who was so well-known in this community that he asked me not to do an introduction. Just to say he's an awful list of memoirs. And when we asked Howard Norman to come and speak, we were lucky to get a twofer. And we got Jane Shore, a famed, well-known, also in this community in beyond, who's going to be reading her poetry. So I'm just going to say one more thing. I cold-called Howard Norman about five years ago to come speak to our book group. And he did. And then Jane spoke to our book group. I mean, we've been friends ever since. So with a lot to do, Howard's going to come and speak here. They may need to pass the mic onto Jane if she can't reject enough to... I'll go up. Everyone can read her poems. And anyone who hasn't stopped by to get her poems, please pick one up or we can pass them around so that you can follow her as she reads them. So, okay, here's one person over here. So with that to do, we're going to bring Howard into the mic. Andre Mulrow said marriage is a conversation that ends too soon. The great Polish poet Cymborski said, really, you must look directly at the truth. Poets are married to language. It occurred to me that in my 40-year marriage with Jane, we've had simply put two kinds of conversations. There is the conversation of just daily life, of what to have for dinner, of too much or too little salt. The conversation about our daughter Emma, which it seems to me should be and is endless. The conversation of how to resolve this or that problem, of time passing, the ongoingness of things, ongoingness, ongoingness, of how to keep one's dignity and one's passionate engagements, of illness and injury and of aging in place, of falling and getting back up, of exuberance of the spirit and of the exhaustion of the spirit, of sadness and joy. The conversation about friends, of friendship, of how to put loneliness to good use. It's a conversation as Lee Chimans put it, of the 10,000 things. But there is a second conversation, often parallel and sometimes interwoven with the first. And that is the conversation about the constant presence of and constant preoccupation and engagement with literature. The conversation about the writing of books as a way to organize our emotions. Because what fate awaits a person who cannot organize their emotions? That was one of the questions that haunted Spinoza so much. Now I would not go so far as to agree with Virginia Woolf that nothing is real unless it is written down. Though quite often I feel that way. Being Jewish in a way I was raised to believe that eternity resides in the past and that memory is sank or sank. And the writing of the past, whether the Old Testament novels, poetry, philosophical treatises, that's where you can find every sort of human experience along with all sorts of instruction about how to live and not live one's life. In literature you can discover every destiny transposed by impeccable artistry. Take Chekhov for instance. You are reading a Chekhov story and you think all that is happening is people are having another dinner.  This afternoon I want to speak about something quite full of joy, often startling recognition and both subtle and seismic emotional response. The experience of reading over decades, final versions of Jane's poems. It is part of the intimacy of marriage to be sure, but never sanctimonious. It is far more what Yates meant when he said, the poet is never the person who sits down to breakfast. There is always a phantasmagoria. That is, if I pass Jane the butter and bread, yes, she is the most grounded person I have ever known, but I still cannot ever determine if she is living more inside a poem than just at breakfast, just existing with a poem separately. And why shouldn't she be? On a more basic level, so often I have read a poem of Jane's and said to myself, oh, so that's what my wife thought about that. And it is very, very interesting to live with someone who finds it quite natural to elevate the most quotidian moment to a level of poetic regard. So I've chosen five of Jane's poems that fit what I've described. They provided a kind of chronology in our marriage, but also, of course, stand alone with their autonomous insistences. The first is the title poem of her book Music Minus One. The term Music Minus One refers to published music where the melody part is absent so that a musician can play their instrument along with the background music of the band. This poem is about Jane's father, George Shore, who really became a father to me. Let's see. Sorry, he lost me. Jane's father, George Shore. In the years before and during World War II, George played clarinet, saxophone, and piccolo, and several of the most famous and most popular of the big band era, including the Clyde McCoy Orchestra, with whom he recorded the famous tune, Sugar Blues, and also saw combat in Europe. It's far too complicated to go into at length today, but when George returned from the war, he eventually owned and co-managed with Jane's mother a very elegant women's clothing store in North Bergen, New Jersey, a corduroy village. You will hear all the exacting and provocative aspects of that transition in Jane's poem, but imagine the severity of contrast between, as a very young man, playing in the big bands to going into a study or bedroom or any separate space to play along with the music minus one recording, to in essence disappear into the music, therefore disappear into the past. To say the very least, the symbolism of this was beautiful because it meant George somehow stayed with the music, but it was also heart-wrenching because quite literally George was the one of the big band era was minus of. He had other responsibilities. Something W. H. Auden wrote applies to this poem, I think, quote, a poem can provide a full emotional biography of a person without necessarily providing the complete chronology of their life. So Jane, so this is music minus one. I'm shorter. Thank you, Howard. It's interesting what you said because it's for me also is I don't often know what I'm thinking of or even what anything means until I write it. And usually I spend a long time on each on each poem, so it's an evolution for me, but well, I'll just read it. And I'm going to let Howard do most of the actual talking, which is like not like real life. So I know I know. So I'm going to read this poem and music minus one and Howard explained that it's a record and when we had phonographs. So Sunday afternoons, my father practiced flute in the family room.  Three o'clock and she was still wearing her nightgown and slippers. Our store downstairs was closed. She was sick of looking at dresses all week. Sunday was her day of rest. I sprawled on the floor with my homework, each in our little orbit. My father gave it all up when he married her, abdicated like the Duke of Windsor. Music was no life for a family man. During the war, he had let the band in the Marine Corps in the South Pacific. In the photo, each man poses with his instrument except my father holding a baton. Clarinets and saxophones leaning against their chests like rifles at port arms. It was my job to start the record over. The sheet music staple to the album cover was propped on the music stand. The needle skated its single blade on smaller and smaller circles on black ice. The needle skipped. He was a little rusty. When he lost his place, it left a hole in the music like silence in a conversation. You had to imagine his life before the war. At 15, on the Lower East Side, he played weddings and bar mitzvahs. At 16, he toured with the big bands. You had to imagine him before he changed his name from Joseph Sharfglass to George Shore. You had to imagine him handsome in his baby blue tuxedo when he played with Clyde McCoy's orchestra. Lighting up hotel ballrooms from New York to California and all the road stops in between. One enchanted evening in Connecticut, he saw my mother. A week later, he shipped off to the war. You had to imagine his life before the war. The one night stands, the boys on the bus, and in its wake, the girls with plucked eyebrows and strapless dresses surrounding him like the mannequins as he stood behind the counter of his store waiting for customers in New Jersey on the Palisades. You had to imagine him occupying the uniform now folded neatly in his foot locker under the telescope popped with rust or blood stains, a souvenir from the war. The record spun, he caught his breath. The music raced on without him. I just heard something I hadn't heard before, which was Jane actually participating in the music minus one. You put that on and it reminded me of something Vladimir Horowitz said. I change page turners every two years because they know too much about me. I always found that quite mysterious. Thank you, Jane. The second poem is titled Reprise. Where did that come from? Reprise. We got married on a sultry June day in the backyard of the painter Michael Mazer and poet Gal Mazer. On that morning Jane was being attended to by women friends. My mother was there too. However, right across the street, I was alone in our apartment. Suddenly the phone rang. It was my mother. As far as marriage goes, she said, I have only one piece of advice. Every morning when you wake up, apologize to Jane. This is true. Mom, you don't have much faith in me, I said. It's just about men, she said. This is the time for a 17-page disquisition on my mother's peculiar sense of irony. But there were good friends and good food, a little dancing, a simple sweet ceremony. Later that night, Jane and I repaired to the Ritz Carlton Hotel in Boston for our wedding night. Now I have to mention that Jane's father, George, had born of experience and certitude, very strong opinions and wonderful stories about the famous classic jazz singers of the 1940s and 1950s, especially icons really, Sinatra, Ella Fitzgerald, Bessie Smith, Tony Bennett, and others. But one figure stood out as a real mensch. It was Mel Tormé, also known as the Velvet Fog. As a singer, George thought Mel Tormé had impeccable timing. But what's more, and more importantly to him, treated everyone with professional respect, especially musicians. So Jane and I married for just a few hours, step into the lobby elevator of the Ritz Carlton, and the only other person in the elevator was Mel Tormé. This happened. He was in town for a performance. Now my wedding suit fit pretty nicely. But Mel Tormé had on a suit that looked as if his personal haberdasher was God. His toupee could have been in its perfect coiffed thickness and undulations, been a wave painted by Hokusai. And his shoes, I can't even tell you. And his cufflinks, I should only someday have such cufflinks. On our assent up to the wedding room, to our wedding room, the elevator stopped and with a good evening, off the elevator glided the Velvet Fog. We were incredulous. Not that I was insecure or anything. But what if Jane followed him down the corridor? All kidding aside, well, I think I'm kidding. Once in