Thank you very much for the chance to speak. Yeah, so today I'm going to talk about a project that is extension of my work with Owen Guilhem and his last talk, but maybe focus on a particular example and I think a relevant example for maybe some physical applications. So let me just kind of remind you of a big picture that came up in Owen's talk, which is that the observables of a quantum field there define a factor. So he talked about kind of a very nice simple quantum field theory, the Beta Gamma system in two complex dimensions and studied its factorization algebra. And we saw that, so for instance the Beta Gamma system, and we saw that we were thinking about symmetries of a QFT, which themselves were also measured by some factorization algebra. This was what he called the quantum and classical currents. And symmetries of a QFT implemented themselves as a map of factorization algebras to the observables of a factorization algebra like that. And this was this version of the Notre map here. So in my talk today, my talk I'm going to show how these higher dimensional current algebras, current algebras, which we choose to represent this factorization algebras most of the time, actually appear themselves as the observables of some quantum field theory. So these appear as observables. So I'd like to distinguish this from their appearance in the previous talk in which they appeared as actual symmetries. Now I'm saying they appear as honest observables of a quantum field theory. And I'm going to choose to focus on a very specific example, but hope to maybe give a general picture as well. So first I'd like to maybe state the kind of object that I'd like to focus on. And this thing kind of mysteriously came up in no one's talk, but maybe I'll say a few more words about it. But for any dimension, this is a complex dimension. So this is over C, say D. And any element, theta, this is going to be a symmetric polynomial of order D plus 1 on G. And it's also going to be G invariant. One can define a non-trivial extension of Lie algebras, actually DG Lie algebras of the following form. So you take your Lie algebras G and you consider tensoring with the commutative algebra that basically looks like the space of sections of punctured affine space. So this is punctured algebraic affine space in D dimensions. So we have some non-trivial extension of this form. I'll label it by D and theta like that. Except you need to do something really, really important. You don't just want to consider sections or functions on derived affine space. So these are sections of the trivial bundle, right like this. Just functions on punctured affine space. If you just leave it like this, there's no interesting non-trivial extensions. What you really need to do is look at the derived space of sections. So this Lie algebra was first considered by Owen mentioned in the work of Farente, Ponyon and Kamprana, and they talked about a lot of really nice relationship between this extension and the modulate of G bundles in arbitrary dimensions. And for me, I really want to think about it as kind of the right higher-dimensional analog of the affine algebras, affine cat's moody algebra in CFT. So this algebra will come up and play a fundamental role in my description of certain algebraic observables, but I just wanted to kind of recall this object was floating around in the background during Owen's talk. And maybe I should say that maybe I should write down the formula. So the formula for this extension definitely came up. So the corresponding two-coast cycle, the two-coast cycle just took a tuple of elements inside of this algebra here, this Lie algebra. This is a DG Lie algebra now and mapped it to this higher residue like looking class. So it looks like you use the Lie algebra polynomial to pair off the algebra parts. And then you apply this higher dimensional residue along the 2D minus 1 sphere to that form there. So we have a really explicit model for this. DG Lie algebra has an L infinity algebra if you like given where the D plus 1 operation is given by this formula there. So I'm going to tell you how this DG Lie algebra actually appears inside of some higher dimensional gauge theories, but to give you a flavor for the style of higher dimensional gauge theories I'll talk about I'll first give an example. So these higher dimensional gauge theories are higher dimensional theories than any mention or what I want to call holomorphic field theories. So just as an example, there's a very natural field theory that I want to call holomorphic. And this is holomorphic Tern Simons theory on a Kalabiya 3-fold called that Kalabiya 3-fold x here. And I'm going to let omega be the non-vanishing top form, holomorphic top form. Then the fields, the fields of this holomorphic Tern Simons are just going to be 0 comma 1 forms on x with values and similarly algebra G. So it looks very similar to Tern Simons, except I'm not just looking at all 1 forms, I'm looking at 0 comma 1 forms. In the action, the action is very familiar as well. So I take my ordinary kind of Tern Simons action right like this, 1 half a dA plus 1 third a bracket a a like this. And I wedge with the holomorphic 3-fold. So here I've chosen a non-degenerate pairing on my lead algebra G to write this down just like you do in Tern Simons. So why do I want to think about this as a holomorphic theory? Well, its solutions to the equations of motion generically depend on some interesting complex structure on the underlying objects involved. So for instance, this example, the equations of motion exactly pick out the holomorphic G bundles. In this particular description, I'm just describing deformations of the trivial holomorphic G bundle on x, but you can do this near any holomorphic G bundle as well. But this is the general kind of flavor of theories that I have in mind when I say holomorphic field theory. We saw another example. So there's a slew of examples in physics. And many will come up during the talks this week. But in physics, holomorphic field theories generically arise as twists of many super symmetric field theories. This is kind of a generic fact for any super symmetric field theory. And Owen actually did an example of this. So for instance, this beta gamma system he talked about on C2, say, where the complex manifold is C2. This came from a really simple super symmetric theory that's n equals 1 caromultiply, free caromultiply. And the example I'll focus on today also arises in this way. So maybe I'll state my kind of the main result. And then we'll get into the details. So theorem. So the type of super symmetric theory I'll consider is 5D n equals 1, super Yang-Mills theory. And the first claim that I won't spend too much time on is that this theory admits a twist to a 5D gauge theory. Maybe I'll say holomorphic, put holomorphic in quotation marks for now, gauge theory on C2 cross R. And I can actually put this gauge theory on this manifold C2 cross R bigger than equal to 0. So now this is a 5-manifold boundary. And if you don't know anything about super symmetric field theory or super Yang-Mills, you could just start with this description of this 5D holomorphic gauge theory. So itself has a nice mathematical description. There's some natural objects that pop out of the quotient motion here that I'll talk about in a minute. And by holomorphic, I'll just say, it's kind of holomorphic in the maximal sense here. So it depends holomorphically in this direction, the C2 direction, and then it has some topological direction in the transverse direction. So that's kind of what I mean by holomorphic. So it doesn't exactly fit into the style that I showed here. But what I show is that there's a boundary condition. So that is a theory on C2 cross 0. It's a boundary condition of this 5D gauge theory. So now it exists just on the C2 guy, whose boundary observables. So the observables on C2 are equal to the higher dimensional cat's moody current algebra. That Owen introduced in his talk. So this higher dimensional current algebra, as we just kind of recalled up there, this depends on, sorry, so for some element. So to really specify what I mean by cat's moody, I need to specify some degree 3 polynomial, some 3G dual inside of G there. And I'll say what it is for this example. So you can think about this as being kind of like a higher dimensional version of the level in ordinary cat's moody. So what it's saying is that the, what this result is saying is that the boundary to some 5D gauge theory there appears a higher dimensional cat's moody at some non-trivial, with some non-trivial central extension labeled by this theta. And I'll say what that theta is for this example later in the talk. So any questions on this statement so far? So that's the general direction we're going to go in. What if it could be usual topological conditions in dimension three and one where it also uses homework structure? Yeah, so I'll recall that. The second side, yeah. What's that? But in the usual kind of classical story, it says there's no complex direction towards the topological side, but it's on one where it's hallowed. Exactly, yeah. Yeah, so here it's not even topological, you're right. Yeah, there's still some really, some holomorphic. But even in, even in turned simons, there's kind of a critical version of turned simons that is not topological. And even there, you do see kind of critical level cat's moody. So I'll say a word about, yeah, we all recall that. So I do like to think about this as the kind of higher dimensional extension of a very well-known correspondence between Trin Simons theory and WZW, Cairo WZW. And I'll say a few words about that now just to set ourselves up. So example, this