I think we're about ready to begin. If you'd take your seats, please. One more time, please. Could you take your seats? And we'll begin our session here. Well, we'll begin with Dr. Callaghan. I guess I have a very fundamental kind of question. Dr. Aaron, in Dr. Aaron's fine book, which laid out much of this, he talked about the need for rationing. But that was not part of this discussion. I would wish you would say a good deal more. Where do you see rationing fitting into the future of American health care? An entirely fair question, since I've been involved with two studies that examined comparative levels of care in Great Britain and the United States for a number of specific procedures. In most, but not all of which, the United States provides higher levels of care. Strikingly, not at all. In some, the British are as generous and as open-handed as we are in the United States. There are reasons for the different relative differences between the two countries that these two studies addressed. The reason I chose not to focus on that today is that after a very long time of thinking about those questions, and despite a deeply held view that we will never successfully reign in the relatively uncontrolled growth of health care spending without confronting the issue of rationing, we are simply a long way from it because we do not have an institutional framework in which that dialogue currently can occur. If you think about the US health care system, I just really misspoke, if you think about the current US health care financing arrangements, there is no system. No, I'm quite serious about that. If you look at differences in levels of care, in styles of medicine, in how people receive care, the penetration of health maintenance organizations, the likelihood of being admitted to hospitals, the differences in usage in the United States, within the United States, are as great as they are within the European Union, which consists of many separate nations, and which makes no pretense to have a European-wide system. We have 50 different Medicaid systems that are radically different in the way in which they provide access to care. We don't have a system. What we have is a fragmented set of financial arrangements, no one of which, other than Medicare, has sufficient leverage to influence the practice of medicine in a significant way. The Twin Cities may be an exception because of the relative concentration of financing, but it's a rare exception. So, pardon me, Medicare, by statutory limitation, is debarred, dating back to when it was enacted in 1965 and the opposition then from the American Medical Association, is debarred from interfering in any way in the practice of medicine. So we don't have any way of confronting or framing of having an intelligent debate that balances our demands for care on the one side versus how much we're willing to spend for it on the other. For that reason, I think it is important to emphasize, from a different from traditional vantage point, the importance of universal coverage, what we have to have is a system in which everybody is assured of financial access to care before we can have an intelligent and effective national debate about how to constrain the total amount of resources that should be allocated to medical care and to force a debate on which forms of care we think are worth what they cost. So my reason was, if you will, influenced by events, not by any change in intellectual sentiment. I also believe, as I probably have made overemphasized excessive length, I also believe that the public debate currently is seriously off the track and is being shunted onto a side road concerning just public spending obligations when we must, if we are to deal effectively with our public spending obligations, recognize that they are tied up inextricably with the health care system as a whole in which we all participate. OK. Anything else? Just a comment in this vein. I was impressed, as many were, that during the mid-1990s with the HMO movement, the HMO movement did manage to curb cost in great part by putting in practice various policies that seemed to work very effectively, but were highly unpopular with the general public and with the medical profession. So I really would suggest the problem is a deeper one of American culture. I agree with you totally in the need for universal health care. But universal health care would have to actually, in a way, look like those HMOs in the mid-1990s. It would have to say no, no, no to many things. And I guess the question is, how do we deal with this cultural block, so to speak? Well, I'm not sure that it has to look like that. I think it could look like that. And that certainly would be one instrument by which trade-off decisions could be made about what was worth spending. The story on HMOs is that they have, all along, had average costs somewhat lower than did ordinary fee-for-service medicine. They spent more on some things less on others than other forms of medical care. During the 1990s, the movement began to spread. But I honestly think they must have hired, whatever a public relations expert is, in the world of anti-matter, what is the opposite of public relations, they must have hired them to manage their public policies. They managed to alienate the public massively by doing things like telling pregnant women they had to go home the same day and other such measures. Not pregnant, new mothers that they had to go home the same day that, what were they thinking, that did have the effect of alienating the public. Something else happened, which was Medicare somewhat changed its financing of enrollment of Medicare patients in HMOs. And it had the effect of reducing. HMOs were always concentrated in just a few places. They were concentrated there because payments in those areas were higher than the national average to HMOs. And Medicare, Congress took a look at them and said, oh, that's not a good thing. There's too much payment going on there and not enough going on here. So they lowered the payments in the high areas, raised them a bit in the low areas. But what they did was lower them enough in the high areas to make it unattractive. But they didn't raise it enough in the low areas to make it attractive. And so enrollments fell off through Medicare. You put those two things together and it looked like health maintenance organizations were going the way of the dinosaur. I don't think that's the case. Part of the Medicare Modernization Act in 2003 was the institution of overly generous payments through Medicare to people who enroll in HMOs. And there is a resurgence of Medicare interest in such organizations and all kinds of non-traditional Medicare enrollment arrangements. And I think we may well see a resurgence of interest in health maintenance organizations as regulatory devices in the future. But right now, they're sort of in the pits. Well, kind of following along this, please comment on the Massachusetts health care model and whether that may be a realistic statewide approach to access and funding. I think it is a realistic approach. It is not a perfect approach. I am not a Massachusetts resident and I haven't been intimately involved with that system. But I know people who have, including if there were a list of four or five health economists that I would say were the best in the country, one of them was intimately involved in planning the effort. And his reaction to it is, I think it hangs together. It's not, it's going to need tinkering and adjustment. But if, and it may take a bit more money than has been currently appropriated. I think the way to interpret Massachusetts is not necessarily that it is a template for all other states, but in a design sense. But that it is a bellwether in a political sense of interest in many states around the nation in a variety of approaches to extending coverage to their residents. I included a sort of a throwaway line in my comments that there was a liberal way, a conservative way, and what I'll call a federalist way, to approaching universal coverage. I act, my own personal belief is that the federalist approach is the one that has the best prospect of making progress in the near future if the federal government smiles upon such efforts. By smiling, I mean two things. Providing some money to help states bear what will be additional costs of covering everybody, and some legislative flexibility in moving funds around among different pots that are restrained by current law from being used for purposes other than those stipulated in law. This is an approach, I'm going to put a full-blown plug here, this is an approach that I thought of about four or five years ago. Actually, I thought of six years ago. But nobody was interested six years ago. I discovered that another policy analyst at an organization I have almost no agreement with on anything, the Heritage Foundation, had come to a similar view. Both our views were that the state child health insurance program, so-called SCHIP, which is a program under which the federal government gives money to states so that they can extend health coverage to children in a wide variety of different ways, which has been quite successful, was probably a model that could be followed for general health insurance coverage. And we've worked together on that for some time. As it happens, there are now two, and I think soon will be three, bipartisanly sponsored bills introduced into Congress, one in the Senate already, one in the House, and another one in the Cooker for the Senate. The Senate bill is Senators Voynevich and Bingaman. The House bill blends two people who really do never agree on anything, Tom Price, a very conservative Republican from Georgia, and Tammy Baldwin, a very liberal Democrat from Wisconsin, and two other members of Congress, one Democrat, one Republican. The next Senate bill, which is being worked on now, there's discussions between Senators Fine Gold and Lindsey Graham. I think there's a lot of interest in Congress in this approach, and there should be. There should be because there is no prayer. There isn't a prayer in the hell of the advocates of any of the pure strategies getting a majority in both houses of Congress, certainly in the Senate that could override a filibuster. But there is a willingness, I think, a growing willingness on the part of elected officials who recognize that the electorate is getting worried and frightened that something does need to be done, and our Washington officials can go back to their constituents and say, we did something, and we did something real by facilitating action by state legislatures and governors. So I believe that in the next year or two, you may see more of that strategy. I think it's the most promising one. It's not anybody's first choice. I have my own preferred ways of achieving insurance coverage for everybody. I'm sure other people here do too, and that isn't it. But as a realistic person who wants to see action rather than another seven decades of deadlock, it seems to me to be the most hopeful approach. Quick footnote. Canada started that way. Yes, of course. Historically, Saskatchewan in 1947, then to Alberta, and finally to the federal level. But it still is a provincial system. I have a cluster of questions here. I'm trying to guess at the age group that we're talking about here. They all have to do with the cost of drugs. Any comment on drug costs? How much is the cost of medicine due to high costs? Let's see. What percentage of American health care costs are attributable to prescription medication? And what can we do to hold costs down? Medications back around 1960 or