our hotel room, I said something that might have made Freud turn over in his grave. But I felt such exhilarated urgency. I said to Jane, I really think we have to call your father and tell him. And Jane understood everything. As Jane reads the poem Reprise, you'll notice it has several spectral elements. This is one of the things that always strikes deep chords with me. Not the least of which is Jane listening on a tape recorder to the voices of her dearly departed mom and dad. The rest of this is badly written. Jane, you should read this poem. Reprise. I can fill the rest in. So I should mention also that my father, besides, he played classical guitar after he retired, you know, retired from music. And the whole time he worked in the store, he also made animated films and he was a huge home movie enthusiast. And then he got into tape recording and, I mean, he was pretty fantastic. Howard's pretty great too. But let me read this. So my father, you know, had a collection of tapes and videos and things like that. So this is called Reprise. Rummaging through the old cassettes, my father taped off the classical radio station. My daughter finds, among Mozart and Bach, cataloged and labeled in his elegant hand, Jane and Howard's wedding, 1984. I didn't know my father taped that too. Disappearing with the boombox, my daughter shuts the master bedroom's door. An hour later, I walk in on her gate crashing our wedding, sprawling on our mattress bed, ear to the speaker. When she was younger, she used to insist that she was there at our wedding and we've told her it's impossible. She wasn't born yet, that she was there in spirit. She's not convinced. Hasn't she always been there, even when she wasn't? She laughs at the wedding march while her dad and I shakily walk down the aisle under the rented yellow and white tent, filling Mike and Gale's walnut-av backyard. Eavesdropping on the prayers, we repeat after the rabbi, phrased by Hebrew phrase. She claps when the rabbi pronounces us husband and wife and we kiss to applause. Her future father stomps on the goblet wrapped in the caterer's cloth napkin and glass shatters safely underfoot. She rewinds the tape back to the beginning to what she calls the really funny part. Back to before our murmuring guests sit down in the rented chairs on that sweltering June Sunday, 96 degrees, freezer wilting, family close to fainting, whipped cream on the cake about to turn. Back to before we stand under the canopy, back to before the ceremony, back to when my father presses the record button, clears his throat and says into the microphone, testing, testing a voice I last heard many years ago, a few days before he died. Shocked, I hear my dead mother say, George, are you sure the tape recorder's working? And my father says, I'm sure. My mother says, George, are you sure the batteries aren't dead? And my father answers patiently at first, then wearily, Essie, I'm sure. She asks him again, and he answers again. And here they are arguing in my bedroom, in the house my mother never stepped foot in. My daughter's eyes shine with laughter, mine with tears. Although I give anything to have them back, even for a moment, I clamp my hands over my ears, just as I used to when I was growing up, and shut them out again. So, in the summer of 2003, in the summer of 2003, a 40-year-old poet named Meridic of Vasirani was house-sitting our house in Washington, D.C., with her two-year-old son, Jahan.  We were at home in East Calus. I apologize for describing this so graphically, but it is what occurred. I wrote at length about the aftermath in a memoir called I Hate to Leave This Beautiful Place. And eventually, we were able to speak in public about this with Susan Stanberg on NPR. Really, we barely got through that. But what I really want to say here most is that before our conversation with Susan Stanberg, Jane somehow organized her emotions. I really don't know how she managed this and wrote a poem called Fugue. Of course, a fugue is a contrapuntal polyphonic composition in which a short phrasing is introduced by one instrument, and then all the other parts are eventually interwoven in to make the whole. And I think you will hear, or I think what can't help be heard in Jane's reading of Fugue, but allow me to say that when I first read it, I was quite taken aback given the almost pulmonary force of emotion that had to be at work, how carefully structured it really had to be. And I remember William Merwin in a letter using the word bulwark, and he meant it, and it was about this poem, and he meant it in the sense of scriptures, quote, how strong our edifices must be, how strong the very bulwarks of memory must be, that ye may preserve and tell difficult stories to the generation that follows. So, Jane, this is Fugue. Of course, when something like that happens, it's so unimaginable. We were really out of our minds. This was an acquaintance, it wasn't a family member, but she did live in our house, and it was unimaginable.  So I had a wonderful physician who called me up and said, do you need any pills? Like, do you need some tranquilizers? And yes, I did. And then she said this fantastic phrase, which this is the phrase that I've used throughout the poem. She said, it wasn't your story, it was theirs. It was like, you know, somehow, she wasn't my psychiatrist, but she kind of was.  So I was able to, not right away, but I did write down the phrase that she had said, and then when I was able to, wrote this poem, along with a couple of others, but that's all that I've written, and it's called Fugue. It was not our story, it was hers. That's how friends told us to think of it. It was not our story, it was hers. In what book does it say that you're supposed to live until you're 80? Our house was hers for the summer, our forks and knives and spoons. She seemed happy, waving goodbye. We said, so long, take care, enjoy. It was not our problem, it was hers. Her clothes hung in our closets, her little boy slept in our daughter's bed and played with our daughter's old toys. It was not our sadness, it was hers. Her sadness had nothing to do with us. She borrowed books from the library, scrubbed the bathtub, baked a pie. We were just going about our business. We were hundreds of miles away. It was not our madness, it was hers. She finished the book, sealed a letter in the envelope telling why.  We stained the new boards to match the old ones, a deep reddish strain. Our daughter first thought was blood until we told her it was not blood. And not our depression, it was hers. It was scraped, sanded, varnished. No one can tell. It could have happened to anyone, but it happened to us. We barely knew her, we weren't there. We didn't want to make their tragedy our tragedy. It was not our story. They had their story. We have ours. Harder poem to clap to. I know, I know. Thank you Jane. Perhaps any other poem might strike a lighter note. This next one is called Symbolism. And I don't think you have to have children to recognize this moment, but those of you that do have children or raise children will in your own way. And in Symbolism as you will hear, that title is heavily freighted with self-recognition as parents. And it also in style and tone has what feels like almost stenographic recall. The only other sense of recognition to mention here is that once you own up to the fact that you are capable of haplessly violating the absolutely powerful sense of dignity your child has, you then experience that child's response. And the sheer savviness and fearlessness in that response provides an almost uncanny sense of solace. She is going to be all right in this life. She's going to find her way. She already is finding it.  So this one is called Symbolism. Well, my daughter, our daughter, having lived with two college professors, writers for ever. You used to hear us talk about our students all the time and, you know, different phrases, metaphors, symbols, etc. So this shocked both of us when this happened. This is lighter, so don't worry. Symbolism. I think it's our come up as parents and writers. Reading in bed, I hear my eight-year-old railing at her dad who's downstairs quietly trying to reason with her as she perches on a step halfway up between our first and second floors, halfway between her father and me, the center hallway and echo chamber for her meltdown that must have started down in the dining room, dessert plate still on the table, sparked with a teasing word, a joke misunderstood, the car of their argument accelerating from one to sixty, her foot on the gas and her father the fuel.   A cloud is a symbol of sadness.   I crack the door open and tiptoe down the stairs to sit on the step beside her, just as her father climbs halfway up, waving a box of Kleenex. We like to tell stories about Emma, and I'll just mention one really quickly. You know, we had different writers and visit. I know. Her first grade teacher. Yes, Jane wrote a poem about Miss Moulton. We had a lot of writers coming through and staying with us, and it was really lovely. But one night at dinner, a particular writer was holding forth way too long and with a kind of academic reductionist way of viewing something, and it was going on and on and on. You know, sort of brilliant disquisition, but, and Emma was quite little. She was at the table and into this about eight or ten minutes, and I was like, check please. And so the next day, there was an equally, equally if not a greater tedious event, which was a faculty meeting. And during the faculty meeting, the department chair was going on and on at length. And one of the other writers who was at the table was sitting across, who I talked with, and in the middle of this person going on and on and on, he caught my eye and I cut his eye and he went, just like that. And both of us burst into this terribly violating laughter, and we just had to leave the room. But I can't ever say check please without thinking of that moment. It was just great. I just learned something again. You know, I never would have thought about comeuppance, but I guess it was, you know, sort of many things at once, that little moment. I just felt very relieved afterwards that she had such toughness. I wanted to end with a Vermont poem because for obvious reasons, it's called Where to Find Us. And ostensibly, it's a poem about giving directions to one's own house to someone unfamiliar with the area. And remember, this is before GPS navigational devices. And so I'm imagining that many of you have had this experience where one of you is giving directions, and then the other person has a different way of giving directions. You're working with phenomenologically two pieces of data, a starting point and a destination point. How can things be so metaphysically misconstrued between those two things? And it happens all the time, I think. Ostensibly, it's a poem about giving directions, as I said. I'm the farthest thing from academic, and this poem does remind us