From Klein to Kan / Q&A / Grothendieck's Universe (contd.)

0:00 Okay, our last speaker this afternoon is Michaila Etini. She is a colleague of John Stachel, our organiser, here in Boston, and she came to Boston in 2002 from Romania, where she did her PhD in differential geometry, of which there is, I happen to know myself, a conference of Romanian differential geometry only an hour ago. Extremely, extremely flourishing, and very popular school in Romania. Her main field is general relativity. But today she's actually going to talk to us on a historical subject. She's going to talk to us on the subject of Brodendieck's universe. So here we go. Thank you. It's done with really nice light, and you can kind of have a little bit of visual discussion with each other, and grow the teaching model. Can you speak louder, please? Can we even turn the microphone up? Anyone on that? Yeah, good question. It's not very loud. No, is there anyone turning up the volume on it? Do your best, don't worry. Aleksandr Grudny is one of the greatest mathematicians of the 20th century, the mathematician of the 19th century, who gave the distinct mathematical found perception and evident lines, rhythms. He changed the landscape of mathematics to the viewpoint that is caught through the journals and the archives. We will start with a short bio. Aleksandr Grudny was born in March of 1928 in Berlin. His father Shapiro is a Russian Jewish American. Elibret was born in 1922 and he met his future wife, Hanka. Hanka came from a family at Lutheran County, which was developed against the prediction of our plan. Both parents, Shafiro and Hanka, have a father. Shafiro died in a concentration camp.

2:30 He took his name from that of the government, and here's a picture of him. By the time the war ended, he and his mother moved to France, the south front, the region called Montpellier, and he ruled the university. The University of Orkney at the time, as your domain was mentioning, it was a month and a half back when I was training as a teacher in the class. Over time I was understanding the university courses less and less, which is found in the teachers promoting and teaching what works for them. In that uninspiring environment, I developed a close-knit experience in the area by training the guys that we had. On his own, he intentionally rediscovered measure theory, the Lebesgue integral, a similar habit to Einstein, which he developed on his own. He applied for the scholarship in 19... Sorry. I don't know how his heart beats. One of the interviews, I think, is according to the application, and the thing about her is that she will show me those formulas again. I think there should be a extraordinary amount of involvement in some of these applications. Thales, in the meeting with Henry Cartan, the son of Henry Cartan, when Groden is arriving in Thales, he shows mathematicians what he creates out of the movement of the air, the results of course, and then he comes. He wasn't this boy. In fact, he saw it as air, and he saw the creeps, and he saw it as mathematics. And in his own words, without knowing it, I learned that solitude was essentially the method of mathematics, something that no master can truly do.

5:00 Without having been told, I nevertheless knew in my dance that I was a mathematician. At that time, I was running a medical seminar for the Colonial Maths Studio in Paris. Learning to think out for the first time made me feel so much more efficient today. Including, um, the speakers. Professor Ducati, yes. Thank you. I'd like to thank you all. Thank you. My name is Chevalier. My name is Diogo. Thank you. Thank you. Thank you. Thank you. Cassandre and his group share a common background. He speaks German, he graduates, as they call him, but Grodenbeek joins the Cassandre seminar. He was an outsider, a journalist, a German speaker, living in a home in France, so his media education has been such a challenge that he found himself here. Grodenbeek's thoughts related warmly to the group. He has nice memories and he said that I found myself struggling to understand what was built around me, things to grab. I need to be a playwright later on. This may have been the reason why, in 1949, we moved to Nancy. The University of Nancy in Lakewood was one of the strongest mathematical centers in France. Nancy faculty included Gildonet and Schwartz. They all remind us that mathematicians put part in the craft of our pre-writing and our mathematics and liberal arts. The place in Nancy was less active than in Paris, and professors had more time for this year. Among Grosvenig's fellows were Leon, Germain Malagrange, and Paolo Di Caprio. Grosvenig started to work in the area of functional mathematics with the two professors, and he wrote a literature for them. I'm sure you've heard of this guy. He was a joker. Before that, he was 60.

