Everybody forced here ripping 20 23 chrome hobby and jumbo a box mission number 29 Random teams find the results of late sports cards calm any time. Let's get started. It's Chargers Dolphins game is a good game Like in this one got high scoring So it's all I care about it's high scoring. It's all I care about. All right guys. Let me tweet out that iMac You got plenty of soccer to fill up soon. So let's do that stadium club chrome and you a fa sapphire all right for hobby boxes Patriots scored again. Is that what happens? Oh, we'll just Refractor aesthetic Mullins The surprising enemy is illegal. It's it even been one of the crazier Eagles fans in chat Ricky prism is Ryan Nelson No, but I mean like today Fractor Brian Reynolds he post the Eagles emojis of once but dude Steven and Rico are just going Yeah, Chris Sains guy Ricky refractor Garcia for the A's Chris what I say to you goes. I probably would have turned chat off. All right. That's it Yeah, I gotta draw the line somewhere purple speckled rookie Nelson Velasquez Cubs at 299 Let's do a color Fractor Ian Hap Prism is jury for the angels Boys are making moves Would that be nuts that would make gold wave nice hit here Christopher morale rookie out at a 50 for the Cubs Nice hit from Michael Y DL Hall rookie refractor Baltimore Some rookie prism is Woods Richardson twins Fractor Michael Conforto Like a three-card back two card back two cards Parazza rookie refractor Yankees Magenta Kyle shorebird a 399 for the Phillies you see he has the same amount of home runs as singles That's the best that Got prism a bray you for the Astros 41 home runs like 42 singles That's just amazing guys live in the dream Over through Can't even tell refractor bias for the Tigers Watching a game while breaking is like having no idea what's really going on got a photo negative rookie for the A's is JJ Able a day prison rookie Josh Smith for the Rangers Illegal needs to get his head checked third and ten Yoshida base You stop here if you got some time Very very little time, but sometimes Tyler O'Neill refractor Prism rookie Volpe for the Yankees Right now you had a game today man But I didn't play him anywhere Ruchman rookie refractor is Prato for the Royals That's terrible Fractor Mookie bets Corleis dude better needs to be elite needs to be legal here rookie refractors Moreno for the Diamondbacks Like to where I can just bet for my for my phone like nice prism Corbin Carroll rookie for the Diamondbacks in 360p looks like Sean has way more hair. What about me? What about me like the Like 1080p is like the high resolution when it's like all crappy Wave refractor rookie Carlos Perez white sauce number to 75 Ricky refractor is Duran for the Rangers It's a gunner. He got it. What's gonna be tie Prism Kershaw Dodgers must be the chain that makes the hair fluffy It's all the plutonium is radioactive And rookie Otto Josh Smith blue ray wave to 150 for Texas Sorry about me Everybody's just coming at me. I didn't do anything I'm just on the internet Prism is Andrew Bogart's for the Padres on the target Rikki refractor Volpe for the Yankees. They must have taken it seriously when I said the paths are gonna win by 30 I Gunner Henderson future stars because it was like late last night I hopped in chat. I know Donnie's era So I'm just like I'm thinking yeah Pats by 30. They can rest the starters in the fourth.  He can't really protect sarcasm. So Either that or just or the he just wasn't having any of it Refractal Contra and all the Eagles fans ganged up on me now Magenta speckle is Diaz the 350 for the Reds Carol rookie refractor Groshan's Marlins Volpe prism rookie Ethan small brewers Yes, you can try to do the The mullet again Okay, maybe one more play here for the for the for the Dolphins Orange rookie auto Connor Cappell to 25 Oakland Good break for Oakland here Fractors ladolo Prism Bryce Harper for the Phillies refractor Royce Lewis Rikki refractor is Coloss for the White Sox inch CJ Crone Rockies the 25 two oranges in the box Wow Three extra points for here factor Corbin Carroll for the Dynamax glad the Pat's didn't pay JC Jackson Wow, I can't believe they're about to get three points on a pass interference call Prism Alcantra for the Marlins or at least an attempt at three points Why is there wind are they in a dome? Oh So that drive the Chargers had did not even matter Because that pass interference Fractor Rizzo It's like it's like syrup and like what hot sauce and stuff you said Chris photo negative Josh Smith Rikki for the Rangers Took a shot to the hot sauce and Prism rookie Pirates Cal Mitchell gallon prism Adam is for the Brewers Fractor Jordan Alvarez that one sounds the best Sweet mustard sounds fire Any more catering this weekend You know what I should have done is taking that pan of French toast on the other day that was still sitting there I just made bread pudding with it gas Would have been gas Because I came in the next day like they were there the next day than the day after they were just gone Like we threw that out, but we could like just throw the eggs out put the French toast in there There's French toast you just toss in the air fryer. Oh, yeah prism Jared Walls for the angels I didn't understand that if you refractor Massey for the Royals No, oh no like eggs that are already cooked you don't want to keep especially in that quantity I Jentus speckle jock Peterson a 350 for the Giants got prism Ricky Brian Bale Red Sox Rookie refractor auto cubs the 499 is Jared young Connor Henderson. All right for jumbos now Watch out the jumbos are checking spots. See we're out. We got a ways to go on soccer guys Let's get soccer filled on up still want to go on iMac next and then four and nine to go still on stadium club chrome 13 and 16 on Sapphire UEFA Football spots are coming in though 11 to go now on specter basketball Chris September 24th That evening. It's like a 730 game Riches buddy TV 12 rookie auto codice Senga for the Mets refractor to 499 Nice hit Mets Cori seager Want to go on iMac baseball divisions next everybody. There's a carol base Suzuki photo negative cubs Prism rookie is Vargas for the Dodgers Rookie are not refractor rookie refractor Fractor Kyle soccer not rookie prism rookie a ronda for the rays Peterson refractor Rookie auto lending so stuff for the white Sox rookie refractor Rosario Padres Got Bowman chrome on a Wednesday everybody got breaks listed through Thursday currently We'll also be doing Wednesday off and acts live as well Prism rookie Moreno for the Diamondbacks rookie refractor VR Giants Wave refractor Mullins the 75 Baltimore prism Bregman Astros Cutch, I didn't see you score for the Broncos. Dang it orange wave Rookie auto Ryan Nelson 13 of 25 Diamondbacks now Refractor rookie Nolan Jones for Colorado Henderson Prism is Mookie bets Dodgers Rookie refractor totally Iraqis Cody Clemens Illegal did you write a three paragraph email the rich about it got prism Manoa for the Blue Jays Carlos Correa refractor If you if you haven't you probably should Time to do list. I know you're very busy, but if you could fit that in your schedule, I would appreciate that You got Gunnar Henderson Prism Javier Bayez Tigers Here factor drew waters Royals illegals incredibly busy That's gonna have time to go to Korea for a week Gold wave is McMahon the 54 the Rockies. Yeah, two weeks. I forgot about that prism Tatis Padres Rookie refractor Parazza for the Yankees. It's a long I Can imagine I have to pay someone to edit it Get a publisher get rookie auto Conor Kapell for the A's refractor Tatis Mullins refractor Are they? Prism is Gulch mit for the Cardinals refractor Adames Prism Adames Brewers refractor rookie For the A's is dermis Garcia Dermis like skin. Come on camera. It's just to focus on the cards. I'm gonna fire this camera Rookie auto Conor Kapell for the A's Refractor rookie is Aranda for the rays Got photo negative Anderson for the White Sox Prism O'Neill for the Cardinals refractor Bregman Aaron Jones Prism rookie is drew waters Royals Camera will fire me. How is that gonna happen illegal? Purple rookie Cody Thomas on the auto to 250 for the A's again refractor Alec Winoa the A's been hidden The all-hall rookie refractor for Baltimore Keep getting paper cuts. Got one earlier The pristine cards are sharp though They'll get you Still got that one spot left on iMac next and we still got we still have plenty of spots and soccer as well as football And basketball tonight at everybody purple speckle Michael totally a rookie auto to 299 for the Rockies negative Bieber guardians They are rookie refractor Red Sox Prism rookie Riley Greene Tigers rookie refractor was Richardson for the Twins Papa John's garlic stuffed crusts crunchy something. I don't even know what I just saw But it wasn't pizza look like the crust was mozzarella sticks Prism Jared Walsh for the Angels rookie refractor Cal Mitchell Pirates That's kind of pizza. I'm trying to eat is a mozzarella stick on the crust or just the whole thing made of mozzarella's like a big gigantic flat fried mozzarella Fractor of bray you there are lots of Papa John's and sale Really, that's funny blue refractor rookie auto Jared young cubs the 150 Rikki refractor Ryan Nelsen Dimebacks Yeah, I saw that lane towards UCL That's a long time though because Bryce Harper came back in a few months started hitting. I don't know why they can't just DH him Dump Stanton orange wave is hunter Greene to 25 or sincey Prism rookie Woods Richardson twins and refractor Brandon Drury Say a wool Masataki Yoshida rookie base auto for the Red Sox Heck yeah, Boston nice Mount Castle refractor with a good tops chrome mixer here with the low refractor Got a jersey