of perhaps the different ways men and women see the world. I quote from a Lewis and Clark expedition report, quote, out here in the wilderness, one can feel quite lost without taking a single step. And, you know, you're sort of in your own house, and you may actually be giving directions to somebody that is going to get them lost, even though the details you think are very specific. You'll also notice, I think, in this poem, what Helen Vendler, critic, referred to. She wrote a long piece about Emily Dickinson's, a particular poem of Emily Dickinson's, which she referred to as a posthumous narration. Once you hear another way you might look at it is that the poet is getting the last word, and I'll come in on this a little bit after Jane reads this poem. Where to find us? After you've crossed the singing bridge and passed Le Geur's farm market, fresh pumpkins, peas, pick your own strawberries, drive two more miles, give or take a tenth. Here's where my husband always said, at Peck Hill Road hang a sharp left. And I'd add my two cents just to irk him, but you're not at Peck Hill Road yet. I always hated when he interrupted me giving directions, and he hated when I'd point out every landmark along the way. My woman's crow's nest view, not my husband's God's eye view. Directions we bickered over for 40 years. Watch for the tilted green wooden pole. You'll miss it. Everybody misses the turn the first time. For a century and a half it was left at the old sugar shack, and people knew exactly where to turn until it collapsed and was dismantled. Its barn board sold as fancy wainscotting for designer kitchens. You may see only an empty space, but to us that shack still disappearing board by board. When was the last time you saw us? You'd have to be blind not to see our three-story barn's rusted roof up ahead and our 1840s farmhouse. Are the clabberts still white? This house just didn't want to be painted. It liked being naked no matter how many coats we'd apply. It blistered and peeled the moment after the paint dried. If you're not stuck behind a swaying hay wagon or snow plow, from on peeler it should take you 20 minutes tops. Stick to my directions. You won't get lost. If you'd listen to my husband you'd be halfway to Montreal. Though it may look like no one's home, the mudroom door is always open. We're in the back pasture waiting buried under the crab apple tree. So it's a complicated overlapping panels of experience talking about Jane's poems. But you go through life with a person, I guess through time and space and dealing with the inevitable unrequited love with the world itself. And perhaps you want marriage to be a conversation that does not end. As Bill Merwin wrote in a letter to me, me and Paula, his wife, talk in many rooms. But it seems to me we also talk between the rooms. That way the very architectural space of our house is expanded to accommodate ever more conversation. Of course he's referring to Emily Dickinson's poem, I died for beauty but was scarce adjusted in the tomb. When one who died for truth was lain in an adjoining room. He questioned softly why I failed. For beauty, I replied, and I for truth. The two are one. We brethren are, he said. And so as kinsmen met a night, we talked between the rooms until the moss had reached our lips and covered up our names. So thank you for coming all this way. I wanted to say to Jane, you know, just after both of our birthdays, thank you for talking with me in rooms and between rooms. So we, I don't know if anyone would have any questions or anything but are you, is that okay? Yeah, yeah, if anybody. But thank you for coming. I know this is a complicated thing because the, it's almost, I remember very much when Jane and I were first going out. She let me stay in her apartment in Cambridge to work when she was teaching and I was snooping and I went into one of the office drawers and I pulled out a file cabinet. We really didn't know each other very well. I was already over the moon but we didn't really know each other. And I found this file, just a folder, regular folder like this. There were many of them. And it was literally, literally hundreds of drafts of a poem. And I thought to myself right then, this is the kind of person that I want to be with but also it was the first moment that answers the question of the talk today, what it's like to be married to a poet. No hurrying, just devotion to language and to a craft but also sort of the habitual nature of trying to get things right. And so that always comes back to me. So it's hard in a short talk to answer the question of what it's like but you could tell for the range of just those poems. Jane has attended to things that happen not just in the world but right in the house and it can be very strange experience but also one I'm very grateful for. So thank you for your beautiful reading, Jane. And I don't know if anyone has any questions. Yes. When we were first together, we read everything that each other wrote. And then, I don't know how many years later, when Howard got a really good editor, I figured and especially I'm not a prose writer and next year I want to give a talk if you guys will let me on what it's like to be married to a prose writer. And also Howard, thank you so much. I'm overwhelmed actually. Thank you. So we used to look at each other's work all the time but then it seemed to me because I didn't know how to write prose and she was a real editor. So sometimes now we read each other's work only when we ask each other or when something is finished. Howard, for me anyway, I don't know how I help you at all but with Howard it's like what's the through line of the poem? Or is it getting too wrought up and too much ornate symbolism and it's too long here. So that's what it's like. But yeah, we did do it all the time and we morphed into a different kind of relationship with it. But of course I couldn't really be the kind of poet in terms of being taken seriously by my mate because I wasn't married to Howard. And I was thinking yesterday I think, what if I married Billy Steinberg, the doctor? How would my life be different? And I realized being married to Howard is also like being married to literature and to like, it is! Because we have totally different tastes in things. I don't know how to use a stethoscope. He wouldn't have understood me anyway. But I mean it's seriously, my life has changed because of who I'm married to and how seriously I'm taken by him and vice versa I hope. I mean I can't yet. Because there's 10,000 moments within that question. But I would say I'm looking at Nadal and I'm thinking, you know, I think really the truth is that without being pollyannish about this, if you love poetry and I don't know, I really can't speak much about poetry. But I can say that you're around the utmost, I think Joseph Brotsky put it best, the utmost use of the language. And that is, unless you're another poet, I think you should just sort of stay away from that and make a few little comments.  It's just not the way I think and it's not what I can recognize. But you do feel it when you're feeling it. I think that's really the answer for me is that there's a point in which very clearly something is going on with the language that I just, you know, you need to turn that over to other people. And that happens all the time. So I'm sure Victor knows exactly what I'm talking about because this is just, language for a prose writer is very different, I feel. It's another, for another topic, but yeah. So many of our friends have heard all this so much, know this so much about us already. Yeah, okay. First, I just love the admiration that you two have for one another. Oh. Having never been married. Well, Jane had a model, a good model, and I had a terrible model. So I think I adopted, I was happy to adopt Jane's parents in that regard. You know, my father left when I was very little boy and, you know, my mother did the best she could. But you know, so I think you, yeah. But thank you, I do. She's a photographer, but she also is a good writer. She's big appetites for life. She's finding her way. She writes a lot. And one thing she writes is handwritten letters. She, she has an old-fashioned epistolary life, which is really great. Yeah. And she's a very good critic, I have to say. She really speaks directly to you about stuff that you write, yeah. And friends. How was she in a restaurant? Check, please. Check, please. Yeah, it was so funny. And it didn't stop the guy, by the way. He just kept going. But, um, yeah. So thank you so much. Some of you drove a long way. Really appreciate it. Thank you. I just wanted to say that Howard said, I don't want to give a speech where everyone asks questions like, how often do you write? Do you have a schedule? Do you need a chair? Do you have a table? But you should be asking him those questions now because he said he would take questions. I'm kind of getting inspired about doing that. Please do it now. But, yeah, Howard and I joined with you.  I mean, I feel like I have to go back and get annotations on the people you've quoted about the words. Oh, I hope that did sound like name-dropping. But it's really interesting, if I see it by depth. It really was interesting, however, how people respond to things that happen to you. I feel in a way like you should publish it. You should put it together in an essay with what you wrote and then have James Poles and then do it. I mean, it's just really too good to just be at the senior center. Bye, Erica. Bye, Tom. Thank you for driving all this way. On Marsh Wednesday. But in any event, one other thing. I've read almost all of Howard's books, but the reason I wasn't here quite on time was I was looking for Jane's book. And by the way, Jane has books over here if anyone wants to buy one. And I couldn't find mine, but I found a book of Howard's that I hadn't read. It was a book of essays, so I was going to chat with him after this conversation to ask him.  I've owned it for like 20 years. I didn't even know I had it. But in any event, I'm going on and on. So next Wednesday is our last meeting. What else am I supposed to tell them? The last three films. Oh, and then we have the three films that are over at Savoy Theatre. And do they also start at 130? Yes. And they also started at 130. So if you've bought the whole subscription series, then you get to go. Hi, Bob. Bob just had his 85th birthday. Oh, Roosevelt. So in any event, yes, plan to come next week. I can't remember what the subject matter is, but Allison will remind me. President, this is the one. Oh, the election. Oh, yes. We have a professor from Middlebury College come in to talk to us about the election. So you want to finish on a strong point that's completely different than poetry. It's the world today. So in any event, come next week for 130. And then three movies. Matt and Mike is the first one. And I can't remember the other two. But thank you so much for coming today. Thank you.


