Dr. Larry Graham, thank you for joining us here at the Hey, Think Tech Hawaii's wonderful program. Don't just age engage and that's my personal program for you all in which I explore the issues of aging, mostly from the internal point of view. What are you doing that is the best practice for you in aging in this community and in this culture. Today we are going to explore one of those people we're going to ask about that from one person that they're very good friend of mine named Philip McManus available join us in just a bit. But what I'm doing is saying that it's the most important for us to look at models that we can claim opportunity that present us with opportunities to grow and to function in ways we want to. We are excellent as Western civilization at studying the problem. We study problems until we don't know what we're looking at sometimes but what we what I like to do is to study solutions, study examples of people who are in fact aging in such a way that their life is what they would call full and wonderful. And that we would look at and say, that is pretty extraordinary. Philip McManus. Welcome to my program. Thank you so much my friend for joining me here today and and sharing some of your story with us. And I've always said that the most important thing we can do is tell our story, and you do such a beautiful job Philip would you just do an introduction for our viewers. Well, thank you for having me as they say in Nepal. Namaste. I've known Larry since we were in high school, and we ended up in Hawaii together back and forth. I've been crawling quite a bit. I've been in music since college which let me travel all over the place. And then I got involved in video over the last 10 years or so and started chronicling what I was doing. And that's basically the place I came from music is a great way to meet people because it goes right to the heart, and they forget that you're watching them too. So what kind of music do you like the most what do you, what is the music that is your music. My father was a pipe organ builder and concert organist is some repeat so I was in piano and cello and voice up through college and picked up guitar 19. And that became my money making instrument, but also my most passionate instrument, although I still play the cello. I've been playing the cello because I haven't played her about 35 years. So when you're putting your finger down on the, on the fingerboard it's wherever your finger is with the note is so you're constantly making and creating a new note every time you put your finger down as opposed to a piano key so I would call it an approximation, a very humbling experience, because you're never tuned but it sure feels good and it's not a question of arrival is a question of being somewhere around kind of how it works. So I would say I love cello I'm playing classical music but my own music and and guitar I can't tell you what it is but I have these beautiful guitars I've acquired over the years that seduce me constantly to play them. Well it sounds like a good description for what I would say is the aging process. You can't really don't know what you're going to get to it's maybe not going to be the exact note, but you're in the process of getting to it. Well there is, yeah there is no exact note I guess it's all an approximation and a quest, or not even a quest, just a discovery. There is no rival there's a wonderful quote that goes when you seek outcomes you get consequences. It doesn't work out the way you always want. And as to the viewers I want to say that Philip has made some tremendous. I think accomplishments in his elderhood. He not only enjoys the music he produces, but he also has some achievements that he's made. And I'd like to get to those and a little bit will share a little bit of video of what he's done, where he's been over the past few years. And the encouragement that he brings I think to anyone who knows him. He has been an inspiration for me. I am here in Hawaii because he invited me to come. And it was his adventurous spirit that helped to turn me into an adventure myself. And I hope that you've confined in this few minutes some of that same electricity about his, his life and his adventuresome spirit. But tell me Philip tell the viewers if you will what do you think is the most important thing to hold on to for what has been the strongest motivator or or enabling factor for you in your elder years now to have such a fulfillment such a strong and adventures in life. Well I never considered myself to be an aid, not having had children. You don't get to measure yourself in the age and the aging of your own children. First, so it would be elder good to me has been more a matter of change, things changing in me and recognizing it, but I didn't associate it with anything in particular. So it's a matter of how do I, I'll never play volleyball again really I'll never run again, but I did a lot of that for years but realizing that my passions in many ways not just in volleyball or running or something physical but other things that I can do. Just shift that passion off to something else it's not a question of, of my favorite uncle was a Baptist minister.   Listen to the stories I've never heard and then in a pause, Theron Uncle Theron said in a small voice, I think my life is just a collection of my loves. I am what I love and I was 19 and you're always kind of looking for yourself at that age if you're lucky. And that moment I found myself I am what I love. The essence was not what I love that I love the act of loving keeps you supple keeps you wiggling. My father died at 91 and he says age affects only those who are not children.   Yeah, which is worth discussing at some point. Yeah. Well thank you for that those are inspiring words, and I would like to highlight for the audience that as a personal coach for life and faith and personal coach for your childhood, I want to coach people into extraordinary elder hoods.  You have your elder hood. And when we look at elder hood as a, or aging as a stage of life. It simply has its own unique characteristics, which each of us has to explore and and discover ourselves we once again ask the question, who am I, who am I at this stage of life, and the answers that we come up with our own world guide us in the decisions that we make. So, having a certain excitement about that having a discovery and having a confidence in what you discover, I think is very important. And Philip embodies that in so many ways that confidence that whatever comes comes and he'll make it through. And physical issues, physical occurrences problems, don't need to enumerate them but what has helped you be so resilient, dealing with these physical problems. I think, first of all, accepting the fact that I'm, they say that life is essentially transmitted disease with the fatal prognosis. Since I have accepted the fact that I'm riding on a on a mortal body that's slowly falling apart and accept that to be part of the game. Then it's no longer an issue. It's also a question of not having things have to work out in a certain way for me to be happy. I was hiking around in the T roll with my friend Stephanie when I started feeling really, really bad and I said man these pills I'm taking from my blood pressure really are making it difficult to move around turned out I was having a heart attack. But in the course of it. I first of all I didn't get to eat my, my goulash and wonderful salad that was served to me really irritated me but I made it to the hospital and that the most interesting people. And I got to watch and do the, the stint at my arm and, but so it really had nothing to do with anything because that was another amazing experience and happily I got in travelers insurance two days previously so who helped for some of it anyway. So I hear two things right now fill up and one is not to expect outcomes and to conform to what you want, but to be resilient with whatever comes, and then the other to be confident in what what what you can manage that you whatever comes you're going to you're going to deal with it in some ways that am I hearing you correctly. To you to a point, but the point being there was nothing to deal with this. I'm not the. I'm not what happens and what I'm watching what happens but I am not what happens I'm the watcher. This is oh look what looks going into operation right now. It's me. I mean it's, it's, it's carrying me around like I'm watching HBO or Netflix, you know, it's my life I'm watching, but it didn't. Yeah, yeah, that makes any sense at all maybe I was in they call too long and part of the game you said is, is that this this body does change. Does have its own decline. We would call it decline or it's, I'd like to think of it as check transformations and and transitions. Okay, okay, go ahead. We were speaking earlier about that about when you're young. You start gaining new talents and experiences and strength that you didn't even miss because you never knew it could have them but then as you grow older. You start losing these things but then again you have other talents and skills that are infinitely more developed than when you were a child. So to let the things go that aren't relevant anymore and really focus on what I'm into and able to be. Yes, yes. And what he has been into my friends is pretty phenomenal itself. One of the things that I can report to you that he did was to organize a canal trip to well a couple of canal trips in in France. Tell us about the canal trip the one that we're going to view we're going to view some of this video of this. This was on the canal to me be which is a canal that was built in the late 1700s early 1800s to connect the Atlantic with Mediterranean, avoiding having to go around around Spain, the Iberian Peninsula to get from one place to another. I had owned the river boat in Hamburg 100 foot long 1922 river boat that I just stumbled across or splashed across back in 2000 and had it for several years and learned how to really manage a flat bottom boat so I hired a ship and had two ships actually and had my friend Stephanie captain one and I kept on the other and for two weeks we navigated this canal, which has bicycle paths on the sides and it only went like 130 miles and two weeks so, but it's just such a rich environment which maybe the video might show you and I had a drone that I've really been enjoying that I did some video in any case that was the trip I had eight women with me between 21 and 80, and I would not recommend that. But the loan mail but we had a good time. We're going to look at the video in just a minute a couple of minute video but you have another trip coming up that you're going to go into. Yeah, I think I do repeat for those of us who've gotten our second shots in September. Hopefully France will be back open if not we will just delay it get our money back and go later. But do it again because there are things I didn't get to see now that I know more about it. I don't know what you're going to have in my, my stuff below but have lots of videos from this on my YouTube channel on your YouTube channel. Okay, well and well let's go to the, to the, to the video. We're going to be able to do that kind of a trip in our elderhood, but one of the things that I'm most amazed at Phillip is that you took something that's been a part of you for many years and, and just three years ago, three years ago I think it was just created this event and this opportunity for people. It was that I mentioned that he's adventuresome. I can tell you that I had just had Nick surgery the week before from having been hit by a car in Chinatown and not a little, but that was, I was fine. And also the two of the women who are in that are gone now they died. And they were, you know, 79 and 81. So, so they were living their elderhood they did it. Oh man I can barely walk. But they were fine. I mean they were, they drank more than I did. But take advantage of it because one never knows what their time schedules are.  