there about took about 14% of our health care dollar. They're then ensued a lengthy period during which other forms of medical care came on stream. We got new kinds of radiological procedures, CT, MRI, coronary artery surgery, joint replacements, you name it. And there were relatively few expensive drugs coming on stream. The share of health care spending dropped to 7%. Sometime I think during the 80s. They're back up to 14% now. Is that too much or too little? Well, there are two ways of looking at this. And boy, am I going to earn this. My stripes isn't on the one hand on the other hand economist. On the one hand, they are very expensive. And the share of spending has been going up. There's every indication it may not go up at the same rate as it has in the past, but drug costs are going to keep going up. On the other hand, drugs are a substitute for hospitalization and in many cases, slow progress of disease or prevent the onset of disease. How many in the room here are taking statins? OK, well, you and I and everybody else here are hoping that's not going to lead to a congestive heart failure or coronary artery disease that would lead to a heart attack. But they're not cheap unless we take zochor in which case it's a little cheaper now since it just went off patent. So on the one hand, yes, they've been going up a lot as a share of health care spending. On the other hand, they do replace other medical expenditures. And there are some reputable studies that suggest that the net effect of increasing drug spending has been a net reduction in total health care spending. I'm not prepared to endorse or disavow that, but you should be aware that there are respectable studies that make that case. The other on the one hand, on the other hand, is there are two prices that are, if you will, polar choices for how you would price drugs. How much does it cost to make the pill? Well, in most cases, not all, there are some biologics that are quite expensive to make. But in most cases, the cost of making the pill is very small pennies, not the several dollars a pill or even hundreds of dollars a pill that may be charged in some cases. In other case, the other poll is the cost that will enable the drug company to finance a level of operations similar to the one that it is currently operating. And that price means that if you have a successful drug and no close competitor, you charge a lot of money for it, and you use those proceeds for some good things and some not so good things. First of all, you do use it to fund the laboratories that will try to be developing the next generation of drugs. And high drug prices do pay for the drug research on the next generation. They also pay for drug detail men that go around and try and persuade doctors to recommend this pill. And it goes for direct consumer advertising that tries to get you to go to the doctor and ask for the pill. And it goes for high dividends for the stockholders. So somewhere between the price of making the pill, which would mean there wasn't any money around for all of those other things, all of those other things, not just the dividends for the shareholders and not just the direct consumer advertising, but also the research for the next generation of drugs. Somewhere between that price, which is what economists call the marginal cost of producing the pill, and the average cost of basically sustaining the business enterprise is the range within which drug companies decide how to price pills. And you can make an argument for both of those. I have sometimes thought that it might make sense if instead of granting patents to drug companies, which authorize that, give them a monopoly, say you can charge whatever you want, that the government appraises the usefulness and value of the drug and pays the drug company a lump sum and then the pill is made available at marginal cost. There are a whole host of actual operational problems who are trying to do something like that. And it may not be a good idea, but there's a real dilemma here, a real problem. And there is no getting away that whichever way you do it, you've got a host of difficulties. We have this crazy system in the United States where we grant monopolies, authorizing companies to charge a whole lot of money, but then we socialize the cost through insurance. We all end up paying higher premiums one way or another for our insurance, which covers those of us who have drug plans. And oh, yes, there is the detail of those without drug plans. They are stuck with very high drug costs.  Well, here's another problem. It has to do with medical education. It says, in the US, more doctors are going into specializations and away from primary care significantly. It says it was 50%, now 20%. It says, in our ER, Medicare reimburses $29, and private insurance pays $150 for a patient. What new grad from med school can afford that? The average loans, I suspect, are $60,000 to $80,000. The second question is, is a cardiothoracic surgeon really worth 10 to 20 times as much as a psychiatrist or a pediatrician? And is there a possibility that medical education should be completely paid for by the government as opposed to partially subsidized? Next question. I think there's a different age group involved this way. I said, next question. Next question. Where should I begin? How about just a question about medical education? I think there is a case for public support for medical education. It would have the effect of freeing newly-trained physicians from the financial pressure that they now confront. And that has, I think, fairly pervasive effects on what newly-trained physicians in fact can do, because they do face these debts. There was a government program that forgave medical loans if individuals agreed to practice in underserved areas. And I confess, somebody here may know whether that program has survived. I do not know. But it seems to me that perhaps broadening that program to include a larger list of activities that would earn forgiveness for medical loans is something that does merit serious consideration. Our cardiothoracic surgeon is worth more than psychiatrists. Some are, and some aren't. Here's our last question. I don't know whether he's completely serious or not here. How about asking Walmart to take over medical care for the primary and secondary care to minimize health care costs? You know, sometimes I get jealous of physicians and think they just earn more money than I do and too much more money than I do. But you know, angry as I may be sometimes, I wouldn't wish that on them. Thank you very much. That'll conclude our session here. We'll reassemble at 3 o'clock for our final talk by Dr. Webb.


I don't think I'm a bad driver, you know, I don't think I'm malicious, I'm not going like 30, 40 miles over speed limit. Sometimes I'm just trying to get somewhere and I go a little bit faster than normal. Everywhere you go, it's some type of fee, it's some type of violation.  On the midst of me trying to get the money to afford those tickets, they would double. So if I couldn't afford it initially, you know, how can I afford it if it doubles? I know I stay in the city and a lot of people take public transportation, but a lot of my work, you know, I can end up in Elgin and Schaumburg and Bolenbrook and different places. Rosie is my 2010 Nissan Versa.  Being Rosie in our lives is very important and essential to my everyday life. Bankruptcy is a band aid for my problems. Did it help me dramatically? Yes. But it just shouldn't have to get to this point. They're not over tickets. My awesome speed violations. Do I put gas in my car to get to work or do I pay this ticket? Do I pay the light bill or do I pay this ticket? This sucks, you know, for every time you make a little bitty mistake for there to be a dollar sign attached to it.


Good morning, good afternoon, good evening, wherever you are. Welcome to the AI for Good Global Summit, all year always online. I'm Charlotte Kahn from the ITU, the International Telecommunication Union. Like most of the world, the AI for Good Global Summit has gone digital, with weekly online programming, allowing us to reach even more people in 2020. AI for Good perspectives offer expert insights, global visions, and shared solutions from the AI for Good community. Today we bring you the third episode of ATRI's AI for Making a Better Tomorrow on the subject of AI for Security and Privacy. ATRI is the National AI Research Institute of the Republic of Korea, so let's take a look at a short video about them. Artificial Intelligence Research Laboratory is the main R&D branch of ATRI, the nation's finest General Intelligence Research Institute for shaping our future society. We are in charge of research and development in the field of superintelligence and superperformance, to build the foundation of a superintelligent information society co-existing with human-based autonomous intelligence to materialize superperformance computing to overcome the technological limits of existing computers. For the realization of superperformance computing, Future Computing Research Division revolutionizes the CPU-centric computing system into next-generation memory-centric computing system. With our memory-centric computing systems, massive amounts of data, such as AI-powered financial predictions, biotechnology, big data analytics, etc., can be processed much faster than today's computing technologies. In addition, our innovative memory-centric computing system can be integrated with multi-cloud technology to spread a variety of high-speed AI services around the world. The AISOC Research Division has developed a high-performance artificial intelligence processor chip for servers to accelerate artificial neural network, as well as an ultra-low-power visual intelligence processor chip for mobiles that visually detects and recognizes objects. This technology will be used as a base in the future research on the 64-bit processors for supercomputing and AI accelerating. In this field of superperformance research, we will endeavor for a realization of the superperformance computing, which overcomes the limit of performance through a memory-centric computing system and AI processor technology. In the future, Atree Artificial Intelligence Research Lab will do its best to advance Korea's artificial intelligence technology to the next level through the development of next-generation AI core technology and to achieve the fourth industrial revolution through intelligent innovation in the manufacturing and ICT industries, which are the strengths of Korea. Now, let me hand over to our expert host, Dr. Miran Choi. Dr. Choi is principal researcher and standardization specialist at Atree. Dr. Choi. Thank you, Charlotte. Ladies and gentlemen, I'm Miran Choi from Atree Korea. Thank you very much for joining us in this session. The subject of this session is on AI for security and privacy. AI technologies have been wildly developed on many areas, including ICT, in order to make human lives richer, safer, and more convenient. Especially on intelligent CCTV technology, to recognize interesting situations by analyzing CCTV videos is applied to many safety-guaranteed domains, such as national infrastructures, cities of balance systems, videos of balance as a service, and so on. On the other hand, those extensions of AI CCTV and increasing CCTV data surely cause the critical side effects, such as invasion of privacy, misuse in crime, and other security threats. So, in this session, security issues on the intelligent CCTV and some video security technologies preventing them will be discussed. Okay, next I will