7:30 Why 60? Why? Am I turning 60? He was not a guy who would admit to being an expert. Nevertheless, he was a extraordinary talent for a time. He could be extremely intense. He was not me. It was very demanding of him to be such an expert. He had very few books, but rather than learning things by reading them, he would try to do something with them. He was very hardworking. He did the twice as much. He used to say to his college students, You seem to be a nice, well-balanced young man. You should make friends. Go eat. And do something. But that was not really what he said. In 1996, Rodenby had a position in the Center for National Leadership, but it was merely a fellowship at the time. Because he was a professor. Because, yes. Rodenby Ph.D. thesis was on Rodenby and Suryata Poloshetian's training lab, a campus product. It was published in 1994 and it appears in the North American Institute of Science. If Ph.D.C.C. showed the first signs of a germ, they were thinking that some characterized the type of mathematical life. Those arguments were the first to realize that the algebraic category of mathematical physics is infinite. And so then some could have it. In some and many other ways, gravity was the first sign. But I just... On Hilbert space, and nuclear space, there are many ways to define the product of the topology, the product of the tensor product, while on Banach it's quite a job. Much of the theory is nuclear space, and we don't have very much of a way to define the tensor product. A grammar instructor will terminate a job as long as he or she can do, so it's painless and it's not a very good thing.

10:00 Frowning is kind of difficult. It should have been wrong in the world, but it isn't. But sometimes you can see that you're learning how to do it right. Should I help grammar teachers get visitors to Brazil in the next few years and suggest to people that they should make a student? The following is a bit distracted, but again, Grozny received a top-up, the best he could get in the University of Khao Kha. Grozny made a special announcement that he would be able to attend the Spanish University of Khao Kha in 1994. He survived while the duo remained, just like Shane, all the way to the U.S. in the 1940s. Bale came to Khao Kha in 1945 and he was in the 1970s. For the whole year in Chiao Pao, we tried to make a head start in the problem of socialization of the world, and then he told us that he was going to say, we need to get used to it, not to the problem of socialization of the world, but to the problem of socialization of the world, and that's what we did, and that's what we did, and that's what we did, and that's what we did, and that's what we did. In his own words, it was the only time in my life when three mathematicians and physicists could live. This frustration taught me a lesson, always that several mathematicians and physicists can survive, so that quantum should be used out to do something that works. Prodigy led a somewhat certain and long-existing vision of milk and bananas and really much research on mathematics. Thank you for listening. There's a lot of time for resilience and trench, you know, mathematics. Oh, the trench area, hydrographics? Well, this connection from the newborn to the newborn. We've been born from the newborn. Not from time to time. Well, if you know that we're doing cuisine, you need an energy note, you'll be sparked.

12:30 Probably more spark than a bath time. Gurdjieff was talking about changing fields. He was very, very patient. He could sense that drive. He had to do something fundamental for the field. After living with the ethical position at the University of Kansas, the campus of Gurdjieff began to invest in anthropological education. He developed a group of experts who were really interested in this kind of work. This is another paper that came out in the same year, in 2013, which is under the direction of science fiction, science fiction. Yes, yes, exactly. This is the beginning of a lot of social interaction and is some concept that Rodin was not one for keeping up. The latest knowledge of classical algebra has turned him into a practical student, but that's a different question. My own knowledge of classical algebra has turned him into a little bit better. But not very much, but I tried to help them with that. But there were so many open questions that we didn't have. Sarah was able to digest ideas that we discussed and in a way that Grodin found special to him. Grodin called Sarah, a lesbian, who wanted to divide the park, and instead of you, Grodin, Grodin called Sarah. And Grodin returned to France and ran a history class at the Indian Academy. He held a position at the same time. And most of the time it's at the end of that particular question. And then you just look to your language, collocation, expression, direction, direction, and so on and so forth.