Okay, we're back here at IBM Edge in Las Vegas. This is ground zero for the transformation of infrastructure. Storage is a platform. Storage is the center of the value purposes and the transformation of the marketplace, where data is the new competitive advantage. This is SiliconANGLE and Wikibon's coverage of theCUBE, our flagship program. We'll go out to the events. Thanks for coming from the North. I'm John Furrier, the founder of SiliconANGLE. I'm Joe, I'm the co-host. Hi, everybody. I'm Dave Vellante of wikibon.org. Sebastian Krauss is here. He's the vice president of global sales for IBM Storage Group. Sebastian, welcome back. What has transpired since April 11th in the client base in terms of the uptake and the enthusiasm around flash? Well, Dave, as you said, on April 11th, we made the big flesh forward initiative, which we have announced in New York after we have done all the bluewashing on the products of Texas Memory System, a company we acquired in August. Since then, we have seen a tremendous dynamic in the marketplace on this initiative. We've been working on it for a long time. There is a tremendous dynamic in the marketplace on this initiative. I believe there is not a single customer in an industry that currently is not thinking about how to replace mechanical drives with flash drives. For many reasons. A, companies are running out of space. They want to be more energy efficient. Certainly also the performance on the application side is something which is extremely important to them. And since we've talked last time here in theCUBE, I think it has become an even more compelling reason to think about flash initiatives and leveraging flash as a technology. Sebastian, what's your strategy for storage or data? How do you respond? Well, I think there are, first of all, we are taking it from an angle of client needs and clients' requirements. I think which is the wise thing to do when you are forming your strategy. So first thing, customers have different needs and even the same customer can have different needs. So if you think about what Ambusch mentioned this morning about business critical needs and the economic impact of not complying to that, that you would have your system down, you would lose millions or hundreds of millions of dollars in your business, that is something that customers cannot afford. And for every industry, for every customer, it means something different. But it's on us to ensure that we provide these high mission critical application systems supporting or being supported by storage systems, making sure that they can stay online. That's the piece where Ambusch talked about it needs to be open. It needs to be industry specific and basically partners should be able to basically plug on their application and their programmable solutions on top of it. And then there is really the third piece which is the data intensity, which is more like a solution orientation which could be data protection and retention which could be something in the high-end scale or file systems for certain industry. Think about, for example, in the university area in the medical area, that's the third leg of the stool. And then last but certainly not least, that's flesh. And flesh is basically almost everywhere. And then there is really the third piece which is the data intensity, which is more like a solution orientation which could be data protection and retention which could be something in the high-end scale or file systems for certain industry. Think about, for example, in the university area in the medical area, that's the third leg of the stool. And then last but certainly not least, that's flesh. And flesh is basically almost everywhere right now. Flesh place is a market segment by itself when it comes to application performance, database acceleration, but it also plays in the other three areas. So can you talk about the open pieces? People are very interested by that open angle. I think it's, I mean, if you think about how our industry went along, it's all about creating a platform enabling the industry participants, whether these are ISVs, whether these are partners, whether these are clients by itself to basically plug on that platform to basically satisfy their needs and to ensure that they can harmonize within their infrastructure what they would like to do. Do you guys agree with that? I mean, obviously, this still may be certainly faster, more or less expensive, but flesh is not going to overtake some say that quickly. Do you have a perspective on that? John, I would take a look at that from two angles. First of all, I don't think that anytime soon the data explosion is going to stop with all the different medias that we are having at this point in time, with the social media, with the different devices that are coming in both on the consumer side but more importantly now also on the business side. Where customers really have to cope with this majority of the data, with the vast explosion that is happening, that is clearly something which they have to take care of. So data volumes will increase significantly between 50, maybe even up to 70% a year. But the way to handle this, I think, has become definitely different. First of all, we talked about tiering for a long period of time. So tiering is a technology that will enable customers to use flesh almost immediately as a plug-in, but then also to reduce the total cost of ownership of the entire infrastructure. So where flesh basically improves the performance of the application of the entire infrastructure and gives you that edge that you need, basically a fast IOPS, and give it an edge towards your customer experience and your client experience on the web. It also provides you with a tier that you can seamlessly integrate into your tiered infrastructure. So you're seeing the accelerated phase and we're talking about the kind of dynamic you're seeing because those kinds of customers are bringing improved concepts and enrolling them out fast. Are they highly accelerated now? And let's add some color to these proof of concepts as they dig in and invest. They are. Proof of concepts more than I think any time that I have seen it in the past are currently providing the proof points to the customer, the value to the customer to go down the path of the strategy we just discussed and to implement it fast. So basically, get it fixed for now but also have the strategic angle. So customers are requiring those proof of concepts in most of those cases that I'm aware of customers stay with that proof of concept gear that they have and they basically implement that solution immediately. Okay, Sebastian Kruss here at IBM obviously talking to customers, there's a huge demand for the quick fix deal of the tsunami of data and new technology as well as build the road map. Congratulations, thanks for your time. This is the cue of our flagship program about the events. Extract the ceiling from the noise. I'm John Furrier with Dave Vellante. We'll be right back with our next guest after this short break.


New intro because we weren't recording the first one and I wonder why it was gold. It was probably might be the best intro We've ever had the greatest of all time Would have instantly gone viral Quadrupled our subscriber count It definitely was another sex joke for sure Yep, no, it probably was Hey, welcome back to first people directs is the Corbyn. I'm Rick you can also Instagram Twitter More juice gone to the next page from falsehood account described like button what you got in the cup there vodka No with ice. Is it just ice water? Yeah. Oh good for you I usually have ice water over here with coffee.  Yeah Today a is chopped yesterday. It's the jailer release date announcement JLo awesome JLo the JLo release announcement Not to be confused with the Shakira release announcement in fact in case she's arrested for tax evasion see the movie Elizabeth Konomi for an Oscar a few years ago. Yeah, is that the about Queen Elizabeth? Yeah. Yes Same director as Bandit Queen Wait what yeah, no, yeah The the movie Elizabeth was directed by the same person who directed Bandit Queen Yeah, well just because the name of the film is in the credits doesn't mean that that was their directing credit It's the one with well look at that With oh, that's that's not the one that oh a yet another few years ago on its cape lunch out Oh, yeah, that's why I was thinking yeah, that is the one you're thinking of you're absolutely right I had no freaking clue. How'd you find out about that people told me? Oh, yeah today the jailer released Date announcements, and you know how they do those because we start Russian come superstar Directed by Nelson. He's like honey comes out in August. Yeah, now. There's three big films at minimum coming out in August Well, I think it was the time. I'm not seeing any of them. The 25th is jaw on Hashtag be lazy This is I think early August and then animal Ranbeer's film comes out in August Yeah, but are we ever interested in anything Ranbeer does Ranbeer? Oh beer oh Not beer got it beer Not all Indians are the same brick. Okay, they're not racist Anyway, so yeah, so this is a little kind of teaser kind of your mom's a teaser release date announcement Here we go superstar Superstar Rajnikanth best wigs in the business Zaddy now is Mohanlal. I believe his intro music is always Look at that wig That's glorious one of my favorite. I love that's great. Love the music by the way Yeah, he And I guess it goes without saying that he should have the