introduce the speaker of this session. Dr. Kono Kim is the manager of physical security and authentication technology section. He has been developing intelligent CCTV technologies for 13 years. Recently, he is involved in developing deep learning technology for CCTV analysis. In addition, the privacy and security issue is also one of his research topics. Now, let's watch the presentation. Hello, everyone. Let me introduce myself. My name is Kono Kim from ATRIE, Electronic and Telecommunication Research Institute, Korea. During the last two weeks, a few AI technologies developed by ATRIE were introduced. And in this presentation, I'm going to talk about the opposite side of the artificial intelligence, security and privacy. Today, the artificial intelligence is everywhere and melting into most systems from front-end devices to back-end large-scale platforming servers. Anyway, some may be satisfied with the performance of AI, but who are satisfied with the security of AI may not be many. Until now, we are focusing on the performance to arrive at the level of human intelligence, but we are not interested in the other aspect of artificial intelligence, which may be dark. There are issues about security and privacy. In this presentation, I would like to focus on security and privacy issues and related technologies by intelligent CCTV systems. The intelligent system is supposed to be a highly probable solution responsible for social safety, which is most of the time. As we can see in many cases, CCTV plays a critical role and generates crucial evidence. Our every history is stored in CCTV videos, monitored, validated and analyzed by other people. Furthermore, intelligence has been added to the CCTV systems, and everything is attempted to be automatically identified. But on the negative side, our privacy is forced to open. Even though CCTV guarantees our safety, they don't protect our privacy. If privacy is not guaranteed, everything you can see may be broken down and become dangerous. In this slide, I would like to introduce a few privacy-invasion cases by CCTV applications. There is an internet site listing IP cameras accessible by everyone without any authentication process. The accessible IP cameras are kindly categorized by nations, manufacturers and deployed places. This is caused because the default password is not reset and continuously used. Everyone can feed other private lives through the indoor cameras. Actually, this type of accident can be prevented with a little concern. This is caused by security weakness of deployed systems. Most IP cameras are connected to the router, so once the router is exploited, CCTV security systems collapse and private lives are streamed all over the world. The router exploited is known to be very easy, and we can simply gather the hacking program in the internet. You can be a main character of the movie through a show like Jim Carrey. This scenario is caused by IP cameras invoking security weakness, namely backdoor program. Once the backdoor program is installed, all security software are useless. Attackers who know the backdoor program can illegally access the IP cameras and sneak look at the CCTV videos. As another security-broken case, CCTV was used for attacking other systems, meaning Burnett. About 25,000 CCTVs over the 100 nations were hacked and illegally controlled to launch DDoS attack. These CCTVs have successfully performed a law as an intermediate control center for attacking victims. This is because the CCTVs are already connected and they have their own computing power. But most of the important thing of all is that no one pays attention to the CCTV status. And all you want is just monitoring. The connectivity and concern enable our CCTVs to attack the remote target victim systems without us knowing. Until now, we are making our best effort to protect our treasure by manufacturing strong safe against illegal attacks. So as the attacks are getting powerful, the safe needs to be supplemented or renovated. But the way of strong safe has no choice but to follow the attacks and damage is already expected.  The only authorized access can restore the original value from the fake money. I would like to introduce a few security technologies for this purpose. This video shows a regular privacy masking method that many people are used to and normally imagine. First of all, private reasons are detected, including human body's faces, license number plate, private spaces, and something like that. And then the detected private reasons are processed to be unrecognized using privacy masking methods like pixel blurring, blackout, or mosaic process. From the security aspect, this method is perfect because the privacy is removed forever, but this is a serious demerit. Most critical demerit is that original video cannot be restored from the masked video because the original information has been already damaged and not installable. So this method is usually used for external carryout of existing videos and the original existing video is stored in storage, which is expected to be secure. When the stored original existing videos are getting dangerous, every private information is revealed and security systems are broken down. This video shows the existing privacy masking technology we developed. The left video is original, the central video is privacy masked, and the right video is a restored result. The advantage of this method is that system videos are securely can be managed during their lifecycle in encrypted format. Whenever system videos are captured, they are immediately privacy masked, transferred, stored, monitored, and deleted. During their lifecycle, the only authorized access can restore the original video, and other people can monitor only the central masked videos. You don't need any further information for restoration, only the masked video is enough. For the restore of privacy masking, we have to overcome some hurdles. First of all, we have to solve the conflict between legacy codec applications and our privacy mechanisms. Legacy codec systems adapt to loss compression for high reduction of file size, so RGB information in each pixel is changed, but human eyes cannot notice that. But for our privacy masking, encryption is recommended, and the operation is valid only when the integrity is guaranteed, so for the actual privacy masking, it must be compliant with the legacy coding mechanisms. There are three types of privacy masking deployment. In first approach, the privacy masking operation is done between the encoding applications and decoding applications. In this case, the privacy masking application should be implemented according to the encoder types. Unfortunately, the private masking depends on the codec applications. In second approach, the privacy masking implementations are integrated into legacy codec systems. This may be most efficient from the performance view, but every codec application must be implemented and provide privacy masking functions. In the last approach, the privacy masking is done out of the boundary of the codec applications. For making it possible, the private masking mechanism should be robust against the unexpected data modification of codec systems. We adopted the last option. Another option is video encryption. In previous privacy masking, we have to detect private areas in each video frame, and then transform them into the unrecognized format. But in video encryption, we don't need a private area detection, but just apply it to the every video frame. Here, our consideration is how the encryption is performed in the lightweight manner. The key idea is to use the encoding mechanism of video codec applications. In legacy codec applications, whenever anchor information is encrypted, and the follow-up information would be automatically unrecognized. This reduces computation to the 30% compared to the overall data encryption method. Also, this application can be installed in the conventional IP camera platform. The original video frames are surely restored by the authorized access with a private key. The left video shows the original, the central video shows the encrypted, and the right video shows the decrypted result. In this page, I would like to introduce a new concept of security, applying privacy masking. In a private world where we live, you can see everything with eyes and privacy is not considered. The moment of frame data is transferred to the online world, privacy is getting important. It's including human bodies, faces, private information, license numbers, and everything private. So, we would like to change our ways of thinking. We want to make offline world secure, and the private information can be seen only in the online world. Of course, the access should be securely authorized. As seen in the video, private information on paper, screen, or any offline media is masked, and no one can recognize it naturally. If someone has a privilege to see that, you can restore the original private information like the light of a figure. In our test, we use mobile phone and smart glasses for secure restorations. I would like to conclude with the sentence, Security for AI makes AI mature. Security is not option anymore, and can be less than pleasure for AI perfection. Thank you for listening. Thank you for your presentation, Dr. Kim. I hope you have a good achievement in AI-based security and privacy area. Now, I will ask two questions on your presentation for the audience. My first question is, what is the difference between your privacy masking technology and other widely used privacy masking technologies? As I mentioned in my presentations, it's matter of whether the original video information is reserved or not. Other privacy masking technologies is adapting, only transformation is not restored, and the original information is not useful anymore. And the moment the original video information is damaged, the worth is getting invalid. Whereas, our privacy masking technologies guarantees the restorations. It's very important and should be mandatory. Privacy can be supported along the CCTV videos' life cycle. Even though the CCTV videos are illegally stolen by hackers, our sensitive information is not recognizable. The concept of your proposed offline privacy masking technology is not familiar to me. Can you explain the concept compared to the QR code method in more detail? We actually recognized why the only online private information is respected. In offline world, the private information can be found anywhere. The offline privacy masking technology has departed from these considerations. We would like to reserve our common notion, that is, our private information is scattered over the offline world in a secure manner and others cannot identify them. The only authorized personnel devices can confirm the original information. Confirmed to the QR code method, our offline privacy masking technologies can support a typical format. Our offline privacy masking technologies can contain the original characteristics, such as writing styles, image information, and signature and others, without any online connection to server. Thank you, Dr. Kim, for your detailed explanation. Okay, I hope you all have enjoyed the episode 3 of AI for a Good Perspective, presented by Etri today. Thank you for your participation. Let me hand back over to Charlotte for the closing. Well, thank you Dr. Choi and Dr. Kim for the presentations and inspiring discussions. I hope you have enjoyed these insightful episodes from Etri. Stay tuned for much more on how AI can be used to make the world a better place by joining us all year, always online.