15:00 What's their point as far as she's concerned? Wouldn't you be afraid when she's here to come to the radio and fix it? We couldn't fix it. This is a big question. In general, it would be wrong. When Rodney got more and more interested in mathematics, he was involved with Atiyah. I'm sure that some persuasions came out of him, but then what came to him was not much higher than I expected. It was his virtue to do my work, and I thought to myself, you know, this is only a matter of time. In July 1967, Rodney was spoken to as an astrologer. There is a wide range of questions that arise, because most of them are fascinating to me, especially the small ones, which are that mathematics has not been able to help us understand what is going on, and the proof is pretty much the same. So he did a lot. He had many other things to do, but he wasn't able to do it right now. This year, I would also like, in 1969, in the back, to apply Gurdjieff to this conference and to write the right for the ground system. I think it's a good plan. So anyway, I'm going to write the right because it's a good plan. In the course of this course, we will study physics by the example of the cosmology model. Basically, the most universal way to define a computer is to have a computer model. So, it's basically, it uses the language of the category to get the answer, to get the answer.

17:30 What do you mean by so-called, all the keys, and they provide the structure of the whole of algebra? No. Basically, all those are the basic parts. You know, that's what you think from your own journey or from other countries. This is a picture of a professor in my class. The basic idea, I think, is that you have to learn how to do it. It's a far-reaching result of a miracle. Generally, you have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. You have to learn how to do it. I didn't put any equations there. The Riemann Rotsch facts, what exactly they are, they relate to all the characteristics of the political environment. The cohomology is a factor, but the topological features are more general than the characteristics of the cohomology. For example, the classical Riemann Rotsch theory is very strange. But what exactly means, basically, the dimension minus the collection is the degree minus the plus the g minus one. So it's basically the linear dimension, the distance between the two dimensions that is needed for the g to be equal. The history of Riemann-Roch theory generalizes this Riemann-Roch theory, in fact the one is from the Manifold. The Riemann-Roch theorem for curves was proven for Riemann surfaces by the Riemann-Roch in 1850 and for algebraic curves in 1923-1939. The Heathbrook Riemann-Roch theorem was proven by Riemann and Westerly-Roch for Heathbrook in 1924.

20:00 And he proved the theorem for complex algorithms for algebraic scores. I appreciate your attention. Thank you. The Hitzburg-Riemann logic applies to any hollow world except the one of the complex manifolds, and we calculated the hollow-molecular galaxies between the left-hand side and the right-hand side, which is a combination of an algorithmic term of dimension and a coherent algorithmic term, so we have the left-hand side of all the galaxies in the right-hand side, which are the main dimensions of the whole universe. In other words, computables, the likes of which I've been talking about in terms of the chess class, which we've been talking about a lot, the chess class is a real nightmare. It's just, it's much easier to fight it. The growing need for this to glean out much theory. Well, we've spent most of the year in a relative situation, you know, with physics and mathematics. It changes the Riemann-Witsch theorem from a statement about a single model to one applying to chain-complexing machines. The theorem gives the precise measure of the last theorem, which is taking the push-forwards of the chain characters, which is the logical combination of the chain-collapses. So what happens is that it interferes with the chain-collapses of the characters, which is very much the story of Morse's theorem, in that it takes the push-forwards. This theorem is a generalization of the theorem and it has further generalizations for most of the cases and also some other generalizations later on in the idea. This was not the last time Brodny developed his work on this subject, and it kept happening over and over again, where he would come upon some problems that people had thought about in some cases for hundreds of years, which have contributed a lot for our people.

22:30 Brodny was not only sold in our time, he was rewarded for that. It was a very great experience. And we're going to summarize the main achievements of the Labiglione, the first and the last because he was the leftist of the total center of physics. Let's have a go at this part of the interaction because it's a beautiful writing. And the main idea of the topology is to replace detail with net calculation, which was part of the theory. He left the business market out to try to, in a way, emphasize what comes with the relationship between the good and the bad, which is about mathematical objects, the math and the physics, the objects themselves. And here's the list of the mathematical contributions of the good and the bad. So the first is the whole of the mathematics of physics. And the second is the theory of mathematics of physics. So, um, we'll be right back here. Key words may include the students of the faculty of the faculty of the faculty of the faculty of the faculty of the faculty of He was the founding member of the Institute of Mathematics. He received his field-maths in 1963. He was the founder of Craftify in 1988. He worked in the North United States of California in 1988.