Now along the canal you disembarked into various villages and while you were in the villages did you learn anything or did you learn I like Beaujolais more than I learned that there's a natural support to life and you don't have to know why the water supports you just have to know that it does, you know, wonderful, wonderful. Well and everybody learned as they went they were still growing they were still coming to new understandings and actually they a lot of issues came up that you know when you're living your what you love you also uncover things that you haven't dealt with. But because we were in a group. It was talked about you know you can only be polite for three days I think and we're together for 14. Lots of things changing so there were some people acting out but they took care of them, you know, and everybody was delighted by the end of the trip so that's wonderful. But that itself is such a learning experience in my opinion, being able to grow from self revelation and self understanding. And sometimes getting outside of our comfort zones and being dislocated into another place can be the opportunity to have that growth experience. I think they were fortunate, fortunate to have you along and sensitive to that dynamic. So we go from there to another amazing adventure.  Tell us something about this would you. Well, I have, when I first went to Europe I, I have a private club that I've had, making it practical to have fun. And I first went to Europe meeting a woman online 24 years ago and we had a food stand in the town square of Humber. We're selling lobster and champagne everybody else is selling bratwurst and beer and pretzels. And it was kind of like a fishing expedition to meet interesting people and I met a guy who was doing expeditions with mayor submarines these mini submarines that go down six kilometers in under the sea. And this was right after the Soviet Union had come apart, pretty much, and these guys are having a difficult time so he hired the ships to do interesting tours and he was doing the Bismarck. I mean doing the Titanic with the submarines charging 35,000 and I said, Oh, hey, Mike, can I sell some of these trips on the internet the new internet he said sure I sold a bunch, not a nice commission. And he said where should we go next till I've been in the military European military history for years I said how about the Bismarck I know it's been just discovered. And he said sure why don't you come. Really. So we he organized everything. And I came along. And we had been the Bismarck of it discovered by Robert Ballard but never explored. He had a camera on the string to see if we went down with these two mirror submarine with the big lights and it was three hours down three hours up eight hours on the bottom on a two meter space with three of us inside this titanium ball flying around, we got stuck underneath propellers and the back. The other sub had to come tell us how to back out properly. It was very wonderfully exciting. Philip, we, we, there's going to be a question after this video, and then I want to turn to thank you for that. I'm thankful for the viewer for asking a question. We'll get to it after this video but in this video, Philip also has is reciting a poem that he wrote that he having been moved by this experience right Philip. Right. Let's go directly to the video then now Melissa thanks. Three miles to the ocean floor aliens from a different orb to a world beyond mortal cycles untouched by waves winds or storms nights or days seasons nations lives or generations to a quiet place whose darkness has remained untempered by sun moon or stars. The darkness that has prevailed long before earth the life had remembered itself. We have found a lost prop from a long close play and with it the final scene from that lost director's cut. I am a member of the last undeserving audience of a few souls with thousands once had attended some 60 years ago. The giant sunken ship again seen by mortals who briefly give her back her name and her story is no longer just a strangely shaped stone among many or a garden for delicate anemones. But for a few hours becomes the silent echo of past dreams and glory terror fire destruction and despair all projected on to her through 17 centimeter thick portals. Our alien lights briefly materialize a tapestry of rusticles and flowering creatures rivaling the beauty of Buddha's sin and dollars which fade again into timeless darkness as we turn away. All my life I've known the story of the Bismarck in her final days imagining her fine and proud as if she had never died. But that image has been ruined as I see her broken in her open coffin just as after seeing my mother cold and dead it took me years to remember her any other way. For me the memory of the Bismarck shall be the same so much for glory and for fame a hero's death both slayer and the slain. Now the spirit lies not on the ship but with the men who sailed her once former foes and worked together to write this final chapter. It is my honor to admit them we have made these memories treasure. The men who sailed them oh my gosh that really that got me in my throat. It gets me all the time. And that boot that single boot was very moving to me to see that. That's a profound experience and one that you hope to replicate or repeat. We can if we had the people that wanted to do it I know the folks to do it. Made friends with a lot of Russians for some reason I've been hanging around Russians for years. I hired a three hundred and fifteen foot tall ship for six weeks in the eastern Caribbean 20 years ago all sorts of stuff. So they're Russian run. Yeah, we can wait. Would we address direct people to oceanographic.com actually my email would be good the best way to go. Okay, check it out with his email. We do have one question from a viewer which I'd love to have you respond to please. And that is how to pick a destination for an adventurous trip like the one you describe. How did you hear of such a destination and then what did you consider as you were deciding that it would be your next destination, but were your considerations for that choice. French trip. I knew the canal I had gone the year before in Burgundy. The canal guy I knew the canal the media existed, but didn't think in terms of hiring a boat and putting my friends on board with me. So it's sort of what's your heart's desire what's on the periphery. What's what's saying oh you're saying oh I can't possibly do that but it's very attractive like the beautiful woman across the dance floor. You can go over and walk to her and say would you like to dance that we're still say no, but you can always investigate. That's important. What makes you crazy what sounds good and see if it's possible. Sometimes it isn't but it's amazing, much more as possible. That is spectacular and I am so grateful that you've been on on my show here and able to really share part of yourself and part of your, along with your interests. Thank you very much for those questions viewer and we will I hope we answered for you if not, please connect with Phillips email at. I'd be delighted. Yeah, I'd be delighted. I stepped on you sorry. And so every two weeks, we have don't just age, engage to encourage you to have the most extraordinary elder hood you possibly can make it me. Thank you to think tech Hawaii for their wonderful support for their wonderful encouragement. Thank you to Philip McManus for joining with me, and we look forward to seeing you back here in two weeks. Blessings.


the sacrifice of worship. Offering to move the heart of God. Sacrifice, sacrifice of worship. Offering to move the heart of God.


And everywhere I go, as I travel the rural parts of our state, I see the evidence of Auburn's research and the great input they have into our state and our economy. Ultimately, we're feeding our people, which is the most important thing. Auburn University is a jewel in the agriculture world. The research that goes on at Auburn is critical to developing new techniques and products that allow us to grow better, healthier livestock, whether it's poultry or whatever, making more economically efficient so farmers can make more money and be more successful. So it's a jewel and I'm glad to be here, glad to be on the Agriculture Committee and in a position to help the mission here at Auburn.


Hi, my name is Glen Jennings. I am the State Driving Coordinator for CFA. Over the years, the driving of CFA vehicles has proven to be a dangerous task for CFA members. Too many CFA members and members of the public have either been killed or injured as a result of a collision with a CFA vehicle. We can only do our job to protect the community if we arrive in a timely manner and in a condition fit and ready to do our role as firefighters. I'd like to cover a few key points in this presentation. The first one is the new 40k rule. On the 1st of July this year, the government and Vic roads introduced a change to the road safety road rules. A new requirement is now for motorists to slow down to 40km an hour when passing a stationary or a slow moving police or emergency vehicle. This has been done to protect the emergency service workers who are doing their job on the side of the road. Therefore, drivers of CFA vehicles do need to slow down to 40km when passing a stationary or slow moving emergency vehicle that is displaying its red or blue lights. It's important that we do this for two reasons. One is to ensure the safety of our fellow emergency service workers who are on the side of the road. The second reason is to provide a good example or set a good example for members of the public, those motoring drivers beside us who can see that we are complying and slowing down to protect the scenes. The second point I'd like to touch on is the wearing of seat belts. CFA has been promoting for many years the benefits of wearing seat belts. We know that seat belts save lives. Therefore, we all have a duty of care to our fellow motorists and to members of our crews to make sure that we buckle up every time we get in the vehicle or on the back of a tanker and we're not directly involved in firefighting operations. So, whether we are the driver, the crew leader or a crew member, it's important we accept the safety of everybody in the vehicle and remind each other to buckle up. The last point I wish to touch on is station doors. Unfortunately, the number of incidents involving station doors is increasing all the time. This has a costly effect on the organisation and also means that we have to replace damaged vehicles with spares which sometimes can be very difficult to find. So therefore, before we pull out of the station, let's just make sure that the doors are all the way up. If there are safety mechanisms, they are locked into place. If the station is fitted with warning lights and tones that we obey those. If the lights are red, no call is that urgent that we need to go through the red light. You need to stop, wait for the light to go green, the tones to cease and it is clear for everybody to exit the station. Thank you for your time to just take a few of these points on board and ensure that we achieve our aim and that is the end of the day all of us return home safely to our families. Thank you and safe driving.


