in fact, Pink's Conjecture. And yeah, I just want to hear, it's also a formulation of Shanwes Conjecture. And maybe I finish up here now. I just want to say that there are many interesting connections here, especially between this functional transcendence theory and logic. And it has already led to many fruitful collaborations. And yeah, I am hopeful that this will continue. And yeah, thank you very much.


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