Thank you very much. So first of all I would of course like to also say Gelukkige verjaardag to Alain Valet. So as Claire said yesterday, I think Alain is like one of the best examples of how to guide PhD students and postdocs. I have seen the effects by hiring some of them afterwards in Leuven. So I think he does an exemplary job in that way. But not only that, I think I learned a lot from Alain's lecture series and talks where he manages in one way or another to have the entire audience leaving the room motivated to start working on something. So I think that that is a wonderful thing that he accomplishes all the time. So I will be talking about von Neumann algebras today and as Bashir already said in the previous talks. So very quickly von Neumann algebras are algebras of operators on a Hilbert space closed in the weak topology and we will be mainly concerned with factors. So factors being the algebras where the center is reduced to the multiples of one. And very importantly there is a notion of a man ability in this world and a man ability for groups has been mentioned already a few times and a man ability of a group gamma would be the same as a man ability of its group von Neumann algebra. But a man ability has an intrinsic definition in terms of von Neumann algebras. It's called injectivity and as introduced by Alain Korn there is also a version that refers to what in the group language would be the existence of an invariant mean on the group. There is something like that. One can formulate given of von Neumann algebra M living somewhere in B of H the existence of a specific functional on B of H playing the role of the mean and being called a hyper trace. So we will be restricting most of the time to so-called type two one factors namely those that admit a tracial state. So a state on the factor that satisfies the trace property and the very fundamental theorem for the entire talk is Alain Korn's theorem from 1976 saying that up to isomorphism there is only one amenable type two one factor and it's a very concrete one. It's the so-called hyperfinite two one factor that was the very first example of a two one factor introduced by Marie and von Neumann and it's very easy to construct this two one factor. You start by putting the two by two matrices in the four by four in the eight by eight by every time putting matrices along the diagonal you take a direct limit that gives you a star algebra and there is a unique way to complete that into a two one factor. So that's the basic object for today the hyperfinite two one factor. So from point of view of classification there is nothing more to say than I mean there is just one I mean there is the unique amenable type two one factor. But on the other hand when you consider sub-algebras of the hyperfinite one factor there is already a very first remark to make sub-algebras inherit amenability. So again up to isomorphism the sub-algebras well they could be like finite dimensional and they could be some center but essentially it's again just the same algebra that that can arise but the way they sit inside can encode extremely rich structures. So something that I won't be talking today at all but that you may know or have heard of is Jones's theory of sub-factors which is like a whole world of considering inclusions of the hyperfinite one factor sitting in one way or another inside the hyperfinite one factor and with all the connections to to all kinds of fields. But that will not be today's topic but it shows how just an inclusion of one in the other can already encode a lot of structure. The topic today rather will be sub-algebras that behave differently. So we will be looking at sub-algebras that satisfy a certain say normality property we call them regular or they were called regular by I think Dix-Mierre and regularity means that the normalizer of the sub-algebra and that consists of all unitaries in the algebra that normalize after conjugacy in this way the sub-algebra. This normalizer should be sufficiently large in the sense that it generates the entire algebra in the von Neumann algebra sense of the word. So that's regularity and then secondly there is a kind of maximality type of assumption in the sense that the only things that can commute with the sub-algebra B inside R should be restricted to the center of B. Now this may sound as a kind of weird set of assumptions and kind of weird why to consider this but I will show you the two extreme cases that will convince you that it's very natural to look at this setting. So the two extreme cases are the cases where B is a billion then this condition reduces to saying that the relative commentant of B inside R is equal to B itself so it's saying that B is a maximal a billion sub-algebra and the other extreme case that I that is very well understood is the case where B is factorial where the center of B is the multiples of one and in that case these are the so-called irreducible regular sub-algebras. So these two cases I will just quickly introduce them they are extremely well understood and then the general case becomes much more intricate. So this is the case where B is a billion and then this definition or this notion amounts to what is called the carton sub-algebra. So a carton sub-algebra B of a two-unfactor is such a regular sub-algebra satisfying the relative commentant condition but now with B a billion so it means that the relative commentant of B is just B itself. Now why is it so natural to look at carton sub-algebras in two-unfactors is because then by the work of Feldman and Moore one can actually realize the two-unfactor as the algebra associated with some other data namely one can realize the two-unfactor M from an equivalence relation. So now I should take some time to explain the concepts so Feldman and Moore showed that any such carton inclusion arises from the following data there is some probability space somewhere x mu x mu arises by writing B the billion algebra as L infinity of a probability space so that gives you x mu then on x mu there is an equivalence relation but it's not just an equivalence relation R is also Borel in the sense that as a subset of x times x it's a Borel set it has countable equivalence classes and then there is a way to express that this equivalence relation preserves the measure so one way to imagine what this means is that if you take a transformation of the space with the graph in the equivalence relation then this transformation should preserve the measure mu and then there is a second ingredient there is a scalar tucco cycle so there is a map from say equivalent triples to the circle somehow making an obstruction to being just just multiplicative and then together so this equivalence relation and the scalar tucco cycle you can define with data to one factor well the factor would come from ergodicity so you can define with data to one factor it contains naturally L infinity of x as a maximum abelian subalgebra and any carton inclusion comes in this way from an equivalence relation so equivalence relation plus tucco cycle goes hand in hand with carton subalgebras what do you mean by countable equivalence relation that that every equivalence class is countable okay so this is what I summarized here now the second fundamental theorem is again a uniqueness theorem by corn Feldman and weiss saying that again if you restrict to the amenable world the word amenable went out well there is a unique ergodic amenable countable probability measure preserving equivalence relation so in in the amenable world there's again a unique object r and not only there is a unique one it has no two homology so here there is a a scalar tucco cycle that appears but in the amenable case the tucco cycle is automatically a co boundary so there is only one equivalence relation that can appear there is no tucco cycle that can appear conclusion just saying the same theorem in other words is that this hyperfina to one factor has a unique carton subalgebra this is up to of course automorphisms of of the algebra no not necessarily inner arbitrary automorphisms okay so again one could say that there is not no extra structure nothing to classify there is just a unique carton subalgebra but let them look at the other extreme case where b is a factor and things already get more interesting so when b is a factor so that here is again the definition we look at regular subalgebras of a two one factor now satisfying the irreducibility assumption so b is a factor and the relative commutant is equally reduced to multiples of one then again there is a way a canonical way to write your algebra not as an algebra of an equivalence relation but from some other data this time and it is as a so-called a co-cycle cross product and what is this group there is a countable group that appears and that's very natural that there is a countable group appearing because the regularity means that the normalizer of b this is a group of unitaries inside m is large enough generates m now an obvious part of the normalizer of b is the unitaries in b itself of course yeah like an inner normalizer if you wish the quotient group in this context where this inclusion is irreducible it's a normal subgroup always and the quotient is a countable group so out of the data comes a countable group and then there is obviously somewhere a two co-cycle or a two comology obstruction because you have this quotient group gamma and you want to associate to every element of gamma a unitary a normalizer here but of course there is no unique choice there is a two co-cycle obstruction that appears extremely naturally and the whole data is then like tautologically say summarized as given by this countable group gamma and a so-called free co-cycle action of the group on the factor so for every group element we have an automorphism alpha g it's not an action it's only an action up to a two co-cycle u and that's just the same as looking at irreducible regular inclusions okay what happens now in the amenable case so the amenable case so m being amenable m being the hyperfinate to one factor amounts exactly to both b being amenable and gamma amenable yeah so in the amenable case when both b and gamma are amenable okneano proved the fundamental results first very surprisingly although there is a wealth of amenable groups the two co-cycle is always a co-boundary I mean there is no way to see this like in a very explicit way but by some miracle if gamma is an amenable group there is always a lift back from the quotient to to the normalizer which is very remarkable and secondly there is essentially only one action as well so essentially there is only one way a count an amenable group gamma can act on the amenable to one factor hyperfinate to one factor b up to the the right notion of conjugacy which in this case would be called co-cycle conjugacy so now there is already something more there is not just uniqueness there is this group gamma that pops up but again there is a complete classification I mean the the regular irreducible subalgebras of the hyperfinate to one factor they are exactly described by this group that's the precise invariant the group in itself up to isomorphism so two such inclusions are isomorphic even only if these quotient groups are the same and this is just a translation of Oknian's theorem of course okay so the the first thing I want to present today is this work that I have been doing recently with Sorin Popa and Dimash Liatenko and it's a very classical topic because let's now just look at the two together so you consider all regular subalgebras satisfying the relative commutant condition and again there is a translation exercise to make because the way the inclusion is written as coming from an equivalence relation in the abelian case or as a cross product in the factorial case I mean all that is kind of straightforward with nowadays techniques so here again there is a straightforward way to summarize what happens but of course you have to put on the same footing an equivalence relation and a group well we know how to put that on the same footing it's by looking at group poets so what will arise is a group poet and I will immediately give some more definitions not to be z of b the center of b is at infinity of x I'm sorry yes I'm sorry the center of b z of b