Hi, I'm Zor. Welcome to InDesire Education. We continue talking about a curl of a vector field. Previous lecture was about two-dimensional curl of the vector field, of two-dimensional vector field. And that's kind of easy, because if you can remember, we were using, let's say, this whiteboard as a two-dimensional surface and we can install a tiny paddle wheel somewhere and rotation of this paddle wheel was basically a characteristic of the vector field, which is defined at every point of this surface. So if it turns this way, it's curl well, negative. If it turns that way, it's curl positive. And basically the intensity of the spinning is a quantitative characteristic of curl at any point wherever we put this wheel. And it was easy because it's flat surface. So there is only one orientation of the this paddle wheel, which we can arrange. Just put it in such a way that the axis of rotation is perpendicular to the plane. In three-dimensional space, it's kind of more difficult because no matter how we put this, it's still kind of different orientation of this wheel and probably we have to put it in some way that rotation is most intensive and that would be the curl. Sounds reasonable, actually. So anyway, that's what will be a subject of today's lecture. This lecture is part of the course called Physics 14's, presented on Unisor.com. I suggest you to watch this lecture from this website because it's a course on the website. Physics 14's is a course. So there is a menu, sub-menu, etc. So everything is logically related. There are notes for each lecture. So not only the video presentation, but also you can just read it as a textbook parallel to the video. There are problems, there are exams, which you can take in any number of times you want and the site is totally free, no advertisement, no strings attached. Okay, so let's go back to three-dimensional curl. So first of all, we have to have a three-dimensional vector field. So this is a vector, which is defined at any point as code in its x, y, z in space. Now every vector in three-dimensional space can be represented by its three components, which I call vx, vy, and vz. At the same time, if you have three components, we can have three unit vectors on each axis. Usually the terminology is i for x vector, j along the y-axis, and k along the z-axis. So we basically represent a vector, this vector, with these three components as sum of unit vectors along the axis, multiplied by corresponding components. This is a plain vector algebra, and we are not talking about the details of this. It's supposed to be known. If it's not, there is a parallel course, prerequisite actually course, called mass proteins on this website, and there are vectors explained there. Okay, also the same mass proteins has calculus part where you can read about partial derivatives, which will be used here. Okay, so that's done. Now, now we have to place our paddle wheel at point x, y, z, and wait. After some time, it will probably orient itself properly, probably when its axis is parallel to the most important kind of direction of the vector field, and it will turn or not turn, and that would characterize the curl. So we're waiting until it basically start spinning or not spinning in a stable kind of way. And that would be our curl of the vector field, but now we have to quantitatively evaluate it. Now, first of all, if this wheel has basically established its position and speed of rotation, how can we characterize the position of this wheel? Well, if you remember some time ago when we were talking about rotation, we characterized speed of rotation with a vector, which is directed along the axis of rotation. So let's say if this is speed of rotation, we associated it with a vector, magnitude of which is basically equal to a speed of rotation and the direction of this vector, one or another side, was such that from the top of this vector, we see the rotation counterclockwise. That's basically a vector. So we can characterize the spin, the rotation of this probe wheel by a vector which is along, which is directed along the axis of finally established the axis of rotation. And the length, the magnitude of this vector would be equal to the speed of rotation. And the gain direction would be in such a way that from the top of the vector you see the rotation counterclockwise. That's basically our agreement. It's convenient because one vector would be basically completely describing the rotation of this pedal wheel at any point in space. Well, let's call this vector K. And by the way, it can also be represented as any vector as a sum of its component. So it's Kx. I assume x, y, z in the parenthesis. So my question right now is, basically my task is to evaluate this vector if I am given this vector. Kind of complex. But we can always try to simplify any problem by dividing it into smaller, simpler problem which we have already solved before. That's exactly how we're going to do. Think about it this way. If my vector of wheel rotation, basically it's a curl, it's a curl vector, if my curl vector has three dimensions and this vector has three dimensions, what I'm kind of assuming would be a natural thing to represent the x-component of the curl, x-component of the rotation. x-component of rotation. This one. As caused by projection of the v vector which is somewhere, let's say, projection onto the y-z plane. So again, rotation around the x-axis is rotation within y-z plane. So I assume that it's a lip of face. I mean, yes, obviously you have to really kind of understand it and agree because it's my assumption which happened to be actually corresponding to the real thing is, obviously experiments can be arranged, etc. that the x-component of the curl of rotation around the x-axis. It's basically a rotation of this vector projected on the y-z plane. So basically I can assume that x is a constant. It doesn't really matter what it is and consider only a function of two arguments, kind of, which basically in a correct representation would be v y of x, y, z times j plus v z of x, y, z times k. So j is along the y, component of vector v along the y-axis. v z is a component along the z-axis and sum of this and this is basically a projection of whole vector onto y, z plane. So we project this to this point y, z and the vector would be somehow, I don't know how, it's the end of this projection. So that would be the projection of the vector v of x, y, and z in three-dimensional space onto y, z plane. And as vector v is rotating in space in different places, I mean the whole vector field, v has certain rotations, certain curls in certain spaces or not half whatever it is. Its projection on the y, z-axis would have basically some kind of a rotation which causes the x-component of the rotation. This is probably the most important part of this lecture to understand this. So again, vector in three-dimensional space is projected on two-dimensional space y and z and if there is any kind of a rotation at point x, y, and z, any kind of a, if the wheel would spin in this particular position in this particular, in some space, then projection of this vector will also have certain wheel and in this case, if we put this wheel onto y, z, its axis would be perpendicular and it will cause basically only the rotation of the curl vector around the x-axis, only the x-component of rotation around the x-axis. This is the most important and that you really have to kind of feel and understand because after that basically everything is easy. How easy? Very easy. It means that kx of x, y, z is a curl of this vector and we have already learned from the previous lecture that rotation in the 2z, which is represented by components according to the coordinates, is the minus dvy of x, y, z by dz. We have already established this in the previous lecture. In the previous lecture we had x and y, x-axis doesn't really matter. In this lecture we have right now y and z only because we started from the x and y and z was the plane of rotation. We will move to y and z obviously. So we have already determined the x-component of the curl of our vector. Now obviously if I want to do this, I have to multiply it by i and I have to multiply this by i and that's what this particular thing is. Absolutely similarly we have ky equals to d so it's xz plane, right? So it's x of x, y, z by dz minus d z dz by dx and finally ky z that's the curl of projection of rotation onto x, y, z. That's the formula which was in the previous lecture dy of x, y, dv, y. dv dv, y at x, y, z by dx minus d vx at x, y, z by dz by dy, sorry. Basically that's it. We finished. We have determined three components of the curl of the vector field. So the vector field has three components. We have basically considered every pair of components which is basically a projection onto corresponding plane. So dy and dz is projection onto yz plane which causes a rotation around x x and z plane is rotation around y and x and y projection is rotation around z. That was exactly what was determined in the previous lecture. We were using x and y. The only problem which I have right now so this should be multiplied by j and that gives me this component and this is supposed to be multiplied by k. This is by j and this is by k and that gives me this component. The only problem is it's kind of cumbersome. I mean people, mathematicians and physics don't like long formulas so I would like to simplify it and it's actually the result is amazingly simple. Here is the simplification of this. Let's say we have two vectors vector p which can be represented as three components p x, p y and p z and vector q which has its own three components. I would like to express in terms of p x, p y, p z, q x, q y and q z vector product of p times q vector product, cross product. Two vectors in three dimensional space everything is supposed to be very simple, right? So three components and three components and multiply each by each and we'll have a result. Now the only thing is I would like to point out that we will end up with multiplication well, constants p x, q x, q y, p y etc will be multiplication, simple. What about the vector multiplication? Do you remember something like first of all is anti-commutative so if you change the order a times a cross product b is minus b cross product a I hope you remember that from the vector product from the cross product and also if you have two vectors which are perpendicular to each other let's say a and b the result of their vector product is the vector perpendicular to both of them which magnitude is equal to times this times this and the direction would be some kind of rule if you will put from if you will rotate from a to b it would be this direction towards us from the port so based on this there are some rules about i and j and k multiplication now multiplication of vector by itself they are basically collinear so sign of angle between them is zero so that would be always zero as well as j by j zero and k by k is zero now as far as i times j it would be a vector perpendicular to both now