best like intro music Just being of who he is, you know, well if it goes without saying why are you saying it? I'm saying it because it goes without saying. Yeah. Oh, hold on. I love doing it. It's a spam call Good this will be great content and you hang up speaking of that I watched the invasion of the body snatchers the original with with Donald Sutherland That's not the original by the way. Well, it's the one that for me is the original You watch the original original. No, the black and white original original. Oh, but that is not the original It is just by the fact that it's the remake of the original. No, it really is. He can't call it the original. It's the original But yeah, I watch it for the first time you said it nice But the andrani song glorious bastards for the first time yesterday We had a back-to-back Quentin Knight one of my favorite and every time feet showed up I told her I said feet fetish. There it is. Yeah, that's a real thing. So yeah, you like body snatchers Yeah, yeah, anyways, but this is one of my favorite remind you anything There you go. Go watch it. It's a good one One of my favorite things obviously about side of his intro music is his moniker that comes up in the beginning of his films It's been the same since I think I think the 90s You mean the actual when lighting in the beginning of the film. Yeah, we haven't seen much of them I don't know it comes up as the the lights the lights still like you they haven't changed it Nice the classic it says superstar Rajnikan kind of like the way Elvis's name was always done up, but they haven't changed it They get why would you the exact as brand as the I think the early 90s And so I like that a lot, but yeah, like I love like because you know what the style of films are gonna be right? They're gonna be The star vehicle and he's gonna be this hero.  I do want to see some of those especially movies more recent ones of that style we've seen some like fight scenes of Certain ones, but I want to get familiar with the vibe the greed that's going on and in these style of films You know and I if I ever need to wear a wig for anything I want whoever makes his wigs because he's got the best in the business and yeah, that is that is Zaddy And was this mohan low? It sure looks like him Sure looks like him Yep. Yep Wow Rajnikan to mohan loud Jackie Shroft Wow Yogi babu Of course if this is supporting character Yogi. Yeah, he's playing it. Yep. I'm really looking forward to the music coming from this Oh, yes if it's good one it has to be epic because it's honey, but it's a superstar Rajnikan Yeah, and so like I'm sure he's been a fan his whole life. I'm sure. Oh, yeah being a person You know just like I think when he did For Vikram, he's a Kamal San fan Yeah, but the intro music and the music behind a Rajnikan film being you know this That's kind of one of the things is the epic background of course behind. Yes, whatever he's doing getting to create a theme for him Come on gotta be cool. It's gonna be great gang tries to rescue their leader from prison where others Where others struck at a pro what where others where others stuck at a problem the jailer of the prison shows off to stop them all and It's not a very good log line, but that's okay. Yeah, it's a weird little little weird kind of If a little bit of a strange log line, but that's okay. So it comes out August 10th Superstar, that's a cast That is a cast how often does a mohan love do Tamil films in Jackie? I mean, I know how often does Jackie Shroff do it to Tamil films as well Now this is Tamil, right? I'm just assuming just because it's superstar Rajnikanth. It's not Hindi. I Assume it's Tamil, right? I think that's a safe assumption I mean, I know he's done Hindi in the past, but if it's a him star, I'd assume it's absolutely right Yeah, it's got you know people from multiple industries, but I think it's Film itself is saying it's a pan India film No, I'm saying it's an Indian film. No, it's a pan Indian. Yeah, I don't every film now is a pan Indian film No, it's we don't we don't need another moniker. It's an Indian film The only moniker you need is superstar rush. That's what I'm talking about Whoa, we do we need to return him because he's got to be working in India There's no reason for him to be on our wall We know No, I need a refresh my wall. We got the wall. Yeah We need a definitely need a superstar Russian if we do need a Rajnikanth up here. Where's Mahanlal? I don't think Mahanlal is out there. Nope Yeah, I need a I need to do a refresher on the wall. Where's Zaddy? What? Oh All three of these people are need to be up on the wall now.  Oh, we do have a tiny tiny little Rajnikanth on the Yeah, he needs to be bigger and we need to be highlighting one of his wigs Because I love his wigs. Yeah, you do love his wigs. I love There I love everything about the wigs. I love the fact that when he's not filming anything He's just showing his normal hair. I'm just has he done a film with his natural all natural look I don't know. It's a good question. I mean, I know it goes against the brand. It does But everybody also knows he's bald exactly and he would I don't think he'd have any problem if he had to play a character That was that was scripted that way at all. That's one of the things I love about him is he's just not at all concerned about image other than other than what they do when they release a film and they Promote the film he himself doesn't seem like a guy who gives a rats patootie about 70, right? Yeah, but his wigs and the film and the makeup and everything He he's evergreen man. He always looks like he's 50 years old Yeah, it's kind of it's kind of actually insane that he's 70 and he's still playing these characters that like absolutely Insane let us know if you're excited for this one obviously and if you're not what's wrong with you I'm very much looking forward to the music. Yeah from this. I can't wait for that Let us know if you're excited about it down below Josh


So, I am Varadaraj Gaonkar, I have secured second rank in the Indian Forest Service examination 2021. I am a mechanical engineering graduate from NITK Sudathakar. For this examination, I chose geology and forestry as my optional subjects. Both subjects were new to me and I had no academic background in these two subjects. So for the preparation of these two subjects, I studied from the basic books and once I was thorough with my basics, I practiced previous year question papers and did mock tests. I practiced mock tests. For forestry, which was one of my optional subjects, I practiced mock tests from the Shankar A.S. Academy. Their timely feedback helped me improve my answers. For the interview stage, I attended various initiatives of Shankar A.S. Academy. I attended their online video lectures and online mock interviews. So all their feedbacks helped me improve my articulation and oral presentation in the final interview at the UPSC. So I would like to thank the entire team of Shankar A.S. and everyone who has helped me in my preparation for this examination. Thank you so much.


The challenge of the Yukon. Honking! The Wonder Dog King, swiftest and strongest of Eskimo lead dogs, blazes the trail through storm and snow for Sergeant Preston as he meets the challenge of the Yukon. Sergeant Preston was typical of the small band of Northwest modern police who preserved law and order in the new Northwest country where the greed for wealth and power led to frequent violence and bloodshed. But in spite of the odds against them, Sergeant Preston and his Wonder Dog King met that challenge and justice ruled triumphant. It was midwinter and in the library of the large house in New York City, two men were talking. Wallace Peters stood with his back to the fireplace. His fists clenched deep in the pockets of his coat. In front of him, Alfred Frank sat quietly, his fleshy face appearing both satisfied and sympathetic. It was a shock that killed her. Well, Wally, you shouldn't take this too hard.  You made sure Mary heard about it, too. I'm sorry. It was a slip of the tongue. You know how much I thought of her. Why would a spare day be possible, Wally? I could have kept my tongue out after I said it while he believed me. Too bad you didn't. Now, wait a minute, old man. You're not yourself. I know all this has been blew to you, but... Yes, you're right. It has been a blow to me. One after the other. First, the business crashing. Crashing because I took your advice about investments. But everyone can make mistakes. I lost money myself. It was bad judgment and... Well, you didn't have to accept my advice. But I did. I accepted it because I trusted you. You've always known I had no business head. You knew that in college. I'm ruined. Ruined, you hear? Lost everything that could be written on the black side of the books. You'll get back on your feet, borrow some cash. No, no. What I lost was my own. I'm down, but I'm not mortgaged. But that's business, man. Be sensible. You take a loss once, you make it up the next time. It's all in the game. Not in my game, it isn't. I'm through. I've got sense enough to see it. Sense enough to see a lot of other things I never thought of before. Well... Yes, oh. I'm going to give this to you straight, Al. Because I'm not the kind that can say one thing and think another.  What? You killed her just as surely as if you'd pushed her down those steps. You're out of your mind. Out of my mind.  