card here, and it is gold and it is a Garrett Cole Yankees number 17 out of 50 Got prism him and as guardians been intending Prism rookies Ryan Nelsen Dimebacks rookie refractor is Coloss for the White Sox Yeah, I'm getting more confused illegal. I'm just gonna not say that the word got Adley Rochman presum you shems key for the Giants Harper refractor last box of the break one more jumbo here guys Another Sunday fun day spot coming in that's not an 18 to go. That is just about halfway full In our first Sunday bond a mixer of the regular season every spot in a regular season Sunday fun day mixer gets you an entry into a Drawing at the end of the regular season the prizes are listed in the break description. There's a Tom Brady helmet There's some panini one football boxes Terry Bradshaw then swan signed helmets a bunch of break credit up for grabs to a nice regular season promo for us this year Rich uh Rich must be feeling pretty good after hanging out with On Face time with Tom Brady to be given one of his helmets away prism Lang Leers rookie for the ace Salvador Perez How about a Bucks with Baker one and oh, yeah, he had a solid game too Magenta 399 Corbin Burns Brewers rookie are not working but prism is Strowman Who ended up winning that Yankees Brewer's game because Corbin Burns had a no-hitter, right? They're like nine innings Blue refractor rookie Otto Marcus Wilson's Mariners to 150 Pools refractor. It's not that where tackle him Yeah Ali Ruchman tackle that guy That's not awesome. Equal Prism rookie costs us for the Red Sox Tobar rookie refractor Rockies Which Kelly is that John Kelly? Who is that John Kelly? Prism Gosman for the Blue Jays McMahon refractor rookie Otto Freddie for me and for the Royals refracted you Darvish Get that guy out of there He's taking all Eckler's yards Yeah, get under the bench. Geez, dude What are they doing out there wave rookie Bryce to rang the 75 Brewers The Yankees one for three and the Brewers had like a no-hitter in the ninth inning. That's just embarrassing dude The Brewers are embarrassing That team is going to the playoffs too, right? Prism Suzuki for the Cubs, dude, that's an easy first-round win if ever plays them Can't even score Alvin's can't stop the run Sean It's a carol base Prism is Nate Eaton for the Royals the rookie there Devers refractor It's where they drafted Joshua Kelly like three years ago, and he hadn't done anything And now all of a sudden he's like a decent Back up to Eckler We were a wave is an Aguilar rookie auto for the Angels Ryan Aguilar Antonio Cruz Do a recap we had magenta to 399 of Schwerber 350 magenta speckled Peterson and Diaz the 299 Velazquez Auto to 50 is morale for the Cubs base autos of Fermin Yoshida Capel, Capel, Lenin Sosa refractor to 499 Jared Young and Kodai Senga Very nice Senga purple speckled the 299 is Togalia purple to 250 Thomas to 150 Jared Young Marcus Wilson Ryan Aguilar Josh Smith an orange to 25 Conor Capel and a Ryan Nelson That'll do it pretty good mixture there. Thanks again everybody onto iMac


Mitch, if you would talk a little bit about, I think Secretary Perez mentioned, some of what helped us get funded was our partnerships. Will you talk a little bit about what the other institutions bring and how that's going to work? Right. Because mission-critical operations cuts across so many different types of industries, one of the things that we looked for as we were putting our project team together and looking at our partners was some of the individual skill sets that each of the different colleges brought to the table. And so some of our partners have very unique skills and very unique programs at their schools that we don't have at our program. For example, Moultrie Tech has a very good representation with connections to the high school levels and getting high school students involved in the technical programs that they have there at Moultrie Tech. And they do a lot of that through the remote telepresence sessions, kind of like what we demonstrated in the labs a little earlier. So working with Moultrie Tech, trying to figure out exactly how we can reach into the high schools and we can kind of grow that pipeline from the high schools up to the college and then on. Wake Tech brings to the table a series of big data analytics and being able to look at all of the information that's generated in the various control systems and being able to look at trends and patterns and try to predict where things are going from there. NASH has an emergency preparedness program and an emergency response program that's also critical to the mission critical side of things. When the lights go out, what do you do now? How do you respond to that? And how do you get the utilities back up and whatnot? And then of course UNC Charlotte as our partner also from the academic standpoint gives us an opportunity to work with developing closely with them a 2 plus 2 program. But they're also recognized for cybersecurity expertise. And so to bring that element of it in and match it up with the industrial networking part of it. And then of course with our program, our automation program here and our IT programs here and kind of putting everything together into the big melting pot, that's where we brought the project from. Well you really embody partnership and again I have the privilege of seeing applications from across the country and to all the colleges that participated that was really the key. I mean I think you've embodied why you were selected because you really had remarkable partners not just in education but employer partners and others. And that is critical and you understand the demand needs of your region. And that's why it's so exciting. If I'm a student here, I would know that if I get through this, you already have a job Ken. And Ken is a representative sample of folks here because you have such a good set of partners. One other thing that we tied into the grant and we do have some partners ISA is here is to get some industry recognized certifications. And so that not only would you have your degree but you would have some certifications, some letters behind your name that said to an employer, okay I can vouch they have these skills. Do you want to talk briefly Jonathan about what the certification part of this means? Yes, so if you're familiar with CompTIA, which is an IT certification organization, we'll be working closely with one of their subsidiaries called Examplify to develop a certification for mission critical operators so that these will be a subject matter expert panel that will be assembled by exemplify identified by employer partners and organizational partners to say, yeah, these folks are the experts in the field. They'll pull those folks together. They'll decide what they'll tell us what needs to be on the certification exam. We'll develop levels of these certifications so that someone could start out at an associate level then move up to a specialist and then an administrative level. But the goal is to get the employers to build the certification so that we can ensure that what we're doing in the classroom directly relates to what is needed in industry. And to also piggyback on employer partnerships and one thing that I think was just outstanding about how Kenneth wound up in the position with Wipro was that they contacted our workforce development office and said, this is the position. Can you tell us, can you give us some applicants basically? And so we then identified students to apply for these positions. And that's the kind of partnership that we want to develop. We want the employers to contact us and say, hey, we have this job. We know that you are developing students to fill these positions. Can you tell us, can you give us an applicant pool? And then from there they choose who they're going to interview. And we just found out just very recently as actually as of this morning that there was another student who was offered a position with Wipro. I won't say any names or anything because none of that is finalized. But there will be a second position just like Kenneth has for another student.


Incomes LSTM networks in 1991 that introduced a long short-term memory cell in place of dumb neurons. This cell has a branch that allows past information to skip a lot of the processing of the current cell and move on to the next. This allows the memory to be retained for longer sequences. Now to that second point, we seem to be able to deal with longer sequences well. Or are we? Well, kind of. Probably if the order of hundreds of words instead of a thousand words. However, to the first point, normal RNNs are slow. But LSTMs are even slower. They're more complex. For these RNN and LSTM networks, input data needs to be passed sequentially or serially, one after the other. We need inputs of the previous state to make any operations on the current state. Such sequential flow does not make use of today's GPUs very well, which are designed for parallel computation.


The presidential candidate of the Labour Party, Pitaovi, has expressed confidence in the unity of Nigeria, will be regretted that politics was the only thing dividing the people, speaking in Onitsha at a meeting with the Muslim community in Anambra State during the Iddo-Fidri break, will be maintained that he had never discriminated against anyone on the basis of religion and would never do so. We have no country, one Nigeria. As the governor of Anambra State, my ADC was the most Muslim of Zarkandu. Idris, and Idris is a good man who will make us today. I'm a Nigerian who believes in Nigeria. I have never discriminated against anybody because of religion and I will never do so.