this is a long x-axis this is a long y-axis so the perpendicular to both will be z-axis and the magnitude would be the product of the magnitude right each magnitude is one it's unit vector so that would be k and then j times k would be i and k times j times i would be j I mean we can always consider all the different combinations if we want k times j it would be minus i etc. so using all these rules which are quite simple I will write the result and if you want intermediate results it's all written in the notes for this lecture but anyway the result is the result is p y qz minus pz q y i plus analogous j plus analogous k and what I would like to say I don't want to spend too much time just rewriting the problem is that if px if p is a nubla nubla is dpdx dpdy dpdz same as previous lecture three components dpdx dpdy and dpdz a triplet of operators nubla and q is our vector v at x y z with components v x y z then this is exactly this which means that I can write a very simple expression for my vector product of nubla times v this is exactly curl of v so this is the simplest formula possible and all these complication results results in this particular formula again I skip a couple of intermediary steps they are absolutely trivial I just don't want to waste my time but in your time but all these results are written on the notes on this website notes for this lecture so I suggest you just to go there well basically that's it we have determined how in a simple form express the curl of our vector field at any point and well you know that my favorite model right now of the vector field is the wind basically you have the wind you can always if you know the velocity of each molecule at each place at some moment in time you can determine where exactly the tornado might be actually located I don't know but maybe those guys who are predicting the weather maybe they're doing something similar to this I don't know okay that's it for today thank you very much I suggest you to read the notes for this lecture they are more detail in some cases than whatever I presented on the board but basically along the same line so thanks very much and good luck


Zero Accounting Software 2023 bank feeds matching deposit from a customer to bank feed deposit.  Here we are first a word from our sponsor. Well actually these are just items that we picked from the YouTube Shopping Affiliate Program but that's actually good for you because these aren't things that were just given to us from some large corporation which we don't even use in exchange for us selling them to you. These are things that we actually researched, purchased and used ourselves. Focusrite Scarlett Solo 3rd Gen USB interface with software suite. I've been using a Focusrite for years for my audio needs before which time I had a USB microphone which plugged directly into the computer but I think you'll find as I have found if you want to increase the quality of your microphone you will need an interface and the Focusrite is the go-to interface as far as I'm concerned. I've been using this for years now. It works well. It's easy to use. It seems quite durably built because I only do the screen recordings. I only need the one solo interface. However if you have multiple microphones you need to plug in or if you have other instruments you need to plug in you can look at a similar model that has more input ports. If you would like a commercial free experience consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com where we have many different courses you can purchase one at a time or have a subscription model given you access to all the courses courses which are well organized have other resources like excel files and pdf files to download and no commercials. In our custom zero homepage going into the company file we started up in a prior presentation the bank feed file duplicating some tabs to put reports in like we do every time right click in the tab up top so we can duplicate it right click in the tab up top again and duplicating again let's go back to the tab to the middle accounting drop down open up our balance sheet report one of the major financial statement reports tab into the right accounting drop down open up the other major financial statement report the income statement changing the date range up top selecting the drop down we want 2022 starting in January ending in December of 2022 and there we have it running and updating that let's go back to the first tab now and go into where our bank feeds are located which we uploaded in a prior presentation accounting drop down located in the bank accounts and then within the bank accounts we got our bank feed up top that we connected to managing the accounts and we're going to go to the account transactions and then I'm going to go to the first tab which is the reconcile tab so we've been basically trying to as best we can construct our books from the bank feeds but now dip it into those areas where we might have a little complexity in doing that and have to come up with some other systems to work around let's go to our flow chart to see what I'm talking about this is from the QuickBooks desktop but we're just really looking at the flow of the forms which are the same for any kind of accounting system we're on the customer cycle here and we're trying to think about how we can fit the bank feeds into a customer cycle when we have an accrual concept we have to put in place meaning we do the work first and therefore has to invoice or bill the client and have to track the accounts receivable so that would be if we had the type of industry would drive whether or not we would have to do that right so if we're in an industry where we have to do that we're going to have to do that we can't just say well I'm not going to I'm just going to be on a cash based system it's like well no people aren't going to do business with you then right so we have to invoice them so that would be like an accounting firm or that could be like a law firm or landscaping we do the work we invoice the client so obviously the invoice doesn't have any cash impacted or affected from that transaction so we can't do that transaction from the bank feeds but then after the invoice has been input when we get paid we saw that it might be possible to connect the bank feeds to the invoice waiting until the payment clears the bank and then connecting it to the invoice however you can only do that if you're getting a payment that isn't the exact same amount as the amount on the invoice and you don't have kind of grouping of multiple invoices or other forms of payments together things that can muddy that up would be if there's credit card charges or a middle person in the transaction that kind of charges fees or groups the deposits like a credit card company or something like a PayPal or Stripe like that then we might not be able to connect the bank feeds to an actual invoice and if they group the payments together meaning we have multiple invoices for example or invoices and sales receipts possibly that are being grouped together by a credit card company or something like that then it's going to hit our bank account in a one lump sum of multiple uh multiple invoices right are combined together and so we're not going to be able to just match it with the bank feeds we're going to have to do the more of a full service system which means we're going to have to receive the payment now when we receive the payment uh that's when we can deposit it into the bank at that point in time however we might need another step there because we might want to set up like a clearing account because again we might have some system where the credit card company is grouping payments together in a way that we cannot easily uh grouped together on our side and therefore put it into a clearing account and then take it out of the clearing account and put it in as a deposit now if we have to do that then we're going to be reliant on the bank feeds just to match so what we want to do is make our deposit in our system the same format the same dollar amount the same grouping of money into the bank as we'll show up on the bank side which will come through the bank feeds we still need to use the bank feeds or can use the bank feeds but the bank feeds will not be recording anything here instead it will be simply helping us to reconcile which is still quite important all right so let's let's see if we can see what i'm talking about here let's pick a payment one of these deposits and kind of do our same thing where we're going to like work backwards to uh get to that deposit amount uh so let me find one first let me stop talking white look all right here we go i found one let's take this hundred and fifty here now now let's imagine that we have multiple invoices that were in play that are making up that hundred and fifty so i'll make multiple invoices and receive the payments on those invoices and you'll kind of see why hopefully we can't just tie the invoice out to here but rather we'll have to you know basically make the deposit on our end so let's imagine we're going to go backwards now i'm going to i'm going to make the invoice which normally would happen first in our time frame but now we're going to we're going to so you're imagining this happened first before that deposit right so let's say this is customer let's make another customer just to uh customer just to switch things up number three customer three i'm so creative with my names my customer names creativity is one of my uh blessings one of my strong points on making up names so then we're going to say this happened on october first let's say the the end date 17th okay that'll work whatever and then let's go down and say that we sold let's just let's just put a random description uh service service item usually we would want to have items that we're describing what we sell because that'll make things easier but that's not where our focus is right now our focus is on this grouping issue so let's say we sold something for a hundred dollars i'm not going to deal with the sales tax because again the sales tax would be we've talked about sales tax but that's not really our point of focus here no team here though what is our point of focus is that this will increase the accounts receivable by one hundred dollars and the other side will go into the sales account for a hundred dollars a uh revenue account however when it came when the deposit came through notice we didn't have a deposit for a hundred dollars we had the deposit for 150 dollars because there was a grouping of some kind of multiple deposits so let's show that let's say we're gonna approve it and add another approve it and add another and let's say this is uh uh customer number four we'll say customer number four to make a new customer and let's say this also happened in october oct one oct one and sounds like a like a username or something oct one act one oct one this is going to be sales of some kind one and this is for the 50 dollars let's say so now the two of these sales add up to