Everything Mary lived for. Everything that had any meaning for her. My friend. My friend who wasn't content to ruin me. Oh, he had to make sure I'd lose everything. Everything. I won't listen to you while in. You'd better get some rest. You'll feel better about it. You'll listen to me all right? Because once I've got this off my mind, so far as I'm concerned, you'll never have to listen to me again. You'll be sorry for this. I can see it all now. When we were both courting her, you were as much in love with her as I was. Weren't you? Yes. I guess I was. Sure you were. But she didn't marry you. She married me. I wasn't good enough for her. I knew it. She was so far above me, I didn't think I stood a chance. You were in her class, Al. You were with all the right clubs. You were the pedigree that goes back to the Mayflower. All the money of Wall Street behind you. What are you driving at? Just this. I tried to make her happy. I tried to do everything she wanted me to. I was doing all right. Except for you. Except that you never forgave her for marrying me instead of you. You're crazy. Oh, no, I'm not crazy. You decided you'd take away everything that was important to marry. Money. All the things she was used to having. Sure, you advised me. Sure, you lost money, too. You could afford to lose a couple of hundred thousand, but I couldn't. You weren't content to ruin me. Oh, you had to tell her. You had to watch the expressions on her face. You had to watch her turn, pay or lose her footing and reach out for something to save her. Only the fall, headlong... You're going too far, Wally. I never want to see you again. Get out of this house. Go on, get out. I'll remember this. I hope you'll never forget it. I won't. Believe me, I'll see to it that you'll never do either. Arranging for his sister to take care of the baby, Wallace Peters left New York as the house in the city was posted for sale. He had an immeasurable sense of loss that was with him no matter where he went or what he did. His skin burned and shriveled with the heat and malaria of the tropics. In waterfront saloons in Singapore or the Argentine, he had the appearance of countless other drifters, purposeless and weary. And then, one day shortly after the news of the discovery of gold on what was North America's last frontier, Alfred Frock, grown fat and heavy jowled, sat talking in his office to the young man who was his secretary. You can start getting the luggage together immediately. Everything will lead. Listen, that flyer you took in South America was all right. Down there we just had to put up with heat and bugs. I don't know anything about this place except that it's cold and a death trap for men who aren't used to the climate. It might be a death trap for other men, but it'll never be one for me. Well, you can send somebody else. Buddy, you are going with me. I may need you, you understand. You and I appreciate each other's myth. Yeah, but I... No buts about it either. I have a reason for going to the Yukon. A good one. In a way, it's a personal score, I want to settle. What do you mean? You've heard me speak about Wally Peters. Peters? Well, sure. Haven't I been checking up on every move he's made these last 15 years? I got a very interesting letter this morning. Peters is in the Yukon. I never did know why you wanted to keep track of him. Wally's found himself as rich a piece of property as any man has ever uncovered. Rich and mighty than you can imagine. Lucky, huh? That all depends on what you call luck. It'll be bad luck for him. Good for us. As long as he went the way of a bum, I let him alone. But now... Now it's stay. I want that gold mine. I'm going to get it, personally. A month later... ...at the small cabin that withstood the icy blasts of wind whipping outside it... ...Wally Peters, swamp in a chair looking bitterly at the two men standing in front of him. His face was bruised and swollen. His hands were tied, the rope cutting his wrists. That's enough, Marty. Have you had enough, my friend? I've met a lot of men who are rotten.  You deserve pretty strong words, Wally. And foolish ones for a man in your position. Too bad you don't look at this the way I do.  You'll never get it. All right, Marty. You said this country was a dead trap, Marty. So it will be for our friend here. Pick him up and put one to sleep. We'll throw him off along the trail, and when he's found... ...it'll look like an accident. Several hours had passed when Sergeant Preston halted his dogs beside the figure on the trail. The Monty revived Wally Peters and listened to the story the man told. Quietly, the great dog King stood close to his master. That's the story, Sergeant. They're at the cabin now. You've got to get back to town.  Easy now. You need rest. How long did he keep you a prisoner? Three days. Sergeant, there's no time to waste. I'm going to put you on the sled. Here, let me help you. You go back to town. I have my snowshoes. I can make them in a couple of hours. But you... I'll go to the cabin and see this man, Alfred Frank. Your dogs. I won't be able to manage them. I'll lead them. In that way, I'll be sure you'll make it to town safely. Be careful. Don't worry. Sergeant Preston's approach to the cabin had been watched. As he stood talking to Alfred Frank, the Monty was unaware of the man standing in the shadows behind him. I've visited the Monty policeman who had him a little surprised. Yes, I imagine you are. You're Alfred Frank. That's right, Sergeant. Mr. Frank, I'll come right to the point. I just found Wally Peters on the trail about a mile from the cabin. Wally Peters? Well, I didn't... He's, uh... He all right. He was able to talk if that's what you're wondering. Oh. There you see. Needless to say, I'll have to put you under arrest for attempted murder. I hadn't found him when I did. He would have died of exposure. There must be some mistake. No, no mistake. This is his cabin. You're occupying it. Everything is pretty much as he said it was. Now, where's the other man he spoke of? What did you put out? What do we do, Al? You rid of him? I don't know. Wait till I have a chance to talk to him. When the Monty regained consciousness, he'd been disarmed. Marty stood beside him holding a gun menacingly while Al Frank slowly paced the floor. You see, Sergeant, that's how it is. I'll meet any price you ask to, uh, forget this unforeseeable chance. You've bought your way out of situations before I take it. Well, more of what you say. You can't bribe me, Frank. Yeah. Maybe I'll inform. Hmm? What's that, Al? The model of the North West might please maintain right. You'll never make any money on the force, Sergeant. A man with your ability and intelligence should travel with any amount of wealth at his fingertips. You're hardly in a position to have much choice, you know? I told you before you can't bribe me, and you can't scare me either. It's my duty to take you in. Hmm, a foolish attitude to take. Well, I did my best anyway. That water's boiling, Marty. I'll take the gun. You get some tea ready. The only pan I see here's this wide one. All right, use that. Two men aren't used to the rugged life, hmm? Need any help? He can manage. The mountain sat silently, his eyes and the man awkwardly making tea. At the same time, he was conscious of every move Al Frank made. For the man holding the gun stood beside him, a deep frown on his face. Preston wondered if Wally Peters had made it back to town. He knew his dogs would carry him safely, but would Peters be able to tell what had happened when he got there? Would Peters be able to send help? Or would he assume Preston was all right? Carefully, Marty Renwick carried the pan of tea to the wooden table. In the corner of his eye, the policeman watched Al Frank, and then casually rose from his chair. I'd like a drink of that tea if you don't mind. Sure, I'll have some myself. As Sergeant Preston turned to reach for a cup, apparently by accident his arm bumped the hand holding the gun, and as Al Frank swayed for a moment, his hand almost touching the pan of tea, he dropped the revolver. The steaming tea splashed.  The tea burned my hand. Marty, the gun, get the gun. Yeah, sure. It splashed and burned your hand, so you want me to reach in and pull it out? Then get the gun for my macadam. Don't step back.  You're in a good spot to stop what they call a hammy. Yeah, sure you can. King, King, old boy. Need any help, Sergeant? Well, it looks like you got those two pretty much where you were. Sam, how'd you get here? All right, and I've got that gun from your macadam, Mr. Frank. Put the handcuffs on him, Sam. Yeah. You law and order commissioner certainly managed to show up at the right time. We managed to show up? Well, I can't, Sergeant.  I harnessed up the dogs and set out here with him leading away. You all right, Sergeant? Wally, I thought I told you to go into three forks and stay there. I couldn't stay there knowing you were here with that rat. I wouldn't trust him any further than I could throw him. Well, it looks like the score's even now, Al. All right, you win. I win. You couldn't let me alone, could you? You heard I struck it rich, and that my son and I would have more money than I ever lost. So you couldn't rest. You started this, and the sergeant here finished it. It seems that you are finished, too. Entierledois. Right has been maintained. Yes, King. The case is closed. These copyrighted dramas originate in the studios of WXYZ Detroit, and all characters, names, places, and incidents used are fictitious. They're sent to you each week at the same time. Jack McCarthy speaking.