25:00 Under this condition, it is mentioned that the Greeks participated in the Game of Rights in the West, and also in the United States. Kronovic withdrew from Marxist society in 1975, and was removed from there for a moment. He dropped out of all of the mathematics seminars and did an ordinary job back in North Korea. I would like to thank the Radical Police for calling. And Roy, Roy Ritzke, who is a physicist at the West Side of the Golden Circle, who was in France at the time, after leaving his work in Le Monde, and who is a high student at the Leclerc University at the time, who is a great physicist at the Leclerc University at the time, who is a great physicist at the Leclerc University at the time. I've got some nice other interesting quotes from John Pace in this portion. Many mathematicians like Ravitcher and Gordon sometimes, but Gordon is more than known. Grotinik was just friendly and at the same time Rai and I reached out to each other and we just came to like each other so that was the beginning of the discussion. People very clearly explained to us, very patiently, these are best practices for the rest of the world. Because I think it is a very special power for one child to be a victim of the same idea. Now I'm 11 years old. We have three children. Roderick had a great capacity for enjoyment. He was charming. He loved to laugh. He could read all kinds of things. He was black and white in all shapes and shapes. And he was honest. He always knew where he was going. Roderick had an incredible idea of his trade. He would wear samples made out of tiles. He thought this was a fantasy. There were a few other kind of things to expect. You make what you have, thank you, and this is a project of mine.

27:30 And it is accepted here in Montreal. As long as I can survive there. Montreal? Montreal. I think this is in Montreal. Montreal is okay. And he said compassion was piano. He's a fellow friend of mine, and we got into a way to decide if he should pass, and he said, I have to pass, and I said, yeah, but I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, and he said, no, I'm not sure if he should pass, He explained what he had been working on. After a little bit of talk for a short time, Rodney went to the board and he liked to do a discussion of sheets of finance information. Still the way it is in the lab, it was like a sea, like a continuous stream of mathematics reports. At the end of it, Rodney said, The next year, he will devote himself to L-functioning, or radicals, that in Lewis should help to write the notes. When he was a professor, he knew nothing about algebraic knowledge. During his studies, he did a math, a new math, and he used it. His lectures were so clear, and he made so many efforts to inform what was necessary over the next year. First he was an expert in physics, then very patient, and others experienced his experience. What was completely amazing, he would then somehow get an interest in something, even something new. It seems to me that a kind of amazing insight into what was good for Robert to be a particular person to think about, and he was somehow much less afraid of the child's mind, so that it seems that he felt it was almost a privilege to be at something that was far too good for him to think about.

30:00 In his own words, until the moment of his first away in 1970, the relationship with my students was like my relationship with my own work, the source of satisfaction and joy, one of the time-forces and future-forces based on the patterns and patterns in my life, in a nightclub, still like this. When I was a child, I loved going to school, but became distracted by dreams, writing, and other things, thinking to play the violin a little while in the school camp. The archaeology of prehistoric matters is captivating. I don't recall anyone being bored. There was the magic of mathematics, the magic of words, the science of mathematics, and some others that we used to do research and research and publish. This is actually the work that I'm going to use to describe and derive. This is the paper of Rima Rouchi, the professor of Rima Rouchi at the college. So I'm saying, this is what I'm talking about. We're going to go through some questions, and I hope that any of you can talk about it. I'll keep it in the background. I should put this in the speech box. I've got it in the back. I've got it in the back. I've got it in the back. I've got it in the back. I've got it in the back. I've got it in the back. And then a couple of things to go and give you my thoughts. I think from my point, I mean, my mind, I just want to call it a show now.