the 150 this is going to increase the accounts receivable and the other side is going to go to revenue uh so let's go ahead and say approve it and let's check it out then let's check it out as soon as i get the green go ahead there it is the green has told me i can move forward so if i go into the accounts receivable into the a to the r the a accounts to the receivables the r as the pirate calls it are the our account there's the uh 50 and the 100 adding up to that 150 if i go back up and i go to my income statement now we recorded the revenue when we did the work so the revenue is already recorded even though we haven't yet got the money it went into the sales account here and if i check that out checking it out right now man checking it there it is and there it is so revenue went up movie b to the n now we're also tracking this a r because we have to collect on the accounts receivable that's the accrual component accounts receivable is an accrual account cash isn't involved with it if it was a cashed based system we wouldn't have a r but we have to have a r in certain industries because we have to track who owes us the money so if i go back to the first tab i can i can track internally in the a r with the business drop down invoices and we can then see we have these awaiting payment items these are the ones awaiting payment uh and so we can kind of track those out here we can also track it by going to our contacts and look at our customers and we can see the outstanding balances the outstanding balances these these balances are outstanding uh that's not a good thing that's not a good but what do you mean they're outstanding anyways uh so these are our outstanding deposits so then if i go back into my business drop down and then i go into my invoices i the point is that when i get a payment let's imagine that the payment processor or whatever is grouping these two together so we saw on the bank feeds it hit the bank feeds as 150 so if i tried to just match these invoices to the bank feeds i waited till i got paid on the bank fees let's go back into the bank feeds and i and i look at that 150 it's gonna be a little difficult to tie out uh these deposits to the bank feeds back to the reconcile and then let's find that 150 it's actually 150 but 150 is how you say it when you're cool that's how cool people say it so anyways here's the 150 and then so it's gonna be difficult to match it over here so if i go over here i could do it right i could go to the matching and say yeah that's gonna be this and this and then boom you're good to go you could do that but normally that's not the most efficient system because that means you're gonna have to do like a bunch of work over on on the reconcile and the reconcile should be the if you have a good accounting system reconciling should be easy and oftentimes these kind of problems are caused by intermediary systems in there like financial institutions like pay pals and stripes and there might be fees involved that kind of mess this up as well so this isn't so if you find yourself kind of having to tick off multiple things to tie out to a deposit you probably don't have the most efficient you know system you could probably do it better uh because again the bank the reconciliation process should be as easy as possible so what would probably be better than is you could say as you get paid when you when you receive the payments you can go into your business drop down invoices and zero has this nice system if i go into the awaiting payment once we receive payment to click these two off now i can click these two off and uh make a deposit of both of them now and i can deposit both of them at the same time uh for the one hundred and fifty dollars and that's great because then i can deposit it directly into the checking account and i'm showing one hundred the fifty and the one hundred detail when i check this out on the customer side but when it hits the bank it'll be there at one hundred and fifty deposit which will match easily zero will probably find it it'll it'll it'll be able to match automatically now i want to just throw one more wrinkle into this that could happen and that is that maybe there's fees that are involved maybe you have a a paypal or a stripe that's going to have fees that kind of messes up the invoice to to when you get the payment uh or uh you might have other kind of receipts that you're also receiving through the credit card company or something for for not invoiced items but sales receipt items or receive payment items if i hit the drop down receive money so in that case you're getting other deposits maybe that aren't simply from invoices that are also being grouped in or you have fees that you're dealing with then this system will still not allow you to just deposit it directly into the checking account that's when you might need a clearing account so that you can put it into the clearing account and then take it out of the clearing account and make sure you deposit into the checking account in the same format as will be seen on the bank statement so let me see let me just show you what that looks like uh if you had to you do that system and it really depends on how complex and what industry you're in usually and what payment methods you're using how are you getting paid so let's go to our bank accounts and what i'm going to do is i'm going to add another bank account but it's just going to be a clearing account i'm not going to connect it to the bank or anything so i'm just going to say add another bank account and it's going to try to connect it to the bank feeds and i'm like no uh so let's say it was bank i'm just going to choose the bank of america and i'm going to say bank of america and then it's going to be like do you want to connect to the bank and i'm just going to say no i just really wanted to set up like an account that's a clearing account but but they don't care about that so you don't have to tell them that but that's what we're doing so then we're going to say the account name is going to be cash clearing account account type i'll just call it uh other we'll say account number i'm making up a number and us dollars minor and us dollars because i'm in the us and we typically transact using the dollar as the form of transaction although inflation is destroying it and uh at the moment which is a little frustrating to savers like myself that have worked hard and put them okay that you're getting off track so so now what i'll do is i'll go back into the business and then we'll go into the invoices and go into the awaiting payment and we'll select these two and i'm going to deposit them into the clearing account so i'm going to say uh deposit actually let's do it one at a time so you can kind of see why the clearing account might be you will now keep it here so i'll deposit into the clearing account make up your mind my mind doesn't like making up it wants to change stuff all the time so we're going to say there's the 50 so this will go into our account let's choose an account and we're going to put it into the cash clearing account i should put an account number on it but the cash clearing account so it's going to go into the clearing account at 150 so if i deposit it uh it wants a reference i'll just put a d for deposit all right boom 150 so now if i go into my my balance sheet and update now we've got in the clearing account uh the cash clearing account the 150 nothing's yet in the checking account and the accounts receivable went back down so ar goes back down if i go into the a to the r r r matey we've got uh this goes back down and the 50 okay and then and so so now the ar went down and we put it into the clearing account and you could see it went into the clearing account not as 100 and 150 but just as $50 so again if if that was the only thing that you needed to do then you could have just we could have just deposited this uh directly into actually it went in here at uh one at 100 and 150 so it's in here as two separate transactions so this might still be useful here because now we're going to we're going to transfer it from the clearing account into the checking account and we're going to do that with uh with one deposit so then it'll go into the checking account as just one lump sum amount which is what we want to see because that's going to be easiest to connect to the bank feeds all right so let's go back and now i'm going to do a transfer i'm going to go back to the first tab and i'm going to imagine that i know that that 150 is now going to be grouped together when it hits the bank account right so that's what that's the system what i have to figure out now notice that if you have fees and stuff involved as well then you can also find different systems to use the clearing account to also help you to kind of figure out the fees and how you're going to deal with the fees with payment processors which is often an issue if you have like online shops like a Shopify or Amazon or something like that there are different systems you can put in place that uh that sometimes have to deal with the fees but anytime you deal with the pay pals and the and the stripes those intermediary the credit card companies fees can come into play as well and a clearing account can help you put a system to deal with the fees all right but in any case i'm going to go to the first tab and i'm just going to go to the transfer now i'm going to make a transfer now i could use a deposit form because i'm depositing into the checking account but when i use a deposit form it will actually show a deposit in the clearing account that is decreasing the clearing account which is like a cash account so that looks a little funny so but you could do that because everything is going into the the checking account but i'm going to use the transfer form because the transfer doesn't look funny on either side right because the transfer could mean a decrease to the to the cash account or an increase to the cash account so i'm going to say it's coming out of the clearing account and it's going into the checking account let's do this on uh october october two let's go uh 2022 uh october and okay and then we're going to say let's just say the seventh and it's going to be for 150 reference deposit all right let's transfer it and then if i go back to the balance sheet and update we've got the clearing account goes away because it's back down to zero checking account has the 150 in it but not two separate transactions for 150 instead having just one 150 150 right there so 150 i thought 150 meant a dollar and 50 cents fitty means 50 cents doesn't it whatever dude 150 you can say it for either 150 or a dollar and 50 cents it's 150 man okay so we're going to go into the checking account let's go back into the bank accounts and then uh drop down here let's go into the account transactions and see if the system matched it out now so i'm going to go into reconcile then look for that 150 and see if zero picked it up as a match and you can see it did now right so now zero was able to recognize zero