thank you of course so the center of b is now abelian of course it's abelian the center of b is l infinity of a probability space that space will be the space of units of the group poet so in the extreme case where we are looking at the reducible inclusions it's one point so that we will get an ordinary group in the other extreme case we will turn to an equivalence relation yeah so that pops up very naturally a group poet with unit space given here should be z of b then of course since b z of b is the center of b your b is written as a direct integral of of two one factors so above every point lifts above above every point of x lives a two one factor b of x and then there is an action of the group poet on on this and this is not very difficult to understand so maybe I should give you one notation so the group poet has units being this space x so this means that there is a source map and there is a target map and we can compose if things match yeah the source of g is the target of h and so what is then an action of such a group poet on on this field of two one factors b well for every element in the group poet you get an isomorphism from the algebra in the source to the algebra in the target and then very naturally it's not exactly an action there is a tucco cycle obstruction so the composition of the two is up to an inner alpha of gh and the use satisfy the obvious tucco cycle relation so this is just a translation exercise well they need in this generality they need not be all isomorphic but they will be isomorphic along the orbits here is no tucco cycle obstruction no no that would be if you would that's because there is already already the algebra it's like really choosing a lift from the group poet to the normalizer say so yeah and then the theorem is as you could expect that what is the full classification of these regular sub algebras it's exactly determined up to isomorphism by the group poet so in the equivalence relation case there was a unique equivalence relation in the in the group case it's classified by the group and in general it's classified by the group poet now if you it's a type of b you mean either type one or type two exactly because you have to be careful that there could be the silly carton case yeah and when you say associated group in itself yes as an abstract I a discrete measured group poet and again in the amenable case of course now this is something like a theorem that should belong actually to the time when when they proved all the other theorems in the 1980s now actually an important thing had been done actually namely the fact that these amenable group poets can act in a unique way that is a theorem from back then proven by sutherland and dakazaki but it's the tucco cycle problem that is the tricky one that was not on so the the question is how to prove that every tucco cycle is a is a co-boundary so now you may for a moment forget about these cross products and and and so on because now I will look at this tucco cycle problem in its own right so you only remember what is a group poet and then a group poet acts on on a field of factors in the sense that from the source algebra to the target algebra you have these and then there is this the inner perturbation and the thing is that tucco cycles vanish actually for amenable group poets acting on any field of two one factors so you don't even need to assume that the field of factors on which you're acting is amenable but it's essential of course to assume that the group poet that is acting is is amenable otherwise this is very much false so whenever you have an amenable group poet for any free co-cycle action on a field of factors like there the the tucco cycle is a co-boundary now first of all we have to look at the case where where the the group poet is just a group so we have just an amenable group and for and the amenable group is having a co-cycle action on on a two one factor b and then actually it's a very recent result of Soren Popa of this summer that in that case the tucco cycle is always a co-boundary and his proof is of course I will not give the proof but I will give the the main point in the proof because it's an extremely remarkable proof because the the main step in the proof is so the existence of a perturbation of the action so one should realize that actually perturbing alpha g with an inner automorphism is something you have always to to allow because that that's kind of random yeah okay so you allow this inner perturbation of the action so after an inner perturbation of the action there all of a sudden exists a copy of the hyperfine a two one factor that's globally preserved by the action what about the yeah and you have to control that as well exactly and you can and then you apply Oknianus theorem because you land you also get the tucco cycle with values in r you have to control everything but you he can and and and you go back to Oknianus theorem for actions on the hyperfine a two one factor and moreover the construction of this globally invariant copy of the hyperfine a two one factor goes through his methods from sub-factor already how do you construct r I mean it's yeah but it could be very small no no but you do construct it in a kind of inductive way by refining refining refining the the partitions and and and then all the time you control that they commute less and less with a pre-given bigger and bigger set of elements yeah what do you see here it's your arbitrary two one factor on which the group is acting and this is even a characterization of a man ability in the sense that being able to always find the copy of the hyperfine a two one factor that's globally invariant can be done even only if the group is amenable so it's it's a sharp result okay so for amenable groups we can annihilate two co cycles all two co cycles are co boundaries I mean in the case where the actual is free then it's equivalent to that so you don't have a co-cycle isa yes in the equivalence relation case you mean yes in the and now I will immediately show because there and then we come indeed to the crux of the matter immediately so here is again the notion of of group poet that I wrote there on the blackboard as well so the group poet actually so let's now consider what is a general group poet that is amenable well first of all there are the isotropic groups so for every for every unit x you have this countable group that's the isotropic group at x and secondly if your group poet is amenable then actually it's not so complicated as an arbitrary group poet in the sense that it's always a semi direct product of this field of amenable groups on which the amenable equivalence relation is acting now what does it mean that the amenable equivalence relation is acting so on top of the field of isotropic groups you have your amenable equivalence relation so you have an equivalence relation on the space x and then for every pair in the equivalence relation for every x i in r there is a an isomorphism between the fiber gamma y and the fiber gamma x and all this just mixes together into a semi direct product which is this amenable group poet and because amenable equivalence relation have no two comologies as Alan was saying there is no more general amenable discrete group poet than such a semi direct product okay so amenable group poets are such a semi direct product of a field of amenable groups and then amenable equivalence relation okay now we look back to the so they're just resuming what I was saying we go back to the co-cycle actions so the group poet is acting on your field of two one factors and now by Soren's theorem we already know that in each fiber you can solve the two co-cycle so for each isotropic group the two co-cycle is co-boundary so say let's not bother about what the notations mean but you can imagine something it's it's co-boundary and you can do that measurably that's not not issue fiber by fiber for each isotropic group you solve the two co-cycle you write it as a co-boundary but now in order to prove that the entire u is a co-boundary you should be able to choose the the the the cycles here in an equivalent way with respect to this equivalence relation that is acting everywhere and a priori you would say that this is impossible so a priori you say that there is an obstruction but actually of course why is there an obstruction if these vx would be unique then because everything is canonical and so on that this would be automatically co-equivariant but they are not unique they are intrinsically non-unique they are only unique up to a one co-cycle of course that is the way co-homology is working so there seems to be an obstruction except that there is a very general lemma and there is a very general lemma so again you can now for a while forget even about group oh it's now we go even some kind of higher level of obstruction just consider the following data some standard probability space and we have a measurable field of groups polish groups metric complete separable acting on polish spaces in a continuous way think of something like a unitary group acting on a two-on-factor by inner automorphisms or an automorphism group yeah well that's the context that will appear later yeah okay now on top of that we have an equivalence relation on x and this is amenable and this equivalence relation acts by what I would call conjugacies of my data in the sense that when x y is in the equivalence relation then say alpha of x y would be a homeomorphism from py to px and delta of x y would be a homeomorphic group isomorphism I mean preserving all the structure present yeah well if the equivalence relation is amenable there is an equivariant choice up to a co-cycle twist that you should always allow but if the if the the amenable the equivalence relation is amenable you can choose such a section that is equivariant with respect to this kind of thing but with one big if if the actions have dense orbits and it's the density of the orbits together with so here is there is one thing to say if the equivalence relation would have finite orbits then of course you can choose equivariantly your your sections now the equivalence relation is only a union of more and more finite sub equivalence relations so you have to do this and you have to make this converge and that you can exactly do if the orbits are dense so this I have to say is kind of abstractization and generalization of several co-homology lemmas that have been used in the 1980s but it's it's put in this very general context now what does this have to do with our topic today there was this obstruction in in solving the two-core cycle where we needed this equivariant choice of cycles solving the the two-core cycles and we can finish the proof if we can verify this kind of hypothesis which will amount and I will explain you in a minute what this means if we can show that the one-core cycles are approximately co-boundaries that is what this density would mean so what we really need as an ingredient now is that for amenable groups one-core cycles are approximately co-boundaries so now we leave the world of group poets you can for a while forget about that and we now just go back to amenable groups acting on two-one factors so the setting is now again very straightforward we have just an amenable group and we have an action by automorphisms of a two-one factor so what is a one-core cycle a one-core cycle is just a family of unitary satisfying the one-core cycle relation what is a co-boundary it's a one-core cycle that looks like this and what is an approximate co-boundary it would mean that instead of exactly writing vg like this there is a sequence of unitaries such that with convergence say in the in the strong topology vg is such a limit of co-boundaries and the theorem that we proved in the paper is that for amenable groups every one-core cycle is approximately co-boundary and even better this is a characterization of amenability so a group is amenable even only if whenever the group is acting on a two-one factor a one-core cycle is approximately a co-boundary now it may be tempting to think that this is something that has to do with just taking a kind of mean over felner sequences but we actually believed for quite a while that this is maybe not true for the following reason think of the much more known case of