So this time I was going to give some applications, but so let me just recall very briefly what I did the first time then. So here we have the big picture, which is like this, that we have some blob up here, which is called beautiful X. So that's a complex manifold. It could be a domain in CEN, it could be an open manifold, or it could be a compact manifold. And then we have a projection map P that goes from this beautiful X down to a base manifold B, which is also a complex manifold. And for instance, this here could be an open set in CEN, and then this could be a linear projection. So there are many possibilities. There are two main cases. One is when it's an open set in CEN, or CEN plus one in that case, because think of this as one dimensional and the relative dimension in this direction would be N. And so there are two main cases. You think of this either as an open set in CEN plus one pseudo convex, and this is a linear projection down to C. Or you think of it as a complex manifold, and then the typical case, all the fibers here we wanted to be compact complex manifold. And then we can think of this here as T-varys, we can think of those fibers as a family of complex manifolds. So I proved some theorems. I'm not going to go through them again, but I put the slides here in case I will want to go back to them. So this was the first theorem that was about the proper vibration. That meant that all the fibers were compact manifold, we have a family of compact manifolds. And then all the time when we have such a fiber, we think of the L2 space or the Bergman space or some holomorphic objects here. In the CEN case there would be holomorphic functions, otherwise there would be N forms with values in a line bundle L. That's what is intended by this notation here, ET. So this is the space for each T, we have a Hilbert space, in this case finite dimensional. And that's the space of holomorphic sections of this bundle, which means that it's an N form with values in L. This means N forms. And then we can compute the L2 norms, they look like that.  So it's a Hermitian vector bundle and the conclusion was that the curvature of this vector bundle with this metric is positive or non-negative. Yes, in this case they will. So that's a non-trivial fact. So in this case it will be. We look at slightly more general cases at the end, and this is not assumed. Or we have in the CEN plus, when this is an open subset of CEN plus one, the CEN plus M in this case, the formulation was a little bit more complicated. Maybe I do not go. Let's just remember that there was some rather complicated statement like this. And the special case of that was that if we have such a pseudo convex domain, and we look for each slice here, we look at the Bergman kernel function here. Then the conclusion was that the logarithm of the Bergman kernel is plurisabharmonic as a function of both the variables T and C. In particular, it's plurisabharmonic with respect to T there. So in case T is one-dimensional, it depends subharmonically on the variable T on the parameter. The plurisabharmonicity with respect to C is a very classical fact, which is always true. Okay, so now we can start with the applications, and maybe I can come back to those things later if we need that. So I'm going to talk first about the Osawa Takigoshi extension theorem. Then I have to draw a very similar picture here. We should not be confused with that one, although it looks almost the same. So we have a domain here, which is now called the D in CN. And we have a, let me write it down here, and we have a hyperplane, no it's not a hyperplane, it's a linear subspace that's supposedly intersects this. So here is V, a chosen coordinates so that the linear subspace is just a space where the first coordinates are equal to zero. And we have a plurisabharmonic function in the big domain here, and we assume that this domain is not very big. So this is the C prime direction here, and this is the C double prime direction. So this should not be confused with the other picture because there is no, yeah, it will, yeah. So I assume that this is not too big here, so I assume that C prime, some normalization is less than or equal to one here, all the time. Okay. And then the theorem is the following, that's the Osawa Takigoshi theorem. It says that if we have a holomorphic function on this slice here, we can extend it holomorphically to the whole domain. So this is a classical fact, but we can do it in such a way that a certain L2 estimate holds, namely we extend it to capital H, and the L2 norm, weighted L2 norm of capital H is bounded by a constant times the weighted L2 norm of small h, which is the function that we extend on V. And the important thing is that C is a universal constant that does not depend on phi. After this, that's where the normalization comes in here. That's what makes the constant universal. So this is a non-trivial fact. It was proved by Osawa and Takigoshi. I should remember when, but I don't. And there are many versions of the theorem for manifolds, et cetera, for sections of line bundles, et cetera, et cetera. And they actually, it's actually a very useful fact. But I'm going to stick to the simplest case in order to show what it has to do with the theorems that I discussed last time. So one question that arose was the following. What is the best constant? We know that the C there is universal. So that was a question of what is the value of C. In a particular case, there was a conjectured answer to this. And the conjecture was called a suites conjecture. If you, yeah, it's probably not so well known. But, and the answer is the following. It was given by Spinger Bloschke and Guan and Shu. They found that the optimal value of C is sigma K, which is just the volume of the unit ball in CK. So that value is obtained. It's attained. If you take just the generic case when V here is just a point, say the origin of the unit ball in CK, and then you take a function there, one, say, and you want to extend it with a small L2 norm as possible. You take phi equal to zero. Then certainly the best extension will be the function that's constant equal to one. And that will give you precisely this bound. So it says that you have a better, this is the worst estimate. So if you formulate it demagogically, you can say that this is the hardest extension problem. This thing, you always get some. You never get the worst estimate than that. That's the theorem of Bloschke and Guan and Shu. And, yeah, so I'm going to describe an approach to prove this, reprove their statement here, and prove maybe something a little bit sharper than that. And this is joint work with Laszlo Lempert. You heard of him, maybe, Thomas? Yeah. Not recently. It was Thomas' advisor. So the idea is this, that we look at DT, which is the subdomain of C, such that the logarithm of mod C prime squared is less than T. So we shrink the domains here. I said that the logarithm of this should be less than T. So when T is now a negative number, it looks like this. I get this is DT here. DT, like this domain here. I look at this family of domains for T less than 0. So we exhaust D by subdomains. And they shrink. When T goes to minus infinity, they shrink just down to this plane here. And you can view this as a special case of what we were looking at before, because you can now construct a domain in one dimension higher, which is the domain I have down there. Beautiful D is a set of tau, C, such that the logarithm of mod C squared minus real part of tau is less than 0. So this corresponds to this picture now. And this is a pseudo convex domain because the function you have there is pleurisabharmonic. It's defined by pleurisabharmonic inequality. So it's pseudo convex. And the DTs are the slices of this domain now. Right? The way I do it. Yeah. So this is how we do it. So we have. And then the theorem with Laszlo is the following, that for each of those domains now, we can apply the Osawa takigoshi, where we can think of the Osawa takigoshi theorem and says that there is an extension here. And we look at the optimal extension. There is always an optimal extension, the one with the smallest norm. We call that HT. And we look at its L2 norm. So that's the index T. That's the L2 norm of a DT. I take, so to speak, the best extension for DT. I take its norm and multiply by this constant, e to the minus kT. So obviously those numbers, the norms here will be smaller and smaller. So I compensate for that by multiplying by e to the minus kT. And then I prove that this is a, we prove that this is a decreasing function for T less than zero. That's the theorem with Laszlo. This is a decreasing function. So what does that mean? It means. Huh? Huh? You mean that T gets more and more negative? Yeah, it still gets more and more negative. Yeah, exactly. What do you say it's decreasing? I really mean that it's decreasing. So, yeah, when, as T increases, yeah, it decreases, yes, yes. So what I want about all is this inequality to hold. So this is the quantity that I really want to estimate. It's the best, when T is equal to zero, I have my original domain. And if I got the decreasing, increasing right, that would be now smaller than the limit when T goes to minus infinity of those things there. There should be an e to the minus kT here. Sorry, e to the minus kT should be there also. Exists? Yeah. Because it's monotone. So I made a mistake that it should be an e to, it should be the same expression here as there. It should be with the e to the minus kT also. And then it's monotone, so there is a limit. And, yeah. Yes, so monotone is, yeah, so, yeah, well, yes, but I have hTT squared e to the minus kT. So I draw this quantity, let's call this AT. It looks something like this then. I said it was decreasing, so it looks something like this, maybe. And then I say that this value here, which is what I'm interested in, would be smaller than the limit here when I go out to minus infinity. Could be, in that case it's not interesting, but so far it's all we claim. But I claim it is not, I claim it cannot really be minus infinity, it cannot really be plus infinity. Actually it will be very easy to compute what the limit is. So the consequence of this here is that optimal constant is sigma k. What is that? Why is that? So the theorem of Lodzky and Guanshu is the consequence of this last inequality there. Because when t is close to minus infinity, I have a very, very thin little strip here. Very thin, it looks like this. So now t is close to minus infinity, I have a very thin. So I want to construct an extension, I can take any extension here. And when t, when this is very thin, I can compute more or less the normal of that and you will see exactly that it gives you the value that you have there. If I got the e to the, I should have had the e to the minus kt there. So the monotonicity is the key to the problem. There is some convexity, yes. So I will get to that because that's the way we prove the monotonicity. So, yeah. So now I want to sketch the proof of this, but I'm not going to sketch it in general. I'm going to sketch it in a special case. So we take the special case when k is equal to n. So that means that the variety here is just the point. Then I can draw a new picture perhaps. Then the domain is just this. I have a point here which is the origin, say. And the dt, this is d. This is dt. Something like that. Looks like this. And yes. And then I want to extend a function, a holomorphic function on the point. That just means the value 1. I want to extend it to a holomorphic function with some estimates. So let's see. This is really a Bergman kernel estimate in disguise because if you remember the Bergman kernel, the Bergman kernel kt for the domain there was the supremum of this quotient. h at the value 0 divided by h, the norm of h. That was the Bergman kernel. Now I can normalize, so I can choose always h0 equal to 1.  