is Trin Simons on, well, Trin Simons makes sense on any three-manifold. And I'm going to do it on a three-manifold with boundary of the following form. So here, sigma is some Riemann's surface, that. And of course, we know what the fields, with respect to this decomposition, I can write as the following. So a looks like az dz plus az bar dz bar. So these are just local coordinates on the Riemann surface, z and z and z bar. And I'll write t for the topological direction, or for the r direction, plus at dt, where all the components are just smooth functions. And at t equals 0, at t equals 0, there is just a boundary condition. And what it does is it takes A. So when I evaluate at t equals 0, of course, this component goes away. And the boundary condition specifies, it projects onto one of the two components here. And the one I'll choose to project to is az dz. So I'm only remembering the kind of holomorphic component of the connection on the boundary. And it's this boundary condition that gives rise to the Keirall WZW model. So maybe I'll just say a very, very modest extension of this, which is the formalism that we like to work in. We can kind of reformulate this, reformulate in the BV formalism, which doesn't really buy you much new kind of structure in this 3D2D example that is very relevant for the five-dimensional 4D example that I've stated in my theorem. So I'll just say it in this Tern Simons case. The fields, the fields in Tern Simons, well, they just look like the diram forms on the three manifold with values in the Lie algebra. And I can write that with respect to this decomposition in the following way. So it looks like, so maybe I'll just write that. So it just looks like star forms sigma cross r bigger than or equal to 0 with values in the Lie algebra. And since I really want gauge fields in degrees 0, I need to shift this down by 1. And then with the complex structure on the Riemann surface, I can write this as 0 star forms in sigma tensor with star forms just all forms on r plus tensor G. So that's one component. And then I have an extra component coming from the holomorphic part in the Riemann surface direction. So that's 1 comma star forms on sigma, tensor forms on r, tensor G. And of course, there's a connecting map here that's just given by the holomorphic diram differential on the Riemann surface that maps a 0 star form to a 1 star form. So I can rewrite the, I'm just rewriting this diram complex in terms of this more complex notation, this holomorphic notation. But in this notation, if I write, so I'm going to write my new fields kind of as a, let me write them as like alpha 0 comma star and alpha 1 comma star. So I'm writing 0 comma star for an element up here and an element down there. The boundary condition that just extends that boundary condition to this full BV space of fields is really simple still. So it just says that alpha at t equals 0. So alpha, I'm just writing as this two component object at t equals 0 is exactly alpha 1 comma star. So locally, which if you wanted to look at, say, the local operators of Carvel WZW, this isn't really telling you anything more. This BV formula doesn't tell you anything more because locally there's no interesting higher cohomology for the local operators. So everything is still considering degrees 0 and we just have functions. The operators in the boundary just look like functions on this holomorphic connection there. But we'll see in the higher dimensional example, it's really necessary for me to remember the derived directions. So the higher dobo directions on the boundary. Any questions on this? So maybe just some remarks on this perspective. So some remarks. So in this BV approach, in our approach to QFT, developed by Kevin Costello and William, as I recall in the beginning of this lecture, the observables form a factorization algebra. So in particular, the observables on the boundary of transimans form a factorization algebra on sigma. So we get some factorization algebra on sigma. And locally, locally on sigma equals c, this recovers the affine cat's moody vertex algebra. And the factorization homology evaluated on closed surfaces recovers the conformal blocks of the vacuum cat's moody. So it's kind of what you would expect from this transimans WDW picture. We're not getting anything new there, but it's nice that it fits into the framework. And there's also the issue about level. So kind of a subtle issue is that if transimans is level k in the bulk, so classically, if you assume that we have a fixed invariant pairing and we're fixing the level to be k, then the cat's moody algebra has level k plus some shift. Call it kc. And this is the critical level. So on the boundary, naively, we'd expect just to see cat's moody at that same level. Cat's moody is also an object that depends on some level. But quantum mechanically, we don't see just the level k, but we see some shift in the level. And this is something that's generated really. If I was being careful here, I would put an h bar in front of kc. So this is really something that's a one loop effect. It's generated a one loop. And there's kind of a nice diagrammatic picture implementing this phenomena. And that's to consider the operator product. So if I put two local operators in on the boundary, this is my boundary Riemann surface. And we have this real direction r bigger than or equal to 0. This critical level is generated by some one loop diagram. And it's of the following form. So what you do is you flow it to the bulk via the propagator. And there's some one loop diagram that's really simple. It's a two vertex wheel. And you show that this thing is proportional to the critical level times some local functional fields that exactly incorporates the central extension of the Katz Moody algebra. So the sense of this thing is one loop, usually right. We keep track of h bar if we're careful. So this critical level is a quantum shift. I really want to stress that because there's a similar shift that happens in my example that I like to think of the critical level and appropriately contextualize in higher dimensions. My last remark is that there's also an extension of this boundary condition to what we call chiral boundary conditions for a wide class of 3D topological field theories that are labeled by a what's called a geometric object called a crown algebra. So these 3D TFTs will be talked about. So by the way, this work here, thinking about generalizations of this boundary condition for more general 3D TFTs is joint with Pavel Sifranov. And Pavel will talk about this example in much more detail in his talk. But I should say that the boundary observables in this case recover a lot of other well-known vertex algebras or factorization algebras, most notably the chiral differential operators and chiral Durand complex as well as many others that are kind of variants of those vertex algebras there. So I won't say too much about that just to stress the fact that in this kind of degenerate limit where I take a crown algebra to something like a vector bundle that lives over some manifold. And you can think about the 3D TFT as basically labeling maps from a 3 manifold into x together with some linear data like sections over the pull back of this bundle, roughly speaking. But in the case that x degenerates into a point, these boundary conditions like the chiral dw exactly become these chiral boundary conditions here. So it gives a nice kind of systematic relationship between CDOs and the cat's moody algebras, if you like. So yes, Pavel will talk much more about that later. I just want to say a word about it and how it fits into this setup. So now I wanted to move on to the main part of my talk, which is to introduce this 5D gauge theory that witnesses these higher cat's moody algebras on the boundary. So the input data I'm going to start with is x. x is going to be a complex surface, which I'm actually going to assume just for simplicity, it's globby yaw. So I have a top form, a degenerate top form. This condition is not necessary. It just makes the theory easier to write down. You'll probably see an obvious way of getting rid of this restriction. And the fields are going to look very close to a term assignments there, right on like this. So there's two components to the fields, a and b. So a, so I'm going to label x locally as z1 and z2. Those are going to be my holomorphic coordinates. And a is going to look like a 0, 1 form. So az1 bar, dz1 bar, plus az2 bar, dz2 bar. And there's a third component that labels what you can think about in the time direction if you like, but some other real direction, t. So here, all of the az bar, i, at. So these are all fields. This is a five dimensional theory. These are all functions, c infinity functions on x cross r. I could use any real one manifold, but I'm just going to look locally in the trans-restriction for now. And then b is very similar, except these things are all proportional to the top form, like this. And then similarly, I have a decomposition of this. And the b, c bar, i's and bt's are also just smooth functions on x cross r. The only way b's are different is they have this extra factor of the Klavier form. And then the action is really easy to write down. It's a trans-simon's type. Looks like this. So there's a kinetic term that looks like. So again, so g here, x is a complex surface. g is the same kind of data you get in trans-simon. So it's a ordinary Lie algebra with an invariant pairing. And I use that in variant pairing just like I do in trans-simon to write down the action. So that's the kind of ordinary kinetic term. d here just represents the Dorem differential on x cross r. And the interaction part