32:30 He's an exceptional man, but he asks, he can try to tell you how he can do it. He's serious, he wants to try to tell you how he can do it. And this is the reply, the reply that we asked him, and he said he's alive, living in a cottage. He doesn't seem to be very much aware of mathematics, but we'll never know. Thank you, Michaela. This is extremely interesting. No, it's very interesting, a nice expose. Does anyone have any questions? I just wanted to know why ETA is never translated? It can be very good. It's a very long book, but it's very simple. Even if I said it, it would pick off everything. How do they start the translation on the British Circle website? Yes, yes, that's so true. Some stuff is translated, some stuff is in the original. And the back points are the actual sites. Yes, that's what I was going to say. There are charts in English on the British Circle website. To me it would be a local priority. I agree, but I... Who is that? It's me writing that. Here, a short technical question. A short technical question. I wanted to mention that Dr. Niemann-Koch quoted me for a review and one of the questions which was really from DPS is defining the term classes including algebra, algebra, algebra, algebra, algebra. and special mechanics, and well-known scientists, and well-known scientists, and then modernly published software in this seminar, in the pool, which is made by flowing after by flowing up to the project department, and which is quite similar to the pool given by Washington. The pool by Washington, too, is especially well-planned by the state department, but it does make a difference.

35:00 When I participated in this seminar on mathematics, he said that the question that he put aside is that you have child glasses and already it's a movement. I emphasized that the child glasses could be used with a few answers. And so we took a kind of such thing as an answer which is what we do. Another question is that doing this seminar includes the K-group. It's interesting that the K-group were considered with some disrespect by the participants in the seminar and so on. And people wanted to make no fuss. They say it's too cheap. For some, it's already one. It's not really what the religion is doing for people. It's not true. You know, you came over to a computer science and you met the one reason why we can't use mathematics and sciences for the life of perception. This came with very small amount of time. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. We had to write a book about this matter. Thank you for your attention and see you in the next lecture. And, of course, now everyone will consider what everyone does and should identify with the way, nor, but already at the time of time, but more and more, you know, the basic science of mathematics. And you only get that later on. Well, why doesn't this do anything good? Very true, of course, very true. There is no unpacking of certain skills, certain skills, certain sheets, certain sheets of work. I have not thought about that. Later on, we understood. How it fits in the general framework, and then it was more how it did grow up, and of course, I mean, to now, if I have to choose to grow up, I mean, well, I did grow up in a very limited world of different subjects, and I think I, I feel, you know, a general definition of what it is, is it's constructed in the sense of five elements, but also a job of growth, I think, is what it is, is what it is, is what it is, is what it is.

37:30 I think one of the most interesting things I've heard was that he was just happy because what he had before this, which is now failing him, he struggled with, right? And more and more, he took support from a very rich group, but he was not naturally good at it. Did he run off as good? Did he run off as low of good? He ran off as good. He ran off as good, of course, of course, of course. After that, he became very established. Okay, what is the relationship of both of these UDNAs? There was talk of being much like Noreni Kudarić, for example, at the University of Montenegro. No, but I'm just telling you that geometry is written up by UDNAs. The summary set of all of what we know about geography comes into view today. You don't believe me? Actually, I have a theory. The history of mathematics is one of the more... The history of mathematics is one of the more... Well, I can tell you the history of mathematics. I didn't like the... I find it more difficult. I took a look at my watch, and I said, no, I won't speak any more. Then, I saw people waiting, and I looked at my door, and said, well, there you are. Thirty minutes to the end, and then we go away. It lasted about ten hours. And then the seminar was over, and I woke up at five. I wrote five pages. And then we did our work, and now my job is finished. At that time, he was president of the University of Czechoslovakia. And he showed me his agenda, which was full of errors.

40:00 Commitments and duties, but it was just, I mean, the real thing was to me, and yet it seems that all of what I've done, I did very little, but every day, every month, every week, it was an incredible discipline in the public for what man would do, but obviously, but it was also, actually, many people took me, but it was, yes, yes, yes, considering the difference in their temperaments, it was, yes, yes. Or for anyone of any particular stature, the world before them. Well, I have a strong sense of the history. And he said that the first of all, he devoted a lot of his time to all the people out on this planet. And then he said, you know, hey, let me find out more as I'm finished my work here. All of the rest of the technical materials of Bobaki's study of quantum physics from the beginning of the 35th to approximately the 60th. And then he felt, I don't know, that doesn't do anything. Bobaki, he is for me, but he gave me this way. And then he stopped. So he went off and wrote a list without a break, John? And then he went off and did something. And now that he finishes, then he devotes a very long series of... Right hand, right hand, hip, right hand, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip, hip. And then we have this book called The History of Geomantic Conformity. Yes, it's amazing. And amazing when the students want to learn not the history but the subject matter. Absolutely. Look at what it is, look at what it is. I remember somebody once saying to me that they give some time of their life to have that book just programmed into their brain.