So to estimate this norm here, it's the same thing as estimating the Bergman kernel. So the theorem I want to prove is equivalent to saying, let me see here. So now we get to the convexity that you asked about. Now I'm going to use the logarithm of the Bergman kernel. It's a convex function of t. It's actually a subharmonic of t, but it only depends on the real part of t. So it's a convex function. Yes. And the theorem is equivalent now to saying that, let me see. So the theorem on the slide is equivalent to saying that this function is increasing because the relation between kt and the norm is 1 over here. So instead of looking at what we had before, we multiplied the norm here by e to the minus mt. Now I get the Bergman kernel multiplied by e to the plus mt. And I want to prove that this is increasing now, this thing. I don't know if this is too confused or is it roughly correct. And now the convexity comes in. Now the convexity comes in because this function here is convex. I add nt to it. It's still convex. The logarithm of the Bergman kernel is convex with respect to t. I added something linear, it's still convex. And moreover I claim that it is easy to see that it is bounded when t goes to minus infinity because then you just need to estimate the Bergman kernel over essentially a small ball in here. And if you have any function which is like that, it's convex. So it doesn't look like that now. Look at that function. So it's defined on the negative half axis. It's convex and it's bounded when you go out to minus infinity. Well, it has to be increasing. So that finishes the proof in that case. So still some... No. So this was actually Laszlo's argument for the suites conjecture. And then I suggested that we should prove that it works for the entire formulation of Savataki Koshiti. This was just a special case from the right. It was a point. But... And then in order to get the full of Savataki Koshiti theorem, when you have higher dimension here and not just a point, we have to use the full formulation of the theorem, not just the theorem about the Bergman kernel, but the full formulation when we had those measures and arbitrary measures, not only Dirac measures. But the principle or the argument is just the same as what I wrote up there. So that somehow gives you the best constant in the Savataki Koshiti. And it also works in more generality for manifolds, et cetera, but I presented the simplest case here. I get back to... Hopefully at the end I will get back to Savataki Koshiti for manifolds a little bit later. Okay, so I leave this. I go to the next topic. So it's some example from Kehler geometry. So this was about Brunning-Kovsky for domain C and the first one. And now we look at... We look at compact manifolds now. So I'm going to this situation here when this is a proper vibration and all of the fibers here are compact manifolds. But I'm only going to look at the special case of it first. I'm going to look at the special case when this vibration is trivial. So I have a cylinder. So I have a manifold here, which is called X. And then I take the product of X with U here. So this thing here is X times U. So all the fibers here, I take a point T in U. All the fibers here are the same. They are all X. So I have a constant family of complex manifolds. And then I also throw in a line bundle. So I take a line bundle on X here. And then I let it define a line bundle on the product here just by pulling it back by the projection map onto X. So I take, so to speak, the same line bundle on each fiber here. So this is L underlined. So then we have a family of manifolds. And over each of these manifolds we have a line bundle. All the same also. Nothing really changes. So what is changing is a metric on the bundle. So I throw in now a metric on this L underlined on this bundle. I have a metric on the total space here. And this may change from fiber to fiber. So I can think of a metric on L underlined as a curve of metrics. So for each T here I get a metric on the fixed manifold and the fixed line bundle. So the only thing that changes is the metric on the line bundle. So I have a curve of metrics on a fixed line bundle over a fixed manifold. That's what I have. What? The metric. The metric, yeah. Semi positive. So I mean that the IDD bar of it should be greater than or equal to zero. So could you take a metric? Here, like this? Yeah. So not really because it has to be a metric on the line bundle. And then if I just take a metric on U here, it would be constant on each fiber. No, I mean pull back from the line. So I have, I could do that also. Yeah, take a metric. But then it would be a constant metric. Then everything would be constant. And then it's not, that's not interesting then because then nothing will change at all from fiber to fiber. It's still allowed. It's still allowed. Okay. And then I can take IDD bar of those things. IDD bar of this. If it's strictly positive on the fibers here, that will be a scalar metric on the fiber. So I have a curve of scalar metrics on the fixed manifold X. And now we specialize further. So we choose a very particular bundle. So we take it to be the dual of the canonical bundle of the fiber. So the dual of the bundle of N0 forms. So I assume that that is positive now, strictly positive on the fibers. That means that the fiber X here is a phano manifold. This is a phano manifold. So I have a family indexed by T in U here of a scalar metrics on a fixed phano manifold. And now I was looking at the fibers of this. You had my vector bundle. They were ET. And they were equal to the space of holomorphic sections over X of K of X plus L, which is now minus K of X. So it looks very trivial. And indeed it is very trivial. This is a trivial bundle. So I just look at the fibers here of the holomorphic functions on X now, in this case. And they are not so many. They are only the constants. So this is a trivial bundle. And the only holomorphic sections are the constants. But still I can do that. So that's really the simplest case of the theorem, if you want. And then you get this theorem. If you now assume that the variation here is semi-positive. So this means that if the IDD bar here should be strictly, it should be greater than or equal to zero on the total space. So it should also be pluralist of our monocle with respect to T. And now I can look at this expression here. A metric on the anti-canonical bundle can be identified with a volume form on the manifold. So I write this somewhat elliptical here so that this stands for the associated volume form. Or alternatively, you could think of it as integral. You take one. The bundle was trivial. It has only constant sections. So one, for instance, you take one squared e to the minus five. And you integrate over x. So that's what I mean by that. And then the conclusion is that if I form this integral here, I get the phi tilde of T. And the conclusion is that this is a subharmonic function. So in particular, if it does not depend on the imaginary part of T, it's convex. So this looks a lot like preco-pasteorem. I mean, if you change x to r and or c and here, it looks exactly like preco-pasteorem. So it's a preco-pasteorem for Fano manifold, if you want. OK. Still no application. We just know this. And I should say that this particular case of the theorem is fairly easy to prove directly. But that's not so important. So there is a converse to this. You can ask this function phi. Yeah, so let's assume here now that we are in the last case here that the metric only depends on the real part of T and not on the imaginary part of T. So then it's convex. And I'll say that it is not really strictly convex, but it's actually linear. So it's linear. What can we get then? Well, the conclusion is that if it is linear, and moreover, you assume that phi T is bounded, just some technical condition, but this is actually quite delicate. So we assume that it is bounded. Then there is a... The conclusion is that then the situation must indeed be trivial. So then there is a holomorphic vector field on manifold X, such that all those calormetrics, they are really the same after applying the flow of the holomorphic vector field. So nothing really changes. Yeah? Yes, yes, yes. So in the previous theorem, it's enough to assume that the anti-canonical is semi-positive. But in this... Well, in this theorem, I want it to be positive. So I really want... I think I do... Maybe I need to check. Maybe it could be. But let's assume it is strictly positive along the fibers. But the variation in this direction does not need to be strictly positive. It can just be semi-positive. It is indeed not strictly positive, but actually only linear in this direction of the integrals. Then as a matter of fact, there is a vector field on X. I can compute the flow. There is a flow associated with that vector field. I apply it to the forms. And applying this, we see all the calorforms would be the same. So then the situation is trivial. So in case you assume that everything here is smooth, et cetera, this follows more or less immediately from the formulas. But if you don't assume that you have any regularity, this is dirty somehow. But still it holds. The only assumption you need on phi is that it's locally bounded. So no singularities. No serious singularities on phi. Okay, so why is this useful? Well, one can use it to prove generalizations of the Bandou-Mabucchi's uniqueness theorem for Keller-Einstein metrics. So when you have Keller-Einstein metrics on a Fano manifold, there is this classical theorem by Bandou-Mabucchi that says that if you have two such metrics, there is a holomorphic vector field on the manifold with the flow, such that if you apply the flow to that, you will transport one metric to the other. So the Keller-Einstein metrics are unique up to the action of holomorphic automorphisms. That's the Bandou-Mabucchi theorem. You can get the proof for that now, and also even in a more general situation as I haven't come to in a while. So this was first observed by Robert Biermann, and then it was generalized to a singular situation by all those people there. And then it was actually used in the work by Chen Donaldson soon on the existence of Keller-Einstein metrics because intimately related to this is the so-called Matsushima theorem about the redactivity of the automorphism group. And this allows for a singular version of the Matsushima theorem. But let's forget about that. I just mentioned this as applications of the proof. So let me sketch very rapidly how this goes, then it's a little bit embarrassing because there are some real experts on this matter here, but maybe I should... I'll sketch it rapidly. So we have to introduce first in order to understand if we have to introduce the Montchampère energy of a metric, and it's defined in this way. So the classical definition is that you define the E of phi. E is the energy of phi. It's defined up to a constant by saying how it varies when phi varies. So the derivative of E of phi with respect to t should be this thing. And actually I probably should have a plus sign here if I want to have it consistent with what I get later. Let's be generous about that. So you define this function of the Montchampère by saying what its derivative is. You can write down an explicit formula also. And then you cook up the so-called ding functional after ding that discovered it, which here would be minus L phi plus the Montchampère energy. And L phi is precisely this logarithmic integral that I had before. Now, the relevance of this for Kell-Einstein matrix is that Kell-Einstein matrix are the critical points of the ding functional. If you take the derivative of this thing with respect to... If phi depends on t and you differentiate with respect to t, say the derivative is phi. If psi, you get the derivative of the first thing here will be integral of psi here with a minus sign. Ah! Yeah, too many minus signs. Maybe I was right as it's written here. So you get this and this from differentiating the logarithm. And then we define the Montchampère energy so that the last thing holds here also. If I get the signs right now, you will see that this is zero for all the choices of psi if and only if e to the minus phi is equal to omega phi raised to the power n modulo constant. And that's exactly the Kell-Einstein equation. It means that you take the logarithm of this and you take dd bar, you get the Ricci and then you get omega phi on the other side. So that must be equal. So this is the way of writing the Kell-Einstein equation. So Kell-Einstein matrix are critical points of this function. And then there is a notion of geodesic. I'll skip over what that means. And it follows from the theorem that the ding functional is convex along geodesics. Because, yeah. And then there is a theorem by Chen. In this case it's easier because you don't need a full force of Chen's theorem, but never mind. Any two points in any such matrix can be connected with geodesic. So the ding functional, if you take a geodesic that connects two critical points, you get a curve there. The ding functional is convex along it. The two end points, the derivative is zero. So the only possibility for this is that the ding functional is actually linear along the geodesic. So here is a Kell-Einstein metric. It's not a Kell-Einstein metric. The ding functional is a geodesic between them. And the ding functional, d of t along the geodesic will be like this. But the derivative at the two end points is zero. So it must actually, the ding functional must actually be a constant. Ding functional must be constant if it's convex. And therefore the L functional must be linear. And then the converse theorem says that we have all those automorphisms that relate to metrics. Because the converse said that if the L functional is linear along some curve, then the curve must arise from holomorphic automorphisms. So this way you get the uniqueness of Kell-Einstein metrics of automorphism. And the point, one point with this proof is that it applies with less regularity. You can study, for instance, a twisted Kell-Einstein equation where this function here can have singularities. So it includes metrics with conical singularities, for instance. And it also applies to Kell-Erich's solitons. Something which Janir asked me to study. But actually it works perfectly well for solitons also. So that's the way you get the theorem by Tian and