just looks like b. So it's linear in b in the second component and brackets a with itself. And you don't use cubic plenum at all? It's cubic in the total sense. It's cubic as a function of both b and a. Yeah. Yeah. Yeah, b and a kind of play similar roles here. So I want to. So it's double the arches with get cubic and valent cubic. Yeah. That's right. Yeah. Does it transform the same way in the case of the transformation? The action. I just am wondering what you think. So the gate transformations are exactly. So I should say that the equation of motion, what does it say? You can work this out. So for a, for a at least, what it tells you is that you have a holomorphic G bundle on x and together with a flat that is flat in the r direction. So if you like, you can think about this as saying I have a flat family of holomorphic G bundles on x. So this r direction just coincides with an ordinary transimus direction. It's flat. It gives a topological direction in the field theory. So it's like saying I have a flat family, but I have some interesting G bundles on the x direction. So the gate transformations you can understand is saying, well, I can always perform ordinary gate transformations in the r direction just by a flat connection. You're near a gate transformation of a flat connection, but then I can perform holomorphic gate transformations in the x direction. Does that help? And similarly for b as well. So it's very, very good. One-dimensional relations, transversals, holomorphics. You can think about it like that. Yep, absolutely, yeah. Question? Yeah. So variation or b gives equation for motion for a and for b. h gives for b, and for b it will contribute very well. Yeah, b, it's not so easy maybe to interpret. So for a is that it's a semi-platform. Shouldn't b be dA plus commutator p in the direction? Isn't it 1.0 in the second term? Oh, this is 1.5. Thank you, thank you. Yeah, thanks. So it's like B-curve theory. And this is not. I just mixed up my factors. Thanks. Yeah, this is like a BF theory. Yeah. What if you don't consider like separate fields and b, but write the same action by just using the t-field? Like if you say this b is omega h8, this is a functional field, a. So writing it that way, you can arrive at more interesting. There's like more interesting deformations you can write down in this theory that are, yeah, that's easier to interpret in that language. But for the boundary dimensions to write down, it's a little easier to think about as like two components like this. But yeah, that's certainly something you can do. I'm not sure it'll play such relevance in my talk today. So Owen mentioned kind of a nice computational result of these types of holomorphic theories that I've considered. Now, this is not exactly a holomorphic theory. It's really like holomorphic plus 1 theory. I have this holomorphic structure in two directions, but then I have this topological structure. But this kind of normalization result still applies. So I'll just write it. So this follows some calculations in my thesis, modest extensions thereof. But there exists a one loop, actually finite quantization of this theory, of this 5D theory, at least on flat space. And the main result I'm going to state today is a property of this one loop quantization. And by finite, I mean, so as I mentioned in the last talk, finite, I mean the finite terms you write down are strictly finite without the introduction of counter terms. So there's a really nice kind of explicit quantization you can write down for this class of holomorphic theories, even if they're not exactly holomorphic, but kind of maximally holomorphic. So the next thing I want to do is to consider this 5D theory, not just on this open space, but now on a 5-manifold with boundary. And actually, sorry, maybe before I do that, I'll just remark then there's an extension in the BV formalism. So this is going to be really important for my result. So here, we have two fields, alpha and beta. So here alpha, the 0 component of alpha, or the degree 0 part of alpha 0 is what I was calling A over there. The degree 0 part of beta is what I'm calling B. So I'm just going to write down all of the ghosts and anti-fields together in this BV language. They look like this. So you have a 0 star form on x. This, again, works for any complex surface, but I'll really be focusing on C2. So it looks very similar to this Trent Simons that I wrote down in three dimensions. And there's a nice way of thinking about this in the BV formalism. Well, this top thing, I'll never forget about the shift. That's just a dg-le algebra. g is a le algebra, and I'm tensing with a commutative algebra. The differential is this d bar plus this dram differential in the r direction. The bottom line is clearly a module for that dg-le algebra, where I just act by the adjoin action and then by the wedge power of forms. So when I'm running down, when I write down the action in the BV formalism, I just use that structure that I have a dg-le algebra in the top, and the bottom thing is a module for it. That's why it generically has this BF type formula, why the action looks like that. And maybe I'll just claim, I'm not going to go into too much detail here, but the claim is that the 5D super Yang-Mills n equals 1 super Yang-Mills admits a twist to this 5D theory on C2 cross r. So if you like, I'm describing the holomorphic twist of 5D n equals 1 in this BF language. This perspective is not really important for my talk, so I just wanted to stay that as a kind of motivation, maybe, for considering this class. When you say 5D n equal to 1, what's the, so you just write down a Poissonic field, and then some thermonics. So something happens in the twisting. The fermionic direction gets twisted into a comological BRST direction. So a lot of the fermions that were present in this n equals 1 theory actually became ghost and or anti-fields and anti-fields in this theory here. So there's no Z2 grading in this. There's no parity here. There's just a total BRST grading. So this is 5D n equal 1 with 3-0 matter? No matter, yeah, just pure, yeah. And if you add magic, is there a similar twist there? Yes, yeah, yeah. We'll be throwing in some representations down on this side, yeah. OK, so maybe I'll write down. So there is a boundary condition at t equals, oh, so for the theory on C2 plus r bigger than or equal to 0 now. So I'm putting the 5D theory here. I'm looking at the boundary, t equals 0. And what I do is I take this two-component field at t equals 0, and I just project out to one of the components. So I just project out alpha to 0, and then beta, the field beta, at t equals 0. I'll keep that up. So what do I, there's some really basic things I can extract from this. So clearly the operators then on the boundary, the boundary operators, the boundary operators are boundary observables. Well, they only depend on beta. There's no alpha terms by the boundary condition there. We can write down a kind of a generating basis for the local operators in the following way. So I'm going to call these, I'm going to label these things. I'll call it O for operator. It's labeled by x, which is going to be an element of the Lie algebra. It's going to be a vector, integer vector. What am I calling it? N like this. So N is just a two component vector, N1 and N2. And integers, positive, non-negative integers. And then W is just going to be a point on C2. So it's a local operator, so it's supported at a point. That's where the observable is supported at. And what it does is it just takes beta t2z. So that's, this is something now that lives, this is not in BRST degree 0, it's in some non-trivial BRST degree according to my conventions. I'll say what I mean by that in a minute. But it takes something like this. So here beta is just a function on the C2. And it maps it to the following. So I take beta, I pair it with x. Sorry, so beta is an element. It's a Lie algebra value function on C2. So I just pair it with my Lie algebra pairing. Now this is just a function and I take its derivative d by dz1 and 1 times d by dz2 and 2 times C and evaluate it W. So notice, really important, it was really necessary for me to be working in this BV setting. Or else I wouldn't have seen anything interesting because these all have degree. This has BRST degree plus 1. Because beta d2z, if you look back to my formula there, that thing lives in BRST degree minus 1 of level of field. So the operator's degree plus 1 gets flipped. So I want to check, that's my first check, for my main result to have any chance of being true. I want to check that these local operators that I've given here agrees with the description of the state space of this higher dimensional cat's moody algebra that we wrote in the last lecture here. So remember, for the higher dimensional cat's moody algebra factorization algebra on C2, let's just recall what it is. Well, it takes any open set inside of C2 and it maps it to some Li-algebra homology-looking guy. So it looks like the Li-algebra homology of 0 comma star forms compactly supported. That was really important on U with values in G, like that. And classically, this is exactly it. There's also, which we'll see quantum mechanically, it gives rise to an extension of this. We don't just look at least Li-algebra, we look at an extension of it. We just work classically for a moment now to see that the operators agree. So on U equals all of C2, if U is just all of C2, we can just calculate compact-supported functions on C2, values in G. So this looks like some big symmetric algebra on compact-supported double-forms on C2. Tenser G shifted down by 1. And then there's some non-trivial differentials. There's the linear part of the differential that's D-bar acting on the 0 star part. And then there's some Li-algebra part, Chevrolet-Ammberg part acting there. OK. So why does this look good? Well, first is 0 star C1 C2 has co-homology only in degree plus 2. So it only has co-homology in degree h2 D-bar of C2. So this thing is actually quasi-somorphic to this. If I could support it, if you like, this is some serduality. But I want to choose to identify this. I want to identify inside of here a really nice subspace, in fact, a dense subspace via a higher-dimensional version of the residue pairing. So this is, if you like, you can think about this as the residue pairing. And the space I'll write down is the following. So you look at two holomorphic two-forms on the disk, on the two-disc dual. So why would you expect this to be a higher residue pairing? Well, what I do is I take a some, sorry, maybe I should. So I want to think about this as being isomorphic to the following Laurent polynomial-like-looking space. So I look at the purely negative Laurent tails in polynomial variables, z1 and z2 inverse.  