Thank you, and let me first thank the organizers for the opportunity to speak here today and the whole Month that I'm spending here, which is very nice so I'm going to talk about the stability of the quite flow and first of all I should introduce the Navier-Stokes equation So the equation is as follows Where nu is a positive coefficient, which is called the viscosity And if nu equals zero the equation is called Euler equation And there is a divergence free condition the divergence of u is Zero okay, so u is valued in r3 and It's a function of t x y z x is in the torus y is in the real space and z is also on the torus So I agree there is a few fluids that live in such a geometry nevertheless it has the advantage of Getting rid of boundaries so what I want to discuss today is the stability of shear flows and And So it's already a complicated question and if you add boundaries it adds a number of difficulties Which I don't want to consider today So this particular geometry allows one to have shear flows without boundaries So what is a shear flow? A shear flow is a flow of the type say f of y zero zero And the particular flow that I want to look at is the Couette flow where f is a Just a linear function So you have y Zero zero, this is the Couette flow and this is a solution of Navier-Stokes for any new positive so the stability of shear flows in general is a difficult question and What we discussed today is the stability of this particular shear flow, which is simpler for reasons that we will see So maybe I should draw a picture So this is y this is x and this is z and So the velocity of the fluid at the point on the y-axis Goes like that. So you see there is a linear shear So I hope you get a sense for the geometry that we are looking at So the question that we want to understand is the stability of this flow which is a Stationary solution of Navier-Stokes and maybe even the asymptotic stability. It does not have finite energy Okay, so what can we say about stability so The first point is that you need to take a positive viscosity coefficient, otherwise you pretty much have No chance. Okay, so you have to be positive So next thing you do is try and look at the linearized problem so informally speaking you just drop the Convection term and what you keep essentially is the heat equation So it's a bit more complicated because you need to linearize around the the quiet flow But essentially you get a linear heat equation With some more complicated terms which are lower order But what you see immediately is that the linearized problem is stable And it's even very stable in that you get a spectral gap So once you have such a strong spectral information, it's not hard to reduce Nonlinear stability. Can I ask a question? Yes Spectrum depends on the space And we have an infinite energy flow. So now we need a that's to a finite energy Protubation and just L2. Is that what you want? Yeah, so let me remain a little bit informal at this point, but say yeah in L2 for instance Okay However, there is something which in hydrodynamic stability is known as the sommerfeld paradox so It's it's true for the quiet flow and for many other Shear flows. So what happens is that the flow is Linearly stable as we saw but experimentally unstable Okay, so it's called sommerfeld paradox So linear stability But experimental Instability yes, yes Okay, so of course, it's it's not really a paradox really what it underlines is that The the important notion is not so much nonlinear stability as the size of the basin of attraction of the quiet flow Okay, so if you want the resolution of the paradox is just saying that the important Idea say is to sort of quantify Nonlinear stability in finding the size of the basin of attraction and This was already underlined by Kelvin And finally there is a last idea which maybe we're not so used to in Partial differential equations, which is that the the size of the basin of attraction Really depends strongly on the topology that you choose. Okay, and this idea goes back to Reynolds Though he phrased it in more physical terms so If you put all of this together, you see that the right question is the following so maybe let me call Let me change notations a little bit. Let me now call you not the perturbation of the quiet floor initial perturbation of the quiet floor and you To be the perturbation of the quiet floor at later times as it is given by just solving the logistics equation For later times. So I hope I convinced you that the right question is the following If you give me say a banner space X with the norm associated to it Then what you want to find is what is the smallest? real number gamma Such that if the initial perturbation is Less than new to the gamma so remember new is The size of the viscosity and the more viscosity you add the more stable the flow So it it makes sense that the dependencies is like that so then you might ask Why should the dependence be? power like Well, it's it's simply what the experience teaches us so what you want is that if the Look numeric Theory it all gives this sort of dependence small new yes This implies first that you of T In X remains small and second that you goes to zero as T Goes to infinity. Okay. So in other words what we're asking is to really quantify the size of the basin of attraction of quets What we're asking for is asymptotic stability if you're sufficient sufficiently close to To quit initially Okay So there has been a lot of work on on this question So I'm just gonna mention a few a few names Yes, that's right, that's true. Yeah I mean of course you could ask You know, you could ask her for that you remain close to quit for a large time, but I don't think this has been too much looked at Right, so there has been a lot of heuristic or numerical works So, okay, let me just mention a few names. There is baguette Driscoll Traffitin There is baguette and traffitin There is valet there's Chapman okay, and many other and Well, they actually don't really agree they find that gamma lies between one and Seven quarters depending who you believe Okay, so that's one set of work where The authors did not really care about the importance of the topology, right? So they just considered perturbations without really mentioning what sort of perturbations And then there is another work by ready Schmidt Baguette Henningson Where the authors find gamma equals three half for what they call rough perturbations Okay, meaning you perturb quit by something which is like white noise Whereas here they were more perturbing by Gaussian say Okay, and there is also vigorous results So it started with Romanov who looked at the case of a channel rather than the whole space And then there is Christ Loonblad Henningson, okay, and once again, there is many references. I don't cite everybody But the the world record was gamma less or equal than four by rigorous means in dimension three so everything is in dimension three and in Subol-F topology Okay, so that that was the state of the art Now let me describe our results So this is So maybe let me first But the three decays and then I'm gonna say word about what happens in 2d. So in the 3d case There is two topologies that you can consider either Jeuvret topology or Subol-F Topology so in Jeuvret topology we found gamma equals one and In Subol-F topology we found gamma less than or equal to three half. So this is a joint work with Jacob Bedrosian Who's in Maryland and Who's at NYU So what's very nice is that it settles the debates, right? We have theorems, which actually say that in Jeuvret topology gamma is one and in Subol-F Gamma is less than or equal to three halfs. We are furthermore able to say that this result is optimal and That's why I Stated it as gamma equals one this one. We suspect it is optimal because it agrees very much with What these guys found for rough data and Subol-F topology is certainly rougher than Jeuvret So we suspect it is optimal, but we could not really prove it Yeah, do you gain anything from an authenticity? Yes. Oh, you mean if you go further to analytic No, no, you would Keep the same the same exponent so Maybe it doesn't depend on Jeuvret's exponent. Yes. So here what I mean by Jeuvret is Say e to the d to the one half plus F in M2 And what I mean by Subol-F is D to the 5 sorry to be you not 5 half plus you not In L2, okay So that's that's what we did with Jacob and Nader But there is also results on the 2d case. So which really give a full picture so in Jeuvret Topology so This is where everything started you find gamma equals zero and this is due to Bedrosian and my smoothie So that's for the case new equals zero and then it was extended by Bedrosian my smoothie and The call to the case of positive viscosity and Recently the case of Subol-F in 2d has been treated Here you find gamma less than or equal to a half and this is due to Bedrosian recall and Wang Okay, so it's it's really nice because for this particular flow it's possible to get a pretty complete picture of what happens in terms of stability and There is this this nice feature that you have a Dependence on the I mean this interesting feature that it's dependent on the topology, which maybe It's not so common in in PD What about us exponents or exponents he doesn't doesn't matter if you go Yeah, yeah, so anything above five halves we believe should give three halves and then if you go to very low regularity Then maybe something else happens if you go to very low, but oh and say my mistake I think I said five halves, but it should be So this is dimension three, right? This is dimension three and in 2d The Gevry exponent remains the same and the Subol-F exponent is three halves. I think if Vlad is here Okay, so that's that's The results so now I'm going to explain what the picture is in in 3d So Right, so the first thing to do is to consider the perturbed Equation around quit Okay, so you want to avoid something like you know Pretty much since you have viscosity It's possible that maybe you start very close to quit does a lot of completely insane things and comes back to quit, right? So this we don't count as a stability, right? We count it as stability if you remain always very close to to quit You see what I mean Straight to me these are these ideas of Trapehton of a non-self-adjoint Flows where they're large transients. Oh, yeah, so I'm going to explain that It's indeed this the fact that the linearized problem is not self-adjoint That gives transient growth and which is ultimately I think responsible for this difference depending on the topology you consider So I'm going to try and explain that Okay, so the perturbed equation So as I was saying we consider a solution of Navier-Stokes of The form quit that is y zero zero Plus you so now you is the perturbation of Navier-Stokes Okay, so if you do a small computation You realize that you solve this equation Okay, and so this this this part is is not a self-adjoint And of course the divergence of you is still zero, okay, so It turns out that it's a good idea to try and remove this Convection term and this can be done easily by changing the Independent variables though it comes to the expense of modifying the differential operators. So let's do that So if you to remove y dx u What you do is you set capital X equals X minus T y capital Y equals Y capital Z equals Z and You rewrite the equation in this new variables It has the effect of turning gradient into what we call grad L which is dy minus T dx dx dz and Laplacian into Laplacian L which is grad L square Okay, so in this new coordinates, let me call also capital U of T Equals little u of T x y z so in this new coordinates the equation reads Okay, so pretty much we just remove the y dx u And now the differential operators have this more complicated structure Okay, so if you look at the linearized problem Maybe it's best to view it in this new coordinates. Well, it's pretty clear And the pressure term so you can express the pressure term as to grad L Laplacian L inverse dx u okay, so that's the linearized problem and That's the full nonlinear equation So what I'm going to try and explain