Shu that way. So you just change a little bit. So in the case of twisted Kell-Einstein metrics, you look at this function instead. You take e to the minus five, you add the function psi there. And in the second case, you don't change the L functional, but you change the energy a little bit to so-called Shu energy, which I will not go through here. But you can prove uniqueness for solitons and you can prove uniqueness for up to automorphisms for twisted Kell-Einstein metrics also, using this Bruno-Minkowski or Placo-Passo argument here. Okay, is it more or less okay? Yeah, so I go on. So this was a trivial vibration. Now I look at the non-trivial vibrations. Yeah. No, no, no. So that's pretty nice. In the real Precopa case, there is a counterpart of this theorem here for the real Precopa, which says that if you have... So in the real Precopa, you have a convex function of t and x. And if you have, so to speak, equality in the Precopa inequality, then this function has to have a very special form. It has to look like you take one function of x and then you add t times some vector. This is equality in the real case. You take one function that depends only on x and you use the t variable to translate it. That's the only possibility to have equality in Precopa's inequality in the real setting. So this is formally very similar to them. Here you have the flow of a constant vector field. In the other situation, you have a flow of a holomorphic vector field. So somehow all the time the translation is this. You change constants to holomorphic things and then you get the corresponding theorem in the complex setting. That's it. Okay. And now we look briefly at a non-trivial vibration. And we have the same situation. We have a line bundle over the total space, et cetera. And now I will assume, definitely, that i d d borrow phi is strictly positive over the fiber. Because otherwise it will not work. Otherwise it will not even be true. The conclusion I want to write. First, it will not make sense. And second, it will not be true. So let's say now that this b here is a part of c. This is an open set of c. So the base is one dimension. I can think of it as a coordinate patch. It's easier to state them. But now we have a lot of machinery here. So here we have a vector field on the base here, which is dt, which is just d dt. A holomorphic vector field on the base. Now a lift of that field is a field up here. So I have this vector field here. It points like this. Now I can lift it. It's going to look like this. And that it's a lift means that if I apply the p to that, I will get d dt there. So the differential of p acting on the vector field up there should be equal to dt. That's a lift of a vector field, not holomorphic. So it cannot be chosen holomorphic in general. So it's just a real vector field. So therefore you compute the d bar of it to measure how far it is from being holomorphic.  And that is codera Spencer form. So if you take the co homology class of that, it will be the codera Spencer co homology class of the vibration. So if you can choose it holomorph, somehow the vibration is trivial. Infinitesimally trivial means that you can choose to be in a holomorphic way. But now, so the kappa will be one zero form, but the values in vertical vector fields, vector valued zero one form. And by Schumacher, building on the work of by Sioux, there is a canonical lift of this vector field up here. I will not go through how that is obtained, but there is a specific way that you can choose to lift here, depending on the metric data. So but I will not go through that, but there is such a canonical lift. And now again, we look at the same vector bundle, the vector bundle of holomorphic sections over the fiber, and we have the norm defined as before. And now I can compute the curvature of this. So the theorem says that the curvature is positive, but now I can compute the curvature. I can write down an explicit formula. So first I define a function c of phi, which is equal to this. So here I take d bar of phi on the total space and I raise it to the power n plus one. And here I take it, raise it to power n and I wedge it with this. And the quotient between this form and that form is called c of phi. It's going to be some non-negative function. And then we have this formula here. The curvature is explicitly given by this operator. So I take... Yeah, so I introduce u1 is the... is this the Cudela-Spenser form. It operates naturally on the form u. I get u1 and I take the... the telemetric defines the Laplace operator. I take this thing here, the Laplace operator, apply it to u1 and et cetera, et cetera. So that's what the theorem says. It's an explicit formula for the curvature. So why is that useful? Well, this is useful first. So this is the formula. So if we assume now that i d d bar of phi is greater than or equal to zero on the total space, then this will be non-negative. So assume now that the curvature is zero. Then both of the terms will have to be zero because both of the terms are non-negative. So c phi must be zero, and u1 must be zero, which means that kappa must be zero. So the conclusion of this is that the canonical lift is holomorphic. So the vibration is trivial. We can use this holomorphic vector field to trivialize. You change the vibration by the flow of the field. You make it into a trivial vibration, and you can also do it in such a way that all the metrics and everything fall over long. So you really get the situation that you asked about. It's really this trivial situation in disguise. It's a trivial vibration and the line bundle and the metric they all are constant on the fiber after a holomorphic change like this. Here. Yes, if this vector bundle has zero curvature, then both... I have a line bundle L over this space here, and then I push forward the line bundle, or rather the n forms with values in the line bundle. I push it forward, I get the vector bundle down here. If that vector bundle has zero curvature, then everything has to be trivial. Everything has to be trivial. So I think this is related to Torelli-type theorems. But let's come to this later. This is a little bit more general so far here. So this is about any positive L here. Sorry? Yeah, so that's what I'm coming to next, actually. So in the special case now, so now we assume that all of the fibers have positive canonical bundle now. So for instance, if they are one-dimensional, they are Riemann surfaces, positive canonical bundle means that the genus is greater than two. Then I can use that as my L. The previous theorem worked for any L. But now I can apply it for the line bundle, the relative canonical bundle, which is a line bundle on the total space that restricts the canonical on each fiber. I can apply the theorem to that. And in that case, there is an argument by Schumacher. I will do that quickly also, which the conclusion is that in that case, if I choose the phi to be the Kellr-Einstein potential on each fiber, then the C phi will be positive. That's what I want to say here. So IDD bar of phi will be positive, in that case, automatically. So I don't choose, I choose the curve like this. I choose the curve for each xt. I take the Kellr-Einstein potential. Here is another Kellr-Einstein potential. And I, so to speak, I put them together, and then it will be automatic that the variation with respect to t will also be subharmonic, so it fits into the theorem. And this is due to this theorem of Schumacher. That's a non-trivial fact. So we can apply the theorem, and we can get that this space here has positive curvature. So now I put in... So here I have like n forms with values in the canonical bundle. If you think of the case when n is equal to 1 so that the fibers are Riemann surfaces, these are the quadratic differentials. So then it's getting closer to this business, right? And actually, let me spell this out here. So the Cordera Spencer formed, they lived in this space, and this space is isomorphic, too. If you, it's isomorphic to this, n minus 1, 1 forms with values in the anti-canonical bundle. You take a tensor product with that, and you will get that this space is isomorphic to that. This is not entirely trivial, but it's not the deep fact, it's just the computation that this space is actually equivalent to that. And then if you take duals, you will get this space. Here I have hn minus 1, 1, and here I will get h1n minus 1. And then I will say that the space where the Cordera Spencer form lives, that's the tangent space of the Teichmühler space.  So I can look at the Teichmühler space of canonically polarized things in some diffeomorphic class. Yes, so far. So after this point, we have arbitrary dimension. But now the next line I take n equal to 1. So now we have Riemann surfaces. We have families of Riemann surfaces. And then you get that this space h1n minus 1 becomes h1 0, which is hn 0. So for n equal to 1, it becomes this space that we knew something about. We don't know anything. Those spaces, my theorem does not apply to those, but it does apply to this one. So it's okay when the fiber dimension is 1. And then you can think of this, it's the bundle of quadratic differentials. You can think of that as the cotangent bundle of Teichmühler space. And the fact that this has positive curvature at the Teichmühler space itself has negative curvature, which is all first theorem now. And if you look at the explicit formula that I had, it's really exactly, you can translate the formula and you get Scott's formula in this case, when n is equal to 1, and you choose this line bundle on those metrics, et cetera. But you still have to do some computations because if you look at it like this, Richard said that it looks a lot like Scott's formula, but it looks a lot like Scott's formula if you know a lot about these things because formally, you still have to do some computations in order to translate this, too. But it's really the same formula in that case. So if you want to, you can view it as a generalization of what he had. Yeah, to end with something very quick again, which is related a little bit to what you said before about plurigener, et cetera. So we still have a non-trivial vibration. But I don't assume it's a vibration now. So I assume it's just a surjective map. So I don't assume that it's a submersion or anything. So it means that I have things like this. I have a total space here. I have a map P that goes down to some base, B, it can be higher dimensional now. And mostly, it will be a submersion. So the fibers will look like this. But at some points, there will be singularities if it's not a submersion that may have singularities. So what can we say in that case then? Well, I'm maybe a little bit ahead of myself. We have a notion of Bergmann kernel for such things like we had in domains in CN. But the Bergmann kernel will now, if you see, it will depend on choice of trivialization. And it will actually not be a function, but it will be a metric on this bundle. The Bergmann kernel, in this case, will be a metric on this bundle, the twisted relative canonical bundle. And so this is defined, the way I did it is defined when you have a smooth vibration, the Bergmann kernel metric. And then in joint work with Mihai Porn, we extended that to only surreactive maps. So if it's just surreactive, then it's mostly outside the sub-variety, it's a submersion. So we can take the Bergmann kernel metric. But now the theorem says that we can extend it to a singular metric on the total space. So we get a singular metric of positive, no, of semi-positive curvature on the total space. So the Bergmann kernel metric defines a singular metric of non-negative curvature on this bundle. Bye. I started with a phi, which was a metric on L, but now I get another metric. Yes, which is not good. I should have called it something else. Ah, sorry, sorry, sorry. Okay, so I was right. So I allow also, I actually allow the original phi to be singular. So I assume that there is one fiber that has finite L2 norm on, there is one fiber on which there is a section that has finite L2 norm with respect to this original phi. Then this metric, the Bergmann kernel metric will be, will not be identically zero. And it will define a genuine singular metric of non-negative curvature. That's how it was. Yes, yes, yes, yes. Yeah, something like that, yes, yeah. Yeah, I think so, yes, exactly. Well, I don't claim that it should be, that there should be some L2 condition on every fiber. I say that there should be some fiber over which there is a section that has finite L2 norm. No, no, phi is defined, phi is defined over the total space. Phi is defined over the total space. Yes, so I start with a metric, I start with phi, which is a metric on, which is a metric on L. And then I get the Bergmann kernel, I get the phi Bergmann kernel, I get the new metric, which is not a metric on L, it's a metric on the canonical, twisted canonical plus L. So I start with a positive metric on a bundle and I get a new positive metric on a new bundle, on the twisted bundle. I need to have a metric on L to begin with, yes? I think so, yes, yes, yes. Yes, I think in that case so. And it's also, you