And I map it. I map it. So maybe I should say, maybe I'll describe this one first. Sorry, this is getting a little. So I map this to some compactly supported double-form. And I do this using the Bauchner-Martinelli kernel. So maybe I'll say what I mean by that in a minute. But this Bauchner-Martinelli kernel plays the same role as a residue class inside of ordinary complex, one-dimensional complex geometry. So it sends it to the following. You look at d bar applied to z1 minus m1 minus 1, z2 minus m2 minus 1, all times the Bauchner-Martinelli kernel. There. And I need to choose a compact support. So I choose any, yeah, thanks, where f is any compact supportive function, smooth function. If you like, this identification here is more fruitful to think about. So maybe I'll just say a word about this. In the function, just identity is 0, yeah? Cook to 1, 0, right? Yeah, so centered around 0, yeah. So I want it to be radially symmetric, right? So this identification is a little easier. I should have started with this. But all I'm doing is taking a polynomial of this form. So z1 minus m1 minus 1, z2 minus m2 minus 1. This maps to a thing that takes in a. So eta here is any polymorphic 2 form on the disk. And it maps it to the residue around s3. So this is this higher dimensional residue of dz1 m1 dz2 m2 of the Bauchner-Martinelli kernel times eta. So this is the kind of unique thing is residue of around s3 of omega pm with any function fd2z. So let me just choose a basis for polymorphic top forms. This is just the value at f at 0 there. So I'm just kind of floating around a lot of variables here. But the kind of thing I really want to identify is these purely negative romp polynomials, which I'm identifying via a residue pairing with the kind of linear part inside of this factorization algebra here. So keeping those formulas on the board above, you see that there's a natural identification with the local operators I wrote down for the boundary in the following way. Oh yeah, that'd be great. Is that good? So I just take a, I just do kind of the natural thing, c1 minus m1 minus 1, c2 minus m2 minus 1, with values in x. So this is an element inside of, I'm viewing it as an element inside of convex supported forms on c2. So it's a 0, 2 form the way I'm identifying it, tensor g. And this is placed in degree plus 1 as well, as this thing was concentrating in homological degree 2. So 2 minus 1 is 1, so this is in degree plus 1. And it sends it to this operator o x, m at 0. I've chosen to center everything around 0 for this example. So this shows that at least classically, the local operators coincide. Now at the quantum level, it turns out to be simplest to compare kind of a piece of this. So I haven't actually talked anything about the factorization product structure here. I've only evaluated it on a disk and shown that they coincide as vector spaces are really as coaching complexes. So I'd really like to say that the factorization algebra structures are compatible on both sides. That would be kind of the strongest version of this result. Unfortunately, there's not really an efficient way to write down the full OPE structure for a higher dimensional holomorphic factorization like this. This would be like the idea of generalizing power algebras to arbitrary dimensions. So a full kind of definition has not yet been written down in totally algebraically satisfying terms. But there is a related object that gets back to the first object I wrote down here. We can study, we can compare what are called the mode algebras. Mode algebras of higher katsumuni and the boundary operators. So what do I mean by the mode algebras? So before, we were looking at C2 sitting inside of C2 cross r, bigger than or equal to 0, at the boundary. What I'm going to do is not look at all of C2, but just look at C2 minus the point. And if you like, in the 5D theory, what I'm doing is looking at C2 minus the point cross r. And this map came up in Owen's talk. What I'm going to do is take the radial projection of the C2 minus the point. So just look at the modulus. So this produces some real number. And then in here, at the level of the gauge theory, I can think about this as doing, I'm compactifying the gauge theory to r bigger than 0 cross r, bigger than or equal to 0. So this really looks like some, this is like a compactification along S3. So since I have some holomorphic factorization algebra here, there, when I push forward, I get some factorization algebra that turns out to be, or at least has a dense subspace, just as in this description right here, to actually be locally constant. And I can state my main theorem in more precise terms. So this locally constant, this locally constant 1D factorization algebra, defines an associative, or really it defines an A infinity algebra. Algebra, I'll call it, let me just call it A. And we have the following theorem. There's an isomorphism, or there's a quasi-isomorphism. Isomorphism of A with, well, first, there's a quasi-isomorphism of A with, I do the same exact construction, not just for the boundary theory, but I can do this for the higher dimensional, this higher Katz-Mudy algebra on C2. So the first thing is that there's a quasi-isomorphism there, where I'm taking the same construction. I'm looking at the S3, back following along S3. And this has some, with central extension, extension given by theta equals, now I'm going to write down some explicit polynomial. While you look at G in the adjoint, you take its character and project onto the third component. This is some element inside of SIM3, G dual, G. So precisely, we see the higher Katz-Mudy at this extension, at this level here. And in turn, this is related, this is work that I own was talking about in his talk. This is related explicitly to this algebra of Fanta-Penionic and Pranoff. This is given by the enveloping algebra of this G hat 2 comma theta, which extends this derived version of functions on the punctured affine plane with values in G. So explicitly, we've identified then the algebra. Really, an algebra of observables, it came from just a piece of the observables, namely the S3 modes, but we've identified a piece of it with this very explicit A infinity algebra like this. So maybe I will say one word because I wrote down the picture earlier. So the picture that you should have in mind, why this extension comes from. So it doesn't come from, so I have this big kind of space here, the C2 in some real direction, but I'm really just projecting, it's punctured, this is C2 minus the point. I'm projecting onto just the line, right, or bigger than zero. And I think about the bulk as being labeled by another copy of R. And the way this extension arises is not from, like in the ordinary Katz-Mudy, was a correction to a two point function, this two point OPE. It arises as a correction to a three point function, which is really like an A infinity structure set in these more homotopical algebra terms. And the three point function arises as computing a diagram where you put in local operators in this one dimensional direction, which correspond to like sphere operators up here, computing their three point OPE, or factorization algebra structure maps, and it's corrected by some Feynman diagram that looks like this. So it's very similar to this 3D, 2D correspondence where you see a two vertex wheel. This time you see a three vertex wheel, labeled by the propagators like in Owen's talk. And this thing you show is basically proportional to this CH3 of G in the adjoint, like that. Okay, so maybe I'll stop there. Do you know what the E2 algebra is acting on this? Which E2 algebra? The one coming from the bulk. Or maybe it's not E2, but is there some kind of? No, it is gonna be E2. No, it should be working. Yeah, we should be able to work it out. Other questions? Yeah, a question. Yeah, if you start with this invariant cubic polynomial algebra, you can also build five dimensional pure topological theory, yeah? I don't know if it turns out the same way, yeah? Just integrate, imagine five dimensions boundary six dimensions. So add a full term, Simon's term to that. That's correct, yeah. And yeah, this looks a little bit more than what you consider to be, but I think nobody knows what to do here in this theory, because in trivial connection, you get no quadratic term at all. Oh. Yeah, so like integral, like in a billion cases, integral one form, yeah, eight times the eight square. Oh, I see, yeah. Mm-hm. It's also kind of five dimensions. This theory should kind of degenerate into that theory, maybe. Yeah, it's pure topological. Yeah. I think it's not studied yet here. Oh, I see, that's really interesting. Yeah, I'll keep my eye on it. Thanks. Yeah. So what if anything goes wrong with these theories in the bandwagonism? You could still define, instead of having a surface, you have some kind of actual defaults. And this proposition I seem to still have been true of. So you can make some kind of logical commission on the kind of logic of linear algebra or something. That's the one that I like. Yes, yeah. So does something go wrong with the analog of, you try to figure out what this thing is? In higher dimensions. No, so an example in seven, six works as well, where this kind of six-dimensional version of the higher cat's mini pops up. But it's very similar in structure to this, like nothing is really. There's something, does something go wrong if you just try and sort of write the same proof, but replace it with two by D and do the same? Is that something that you have to? No, just interpreting as like, so I should say selfishly, the reason I care about doing this is because it gives kind of insight into maybe seeing some dualities in physics. So I really care about this five, four correspondence for reasons like that. But there's nothing that stops you from doing this in arbitrary dimension if you don't care about kind of relevance to other maybe interesting physical theories. 