homology for a unitary representation so if if we have a unitary representation of your group gamma then there is a notion of a one-core cycle which is nothing else than a map from gamma to the Hilbert space with this one-core cycle relation now a linear one and this is something with the Hayru property and so on the Dalin likes a lot and knows a lot here it's not at all true that for an amenable group one-core cycles are approximately inner by no means so it's and it's not true that you could take them the the mean of the cg over felner sequences and so on it doesn't work at all and so we believed somehow that this should be viewed as the the linear term of that kind of more complicated setting so that maybe there is even an obstruction to have approximate internals of one-core cycles but it's not so and it has to do with another characterization of amenability namely the characterization saying that outractions of the group gamma of an amenable group are never strongly ergodic and this means that there are although there are no not necessarily invariant elements there are always unitaries that are approximately invariant and so here again you may be tempted to say okay that's easy let's just take the mean over a felner sequence but typically that would completely kill the make very small l infinity norm so this is not the the way to go to to prove this yeah okay so how can it be be proven this kind of results so I will just give you a hint of a few of the implications so I will show you how to go from the fact that there is never strong ergodicity to solving or approximately solving one-core cycles and I will also show you how to go from amenability to the fact that that there is no strong ergodicity okay so assume that you have an action of your amenable group on a factor and the tool that we will be using is because we will be looking at approximately invariant elements so we will be looking at sequences of unitaries wn sequences of unitaries that are approximately invariant now in order to express this in a much more convenient way you can view the sequence as an element of the so-called ultra power algebra I will not introduce the ultra power to one factor but there is a way to to to view to put a two-one factor structure on the space of sequences modded out by those that converge to zero okay now in that case strong ergodicity would mean that if you have the group then act on the ultra power that there are that there is nothing except the scalars that there is invariant in the ultra power algebra okay so the first step and this is really actually a method of Alain Cohen if let's assume a little more than just the non-triviality of these fixed points if this is a factor then one-core cycles are approximately co-boundary and that's really Alain's method because what you do is the following assume that you have somewhere a one-core cycle then you build a two by two matrices over b and on the two by two matrices over b you have this action that Alain wrote and then you notice that there are two projections in this algebra that there are two projections in this algebra namely this one and this one they are invariant by construction under bg now our assumption is saying that the fixed points in such a ultra power algebra is always a factor so these two projections must be equivalent now these projections being equivalent in this factor produces you a sequence of unitary sitting in in that position there and it exactly solves you approximately the one-core cycle so this is say classical by now okay so that's for that part then we have to go from the assumption that the group is amenable to producing almost invariant unitaries and this is much more tricky than you would expect because you cannot just take the mean over over a Felner sequence so take an amenable group and let it act on a two-one factor and I will produce for you a sequence of unitaries that's approximately invariant under the group action so because the action is assumed to be by outer automorphisms if you make the cross product the relative commutant of b in this cross product will be reduced to multiples of one and now there is another very interesting result of Sorin Popa in general if you have this kind of situation a subalgebra with trivial relative commutants then you can find in the ultra power of this subalgebra a unitary element that is free with respect to the entire algebra free in the sense of free probability theory if you make all kinds of words between new and elements in the larger algebra you never get one you never get three zero and so on and so forth and and you see that the relative commutant condition is essential because if there would be something in b cross gamma commuting with b yet then it would commute with everything in the ultra power you can never get freeness so it's but whenever the relative commutant is trivial you find in the ultra power of b an element that's completely free with respect to b cross gamma now if you take this element b you now build inside the ultra power algebra you look at this subalgebra and all the ways the group acts on it now if you translate freeness you can you probably have no real idea what this exactly means but what you then find is inside the ultra power b omega you find a free family of copies of b all free with each other indexed by gamma and the way the group is acting the way the group is acting on b so it's acting on b omega and the way that it's acting is just by shifting the the free product around so you find the free Bernoulli shift if you wish inside b omega automatically always and this is the big advantage that this free this is a very concrete thing this is a free Bernoulli shift you can very concretely now construct almost the invariant elements in the for the free Bernoulli shift and and therefore you find it in b omega and therefore you have it in the in the two one factor okay this by now very recently actually it has been shown to be true as well in the type three case so at least for state preserving actions so the similar reasoning works for state preserving actions on arbitrary factors by now that's a result of amin marachi the group is amenable but the factor need not be amenable here it's not supposed to be amenable so what is then the conclusion while we can then put everything together one co cycles are approximately inner that gives you enough of a covariant choice so that you can solve the two co cycle problem and then you have the the classification result that I said for for regular sub algebras but this also poses actually a lot of questions because you could now wonder as serene did in his paper what is this class of groups satisfying two co-mology vanishing for any action on a two one factor with the with the two co cycle so what what serene proved in the group case is that amenable groups have this co-mology vanishing property for obvious reasons if you make a free product then of course if you can solve the two co cycle on gamma one and on gamma two you can do it on the free product so that's so it's stable under free products it's actually even stable under you can amalgamate over finite sub groups that's not not a problem and there are other things that serene could prove for instance property t groups are never inside yes that's the next they always have the high group approximation property they cannot be property t there is no room for commuting things inside so you can in such a group you have no room for a direct product of an infinite group and an amenable group that cannot happen so all this leads to a wild guess that I want to discuss in the final minutes of my talk say you have examples of groups which are not because they could still I mean high group groups could still be such direct products so yeah so say z times f2 would be have the high group property but not be exactly but the guess rather is that it could be the so-called treeable groups and that's a notion that I want to to discuss so this class of groups satisfying co-mology vanishing could be exactly the class of treeable groups so what is a treeable group so countable group is said to be treeable if you can have it act somewhere freely and preserving a probability measure in such a way that the associated orbit equivalence relation so the equivalence relation of lying in the same orbit is treeable now I have to tell you what is a treeable equivalence relation but let me first say what is strongly treeable it would be the same but requiring that for every action free action preserving a probability the relation is is treeable but what is a treeable equivalence relation well this is again not a real definition but still you can put on the orbit structure so you can choose you can put on every tree sorry every orbit for the moment is just a set of points countable set of points you could say okay this countable set of points has actually the structure of a tree that you can always do you just choose a tree in the orbit but then you have to do it measurably throughout being able to do that measurably throughout is what is called treeability but maybe you want to see a much more concrete definition of three that I don't think so I mean I will the concrete definition will will show you what it really means it means that you find that's another definition of treeability a family of elements phi i in the so-called full pseudo group I mean these are partial transformations yes of x with grav in the relation so treeability means that you can find such a family such that no word unless the you make a trivial composition say is the identity somewhere the identity transformation so it's it's really that you can find a free family and generating phi i generate the relation but the group acting freely on a tree would be just a free group it's okay no I see you're right absolutely yeah so everything is up to measure 0 yes everything is up to measure 0 yes so that's the notion of treeability for an equivalence relation and then for a group treeable and and strongly treeable by the way it's a huge open problem whether every treeable group is automatically strongly treeable so that's it would be very interesting I think there should be counter examples but that's a difficult problem now of course in the same way as groups can act group poets can act and there is an obvious notion of treeability for for group poets and there is a similar obvious guess that group poets satisfy to co homology vanishing even only if the group poet is vanishing the even only if the group poet is treeable now there is a little nuance now let's get back to equivalence relations I just defined you treeability of an equivalence relation but I also defined you or gave a hint what is treeability of a group poet so meaning that the group poet is acting somewhere such that the orbit relation is treeable now I have to reinterpret this what this would mean for an equivalence relation I have now two definitions of treeability for an equivalence relation this one and that one now what is the second one meaning um so this was the original definition now if you viewed this in the group poet definition an equivalence relation would be treeable say in the group poet way if there happens something else if there is this orbit relation which would be another equivalence relation it sits higher up there is a treeable equivalence relation s on a space living higher up on a space y and then a factor map measure preserving from y on to x that happens to be bijective on the orbits of the relation now this is just a map that is a subjective and measure preserving yeah and essentially subjective up to measure zero okay now this is weaker so you could call it I mean I don't know whether this is a good notion but let's call it weak treeability just for one minute and now there is an equally open problem whether a weakly treeable equivalence relation is is automatically treeable and this is a question about equivalence relation if you restrict this question to equivalence relation coming from group actions then it's the previous question of course and that's in the yes exactly that's in the and that the sub relation of an equivalent a treeable equivalence relation is treeable which is a theorem of of them yeah and now the guess was that a group poet satisfies two-core muller g vanishing even only if it is treeable so an equivalence relation satisfies two-core muller g vanishing even only if it is treeable now there is some indication but that's something that I don't have time to discuss today instead of just looking at group poets and equivalence relations and groups acting on two one factors you can also have them act on carton inclusions that has to do with normal sub equivalence relations and so on that's another story and there actually you show that if two-core muller g vanishes in that category then automatically the group poet must be weakly treeable so there is a beginning of indication that this could be the the right notion but I cannot go deeper into that so that's all thank you the problem is even that there is no true cosmology theory so but we didn't think of it but it why not no that's right yeah