was able to recognize the 150 you better recognize 150 that's right uh so there we have it so zero recognized it now so now so but now when i add it all it's doing is reconciling it's not going to add anything new to the uh it's not going to add anything new to the transactions so we'll just reconcile that helps us out with our bank reconciliation so nothing new happening to the financial statements here but still important to do because it helps us with that reconciliation process we still want to do bank reconciliations by the way just to make sure i would still you know process a bank wreck which they have a nice report zero does we'll look at it later uh but that's that let's let's see how our financial statements have been constructed thus far tabbing another tab open so i can open the trial balance you better recognize 150 man 150 inflation i used to be fitty i used to be just fitty but now i'm 150 because of inflate report reports okay okay focus trial balance and then we're gonna go uh there okay so so here's what we have it so we can see that this is just the balancing on top of the income statement and we're just constructing this thing as we go the income statement stopping or the balance sheet stopping at retained earnings income statement below that so that debits equal the credits is the same thing as saying that our assets equal our liabilities and our equity the income statement is part of equity because it's being squished together in this one number of uh uh the current year earnings which is the bottom line of the income statement 7609 54 7609 54 on the trial balance we're not grouping that in there into the equity which is going to eventually go into retained earnings this is the prior year equity and then the current activity is broken out in the income statement format accounts


spnice za kratnice zabilitega idejo na napravse, da Sorom načo obočje Fire, pa je to z napravkelju predstavila, da je to napratil, da je to za lango, da je to engajno zwrotno. Salo delanje, da je approvedvo, da je to z kalja, po to, da je to priden. ... stones for, because we have four complex dimensions, and the worth, oops, sorry, and the worth magnificent, stands for the belief that four complex dimensions is somehow the highest possible one where one can play this type of game. And my main goal during this talk is to present some conjecture for some supersymmetric partition function, Zelo še bejte, ki jim se volim, da sem imel dobro izgleda vzelo.  So along RT times R8. With a constant B field, turn on. As I will be more precise in the rest of the talk. But OK. The statement is that this object, which I call zeta K for nD8, in the operator formalism, of course, I can write it as a written index, is a character valid written index. hk je vziv, spas, tudi, tudi je bila g. In sem tazimo, ki je superashelja, je nisem način, nezavodno v tembetarih beta. Po vkroju, ni ne zelo. Však je, zelo se zelo, kaj je motivacija za toz problem. One could be interested in studying the bound states of the brains, for example, the 0D4, the 0D6, the 0D8 are all interesting topics to look at. This is just a character valued version of those computations. Moreover, there is a connection. zelo, ki je začali noženih在a iz nas iz verbenih na vljana, katiljno mi, kaj čojnega začupaj n Primedesitega in z��ila predtitev dvoj delijo deličnih teori, na zelo po vseh izgledaj, da je ta ročnija odličenidela, da je ona začal začal začalam za njih deličnimi delimi deličnih deličnih deličnih, ker so pradi doličenih deljičnih počeri, zato mu je to, da, da ta ročnija bježi nožena iz boži državo. in analogovosti istantično občutij, prejste zelo olačiti, to bi je vsev spina veliko, tko vse vse izjelimo, ne bo vsev spina vsev. In vsev, in kratkivom matematijku, to je srednje do Donaldson-Thomas sprave, da je, zelo, tko kala-biao, torik kala-biao, nekaj sem in vsev počakal lači tko tko priplizirana tko torik kase. Pozorno je, Zeta, kaj sem stojnila, če sem pošljala vzelačenja atlokovana, o kjeva z 0 in finiti, pk, zeta k. Fitne, tkaj to je pletistične prizvače, zelo, da je pletistične prizvače, je tko drog treba, ker sem da bo vzelačenja. Zelo, da je pletistične prizvače. office finitely many numbers for early in so I call this function of n. Yes yes, so Jesus un group element which leaves in a global, a group of Rob In na svejmer. In ja. Tak, je. Tak, ja. Ja võlga. Nama, da vse da, da, z tem,än ta gaurja, pa, tako, da, da, ne, da, domaš več staro, zači, da gauri na odkod nekako, Vesu, ja. Trim sem že v pačjih spodobna, ali je bачiti ampak palecje, in taj palecje sem izbytno za glasboj zameranje. Vse sem je pogleda, nekaj let bo na vse glasboj, na salitku v drže in drže in v Hellenji. To bila zelo vautn Historia, na Fietiliopoloj ste. Je to pripečne, da je srednja dorenje. So. Yeah, and OK, not the way of looking at this is that this low moving approximation is the same thing as basically taking the alpha prime to zero limit. At the same time is killing the field as alpha prime. The remains constant and this n, 1, n, and one would like to study, what is the effective action for this system. Sve, ki sem postančen, porque sem ide, da kako se tudi tako zste kakv. Počakam, da je celo zelo, da je tako zelo, da je zelo, da je zelo, da je izelo. In ja, to je kvantomekanice, ker smo izgledali na teoriče na volume z zelo. To je počkaj. Prostavno, kaj smo počkali, that the 0-d8 system, in kako je skupnila na v10, je to supersymmetrične, kaj bi nekaj zelo, tako je zelo, da se počkala v bps-bondi stati v nekaj kazih. In ja zelo, da je vse zelo, da je vse zelo, da je vse zelo, Tako, zelo igram do vresnega, imam medanje in imam mene, izvečurjo r8 in ni zelo vse zelo. Neselimo, kaj je zelo, kot lahko je, kaj je vse, kot neče zdaj. Zelo igram vse zelo, izvečurjo r8. Vse vse zelo, da sem od 1 do 4 aj, imam 4 zelo, tako, imam vse zelo diagonal, na 4 zelo. Selo, da sem, taj si priberite teori tako zvoru premačenosti taj vzil. Tati, smo že me prirožjali je, anderiji labuSE,先 čas imelo okledoziv. Zato vergodit ja z okídem. Protoč aquí je odrečujela beta. Premačen je doditi supersimetri z vsovvenje kanici, da je čas in gažnja taga, čas je gaž,gaž na katom mody evac. Gažnji ampak je uk, kar gaž enak vzalj taj vzil. To vzaljana je jaz na dosimetrij. ta sekne accim husband ne bo. Prejč covering Lyn Head can come from to type of Alle strings either this is strings stretching from 0, shuttle brain or string stretching from the SVD Nu destructive brains. The other question was about G. I denote this G as an element of the global symmetry group which are called G-flavors and I will explain what it is for this particular model. In... Ja. So let's see. Let's come actually to that question. What are the symmetries of this problem? In principle, so this g-flavor could be... So this g-flavor has various factors. There's an SU4, which is the SU4 inside spin8. So they are 8 as a spin8, but we have to take SU4 in order to preserve the two supercharges that we had before. And then there are two UN, the first UN, small N, I call UN capital N. This N is like a meant to remember, to remind the champaton bundle of the 8. So this is the symmetry group of ND brains, ND brains champaton bundle. And then there is another UN, so same small N, but I denoted with sub capital M. This guy, this UN is not manifest in the geometry. And so in the next few slides I will motivate how it comes about. And there is also a speculative interpretation about it may come. And is that one could introduce in this system another stack of N anti-D8 brains and that M will be the champaton bundle. So same dimension N, small N.  And the charges of the fields, I also list there to show you that there is an anomaly, and such that I will introduce something to compensate it. So it's not a gauge anomaly, so it's not, the system is not broken. It's just that the correlator otherwise will be zero. And so for these two guys, a plus minus five, say the complex combinations, the charge is plus minus two, and it's minus one for these fermions. Yes, yes? Yeah, so that the measure of the, you can write a part integral for the quantum mechanics, and the integrants in the measure will transform with this U1 charge. Sorry? You can think of it as like a ghost anomaly if you want. I mean, these charges, you can read as the charges of the fields in the transverse direction. So this is that interpretation. And then once you write down, I mean, the written index that I wrote before, you can write in the integral language, and the measure, many of these, all these fields will appear in the measure, and that measure will transform. So that's what I meant. That's what I meant. You can, actually, you're not forced to introduce this, because now you can evade it in another way, which is given, which you do anyway, which is given a weight of this type also to the omega background parameters. But one way to avoid it is to introduce an auxiliary system, which I will later call Upsilon. It's just a decouple fermi multiplet, and that does the job of... So at the level of inserting some observable in the partition function, you're inserting some chair classes weighted by those masses m that I talked about before. It's like you make an extra insertion to make the observables non-zero. That would be a way to... I don't know if this satisfies you. Yeah, okay, I don't have another explanation, it's just the measure transforms this way. And yeah, the other relevant multiplets are the current multiplets, and they have two origins. So one comes from the zero to zero sector. And again, I have... So from the zero to zero sector, the main players will be these matrices, B sub A, and this dagger. This index A will always believe the... Always live in the four of SU4, and again, they are K by K matrices. So their representation content is that joint for UK and the four of SU4. And another way of phrasing this is that each BA will live in endomorphism K, and their fermions. And then from the zero to the eight, there is a... So for NS sector, okay, let me say first, for a month sector, you have a bunch of fermions, which will always be there even without B field. But now, because of B field, you have a massless state in the Neveshvat sector, which I call I, and I dagger. And they will live in the B fundamental of UK times the first UN, N. So K times N bar. And again, another way of thinking in terms of vector spaces, they will each I... So I will live in on N, K, and I dagger on K, N. And for all these Keral guys, the bottoms will have charge zero, and the fermions will have charge plus one.  