in the time that remains is a few Striking properties of this linearized problem, which has a lot of very You know striking features And then I'm going to mention a few Important features of the of the nonlinear Okay, so the first linear heuristic is the so-called lift-up effect. So that's the name that This thing is called in the physics literature So this is the the main destabilizing effect in dimension three and it is absent in dimension two So this explains why the exponents in dimension three are less good than in dimension two at least partially Okay, so how does it work? Well A very important idea is that the frequencies which are zero in Capital X behave or little X behave very differently from the frequencies which are not zero in little X and This is because of this shear here So the if you look at the linearized problem the shear will only affect the nonzero frequencies in X So the picture is very different depending on whether you look at zero frequencies or nonzero frequencies in X So here we look at zero frequencies in X and we call F sub not The integral of F DX Which is the same as the integral of capital F D capital X. It doesn't matter just the Zero frequencies in the X variable. So it turns out the linearized problem is extremely simple for zero frequencies because then the DX U2 cancels so the right-hand side cancels and the Delta L Becomes a regular Delta. So the only thing that remains is Dtu Minus new Laplacian U. So I put a zero to indicate that it's the zero frequency in X plus U2 zero zero equals zero So that's very simple and you can actually explicitly solve and you find that you not is So the first coordinate is E new T Laplacian U1 so here I put in for Initial to distinguish from the zero, which is the zero frequency minus T U2 initial E new T Laplacian U2 initial Initial zero right everything is at zero frequency E new T Laplacian U3 initial at time zero So obviously the second and third coordinates are well behaved but this one you see it grows linearly until the Heat coronal kicks in but this happens only at a time T like one over new. Okay, so this gives linear growth until T like one over new And you see in dimension two this does not occur because U2 Zero has to be zero due to the divergence free condition So that's the main source of instability and it's really a 3d effect Okay, so the second piece of Linear heuristics that I want to present is the so-called enhanced dissipation Okay, so let me try and explain the idea in physical terms. So if you look at this picture You see if you have a good physical intuition that if you have something that depends on x Due to the transport in this direction. So this direction is like a tourist direction, right? If you have a data that actually does depend on x This leads to the creation of very high frequencies very fast and these get then eaten up by the viscosity or by the heat equation. Okay, so Maybe it's easier to see it through the equations. So it's actually very easy if we just look at The heat equation in the new coordinates, okay, so that's the heat equation In the new coordinates and let's just forget about the rest of the of the linearist problem. Let's just keep this piece and Remember that delta L. It's dx squared plus dy minus tdx squared plus dz squared So if t becomes very big, of course what matters is this guy here tdx. So essentially what remains is dtf minus new t squared dx squared f Okay, something like that. That's the leading part if t goes to infinity equals zero so you see that the viscosity becomes immense as t goes to infinity and if you switch to a Fourier variable This becomes dtf hat Minus new t squared k squared f hat equals zero and it's easy to solve F hat of tk is something like e minus new t cubed k squared initial So here you have a t cubed instead of a t Okay, so it makes a huge difference and it means viscosity acts extremely fast once you have the shear and so what it means is that the dissipative time scale is Now one over new to the one-third right instead of one over new for regular Heat equations. Okay, so I should say this sort of idea has been exploited first by Bedrosian, Masmoudi and Nikol. Okay, and then there is the last linear effect, which is the famous Invisit damping, which is the Euler version of London damping So linear heuristic three Invisit damping, which is the once again the Euler version of London damping and of course this phenomenon received a lot of attention after the work of Mouot and Villani on London damping for Vlaise of Poisson So it's actually very easy to see in this context There is just a little trick and the little trick is to switch to the new variable q2 Which is Laplacian l u2. Okay? So it looks a bit magic, but it's the standard change of variable that Physicists do for instance and what's very nice is that in this new variable The the equation satisfied by q2 is dt q2 Minus new Laplacian l q2 equals 0 so that's at the Linearized level Sorry Right, so the other variables don't behave that simply so that's why I just single out this one So for simplicity if we just look at the case and u equals 0 So which is really the inviscid case of the Euler case What happens is that q2 is? constant right Because you just get dt q2 and that's at the linearized level. Yeah so it's very simple to Recover u2 u2 is simply 1 over Laplacian l q2 So now if I take the Fourier transform and switch from x yz My Fourier To k eta l You see what comes out is u2 hat Equals 1 over k squared Now given the definition of Laplacian l eta minus kt squared plus L squared times u2 Initial and This formula is extremely instructive Because from this formula you can read two things first What happens as t goes to infinity so as t goes to infinity this guy becomes huge so that u2 hat Goes to zero and then u2 goes to zero as t goes to infinity So this is why it's called inviscid damping So for u equals zero you have a very nice Hamiltonian system no dissipative effect whatsoever Never the less You get this decay of u2 as t goes to infinity and I should say it's not an effect Which is like scattering for say wave equations in the whole space because You don't have space to scatter in the x direction Okay So that's sort of the good side of the picture, but on the other hand if This factor here vanishes T equals eta over k so it means this factor here vanishes and then you get a growth Compared to what happens at time zero. Okay, so there is this two sided effect This one is called inviscid damping and this is rather helping us To prove stability and this one is called the or mechanism And of course it's rather annoying because it means that You have growth At various moments in in time And of course the fact that you have this growth at various moments in time is ultimately Linked to the non-self-adjoint character Of the Linearized operator right since it's non-self-adjoint. It's well known that you should expect growth for the evolution problem Okay, so that's the You can call it intermittency, right because If you look at that it's sort of very nice all the time, but there is One particular moment where it grows and then it decays again So one might call that intermittency Okay So now let me discuss the non-linear problem non-linear heuristics one It's a so-called streak solutions So I should call the I should write again the non-linear the non-linear problem This time in the original variables and an important observation is that there is A large set of explicit solutions to this problem which consists of U2 Depending only on y and z And u3 depending only on y and z as well Just solving the 2d navier-stokes equation While u1 is driven So if you plug that in you see that it works and that u1 is simply driven by u2 and u3 In the following way. Oh, I forgot someone here. There is minus u2 So here you get u1 So u2 the u2 dy plus u3 dz U1 equals minus u2 Okay, so u1 is just Slave to the others and these two solve the 2d navier-stokes. So that's an exact set of solutions And you see So these are called streak solutions because supposedly they look like streaks in experiments And you see they play the role of an attractor Because what the enhanced dissipation does is that very fast it's killing any dependence on x Right, so here to get this very Fast decay you need that kb non-zero. I should have said that So if k is non-zero you get very fast damping what remains does not depend on x And these are streaks. Okay, so these are attractors At least on the time scale one over new to the one-third. Okay, and the Last thing that I would like to emphasize Is the various null forms which are found in this equation So Okay, so there is it's There is a lot, but let me just mention two If you look at the most threatening interactions Well, first the most threatening interaction is due to the growth of u1 up there You see that u1 is growing linearly. So really the worst that could happen is u1 And it's at zero frequency Talking to u1 at zero frequency maybe with derivatives So this would be very bad because both grow linearly. So it would Completely kill the structure. Unfortunately, this does not happen. There is no such interaction another problematic term is the the grad l So if you remember grad u dot grad l It's u1 dx plus u2 Sorry, I should put capital u dy minus t dx Plus u3 dz And so of course this t here is very threatening But luckily it comes paired with u2 and we saw that u2 decays Thanks to inviscid damping. So there is sort of a cancellation Between this t factor here and the u2 which decays Uh, so The proof consists in putting all of this together. So essentially the picture that emerges is that First on a timescale one of a new to the one-third you get this enhanced dissipation which kills all non-zero x modes Okay, then The solution looks like a streak For t larger than one of a new to the one-third like a streak plus something very small And then what happens is the lift-up effect kicks in And you get growth until you reach time one over new And then you pray that you can keep everybody under control And you can do it thanks to these cancellations Which are present in the equation And that's all I wanted to say. Thank you for your attention We've answered So these mechanisms we described that here and where does this And it must there must be a big head Oh, yeah, it's it's a big worry. Yeah, so you need to so that's for this reason that Bejoison and mass moody introduced their toy model in 2d And in 2d that's really the main problem Uh, because they're able to do the case new equals zero in 3d It's not I mean, it's one of the problems, but it's not the only one anymore Yes, so you didn't quite explain the connection between the proof and the fact that you have this difference between between topologies All right. Yeah, so Okay, so what this All mechanism is doing Is that so if say, uh, if you think of eta being big so you look at high frequencies No, sorry, we think of uh, eta being small So what you want to avoid is a high too low cascade, right So that's what our mechanism could do and The best way to avoid a high too low cascade is just to start with very few high frequencies And and that's why It helps so that's that's how it's related That mechanism that at the end of the day It's at the end of the day Jeffrey classes to do that I mean in 2d. Yes in 2d. It's very clear in 3d things are messier and it's Not the only effect that one has to take into account In particular the lift up effect is is is more threatening And and it's yeah, maybe it's it's more the lift up effect in 3d, which is annoying So is there a simple heuristic explanation of the number three over two? No No In in jeuvrette apology the one of a new scale it's easy to explain That's lift up effect, right? Yes, exactly But hadn't you three halves, what is it? So three halves it's less clear. There is no simple Like I cannot point to a single mechanism that that does it All right, no two mechanisms together But why do you think it's it's Optimal Right, we think it's optimal because we tried hard to do better and the numerics give the same I agree, it's uh, you know