42:30 I can't think of what you call it. Well, I know exactly what you meant, I was just trying to read it myself. About the personal relationship between the 20th and the 20th century, then there was the work of the nice 17th century, which may not have had a lot to do with it. I mean, there was a clash. There was a clash between the 20th and the 20th century, especially because, well... There's a name in politics for them, rather conservative. Yes, rather conservative, but very honest. What you could convince him of something, he didn't accept. But, of course, there was a question. Basically, because he wasn't happy to be politically corrective. And then, there was a significant change in his mind. And also, at the same time, then he got a bit of therapy in the same lab. And then, both of them, after he got the IDH test, applied. I want to be frank. He was not that frank. He was not that frank because he refused to become a constituent because he was afraid he could be laughed at. It's only when he was invited to something like that which was clear that he would never be laughed at, that he accepted to become a constituent. Although he wouldn't be free to do it. However, he was free to invest in the United Nations. That's clear. He was so free that he was not accepted by the United Nations. And so on and so forth. And so, ultimately, because it was not a French institution, I mean, it could get, it could at least be positioned in a very academic place, but not the kind of college. The lowest chance is 72 in French academics. After 72, you actually have the liberty. But then, at that time, there was a problem with applying to two or others, so when they were able to get to a provisional position, it was good. Then came the case in which they were able to apply to a permanent position in college. There is so much antagonizing in a half level. In the final goal, you get one boat out of each.

45:00 And then, say what you can do to provide your students with the right information. It was so upset by the beginning. Why do we do this? I'm not going to tell you why I'm in another position. I'm not going to talk to you about it. I'm not going to tell you. Not each one of us is the same. Everyone of us is the best way to recognize and to say anything. And conduct all my devotions in a very good way. And I'm not going to say where I come from. I'm not going to say anything. I'm not going to say anything. I'm not going to say anything. So, it's interesting that there are still, I think, it's interesting that there are still properties. That's one of the things that I care about in the math. We just have a couple of time for a couple more questions, John. Well, one comment and then one question. I, in the course of reading about Brody, sources of my own limitations came to me. Brody was born March 28, 1928. I was born March 29. Clearly, all the brains were given to him and I at the same time, because I told him everything. It wasn't a stock, was it? The question is, when and why did he shave off his head? Was that an ethical decision? No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no. And many of them, because he was an underground scientist, and when he is known, I mean, if you look at him, he is important, I already know that, he has a few names, and so sometimes people ask me, you know, ask me, what is his name? I say, Shapiro. And the fact is that he is known as Shapiro. Shapiro, and Shapiro, it's interesting, because the name of Shapiro, then he made a very timely joke about it, because, well, you know, probably you can't stop.

47:30 And it's a Belogorsky, Belogorsky is somewhere now. At the time it was in Kiev, now it's Russia, but they don't do it, they don't, you know, well, Belarus, in Kiev, and Russia, so Belogorsky, Belogorsky, it was a Jewish town, yeah, a Jewish town, very, very, very, very, very, very, very, very, very, very, very, very, And his father came from a family in Patim, and he was part of this virgin generation of the Buddha, the Jewish kind, the kind of Zionism that was defined by Jesus Christ. What did his father do? Okay. Thank you, Manuel. We do have to be out of the room. Can we thank all of the speakers today? And we reassembled here for a coffee of eight certain tomorrow morning, and we're free on our own for dinner tonight. Thank you. By the way, Jay's, the restaurant across from the hotel where we're staying, has a very good selection.