Hi everyone, Sean with jaspyscasebrakes.com here doing 2021 tops archive signature series retired edition baseball five box break random box number 12 last five boxes from a case that we started with the random box number 9 10 11 and 12 now so uh the way this works five spots for first number all five boxes randomized list of customers names and numbers whatever number you match up with is what number box you get so here's our list of customers Matthew Brister down to Jonathan Arnaldi and the numbers one through five so here are those five boxes we do have a fresh case that I've put in store for random boxes with random box five box break number 13 in the store right now so one on top five on the bottom one so you can see one two three four and five on the boxes let's pop over here to the randomizer turn on the top camera so you still see the boxes there dice world randomized both lists and pair those up four and a three seven times seventh and final time Nelson crew or Nelson Ortiz down to Mike McCarthy and seven times on the numbers seventh and final time two down to four so seven times on the numbers seven times on the customers and seven times on the dice uh Nelson Ortiz with two Jonathan Arnaldi with three Matthew Brister with one Jake Johnston with five and Mike McCarthy with four so there you go Matthew one down to Jake with five let's print out this list and print out some labels and it's ripping and since everybody has one box each we're just going to go with a box order number Babe Ruth cut also I mean most recently we just pulled Ty Cobb and Mickey Mannell like in the last month so I wouldn't I wouldn't be surprised if we had pulled a Babe Ruth before cool so box number one Matthew Brister Mickey's a little bit more common Ty Cobb is definitely not though Ty Cobb that was like the only the second auto I'd ever seen in person of his and I didn't even like I had to be reminded of the first one box number one Matthew Brister it is David Cone 7 out of 60 for the New York Yankees what's that is that Stadium Club what your 1999 Stadium Club David Cone here you go Matthew thank you very much cool looking car like that stuff uh box number two is Nelson Nelson Ortiz number two we're going dock Dwight Good and Doc Good in 17 out of 32 one off his jersey number that's from 1986 Tops NL leaders and wins he was the leader had 24 wins that year very nice box number three is Jonathan Arnaldi there you go pull you a cubby let's see did I do it I did not pull do a red Tony Perez Cincinnati red from tops gallery collection that is 20 out of 29 and it's tops gallery collection 2003 Tony Perez to see almost cubby just wrong wrong there you go Jonathan thank you very much man uh box four is Mike McCarthy box four Mike McCarthy and it's Alfonso Soriano 94 out of 99 Yankee from 2014 tops there you go Mike box number five final box Jake Johnston and it's one of one Mark Mulder that is 2007 tops Mark Mulder one of one to finish it off and there you go Jake congrats with the one of one not that I know of Rex I haven't heard of any and there you go that is 2021 tops archive signature series retired edition baseball five box break random box number 12 from jasphyscasebreaks.com I'm Sean jasphyscasebreaks.com fresh case posted five box break number 13 to start it off in the store jasphyscasebreaks.com thanks for hanging out see you next time


They asked for my ID at the checkpoint. Fake, of course, but the duty boy didn't look at the details, voting his senior officer as soon as he saw the last name. The boss must have been waiting for me all day, picking up the phone in a moment's notice. The duty boy told him that I'm here and he would flood it with orders. The chief of this admirable jail isn't too keen to talk to Foundation agents in person, but he's really fast to perform the required tasks. I've been here four times, never had to wait for anything. The guards, mind or manners, the in-major cooperative, some pleasant working conditions. Duty boy kept nodding and saying yes as the orders were neatly piled upon him. He hung up and suggested I take a seat and wait for my escort. I followed his advice and put my briefcase on my knees. I ended up surrounding lazily. I started humming a song that has stuck on me since morning. Some new hit the aired on the radio, though I couldn't remember the name of the artist. Duty boy took a glance at me. The escort arrived soon after. An obese bloke with a wide smile, a real happy hippo. Really glad to see me as if I was his grandma. I got up feeling the infectious smile spread on my face as well. Alexi Yarin?  We've been waiting for you since this morning. No trouble getting here? That's fine, thank you. How's Miller doing? Just let her down. Need any pups? Just kidding. I know you're eager to start. Follow me. We strode down to bleak corridors. The escort kept flooding his ar- We strode down to bleak corridors. The escort kept flooding his arms while walking, and his gait had such a kick to it. I kept waiting for his shoes to come off. I've never turned down the pleasure of talking to this lad a bit.  Funny thing is, I do remember his name, but not the name of the owner. I wonder. Are you a music fan? I ask. Why'd you ask, he said, looking over his shoulder without slowing down. Heard one this morning.  Try humming the tune. Goes like D-D-D-D-D-D-D-D-D-D-D-D-D-D-D-D. Now that's not up my alley. I rarely ever listen to music. Rather, tell me something. Will they really be taking Boris up a way? If he agrees to it. Very well. Feel free to call me. I'll help with persuasion. Okay, here we are. The interrogation room is very simple and cramped, lit by the dim sunlight. We've cleaned it up before you came around. Thank you. You really shouldn't have. I entered the room and rarely looked at every corner. All I'd need is a table and a couple of chairs, nothing else. Although they think I'm some big cheese, so keeping up appearances of the must. Good, I said condescendingly, taking a seat. The chair's iron legs have a demonic screech as I pulled it out. Are the inmates ready? Oh, are they? Everyone's itching. No doubt some of them are entertaining a naive thought that I'll be releasing them. One to men one by one, exactly as the list goes.  I'm just giving a list. I forward it to the prison director and go talk to the inmates. I'm not taking them prisoner. I get them to agree. It's just that I'm allowed to be persistent. First one is a pale youth, flap-eared, lanky and aggressive. The boy was about to be transferred elsewhere, so we lucked out catching him here. They seated him over against me and left us alone. I took my time, languidly placed the agreement's folder to the right of me, and the empty, for-now folder with signed papers to the left, placed the voice recorder at the corner of the table and turned it on. A happy smile appeared on my face. Good day, Maxim. How do you feel?  Now, aren't you a menace?  To demonstrate that he's serious, the inmate placed his skinny hands on the table, refraining from the throttling bit for now. Now that we've found common ground, I'd like to make you an appealing offer. Wouldn't you like to go? It's not your fault you ended up here. It's all caused by your disease. Here's an agreement, I said, placing the document and a pen in front of the villain. For taking part in testing experimental medicine, these could cure you. Having heard the last phrase, the inmate started pondering. He leered to the paper and started moving his lips without making a sound. So what do you think? So my memory won't be finicky anymore? You have Korsakov syndrome. That's not just your memory being finicky. But by and large, yes, they'll heal you completely. Taking new medicine? The poor fellow can't make up his mind. Yes, and they will release you in a month. This medicine is very important. They'll cut your sentence down if you take part in the experiments. So I'll see my mom in a month? Exactly. The inmate gave an exalted sigh, a second after he picked up the pen and pulled the agreement towards himself. Right here and same place on the other page. That is all. Welcome for you this evening. They all are innocent. Every inmate with a life sentence is blameless. Circumstances are the ones to blame. Depths, poverty, alcohol, disease, those are the true criminals. Which is why inmates will go to great lengths to return their freedom and get rid of the circumstances. They even agree to experiments. Truth be told, that guy would be testing meds.  Saves us the amnestics. The next subject is a tall and lean athlete.  Although his body is not adorned with dragons and sakuras, but with Celtic crosses swastikas barred wired eagles, reminding of Nazism and showing the inmates true colors. He's also struggling not to spit in yours truly space. Stand to slide, Berlogan. Pleased to meet you. Is that so?  Call me Alexi. I'm from the Bessinaw Penal Colony. We offer you a transfer.  An everyday vulgarity, but annoying nonetheless. The state is rolling out an inmate re-socialization project in our colony. You were listed as a candidate for a training course to get rid of ethnic intolerance. I'm not ethnically intolerant. I'm laying the murder on those bastards not for where it came from, but for what they allowed themselves to do in my country. Your education is impressive. Not everyone knows what ethnic intolerance stands for. Still, you see, you're here because of that specifically. Your attitude towards ethnic minorities have led you to a sentence. I'm gonna say that again, but not to lean forward. I only ran into foreigners the police can't be arsed about. Was that the reason why you and your accomplices burned down a bus carrying foreign exchange students with Molotov cocktails? They came here to take our jobs. They're foreign exchange. They will study here and work at home. Could be. But they take stake-funded places our boys could be having. Their state is paying for their tuition, not ours.  Time to weave my tangled web now that he's off balance. I gave him a copy. While you are reading the agreement, I'd like to describe the conditions. Three square meals, shower, gym, computer room, daily therapy sessions, manual labor down to a minimum. If the therapy is deemed successful, your sentence may be changed to 15 years instead of a lifetime, and you'll be settled in a block with those like yourself. That piqued our Nazi's interest. He pulled the agreement closer to him. So, uh, no. At all? Not a single Jew, except for me, of course.  Okay, where do I sign? Taking a class D in the Foundation is not part of one's punishment. We are not picking those who are guiltier than the rest, not at all. Our filters work like this. First, we get death row inmates, a rare commodity in our country. Then we get to those who aren't likely to get anything but life sentences. And out of these, we pick inmates with no next to kin, who aren't likely to be noticed if they go missing. People from orphanages are the best candidates, like that Nazi here. This one pushed inside with a rowdy stout type with a massive forehead. Which I had a forehead like this, I'd hammer nails down with it. They always had to force a short inmate to sit down, but having been seated on a chair, he immediately calmed down. I especially like that sort of people. Good day, Alexander Bereisa. My name is Alexei.  