70 and also the three states. That is also relevant for it. Yeah, that's why I've done that one too, but yeah. Yeah, I don't think anything should be wrong in the system. It just, yeah, I don't know how relevant it is to other. On the questions. Can I ask you about matter again? So this main theorem here, does it have an extension decision when you have matter? Yeah, so you'll see some BRST reduction of the matter and the boundary.  Yeah, you'll see like the higher chiral version of BRST reduction of that module, a representation that you chose. Is it easy to write it though? Yeah, I could give a description. I don't know if it would be useful at all, but yeah. At least I could describe this algebra really explicitly. The infinity algebra is really easy to write down.


is this fact that you probably don't have a compass.  This is getting back to more classical life coaching stuff, but we all need a hierarchy. And we actually need to know what has to exist in my life and what do I want in my life. So for example, if you're a student, you may say, well hey, an education has to happen right now. It can happen later, but man for me has to happen right now. A relationship, I don't know. That changes from man to man. But if you don't have a hierarchy, you'll never know where to put things so that they balance. Does that make sense? For me, I love, there's a couple of things I love. I love rock climbing. I love salsa. I love martial arts. But there's no salsa, there's very little salsa and no martial arts in my life. Why? Because I've chosen rock climbing as the highest priority for my hobbies, yeah? So that's an example. There has to be priority. And you have to actually be willing to knock things out. That's just part of everyday life based on that priority. But all that comes with having this moral compass. But yeah, priority is kind of the key to that. Not a problem, man. Anybody else, guys? Just put your hand up and I'll, oh, yep, fantastic. First of all, thank you for the speech. Not a problem. Your speech is actually quite great. And Nick, thanks for bringing me along. It was my idea to come in. Yep. He had an extra ticket. He told me to come down and I'm kind of, I'm really glad I'm being, a lot of what you said resonated with what I've been thinking about and putting a lot of stuff straight away to you. One question I do have. A few years ago I used to study a bit of philosophy. Yep. And I wanna know, is it all about the pursuit of happiness? Ah, that's a good question. Yes, I would say so. Being in the pursuit of something that you love, I would usually say being in the pursuit of passion or being in the pursuit of love, right? But other people would call it the pursuit of happiness. But it's dangerous because we're all, any human being, we're wired to be in the pursuit of happiness. There's always have been, I don't need to tell you. Guys, stop pursuing unhappiness. Just pursue happiness. Don't worry about that, I'm happy to stop. You know, I'm not making fun of you. I just mean, obviously we're all in wired to do that. So to say, to me to say, being in the pursuit of happiness is dangerous. Why? Because Charlie Sheen is in the pursuit of happiness. You know, he's sleeping with lots of girls, he's doing lots of coke, he's doing what he does in the pursuit of trying to be happy, but it doesn't make him happy. So there's an art form to the pursuit of happiness. And to me that's again, pursuing the right type of happiness in the right way. Does that answer your question? Yeah, yeah, we're wired that way. We're endocrinologically developed that way.  But like I said, you gotta be careful, there's two types of happiness. But yeah, absolutely, as far as I'm concerned, the more happy you are, because that's the way you're developed, the more you're gonna enjoy life. So yeah, I will put it that way. Two more questions guys, yes? Where does the feeling of content fall into play? So contentness? Being content. Yeah, so being content is much closer to eudaimonia, but there's content, which is toleration content, and there's content which is, I'm really happy with who I am content. So content actually kind of has, is another one of those words that has multiple meanings.  Or there's content with, I'm quite happy with things are. If nothing changed, I'm totally happy. There's very different things. So the content which is I'm really happy with things, that's eudaimonia. The content which is where I'm just tolerating for things to keep going on, then it becomes, no, that's all wrong, but it's different definitions for the same word. Cool. Oh, cool. Thanks very much, Damien. Not at all. My question was, why do you think that the stuff that you've talked about isn't valued in our modern society, in our world? Right. Well, that's a big question. In my opinion, part of it is because the stuff that I talk about doesn't make as much money. Essentially, I mean, money drives our commerce, and our commerce has been entirely dependent on people consuming since about the, what is it, the 15 or 1600s, anyone know more about finance than me? Once we invented money lending, which used to be illegal, by the way, called the usury, but once we started inventing that, we had to start spending, because if we didn't keep spending as a culture, in fact, if people, by the way, if everyone pays off their loan at once, our economy disappears and our money has no value. Interesting thought. But yeah, so a lot of it depends on the consumerism, because what you find is the more consumerist country, the lower this eudaimonic happiness becomes. Why? Because to consume, you have to be focused on the fact, on these hedonistic pleasures, you have to be focused on the idea that I can't be happy unless I attain something physical, focused on end point, and you can't be happy with that end point, you have to keep one a new end point so that you drive the economy. So in my mind, why? Because I don't think that there's any one person overarching on the excellence, yes, yes, keep them far away from the eudaimonic goals, but what's happening is just this, the way that our financial culture has to work, for people to be successful financially, people have to keep spending. So what do we do? We create ads that say, you're not perfect until, yeah, you're not cool until, have a cigarette, yeah. So our culture has actually created this whole way. And that's why I believe, I believe it has everything to do with money and our financial system, yeah. Yeah, Damian, thanks for the speech. It was very informative. My question relates kind of what was just asked.  Is that what you're saying? Yes, absolutely. Where do you rate self-actualization, if at all you do? Yeah, no, to me, it's all part of the same thing. I mean, what you're doing when you're fine, can I ask you one more question? Hold on to that, Mike. What do you mean by self-actualization? Because there's a lot of words that have multiple meanings, of course. So just try to explain that a little bit. A point at which you would be content. A point? With where you are at life and I can. Okay, so to me, if you say a point at which you're content becomes an endpoint goal. And if you find someone whose goal was to be content, whose goal was to find that endpoint goal to be content, they're likely not to have found it. If someone's whole life purpose is just to learn to be more and more content on an ongoing basis, they're far more likely to get there. I find it's actually quite dangerous. The idea that a lot of people have, which is when I have this, I'm gonna be content. Because content self-actualization often depends on certain achievements. So to me, I thought once upon a time I was gonna be self-actualized. If people just recognized me as having interesting valuable things to say, and I could have a positive impact on people's lives, and that paid for my livelihood, then I'd be self-actualized. But as you can see, as I was explaining, I don't feel self-actualized as a result because it becomes a point in the future. What you'll find is that monks, even meditative monks, as amazing as they are on an FMRI machine, there are still moments where they go up and down. So there are moments when they feel less content, moments where they feel more content. But their bodies are much better at dealing with those ups and downs. But yeah, I find it dangerous if you look at a point, what you should be in is a constant pursuit of being self-actualized, which is where this, you don't want to compass comes from. What you're doing, you're constantly moving in direction that actualizes, helps you discover more and more about who you are. Understood, yeah, thank you. Thanks, buddy. Fantastic, guys, that's the last question. That's it, that's it. Awesome, thank you very much, guys. And again, just like James said, I love what I do. I love talking to people about work. I love influencing people's lives. I love having a positive impact on the way that they exist. I do love that. So if you want to come and talk to me at any point, please feel free, I'm always available. Again, if I'm annoyed, I'll tell you, I'll just say, leave me alone. Hey, those of you who come up to me and ask questions are the ones who are far more likely to actually progress in life. I noticed that with all my students, the students who actually push the hardest to learn the most and really grasp what they're trying to grasp, they're the ones who get the furthest. So don't be shy, guys. Thank you very much.