Again, they are K by K matrices. So they stay, they live in their joint of UK. And then in the six, which should remind you of the previous, the composition that I reminded you here. So the four are the fermions here, and the six is the here. So you could complain that KAI AB, the index AB run from one to four, but there is a constraint that KAI AB is equal, say, to epsilon ABCD KAI DC dagger. So this gives you the six of SU4. And another way of phrasing this is that they stay, they are living in endomorphism of K with pi. I mean, some projecting because they are fermions. And similarly, and so they have charge under DC1 minus one. And if you add the charges, you see that if you introduce now another fermion multiplet, which we call Upsilon and Upsilon dagger, which is with its auxiliary boson, this time valued in the bifundamental of UK and another UN, which is what we, I hope this read about, is this UN sub M, which charge minus one, then these charges are canceled. And so we just add this auxiliary system to our homological field theory. And again, one can say that it's valued in homomorphism of M to K. So this is more or less my field content. Can you say again? What is the U1? This one? You just invented it. Ah, no, these charges you can just read. I think you can read by observing that this U1 is the transverse one to the array plane. So this should be the correct charges of the field. And then this circle one you assign it. And yet another, okay, now I think about yet another argument is that, so this minus one, I mean minus one times K times N times two, because there is a Upsilon and Upsilon dagger. So this is minus 2KN. And this precise the virtual dimension of the module space that I will, of the instant module space that I will come in the, so that's another way of checking that this should have that dimension. I will come to that in a moment. So, yeah, instead of, okay, like I said, I mean, the action will have a zero to zero sector, which is this reduction, and then the zero to eight sector, which you can, for example, compute, which will have kinetic terms, and then a scalar potential. The interesting part is actually the scalar potential. So let's go on the X branch. Namely, X branch means that there will be a complexified connection, and we go to the branch where this 80 say plus phi is zero. And then we can read off this scalar potential, and it will be positive, and it will be the sum of squares. So I wrote here the first term is trace SAB, S dagger AB, less than B, from one to four, where this first term is just involves the d zero, d zero sector. Namely, it involves those matrices that I just introduced BA. It's like commutator of B, ABB, plus epsilon ABCD, BCBD dagger, and it's actually related to itself in this way. And you can see here already that the SU4 tensor appears, is epsilon ABCD, which means that this guy won't be invariant under a full SO8, but we have to pick an olonomy, and we pick SU4. So this is just, I mean, it's not we pick, it's like the system picks it for us. And the second term is trace some real moment map that comes from the d term in the vector multiplet, which I call mu r, and we can actually, actually V10 itself instructs us to do so that in the presence of V field, we are allowed to introduce a phyethyliopolis term, which I write, which I denote by zeta. So we take it positive for reason that will be clear also later. And this mu r, now is as cross terms, we did zero d8. So it's sum of the commutator and plus ii dagger, where i is rd 08 matrices that I introduced before. And now, the model space I was talking before is this m, which is just the zero set of the potential, of the scalar potential, modded out by UK gauge transformations, where the UK action is the obvious, I mean, is the one that I introduced before, so the B transforms in the joint and the I transforms with the factor. And on this space, okay, I will have a few comments about this, but let me first say that, first of all, it's quite clear that on the space of solutions to these equations, the B is commuter, which comes from the first piece. You can manipulate this SAB and SAB dagger using the epsilon and so on. And you will, this will imply that all the terms, I mean, that all these terms alone should vanish, so that it's a simple computation. So B is commuter, as is the case in the Zilber scheme of points stories. And the second one is that you can, I mean, mu itself has to be equal to zeta, so we can trace it. And so we discovered that the IA dagger must be non-zero and must be equal to K times zeta, where zeta is the FI. And again on this space, which is the space whose virtual dimension is, say, real, is took again, I was talking about before, there's a stability condition type that holds and is that we can take, for every vector V in a capital K that we can take, capital K is that K dimensional space I just introduced. You can, there exist a polynomial, F in four variables, Z1, Z4, and the vector V in N, N is the other relevant vector space, such that this equation is satisfied. So F of B1, B2, B3, B4, applied to I, applied to V is equal, can generate all these. You can generate all these in this way. So now, okay, this curly line is meant the following. I mean, this type of condition is very reminiscent if you are, for example, familiar with the 0D4 case, namely the four dimensional gauge theories, this will be the Hilbert scheme of points on a, say for N equal one, so N capital N one dimensional, this will be the Hilbert scheme of points of C2. And this type of, so for example, if we denote the map phi as this map here, then there is a corresponds by kernel phi and the ideals and vice versa, I mean, vice versa into this space of equations. So this, I mean, this is not a proof, but this is somehow meant to suggest that in this case, the space, I mean, this can be proved, it will be the Hilbert scheme of points of C4 and in higher N will be generalization thereof. And as in 2D, the, now the torus fixed points of this space was the ideas parameterized by the partitions. In this case, like I say again, this is not a proof, that's why you're at this curly arrow and I will come back to it. But this, in this case, the relevant fix points of my actions will be the solid partitions. So for dimensional partitions and moreover will be colored because in general the rank N, small N as rank N, so I take color solid partition. So that just mean to suggest that we should think about this solid partition and that's meant to motivate my next slide, which is an introduction, a brief reminder of this story. So we can think, let me see. And also, yeah, it's very important, I forgot to mention that the silver, I mean, in general this space and already the case N equal one, the Hilbert scheme of C4 is very different from C2. I mean, it's not smooth, it's not type of caler, it's not caler, it's just maybe symplatic quotient. So it may be much more singular, but still we can, this type of localization goes through and the fix point one can extract and are these solid partitions. So there are many analogies with four dimensions, but up to a certain point. For example, in the 0D4, this data somehow is playing the role of desingularizing that space. But here, Hilbert of C4 for i enough k is already singular, is not irreducible. So there are some differences, just to point out. So now the solid partition, let's, yes, yes, yes, you mean, ah, you want the microphone? This one, that's fine. Yeah, I'm just saying that this i and i plus in the middle of the thing, in i dagger, yes. Yeah, i and i dagger. If you really quantize the 0D8 string, because you have co-dimension one, there's an ambiguity of the GSO projection. That's correct. And on one side this exists and the other side is just all massive, if I remember correctly. That is correct, but this word that you are talking about is in the B field space. So I'm talking in the B field parameters. Even when B is zero. No, when B is zero, there is no such thing. Yeah, that's my point. Yeah, okay. When B is zero, this guy's, in this sector is massive, so there is no i. When I turn on B instead, I have it. I see, so you're always working with B non-zero. Correct, yes, yes. I always assume this B is turned on. That's fine. Right, right. Otherwise there is no, and that you may ask, you may ask about wall crossing, for example, like you did. Yeah. And so just quickly, how much time do I have? 15. 15, okay. Okay, so quickly, just a reminder, in four dimensions, the relevant things are, so four dimension for the gauge theory, so d0, d4, and two dimension for the young diagrams. I mean, the relevant objects are the young diagrams, which is just, I call it y, is a collection of non-negative integers, and it's decreasing, and it will be relevant to have its size, which we denote size y, it's just the sum of the integer, and there is an inclusion relation, which is just the objuzer. So this is the picture. Then we can go up one dimension in 3D. I mean, there are many ways of thinking about, I just presented the recursive one, which I think is the most natural, for example, for computation. So the next step is 3D, namely plane partitions. These are relevant for six dimensional gauge theories, namely d0, d4, d6 gauge theories, and you can think now of being in three dimension, stuck in cubes under the, say, going the first octant and put some gravity and stuck in cubes under that force, and they will assemble as a 3D partition. So a 3D partition raw is now a collection of young diagrams, such that it's again decreasing, in the objuzer sense, and we can define its size, which is the sum of the size of the young diagrams. And again there is an inclusion between, say, row 1 and row 2, if all the young diagrams of 1, each young diagrams of 1 is contained in the corresponding young diagrams of 2. And then the ones that are relevant for us are the four-dimensional or solid partitions, which are relevant for these eight-dimensional gauge theories, or d0, d8. Okay, now I'm stuck in hypercube, so I do not know how to draw it, but this is meant to be the analog in four-dimension of the previous picture. So you want to think, yeah, presumably, there's many ways of thinking, yeah, yeah. Yeah, yeah. I mean, this way of thinking is like taking a slice. You cut it by a plane and you read the slice of plane partition. Zoom up, zoom up, yeah, yeah. So for these, I can again define the size, which is the sum of the sizes of the plane partition composing it. And I will actually be interested, like I said, in colored solid partition, say of rank n. And this is just a vector of solid partitions, pi 1, pi n, where each pi i is a solid partition. And for, say, such an object, I will be interested in its character, which again I call capital K, which is the same letter I use for the vector space, so I'm identifying both the vector space and its character. So now the character associated to this pi will depends on the q's and on the n's. And it will be a sum over alpha of the n alpha times the character of each pi alpha. So sum over a point, and this is, again, another way of thinking about, is a two-pulse, four-dimensional two-pulse of non-negative integers, a, b, c, d in pi alpha, and then I take q1 to the a minus one and q2, q2, q3, q4, and so on. And, okay, just, it's not an observation, it's more like a curiosity, is that for 2d and 3d that represented before, the generative function is known by MacMau, I think. And, but in 4d instead it's not known, and people have only worked up to some size, say, 672, or that order. So it's not known how to do it in general. And now I come to the actual computation. So let's go back to the index we want to compute, which I called in the beginning zeta k. And this, in the integral language, as, I mean, let's write formally, is an integration on variables phi, and there will be an action, which I didn't write, which is, will be a functional of these phi's. And, I mean, I also didn't write the supersymmetry transformations, but are the more or less the standard ones. But anyway, the way that one can compute is that, in principle, this would not have periodic boundary condition, because it was twisted, but if we weakly gauge this g, then we can, there's a standard argument that the integral can be written as a periodic boundary condition. And this omega is meant to remind you that now the action itself depends on the parameter. So the same as in the four-dimensional omega background.  