Who are you? He croaked. Can't tell you at the moment. I'd rather you answer my question. Weren't you in prison for an arson attack on a tenement house? Yes, but I didn't. How many people have died? Thirty-one, but not all of them were. How many of those were aliens? I ask without batting an eye. The short guy was looking wary now. No one has talked to him like that. Someone burning down a house is part of his fight against alien invasion and getting him prisoned into a simple jail instead of a mental asylum. This has a simple explanation. The shrinks thought he was faking it. No one believed him. He was deemed sane by three doctors, and another one after he appealed against a judgment. And now he's looking at someone who believes him. Are you kidding me? You think that I came to a jail and managed to get an interview with you just to kid you? No. Not at all. I'm here to give you a collaboration offer. Here's the agreement. The resistance fighter browsed through a few lines and fixed his grim eyes on me. Lord, is he ugly? I understand. You are not willing to take my word on it, I said, putting my hand into an inside pocket of my jacket. But my sincerity can be proven. Here. Familiarize yourself.  He did his brows even more, but then he started looking and with every picture his brows went higher and higher. Soon he would seat them with rage, the phrase I told you so stuck in his throat. Like these, I said, leaning over the table. See this one? All scaly, triangular head. And this one, look, wove itself a nest from its silk. It's not silk, actually, that's just what we call it. The madman was almost mine now, but he was again overcome with doubt. He looked at me sternly, demanding further proof. Not a fake, he asked, poking the photos. Sure isn't. If that wasn't enough to convince you, here's one more thing. Out of a special pocket I pulled a coin with a hole in it. A long string went through the hole. As soon as I opened my palm, the coin fell on the ceiling. The end mate gave a jump almost falling out of his chair.  So, sales for two people, the contract is for a month, after that you decide if you want to do more. Also, tell me the rest of the way there, where do I sign? It is our responsibility to scrutinize the candidates through and through. We must be prepared for the meeting. Everything matters. From the crime committed to grades in school, from mental to dental health, candidate interviews in meticulously directed stage plays, rehearsed for weeks on end. We must delve deep into psychology. Must be familiar with arrest reports, court transcripts, and the end mate's behavior in jail. Hell of a job, all for a wee couple of signatures. Getting prepared for my next client took quite a while, but after we met I just started looking at his mug. For a good couple of minutes I'm just sitting there, chained propped on fists looking at the visage of a 6'6' brute. That visage is remarkable, lacking the left eye with a scar instead of it looking like it was sutured on a sewing machine. Granted, he wasn't a glamour model before that, too. A knife did that, am I right? Yup, an upward stab.  Well the kitchen knife, shrugged a beefcake. Doesn't matter, it went right into your eye. Just a nick, he said, shrugging again. Knife did that to you? That is right. We had a disagreement over the legitimacy of her infidelities, so she went nuts.  Just wanted a soccer one, and then she dropped dead after the first hit.  I merely resorted to self-defense, and killed seven more. The brute spread his hands. What could I do? Other cousins were there. I'll call you Travolta, said I, fetching the necessary agreement from my bolder. Why? You remind me of Face Off. Good flick, he nodded. This here is a government job offer. A month of work and you're free to go. Take a look and give your autograph. The brute quickly browsed with the document and raised a pen. Instead of signing, he went with a question. Could I smoke there? No. You'll be given a nicotine patch. Assure him, he said, signing the agreement. We are restricted to one language, the one the inmate wants, and everyone wants different things. Still, out of the multitude of languages we must unerringly pick one. Proper tone, proper words, proper gestures. We work methodically. As we enter the room, we know every step we take. Recon is crucial. All fares to their credit supplies us with everything we need. In exchange for that, they only require that we don't forge dissenters. They brought in a timid mess of a wimpy lad. As soon as he sat down, I tossed him a pen and a paper saying, Sign this. What is it?  What part of sign this don't you understand, bitch? The wimp grabbed the pen and the agreement. He must have been shaking as much as when his sentence was proclaimed.  I got my signatures. Dismissed. Yes, we're training on that too. Not recommended to use. Works on one person and twenty, at most. Saves a lot of time though, who knows, maybe I'll wrap up early today. Next one spoke first for a change. Are you from the agencies? No, Victor. I'm not from any secret agency. It just adds a pretty nice suit you got there. Compared to what you're used to wear before the jail, this is rags. Did you read my case? Loaded at your social network profile. Victor Rogov fixes me with a piercing glare, arms crossed on his chest, an all-knowing narcissistic smile in his face. Now, who are those dapper people not from secret agencies that need me? Science, I said, getting out of their agreement. We offer you to participate in testing a new non-lethal weapon. Active collaboration might get your sentence commuted. Best case being ten years. Better not to mention actual terms around the shifty fellow. He's too suspicious to believe in life sentence being shortened to a month. Victor took the paper from my hand but didn't even look at it. Not so non-lethal if you need convicts for that. How do I say it? There is a risk. It's like test pilots. They take risks too, but no one wants them to die. What sort of weapon? He asked with a disinterested look. Foam.  You'll be bathing several times a day.  Look suspicious. See, for yourself, I said, opening the folder with unsigned agreements. There's only two more papers in here. You have the third, and those are signed. As you can see, there are five of them, and I'm sitting here since 2pm. The alternative I'm offering looks more and more promising. Victor starts pondering it instead of turning his nose up like a princess. I'd like to go through the details, he said, pouring over the agreement. By all means, please do. All of the more so, the document doesn't contradict my words in the slightest. None of the signed ones do either. Every agreement is custom-made, tailored around a specific cover story. And all of them, a round of applause to the legal department, are composed as you can't raise any claims. This guy has monthly rotation mentioned there, too. I'm not afraid of any reveals and unmaskings. They may read all they want, but man, do they go for a long time. I don't know the details, but they say that every candidate is already assigned to a specific object. They even say they're even assigned to specific experiments. I don't believe that. But I do know that doctors do make overly specific requests. It should not concern me, but a colleague told me once. There were requests for blind people, people with alien hand syndrome, chemically castrated people, ambidextrous people, and consider this. The world's fate depends on whether I can fulfill their request. Of course, not me personally. There are many of us. I'm not even the best in this business. And actually, we don't keep tabs, so I don't know who's the best. Might even be me. One can never tell. When they brought the next one in, I was pacing to and fro next to the window. The young thop, a bit worse for wear after encountering daily prison life, was seated down, and he stared at me blankly, never reminding the jail personnel who haven't left yet. I started talking into the phone. Yes, Peter Romanovich. But just brought him. Doesn't look like he was beaten. Looks alive. No, unfortunately you can't talk to him directly, I… Peter Romanovich, I understand, but now… Peter Romanovich, now is not the time. We're already taking too much risk. Yes, the plan is unchanged. Yes, right, we'll send him out this evening. Not sure about that. Dmitri Stepanovich hasn't called back yet. No, but he did say he'll do everything. And he never failed us before. Yes, okay, talk to you later. I hung up, without actually calling anyone, and offered Peter Romanovich his offspring to the agreement. So lookie here, you sign these papers and we'll transfer you to another jail. Conditions are better than here anyways, and you'll share the sale with your father. Yes, that was him on the phone. He's done us a big favor back then, so we'll be getting you out now. It'll take some time though, can't fix the deal less than a month, but we're working. Got it, said the rich brat without asking for details. Do I sign here? Yeah, put your John Hancock right over there. The other page too. Excellent. This evening you'll be going to your father and after that, well, we'll press on. Thanks, said the young criminal and hurried to the exit. He might even get to meet his father, who's been working for the Foundation for two weeks now. As a matter of fact, I resorted to outright lying. That is, I was obscure earlier, but not a word of truth was spoken now. Very few cases justify that, like this one for instance. The criminal family might have gotten out free. They have veritable contact with the police major, people from the regional administration, a couple of mob bosses, and a serpent's hand. Last one today is a real treat. The one brought to me was not a brutish murderer, not a maniac, not a bomber, not even a legal downloader. This is a mediocre looking man, a bit on the heavy side, who looks like he was beaten. Lumps and bruises sporting every color of the rainbow. We had a long fight with the government over this one. The bastard sold state secret information to terrorists. Investigation confirmed that 53 documents were sold, but there may have been more. He should have gotten a firing squad, but the case went public. Human rights activists crept up from every corner of Russia and beyond. These are okay with protecting any sort of bastards.   Three years of work were put into him. Once they beat every piece of information out of him, he was thrown here. Now he's beaten by his cellmates. A lot of patriots among this bunch too. After we were left alone, I got up, walked to him and put the agreement in front of him. Slowly, languidly, hotly. Placed a pen next to it, and finally started talking. Five officers were stabbed to death with their families. One of the officers was a good friend of mine. The group you sold the info to committed three terrorist attacks. Assaulted a military base, stole weapons. And these are only the episodes obviously connected to the info you leaked. That's a lot of blood on your hands, First Lieutenant. I jabbed my finger at the dotted line. Now you take the pen and put your signature. I set in a quiet but intimidating tone. I won't sign your papers. Listen, do you think you've gotten through the grit of Russian torture? Think you've already had the worst? Look here. I rolled up my trouser leg with a pistol underneath it. That impressed him. I walked into a jail with a weapon and no one bothered to search me. Can you even imagine what kind of person I am? I'll do things to you if no one will come here as you scream.  You may want to turn off the recorder. I shattered the device against the wall. The smart guy lost every bit of self-confidence and put his hand over his head.  Don't make me angry. The bastard started having second thoughts and took the pen. As soon as I made sure the signatures were where they should be, I calmed down and started packing my things. Most excellent, I said while putting the folder into the briefcase. I hope you get Keter duty. What Keter, he said, passes me the signed agreement. That will be explained to you on site. No, you got me wrong. What Keter will I be said to? The one that desiccates water with a look or will you throw me to the living geyser? It was like an electric shock, my eyes widening, jaw slowly dropping.  It felt like we changed places. What were those documents you sold to the fucker? Who were those terrorists?