And we are going to contemplate today how amazing life is on planet Earth right now. All over planet Earth. People, human beings, like you and me, or not like you and me, but human beings here, we've got low legard in the Gulf, right, in the Gulf. A very different culture than what many of us are living in. We've got Europeans here, we've got people from all over the world listening. And there's a lot of people not listening, billions of them. And their life is better today from a material perspective than life on planet Earth has ever been. We live in the richest period in human history. We live from a violence perspective in the safest period, pretty much, in human history. There are fewer wars, there are fewer people dying at the hands of their own government, at the hands of civil wars, at the hands of violence, including crime.  Many of us, again a vast majority of humanity, live today with cell phones and telecommunication devices that are just stunning and amazing. We have opportunities to enjoy, we have time on our hands, time, the most precious thing in the world, the rarest thing in the world, if you will. We have time because we're so wealthy we can basically produce our survival needs relatively easy and relatively quickly and relatively cheaply. And as a consequence of that, we have plenty of time to do other things, to think about other things, to engage in other kind of activities. We don't have to work 24-7. We can engage in hobbies and in artistic pursuits and friendships and in parties laid into the nights and lots of activities that we just couldn't afford. We couldn't have time. We couldn't contemplate even engaging in in a different era in a different time. It's so important to be able to sit back and realize how amazing the world is today, how rich we are, how wealthy we are, how easy, easy in the positive sense our lives are. And then of course it's important to think why that is and what makes that possible. And of course what makes that possible is the genius of so many people, the creative ability of the great people that we live with on this planet. In particular, the people who have the advantage of living in places that are free, in places where they can pursue their values, pursue their ideas, pursue their thoughts, pursue science, pursue new innovation, new ideas, new projects. It is the world around us did not just appear as so many people both left and right today believe. It was not just plopped here by God or somebody. It just didn't just arrive fully formed with iPhones and cars and nice buildings and great restaurants and just it didn't just show up like this. The world in which we live was created. I'm a creationist in this sense. It was created by human beings. It was created by human beings who use their minds to create it. It was created by productive people, by people who built and made and created stuff and thought outside of the box and then took risks and made something, whether they came out west in 100 and something years ago, whether they built up great industries like Carnegie and Rockefeller, whether they pursued a dream and built great companies like Steve Jobs and Bill Gates and the first founders of Genentech and Moderna and BioNTech. They have made this world and of course let's not forget the architects and the real estate developers. I mean we take people for granted. We take their great productive genius for granted but people who imagine, who look at a plot of land that's empty where there's nothing there and they can imagine homes and businesses and offices and gas stations and roads and they can imagine and not only can they imagine it but they can bring all the resources together and build it. I mean I live in this amazing condo connected to other condo buildings in an office building not far and some restaurants downstairs and right on the water and there's an artificial wall that prevents the water from flooding our garage and knocking down this building and somebody had to do all that. Somebody had to do all that. When you look around your neighborhood somebody had to develop and design and build the streets and put in the cables that give you internet and electricity and everything else and you know and it's the great minds that think about this, that imagine it, that make it a reality. It's the workers who actually go and let's not forget. You know the productive workmen who actually go out there and work and build and make and create and and produce all the beautiful thing, the amazing things that we again just live our lives in. This is not nature. We don't live in nature. I'm not thankful to nature. Nature just is here. It just is here. But human life as we live it today is created. It's created by the creators. It's created by the productive and Thanksgiving.  All of that is so far at least negligible, a sideshow as compared to all the good things that are being produced and created every single day. You know we've lived through this COVID epidemic now, pandemic for two years, shockingly for two years and everybody has screwed this up.  The scientists particularly who give us advice at the upper governmental levels. But at the same time there have been people who have been really thinking about this. I mean looking for solutions and looking for rational guidance and as I have mentioned many times on the show two days after the genome of COVID virus was known there was already a vaccine in a sense that the formula was there both at Moderna and at BioNTech. So I am continue to be thankful to Moderna and BioNTech. Not to the FDA, not to the CDC, but to Moderna and BioNTech and all the scientists and all the thinkers and all I mean the Hungarian scientists who stuck with mRNA in spite of not getting government grants and not getting an associate professor I think position at a university and just sticking with it and now she works for BioNTech. The capitalists behind Moderna and the people who worked at Moderna who couldn't have created this platform couldn't find a use for it didn't make any money for years and years and years and years and kept going and kept going and then when COVID hit they found the perfect use for it and you can complain about the vaccines and maybe they haven't lived up to everything we were promised about them and I'll be discussing that maybe you know as well but they have certainly changed our lives made our lives much better made it possible for us to cope with this virus much better much healthier way and even if this virus is relatively mild and COVID is I think when the grand scale of things relatively mild the technology that these thinkers these creators these builders have made is one that will be used for more serious pandemics more serious diseases and if we're smart we'll learn from COVID and when the next one happens we'll be so much better off and if it's deadlier we'll be so much better off to deal with it because we'd live through COVID if we're willing to learn the lessons and I think there are people out there learning the lessons so I'm thankful for all of those I'm thankful for people like Amish Adalja who I think has done a phenomenal job of calling COVID white and yet has been attacked from our sides constantly and I'm sure there are lots of out there physicians and doctors and researchers who have struggled because of these attacks left and right we'll talk more about that again tomorrow and I'll have I'm going to have Amish on the show again soon to update us kind of on where we stand with COVID and vaccines and the latest about vaccines but I am thankful to all those who have again built and created the modern world I read some amazing books this year just recently so they're at the top of my mind right I read the book the code breakers about the the bioengineering revolution that we're living through and about a CRISPR the technology to edit genes and it's stunning it's stunning the the the hero of this Dr. Dowden is an amazing woman a real hero I'm thankful to her you know I think I'm gonna benefit me I'm gonna benefit tremendously in the next 20 years from the technology that she has invented and from the work that she is doing in in bioengineering and in gene therapies and I think all of us are going to so I'm thanking her now and in advance both for being an inspiration and for the technologies that she's developing but one of the things that came across in that book is how many people how many people participate how many people engaged with these kind of achievements these discoveries like how many people added value work productive work