And now, in this step, we can apply, I would say, the standard localization argument. For example, I mentioned before, there is a, I mean, there are various papers studying this. For example, there is a nice paper by Ori, that summarizes this construction for all equal to two system. There is also the previous work by Muren Krasov-Stratashvili, that deals with this kind of... So depending on your taste, you can... Anyhow, the procedure, the first thing that you have to, that one has to do is to, I mean, compute the wall-loop determinants of the field, and one gets a rational function. So just by just inspecting the field content I presented in the table before, one can write down this rational function, kaj k, which is, so, this product of a very different than j, this comes from the vector, this comes from the four, so the chiral multiplets, this comes from the Fermi multiplets, where here A goes to one to four, and here only to three, and this QAB is just a notation for QA times QB, and then there is... So these are the i's, another chiral multiplet, which give you product over i and product over alpha and alpha minus xi, and these are the Fermi multiplets that they call the Upsilon, which gives you N-alpha at the numerator, N-alpha minus xi. And then the procedure, the first step is that the party integral, I mean, there are many subtleties related, for example, to having, I mean, one applies localization and somehow wants to, the result turns out to be a residue, that's because you wanna apply the somehow stock's theorem and what is about boundary terms, the same boundary terms that give you wall crossing, and then by stock's theorem you can write it as a residue, so since we are in higher dimensions the appropriate tool is this object called Jeffrey Kirwan residue, so the result is one over k factorial because of just vile symmetry, and then some over some poles, so I call them U star, just because for listing the poles is better to go to these variables, and then some chi and residue respect to the U, and the interesting thing is that, I mean, the important thing is that the poles will be leaving some m singular, some space of singular hyperplanes, which are determined by chi, I mean, by the field content, and so by chi, and so where at least k linear independent hyperplanes meet, you define a point U star, and then you can compute these objects, which, so for each hyperplane arrangement defined by U star, you compute these objects, and these objects depends on the, so these are another hints of wall crossing, depends on the field heliopolis zeta, not punctually on zeta, just on the chamber, it just depends on the chamber, so this is like standard argument, and then you can manipulate again this expression to write it as a sum, now over the real, the true fix points, which are these colored solid partitions that I just mentioned, of sides k, of course, of a standard residue, the standard iterated residue of the same function chi, now computed at the flag, now, I mean, the iterated residue, the appropriate way of doing it, one appropriate way of doing it, define a flag, this flag will be given precisely by the content of pi, I mean, there will be a correspondence by the content of pi and the flag, once we pick an ordering for the monomials in pi, and also, okay, I use value invariance to get rid of this k, this chi k is value invariance, so we can get rid of it, I mean, and also a curiosity is that this residue itself was also studied by other people, by Parshin, by other mathematician, and again, they come up, I mean, I say this because they, both this jk and this iterated residue, of course, have a representation in term of cycles, so one is really integrating on some cycles, this is well defined, and yeah, that's, that's, okay, let me stop at this, indeed this is like, yeah, yes? Yes, yes, yes, but remember that I had a condition product over q is equal to one, yeah. No, actually, are you asking about value invariance? Of permutation of the x i's, or permutation of? So you're asking about the value symmetry of su4, yes, in that case, you need to enforce the condition product of the q is equal to one, and then it will be, which I always assume it, from this point, oh sorry, from this point on, I assume it, otherwise it's not even supersymmetric, yeah. Let me see if I want to add something. Okay, yeah, now this is, the result, now I come to, back to the, the conjecture that I introduced in the beginning, and that, and the conjecture is that the zeta, the partition function, has a simple free-field representation, so let's define the platistic exponent of some function f of x1, xr, I mean, it's the obvious way, so it's pA, and it's defined as exp, sum over m to one to infinity, one over m, f of the product of the variables, x1 to dm, xr to dm, and then, if we do so, the conjecture states that, if we take the generating function, the one that I wrote at the very beginning, now the dependence on g is made precise in sense that g is parameterized by the qA's, the nA's and the m alpha, and the conjecture is that this guy is equal to the platistic exponent of a simple function fn of q1, q2, q3, q4, minus p, dependence on p, and then the dependence on the Coulomb branch parameters and the masses just through an overall product, n over m alpha, where f more explicitly, if we define bracket of t as t to the one alpha minus t to the minus one alpha, then f is the form bracket q1, q2, q3, q2, q3, which I remind you q1, q2 is q1, q2, divided bracket q1, q2, q3, q4, q4, then the argument I call s effective, so bracket of s effective divided by bracket of p times square root of s effective times bracket of p over square root of s effective, so this is like a simple conjecture that we tested up to some order and so on. On the right, n, you are asking the rank, let's say again, yes? Yes, yes, I understand. Well, it's just, I mean, the form is the same, it will be just in the variable s effective, but formally it's... Yes, so it's in the form of this guy, but you are right, formally I could have dropped the 10, because it's in here if you want. That's true, that's true. And okay, I have a few minutes, right? Or... Okay, good, good, good.  So the conjecture is that the guy is equal to PA with this argument, so that depends on what is in here. Just I just write a dummy variable. So I can affect it because it's a effective U1, it's a product of all the guys divided that way. So in the last few minutes, I just described some mathematical properties of this construction, and it goes as follows, we can introduce a tangent space to this instant-tomoduli space. Yes, yes, thank you. We can introduce a tangent space at a fixed point. So the fixed point will be fixed by some toru section, and the toru section was the maximal torus of g flavor. And the fixed point we know is given by a color, a solid partition, and the tangent I call t, and will be equal to n minus m star times k minus the product from one to three, one minus qa k k star, which we think of as a virtual character, namely, I get before the spaces n and m and identify them with their characters, which are just some of the n's and some of the m's for m. And again, k was the character of the solid partitions that I defined a few slides back. And star just means to replace each of these variables, qa and alpha and so on, by their inverse. And okay, you could guess that this is already, I mean, you could guess that this is like the square root of what you would expect to be the tangent to this moduli space. And in fact, I say this because there will be issues with orientations, namely, one will, since we are taking a square root, one will have to be careful in picking correctly the signs. Otherwise, this is just the trivial, I mean, this is also what happens in the 0D6, the 0D4. There, you don't have this issue. So that's why I'm pointing out. So the first factor is that if you, if we pick a generic parameters m, alpha and n, alpha, generic means that they are not functions of the, of the q's, which, by the way, was also an assumption in the localization computation. Otherwise, somehow you have to resolve it and go back to degenerate cases. Then the tangent at some solid partition is movable, where movable means that, okay, let me explain a bit better. So the tangent t, once we write all the characters, is a sum of monomials in the q's, q inverse, n's, and so on. Sum of monomials with plus or minus signs. And actually, you can, if you look at it, you can convince yourself that there is the same number of monomials with the plus sign and the same number of monomials with the minus signs. And there may be, and there may be, there will be in general cancellations among them. And there will be also, there may also be plus minus one factors. The statement that this guy is movable is that there are no, after you simplify, of course, there are no plus minus one factors in this sum. And this is a fact that you can prove rigorously.  Modulo, the sign that I was talking about. So concretely, the statement is that the iterated residue of chi k, that was at the end of this slide, is equal at some color, the solid partitions pi, is equal to some function of the tangent at again pi. Up to a certain well-defined sign, which I call minus one to the h of pi. And this sign has to do with orientations, namely, I mean, it's a concrete function for the partitions that has the interpretation of orientation of the formation and obstruction bundle to the modulus space. And then finally, the last thing they said, this map, a hat that I wrote there, is just a map that acts on monomial. So if you have monomial r and s in the tangent, then a hat of r is just one over bracket r, and it converts sums to products. And notice that this thing is well-defined because t is movable, otherwise there will be plus, either zero or infinity factors. But since it's movable, this is well-defined. And this is just a map that converts the tangent to product of weights in the equivalent k theory. So, yeah, I think I stop here. So thank you for your attention. Questions for Nicole?