can apply it to, say, elliptic vibrations on a codera. So you can have multiple fibers, for instance. And then you will have also minus infinities or minus infinities on the single fibers. Well, but the point is somehow that if the morale of the theorem is that if L is positive, then this is positive. So the relative canonical always gives something more positive. So somehow, one consequence is that you can start with, say, the canonical here and then you get twice the canonical here, then you can feed in this one here, you get three times the canonical and you get positive metrics on all multiples of relative canonical bundle this way. For instance. What? Yeah, then it doesn't work. So this theorem is mostly interesting when you have some fibers of general type or something like that, yes? Well, unless L is very positive. L is very positive. That there should be a section on some. Yeah, a section. You have to assume that. Because otherwise, I mean, the Bergmann kernel is defined in terms of supremum no sections, et cetera, or something. If there are no sections, there is no Bergmann kernel. Yeah. Yes, yes. But the remarkable thing is somehow that you need a condition only on one fiber to guarantee this. And then you will get something for the whole thing. Yes, so for instance, you can use this somehow or there are variants of this you can use to construct because the invariance of plurian is very much. So maybe I think my time is running out here. But the invariance of plurian is very much tied to the construction of metrics. You want metrics on M times the relative canonical bundle. This line, M is some large, well, maybe not even large, but you want to have metrics of non-negative curvature on this. And this somehow is one way to construct such metrics on this bundle. And once you have positive metrics there, you can apply the Savataki-Gorshi theorem to extend things from a fiber to other fibers. So I just end here by saying that this was extended by Pohn and Takayama who showed that even in this case where you just have a subjective map here, you can take, you can still take the direct image of this thing here and you get a sheaf in general and not a vector bundle, you get a sheaf. They defined metrics on, it's a coherent sheaf. You define metrics on coherent sheaf and they get such metrics with positive curvature or non-negative curvature. And this somehow, this extends, but this gives a metric approach to a theory of a feedback on weak positivity for vector bundles. But that will go too far and I know too little about it, but feedback has a notion of weak positivity for such direct image bundles, and this gives a metric version of that. Because algebraic geometries, they don't speak about positivity in the terms of some curvature tensor being positive. They say that it means that there are sections of something or the other. But here you get genuine such thing. And then finally they applied this to the Itaka conjecture, but I don't think, so this was applied by, this kind of thing was applied by Junyang Xiao and Mihar Pan to prove a special case of the Itaka conjecture for codera dimensions assuming that the base then was the torus. Then they could use those metrics to prove it, but I will not, I don't have time to go through that, so I'll stop here. Thank you.


Hi everybody. Thank you for being here. My name is Sam Utney. I'm the Managing Director of Impact Hub NYC and I'm here to talk to you about a concept that is a very exciting concept, but it's about 2,000 years old. And it's something that I think may actually be the key to the modern innovation, a new model for impact innovation. It's the idea of the marketplace and the marketplace where people come together, where they exchange ideas, where they work together and build a sort of local ecosystem. And what we're doing in New York at Impact Hub NYC is introducing something that we're calling Impact Bizarre, which is a live marketplace for impact innovation. And the idea is that anyone with an idea can come to one place, some idea that they had stuck in the back of their closet that they never thought they might pursue in their lives. They can come in and be met with the tools and resources and guidance that it takes to get a business off the ground or push it to the next stage or actually just sort of test it to see if it has something. It's mentorship, office hours, classes, workshops, lunch served daily, yoga in the morning. We'll have inspiring talks by founders and best practices during lunch. And it's a place where you can simply have someone hear you and hear your idea and give you some feedback and guidance. It will be open Monday through Friday, 9 to 6 p.m. and starting later this month. We've brought ourselves to a state of isolation. We're so connected through digital media and through social networks that we consider ourselves very connected. But as individuals and as entrepreneurs and as innovators, we're extremely isolated. And that can be incredibly lonely. It's also the same state for the organizations that are trying to help entrepreneurs and innovators. They're operating in silos. They're trying to reach these communities. And it can feel like a treadmill trying to actually access the people that they're trying to support with their services and resources. So what we're doing is we're pulling together the best organizations doing great work to support entrepreneurs and innovators and bringing them out of their silos into one space to benefit from a larger aggregate community and let that community benefit from all of their support, let that community benefit from all of their services all in one place. The idea is to really bring together an ecosystem of services, tools, guidance, expertise to let anybody pursue ideas and bring a current business to the next stage. So here are seven reasons why I think Impact Bazaar is a new model for innovation. First, we're mapping the local innovation ecosystem all in one space. All of these organizations, all of these ecosystems exist in every city. Every city is a perfect ecosystem of services, mentors, teachers, entrepreneurs. But it's very difficult to find your right partner, your right investor, your right entrepreneur. We're trying to bring all of these together so that you can simply look up, turn to someone, find out how they're a resource to you and actually have access to them in one space. So we're actually mapping the ecosystem. The ecosystem works incredibly well here at SOCAP. All of these resources are under one roof. But even then, I probably have all of the sponsors for Impact Bazaar I could possibly need. I probably have investors. I probably have all of the entrepreneurs. But even then, I haven't properly been mapped to them. So what we're really focusing on is mapping the ecosystem. And every city has the opportunity to do this. Many organizations have the opportunity to do this. It's just trying to map it. This is a new type of public space. And that's really thinking about market places and the role that they've served in society for thousands of years. It's been a place where people come together and it's fully open and public. It's accessible to everyone. So what we're trying to do is create a space that is truly accessible to everyone. We live in a bootstrap paradise. All of the tools exist right now to build almost any idea. If you have some random idea, you can build a website for it. You can create an online store. You can actually create apps very easily. Everything exists to build almost anything for very cheap or even free. But what we don't have access to and is what's really difficult, especially for a first-time entrepreneur, is that layer of guidance and expertise that sits on top of the tools and resources. So what we're trying to do is build a place where you can come in with this idea and have somebody listen to you and have somebody give you feedback and tell you that idea might be a great idea. But you should try reducing it to this simpler version and maybe it starts as an email list and not a full website. Or maybe you should just talk to that person because that's your right resource. Or maybe you should consider partnering with this person or that person. Or maybe you're not a non-profit.  So giving a layer of expertise and proper sequencing of an idea and understanding this vast world of resources and tools through guidance and mentorship. Part of what makes this a real ecosystem is and part of what will truly allow this to represent everyone is to have everyone's voice included. So this is about creating a space that is provided at a price and a level of accessibility that anyone can experience it. And this is part of why we're reaching out to sponsors and part of why our support from Squarespace is so important to be able to make this accessible at $10 a day right now and it will be free to many of the communities that we've partnered with to actually promote this to the New York City innovation ecosystem. Also, this should not only be accessible to the people who can pay $450 for a monthly membership at a co-working space. We run a co-working space. I'm not trying to put that out of business. In fact, I think that that will help our business, but this kind of space, these kinds of resources should not only be accessible to incubators and co-working spaces and people who attend conferences like SoCAP. This should be available to everyone. We're redefining success and building businesses like we build art. Success can manifest in many ways and not every business needs to be built and have the next $100 million IPO. It's perfectly fine to build a business that can sustain your lifestyle, be something you love to do, and allow you to live out your days doing something that's really a wonderful passion. Not everything needs to be scaled. So if you're happy with your business, we want you to be able to build that kind of business and be supported in doing that. Also, you should be building businesses and we should be building organizations that are like art, something that we want to sign our name to. If you're building a business, we want to encourage people to build something that means so much to them and they are so proud of that they would sign their name in the corner when they're done. That doesn't even need to have a business model to start, but if at the end of building that piece of art, they sign their name and somebody wants to buy it, that's a business. So we're encouraging people to build businesses in the way that they would build art, build something you're proud of, start over if it's not right, give yourself access at a price that isn't forcing you to follow through on an investment that you're so deep into that you can't turn back from. Individuals need companions on this innovation road. It's a really lonely journey building an idea. We need community and to operate in isolation is incredibly isolating and lonely. So what we're doing is trying to build a place where people can come together, but we're also trying to recognize that this is a journey and it's about the journey. Building a business shouldn't be about the launch of the business, it should be about enjoying the entire process of creating it. So we're trying to build a space where you'll enjoy building your ideas. Access is the Trojan horse and social good is the ambush. We're trying to put together a package of tools that is accessible that can build any idea. So by providing access to someone who has this idea buried at the back of their closet that they never thought that they would be able to pursue or at least not now and that they can come in and be met with all of these resources to get it off the ground. That's our Trojan horse. This is about bringing people in to pursue their passions and to pursue their ideas. The ambush is the reality that all of the conversations that we have, all of the context that we put this in, the entire lens that we view this through will be the social impact lens and it will be the new norm of creating businesses. It's not about bringing people in to create social businesses or impact businesses. It's about having a simple reality and recognition that every business moving forward needs to be responsible to its community and to the environment and to its stakeholders. So that should be the new norm. That's the only conversation that we'll have. So really just to sum this up, this is about creating a space. A marketplace or a bizarre is about creating a space and time and all we're really doing is saying that this bizarre will be available in this space at this time. But what builds the bizarre is the creation, is the community that gets involved in it. So the people who come together are what build the bizarre. It's not just the people between the stalls. It's the people providing the services. It's the people offering resources. It's the people filling needs. It's the entire ecosystem there. So if you'd like to be a part of filling this space and time, we invite you to join us later this month in Impact Hub NYC. You can join us there or at impactbizarre.com and I look forward to building this ecosystem with you. Thank you.