creative and added to the value of a CRISPR or any kind of new science and new technology so while they are geniuses and they are real men and women of ability who who are really at the forefront of these things and make them possible and innovate it and push everybody else and two great achievements the achievements are made possible because of the hard work of millions and millions and millions of people who are exemplars of the virtues of productiveness at whatever level they are capable of not everybody's going to be that genius who moves things forward in dramatic ways so I'm thankful all of them all of them primarily to the geniuses because they have the biggest impact on my life so in in spite of it being a very very difficult period for philosophical political reasons it's still inspiring to me to go outside just to see productive activity going on to to catch up on the latest and coolest and greatest technology that's out there the greatest and coolest stuff that that that is being produced and being created I love tech I'm you know I'm always contemplating buying the next little gizmo to play around with I'm pretty good at being disciplined about not always doing it but I love the fact that people are constantly thinking of better ways I love the fact that all those technologies that were really ramped up during during last year because of COVID have now this year just just taken off and become more stable and easier to use and more integrated from zoom to teams to all these things that we became dependent on last year this year have just become robust and and really good so there is a lot a lot to be thankful for Jennifer thank you really appreciate that and of course you know you should in your own life look around you and and and figure out what you should be thankful for what you should be thankful for given your life and and I'm sure there are lots of things there are lots of things out there in the world people you've never met that you're thankful to but there was some sure people in your life that are important to you whether you tell them or whether you just take a minute to appreciate them and to think about it it's always good to tell people you know justice is the virtue of not just condemning people justice is not going after justice is not going after the bad guys justice is not you know putting them in jail and and and and you know condemning evil the primary aspect of justice the most important part of justice is recognizing elevating appreciating thanking the good so whoever in your life is good good for you good for your life good for your happiness good for your success this is the time of year this is this is the period where it's this is your opportunity to say thanks little pat on the back whether it's an employee whether it's a loved one whether it's just a neighbor that inspires you whether it's somebody who I don't know a restaurant owner a waiter a whatever they just do a phenomenal job they just make your life just a little bit better saying good job well done thank you is priceless and it's the true act of justice a true act of justice it's what that virtue really means we we we tend as a culture as a society we tend to focus and obsess about the negative there are a variety of reasons for that actually I'm gonna talk about that in one of the future shows about this because I'm reading Stephen Pinker's book on rationality and it has some interesting things to say about this but we obsess about the negative and and we have a justice system which is supposed to catch the bad guys and the whole concept of justice is skewed towards penalizing evil and it shouldn't be and you shouldn't in your life in your life the concept of justice should be skewed towards thanking appreciating patting on the back the good because what does it mean that somebody is the good it means they add value they add and since you're interacting with them they add value to your life and what's more important in life than those values that make your life better greater happier more successful and if you can say the thank you impact them on the back and increase their motivation and inspire them to do even more then your life becomes better justice is about bringing close to you the good and distancing yourself from the bad surrounding yourself with the good so again this is a great time of the year to think about that to consider who are the good people in your life who do you want to thank who do you want to be close to surround yourself with and who not and who not life is too short to waste it life is too short to waste it on people who don't deserve it life is too short to waste it on people who don't add value to you so positive reinforcement positive that's what you should be doing particularly on Thanksgiving thank you for listening or watching the Iran book show if you'd like to support the show we make it as easy as possible for you to trade with me you get value from listening you get value from watching show your appreciation you can do that by going to iranbookshow.com slash support by going to patreon subscribe star locals and just making a appropriate contribution on any one of those any one of those channels also if you'd like to see the Iran book show grow please consider sharing our content and of course subscribe press that little bell button right down there on youtube so that you get an announcement when we go live and for those of you who are already subscribers and those of you who are already supporters of the show thank you i very much appreciate it


Hello friends, I am Sanjay Gupta. In this video, I am going to demonstrate you how you can add all odd numbers between 1 to N using recursion in C. Before starting, you can subscribe my YouTube channel by clicking on the link which is available at the bottom right corner of this video. You can download my app Techimus that is available on Google Play. You can connect with me by following these details which are available in front of you. Now coming on to the implementation, I am using Dave C++ for program implementation. First statement is header file inclusion. I am including stdio.h for that purpose. Then I am declaring a function sum. This statement is function declaration. This function will receive an integer as input and it will return an integer as output. Then I am implementing main function definition. Inside main, I have declared two variables N and S. Then I am using printf statement and messages enter value of N. This message will be displayed on console. Then the entered value is received by scanf inside N variable. Now I am calling some function and input N is passed inside it. This statement is known as function call. The return value which is available inside S will be displayed on console using this printf statement. This is complete implementation of main. Now I am going to implement definition of sum function. This is function definition. This function will be a recursive function. So here I have to define two properties of recursion. First one is base condition. Base condition is responsible for termination of recursion. And second one is recursive function call. So first I am implementing base condition. That is N equals to 1. If this condition is true, then 1 will be returned. Otherwise return N plus sum of N minus 2. This function will be called again. Here this is base condition and at last return statement is containing recursive function call. This is recursive function call sum N minus 2. And you have to remember that whenever you will be executing this code, you have to enter odd number only as N. So starting from 1 to that odd number, all the odd numbers which are available in between them will be added through this program implementation. So here suppose initial value of N is 7, which is received by this formal parameter N. So 7 is not equals to 1. So base condition is false first time. So return statement will be converted into 7 plus sum of 5. So next time sum of 5 will be called and this 7 plus will be stored inside stack. So suppose 7 plus is stored inside stack and next function calling will be like this 5 plus sum of 3. So sum of 3 will again call this function definition and 5 plus will be stored inside stack. Next time 3 plus sum of 1 will be called. So 3 plus will be stored inside stack and sum of 1 will be called. And this function will be executed and then this base condition will be checked. Right now it is true. So it will return 1. So base condition has stopped recursive function call a process. So 7 plus 5 plus 3 plus 1, all these values are stored inside stack. So 1 plus 3 plus 5 plus 7 will be added and the result will be stored inside the S variable, which is available inside main and which is calling some function and the result sorry here I have to use S. So with the help of this S output will be stored or you can say display on console screen. So I hope you have understood how we can add all odd numbers which are available between 1 to n using this demonstration. Now I am going to compile and execute this code. I am entering 7 it is displaying 16. So suppose we add 1 plus 3 so result will be 4 then we have to add 4 into 5. So result will be 9 and then we have to add 7 into 9. So 9 plus 7 is 16. So you can see that this output is correct. This program is adding all the odd numbers which are available between 1 to n and you have to remember that the n must be an odd number. So implement this code at your own so that you can understand how you can add all the odd numbers between 1 to n using recursion in C. If you want to watch more programming related videos you can connect or you can subscribe my YouTube channel. Thank you for watching this video.