1. Talking About Family. This video is brought to you by the following English learning websites. Let's talk about family. Answering questions about your family. What are some typical questions people might ask about your family? How will you answer them? 1. Tell us about your family. Well, there are six people in my family. I have one brother and two sisters. My mom is a dentist. My dad is a teacher. Let's break that down into sentences. We use there are to indicate the number of people in our family. It's there are because the number is usually plural. This is the most common way to start talking about your family. We can also say I or we have five people in our family. 2. How many brothers and sisters do you have? I have one brother and two sisters. What number are you? I'm number three. I don't have any brothers and sisters. I'm an only child. Note, we do not count ourselves as a brother or sister. If your parents have four kids, you have only three siblings. Siblings are brothers and sisters. Let's describe this family. Pretend you're the young girl in the middle. Family description. There are seven people in my family. My mom, my dad, two brothers, two sisters, and me. I'm number three. I have one older brother and one younger brother. I have one older sister and one younger sister. My sister is the oldest. My baby brother is the youngest. Notes from the picture. In English, we don't have to specify older brother or younger sister, but we often do. Sometimes the youngest child is called the baby regardless of his or her age. Giving more information about family members. You can describe your family members briefly by telling what parents do by saying the names and ages of your siblings or their grades in school. Do not tell the ages of your parents. My mom is a lawyer. My dad is an engineer. My sister, Katie, is nine years old. My brother, Ryan, is in second grade. If you're a parent, you can say, I or we have three children. One son and two daughters. The oldest, Mia, is 18. She just graduated from high school. The youngest, Brianna, is 12. She's in sixth grade. And the middle child, Cameron, is 14. He will start high school next year. If you're married, you can also describe your spouse briefly. My wife works for IBC. She's a general manager. Or my husband is an accountant at Heady Industries. We don't have any kids right now. You don't have to say this unless you want to. Be careful. Some people don't like to be asked a lot of personal questions. In English, it's okay to ask general questions about someone's family, but don't be nosy and ask for too many details. Avoid asking questions like these. Are you married? Why not? Do you have any children? If they want to tell you, they will volunteer the information. Okay, tell us about your family. Hope you enjoyed this video. You can find more information about this topic by clicking on the links in the description below. Talking about family, people, and relationships. Free English lessons. Thanks for watching. For more information, check out the websites below.


Good morning, folks. Steve Rhodes coming to you live from the shores of sunny and a very pleasant Delray Beach, Florida. This year, Lebanese update and a slightly mixed bag. The mix coming from the trannies, which are up three points. So basically flat. Other US indices trading to the downside. As of 11 o'clock, dollars off 137 S&P down 13. NASDAQ is on a point. Russell's off 12. Semis are down three points. You got gold off six bucks. Silver down 29 cents. Slices recruit off 29 pennies. Natural gas off six cents. A 30-year treasure down 14 ticks. Trading out at 108. 27. Let's try to figure out what all that means by looking at that nine panel. Market update chart. We've got the ESMini upper left-hand side. We've got the ESMini right now testing support. Support here is the bottom of its profile. That's at 43.33. A price closed below 43.33 today. It would suggest a run to 42.55. 42.55 fails, then down to 42.35. 50. Spot follow tonics is still above its 50-day exponents moving average. That puts pressure to the downside inside the S&P 500, the ESMini. If we take a look at the NQ, the NQ firmly trading below its bearish structure, the center of its bearish structured daily profile, that typically signals to move all the way back to the bottom of that profile. That's up at the 14. Down at the 14.676 area. I don't see anything else as a support area for the NQ. If we take a look at the US dollar index, it did find resistance at the top of its daily profile. That was at 106.42, moving slightly lower out there, but not having a substantial impact in the markets. Gold is going to complete a TD9 count top today. So long as gold closes above 1941.50. A TD9 count top is going to complete today inside of silver. Yes, it was bar number nine, but it has a new profile that's attempting to form. I've refreshed this a couple different times. Pretty solid as we speak right now. So support inside the silvers at 22.46. Of course, we won't have confirmation of this profile until this evening or tomorrow. We take a look at the LightSuite crude. Not doing much trading with inside its bullish structured daily profile. Well above that center says that LightSuite crude wants to make a move to 9248 or 9125. We take a look at natural gas. It's now trading below 0.618 retracement of its last leg up. Next area of support would be the 0.786 area and that's at 2.94. Below that, we're getting all the way back to the bottom of that swing point. That's a swing point from September of September 26th out there. That range is from 276 up to 290. That's the November contract. We're going to roll that to December here. We take a look at the 30 year treasury. A close today below 10829 says it's headed even further lower. That's just by the by the D point support level. 10829. Folks, stay tuned for the Trader Zed Show. But if you have to start your Thursday, please have a terrific one. Thanks a lot for joining us. We'll look forward to speaking with you again soon. Take care now.


So beyond Light and the beyond, ViDuck is not long been aired. Today we quickly cover what in my opinion are the best and most important parts. Has it gone guys? My name's DPJ and if you enjoyed the video leaving a like, who helps out and if you like what you see I want to see more, be sure to subscribe. Ok so let's go people. So firstly, anybody notice how much weight Luke Smith has lost? I mean jeez dude looks like he just shot out of the camel. But seriously, good game. So it seems now we have Kabul allies, as we see here Savala, Osiris and Tukobar peace on what looks like the same side. We next up see and it's explained that we have to work with the stranger and with that darkness to stop it. Obviously talking about Stasis here, which is what we already know. We then see a titan with a fridge on his back and his secret cold and his belt confirming and all and beyond is returning. I wish. So we then see Europa and it's said to be huge, cold, desolate and beautiful, much like a polar bear's arse. We then see two guardians taking a jug, cyberpunk helmet easter egg confirmed here. We then get a glimpse at what lies under the ice and it hints at secrets and they state they can't wait to see what we find here. Let's just hope it's more than a lost sector. We then see why I believe to be a loading in area to the new raid, the deep stone crypt. We then get a look at a dark mod inventory and wow, I actually like this all jokes aside, this is going to be amazing and if you notice when this subclass changes, we get a gentle glow that changes with it. We then get a quick glimpse at a few of those Stasis subclasses and gameplay with a few details and fragments within those Stasis subclasses. Arc and now we've got Stasis. The idea for Stasis all really came back from the gameplay idea of freezing someone. That was kind of the theme that everyone's kind of rally behind. You know, Dima's an amazing concept artist had some images that really kind of put us on the right path. What really was landing with that was the more crystalline notion. So when we say cosmic ice, that's kind of where the cosmic comes in. Once you freeze it solid, I'm able to hit them again and shatter them in pieces. The pieces break apart and explode and those sharp shards that can damage you. So all that kind of came together when we landed on that theme. Stasis is going to not only change the way that you can attack or approach combat, there's also some really great ways that you can upgrade it. Then you start getting into like the more interesting parts, things that we're calling aspects and fragments, which are additional ways to modify your subclass. Aspects are a little bit more potent and then the fragments are the things that are class agnostic, but depending on what your class is and depending what your aspects are and how you want to play, you're probably going to be starting to select different ones in there. This is just the beginning for Stasis. We're going to continue to expand on it. We're just excited for players to get their hands on this. They're then going to talk about how the audio for Set Stasis and Ice was recorded and well, it includes a breast pump. Okay then. Everyone on the team blocks out about a week where we can say, okay, you're going to go out into the world, microphone recorder, record anything that reminds you of cosmic ice. That gives us the palette that we can build the eventual sounds out of. I found personally that the best way to do it was at night, but doing scream screeches and blood curdling yells is a little scary at night. Then I had a really rumbly stomach and that also was recorded. There was also a breast pump. You have to make use of what you got. We then get a great shot at some new exotics as well as explanations behind some of them. Take a look. See if you noticed that quick glimpse of Omnigul strike here.  You can actually have that on top of the arc sole so you can be your own little mini firing spot you built for it. Another one we have is the laments. It uses up your sword's energy to give yourself a new combo that ends up in a big spinning slash. Probably the largest selling point for a lot of people is that it slices right through barrier champions. I think the largest draw from us people is actually going to be the fact that it is a chainsaw sword. Maybe. Yeah. For Beyond Light we really wanted to create exotic armor pieces that formed a key part of your build around which all the other parts of your build could revolve. For example the Titan gets the Icefall Mantle which is a set of exotic arms that looks like it is crafted from golden age tech.  The Warlock Exotic is Necrotic Grip. If you are facing a wave of thralls running at you you can nail them with your melee attack and it starts to burst and sort of cascade through the whole group. Also as we know the Cosmodrome is back and it's said to be bigger than ever. A friend who hasn't tried it out, here he ends for free players. Last year when New Light launched we brought back a small portion of the Cosmodrome. This year we're bringing back a much larger portion of the destination. It takes some of the experiences that started with the original. We then see the Cosmodrome's new vendor, his name is Shaw Han, rocking those young Ahamkara spine gauntlets. Next up we see Uldren and it's said he doesn't actually know what he's previously done and while his introduction at first gave me goose bumps, check it out. The Cyrus is in trouble and of course you're his only hope. We finally catch up to what we saw at the end of Forsaken where we saw Uldren being brought back to life by a ghost. Uldren who now refers to himself as Crow, he doesn't know what he did. The slate's been wiped clean when he was resurrected as a guardian. We know what he's done and we know what he could be capable of doing so now we're going to spend some time watching him go back and forth. And beyond this people is literally what this season is all about what it will consist of. Take a look. In Season of the Hunt we're partnering with the Crow and Osiris to take down the high celebrant. It's creating these crypto lifts around the system and those crypto lifts are attracting Alixian Cabal and corrupting them. So Zebu Arath is essentially corrupting herself and Armi and it's our job to put a stop to it. I'm really excited to see Zebu Arath flesh out more and to find out more about her relationship with Savathun and what that means for Year 4 of Destiny. Savathun has been placing Dominoes and at the end of Year 4 she's going to knock down the Dominoes. We're going to see what she's doing up to and so this year she's putting the last pieces in place. And well guys we're at the end of the video looking at the world map and the future or the near future. We see what Beyond Light comes with watch through to all players with dates and times as what's to come before the year ends. And on that note guys we are done just a quick roundup of what the latest viaduct offered. I hope you enjoyed it. If you did leave me a like really helps out and if you do want to watch the full thing I will link it with in the video description but guys thanks as always for stopping by. Hopefully you enjoyed the video and hopefully I will see you on that next one.


The first thing that the that the NIV does is it attacks the gospel and the person of Jesus Christ. Look at Hebrews chapter 4. Remember that God's rest is is being used as a picture of salvation in Hebrews chapter 4, but in Hebrews chapter 3 we're comparing the wilderness, the people in the wilderness for 40 years, not being able to enter into the promised land is a picture of not being able to be saved through unbelief. Let me read you Hebrews chapter 4 verse number 5 and verse number 6 from the King James Bible. Look what it says. It says, And in this place again, if they shall enter into my rest, talking about salvation, seeing therefore, it remaineth that some must enter therein, and they to whom it was first preached entered not in because of, here it is again, how many times we have to say it, unbelief. Why is any man going to go to hell?   That's why. But look what the NIV says. So we just see this again and again and again. God's rest is salvation and why didn't the people go into the promised land because of unbelief? Why aren't you going to be saved? Unbelief. Unbelief. Belief. Unbelief. This is just over and over and over. Now look at the NIV in verse number 5 and it says, And again, passage above he says, They shall never enter my rest. Verse 6, Therefore, since it still remains for some to enter that rest, read along in your King James Bible. And since those who formerly had the good news, that's what modern church is constantly called the gospel, by the way, the good news. Proclaimed to them that did not go in because of their disobedience. Whoa. It says it changes unbelief to disobedience. What is disobedience? Disobedience. If my children are disobedient to me, you know what that means? It means they're not doing what I say they're supposed to do. You see what we did here? We just turned the gospel into workspace salvation in one verse in the Bible. If you're disobedient, how many times have you heard that out soul winning? Believe in Jesus, but you have to be obedient. Look, this is not harmless because people believe this. False prophets, false teachers, they're getting up and they're using this verse to attach works to salvation. Go to Mark chapter 10, verse 24. Look, folks, I can't give you all the examples. I can't give you all the examples where the NIV is discrediting the gospel, is discrediting our Lord and Savior Jesus Christ. I can't give you all the examples. I can just give you a few. Go to Mark chapter 10, look at verse number 24. And Jesus looked around about and said unto disciples, How hardly shall they that have riches enter into the kingdom of God? And the disciples were astonished at His words, but Jesus answered again and said unto them, Children, how hard is it for them that trust in riches to enter into the kingdom of God? Look, He's saying it's hard for them that trust in riches, because what do you have to trust in to be saved? Believe on equals trust, folks. You have to trust in Jesus. And if you're trusting in something else, it's going to be impossible for you to get saved. This is what Jesus is saying. He's saying it's going to be hard for somebody who trusts in riches to get saved. He didn't say it's impossible for a rich person to go to heaven, but it's easier for a camel to go through the eye of a needle than for a rich man to enter into the kingdom of God. Why? Because of the verse before, they're trusting in riches, folks. But look what the NIV does. So why was it, why did Jesus say it was hard for that man to go to heaven? It was hard for him to go to heaven because not because of work that he had to do, but because what he was trusting in. You have to remove, look, you have to repent. Meaning, what does repent mean? It means to change your mind. You have to repent.  That's it. That's why. But for somebody that's trusting in riches, Jesus is basically saying, it's impossible if you're trusting in riches to get saved. And that's the truth. But let's look at what the NIV says. The NIV says in verse number 24, where the Bible says, how hard is it for them that trust in riches? Here's what the NIV says. The disciples were amazed at, this is the NIV. The disciples were amazed at his words, but Jesus said again, children, how hard is it to enter the kingdom of God? Inverse. The NIV here is saying that it's hard to enter into the kingdom of God. Look, is it hard to receive a gift? It is not hard to enter into the kingdom of God. Few will enter, but it's because they're trusting something else. It's not hard. They took out the trusting part. They took out the trusting in riches part of the Bible. So the NIV makes salvation. It adds works to salvation, and it makes it hard. It makes it hard to be saved. First Corinthians chapter 1, verse number 18. Look at your King James Bible. The Bible says, for preaching of the cross is to them that perish foolishness. But not to us which are saved, it is the power of God. I have those words which are saved underlined in my Bible. Because here's the thing folks, you're either saved or you're not. When you believe on the Lord Jesus Christ, you have everlasting life. It says in John chapter 3, verse number 36. It's in a moment. And then you're sealed by the Holy Spirit. It says in Ephesians chapter 1. It's in a moment when you trust on him. It's done just like that. You are saved or you are not saved, depending on whether you have believed or you are still in unbelief. Here's what the NIV says. Here's what the NIV says. It says, for the message of the cross is foolishness to those who are perishing, pretty close. But to us who are being saved, it is the power of God. The NIV turns salvation into a process. How many people have you talked to, soul-owners at the door, who believe that salvation is a process, who believe that not only do you have to, you know, have faith, but you have to go through this process of living this life and living for the Lord and following the commandments they'll say. Just look, the only way salvation is a process is if you have to work to get it. You are not being saved. You either are saved or are not saved. The NIV destroys the Gospel, is what I'm trying to get you to understand. It adds works to the Gospel. It makes salvation hard, it says. And it makes salvation this process that we must get through in our lives. This is workspace salvation.


Archeosomes are liposomes derived from archaea that exhibit high pH and thermal stability and can induce strong immune responses in mice. The new class of adjuvants developed by the authors, comprising a sulfated saccharide group covalently linked to an archaeal core lipid, sulfated S-lactosalarchyl SLA, mixed with uncharged glycolipid, lactosalarchyl LA, can be easily synthesized and retain strong immunostimulatory activity. The authors demonstrate the safety of SLA-LA archaeosomes following intramuscular injection to mice and evaluate their immunogenicity in vivo distribution and cellular uptake of antigen, ovalbumin, encapsulated into them. They find that semisynthetic sulfated glycolipid archaeosomes are a safe and effective novel class of adjuvants capable of inducing strong antigen-specific immune responses in mice and protection against subsequent B-16 melanoma tumor challenge, with the recruitment of immune cells to the injection site and subsequent trafficking of antigen to local draining lymph nodes being a key step in their mechanism of action. This article was authored by Bassler Catch, Felicity C. Stark, Umar Iqbal, and others. We are article.tv, links in the description below.


This research suggests that cancer cells release macrovesicles containing genetic material that promotes tumor growth and metastasis by stimulating angiogenesis. This article was authored by Kim Yoon-kin, Choi Dong-sik, Kim Ji, and others.