First Bank of Nigeria says it has lost confidence in Justice Rabi Haliru over a case between its former December branch manager and the financial institution. After the court hearing, the Defense Council Oninye Noli wrote the industrial court requesting a transfer of suit from the judge to any other on the ground of buyers. Responding, the Prosecution Council Monday Mawa rejected the call, asking the industrial court to disregard the purported letter. That the matter, there is no way anybody can be compromising the matter. And we were very happy. We were very satisfied and we let the office at it. But our greatest surprise yesterday, we received a letter from the false bank, asking that my lord, the judge handling the matter, Honourable Justice Rabi, should have hands off the case for no reason. The only reason we were able to profile in the letter was that one that he said, Mosul, the claimant, was only used as a scapegoat. And I think another policy is used that they did not sue Djangeli, the main contractor in the matter. And to me that this is laughable. And the only thing I can say prompted this letter, yes, they were going to my lord told us in the chamber that there was a point from Bessie Pender to bribe her. And she even has to jail, though, that came to bribe her. And as far as I'm concerned, there is nothing that has been done so far to suggest or to the people and me of the party to drug inference that my lord, the Honourable Justice Rabi, will be biased.


wasted chewing gum bacterium. I mentioned that it appeared in scientific reports like one year ago, but what is this paper about? So the first thing what they did was like asking a question. So we're just surprised to see that no one before had studied the microbial diversity in wasted chewing gums. So we all know that wasted chewing gums are a contamination and esthetical problem in so many cities because they are stuck on the pavement. If the pavement is light and the chewing gums become dark, it's not something very nice to see. And we all know that it takes very, very long to disappear from the ground. So what we did was taking profit that we were on holidays like before the pandemics. And we were all traveling, at least I always do that, with the sterile fiber tubes. And we took samples from different countries of wasted chewing gum stuck on the pavement. So we did that, of course, from Valencia, from Spain, from France, Paris, from Greece, from Istanbul in Turkey, from Singapore. And there were other samples that unfortunately didn't work well because they were taken from Indonesia from Bali. So sorry, and this picture here shows the diversity that we found. The number of samples is not high enough to make a relation between geography and microbial taxonomy. But what we can already say is that it's a huge diversity of typical environmental bacteria there. This already suggested that chewing gums were not simply something inert there, but they were home of a quite amazing diversity of microorganisms. Some of them can be found, of course, in our environments. And no two chewing gums were alive. So there's quite an interesting variation. Another thing that we did back in Valencia was to answer a very simple question. So if you have a chewing gum after a while and people step on it, etc., you get a very, very thin layer of this plastic-like gum or matter attached to the pavement. But even if it's thin, it might have like a couple or three millimeters. So the question was, is it the microbial profile the same in the surface of the pavement or in the internal part or in the one that is attached to the pavement? Because the availability of water can be different. Of course, the effect of irradiation is very different depending on whether you are on top or in the middle part. And then what we did was taking just one chewing gum and slicing it, making like salami pieces of it, one top part, one intermediate part, and one bottom part. And to our surprise, they were basically the same. So you can see in these three histograms down there that they are small faint differences, but basically the composition of the chewing gum, the bacterial composition, is basically the same, which suggests the chewing gum is not something that is sticky and that attached bacteria on its surface because of its stickiness, but it's an environmentally, microbially an environmental environment by itself. And it has a relatively homogeneous distribution of bacteria and other microorganisms inside it. After that, we wonder whether the bacteria that we were identifying there could be able to grow on chewing gum. And in order to answer that question, what we did was setting up a small collection of microorganisms that we isolated from chewing them and giving them as the sole carbon source different compounds. So some of these compounds were ones that we bought and that are regular ingredients in chewing gum, for example, glycerol, aspartame, xylitol, sorbitol, blue sucrose, etc. And another thing that we did was preparing just the suspension of pure chewing gum that we bought in the supermarket and use that as a carbon source, sorry, for the bacteria that we were able to isolate from old wasted chewing gums. And as you can see here in this kit, many of those bacteria are able to use those compounds as a carbon source. And in the petri dishes there, you can see that some bacteria grow much better when the medium is supplemented, for example, with powder, with powdered chewing gum. So they are eating some of the components of the chewing gum. Of course there is a plastic matrix there, which is very difficult to buy at the grade, but the others can be used by microorganisms to eat. Okay, figure A here shows the diversity that we found, the observed diversity, Shannon and Simpson. And basically it follows like an A truth in which the diversity is maximum at the middle and is significantly lesser at the beginning and at the end. But at the beginning, at the end of what? So what we did here was an experiment in Valencia and I think this is something that contributed a lot for us to get the ignoble price because it's a fun experiment. So one of the researchers who did this, Leila Satari, the first author of the vapor, she was chewing gum every day and she was spitting the chewing gum in front of our institute here. You can still see the stains on the floor and then she was able to recover the wasted chewing gums after one week, two weeks, three weeks, etc. So we were able to set a collection of wasted chewing gum, the age of which was perfectly known because it was us who made this and who put the wasted chewing gum on the floor. The first chewing gum was not put on the floor, was a console one, and then we analyzed directly after viewing chewed by Leila. So at the beginning we had the microbial community of her mouth in this case and at the end we have the microbial community that had stabilized on the chewing gum. This central slide shows the diversity, a lot of bacteria at the beginning, very oral mouth bacteria at the end, very environmental ones, and in between, the highest diversity, both of them. And the C-figures shows a principal components analysis in which the classification of all these samples tends to grow according to their age. In other words, as you can see here, sample 1, 2, 3, 4, so the first samples, the ones that were younger, that were just more directly related to the console ones, the recently formed a group, and then samples 5, 7, 8, etc. Another one in red this, and then in purple the other one. So there is a clear relationship between the bacteria you can find at chewing gum and how old that chewing gum has been stuck into the pavement. In order to see that more clearly, what we did was a very simple visualization of our results. So if you took the main, the four main genera that they are present in the console sample, you remember that the console sample was that one that was not stuck on the floor, similarly just recently too. So if you represent that, you get this figure, figure A in which you can see that bacteria that are typical from the mouth are very present at the beginning, this is expected, and then they decrease in frequency, but they can be detected all along this 84 days assay. In other words, bacteria from a chewing gum are full of oral bacteria at the beginning, and once they are on the floor, their presence is decreased, but you can still find them, so they are very stable, at least you can detect them, it doesn't mean that they are alive, that's true. In the figure B here, what we did was something, it's the opposite visualization impact. We selected the main taxa that were present at the last part of the experiment, so day 84, and we made this representation. And as you can see, some of these bacteria have been all the time there, but some bacteria are specifically increasing their presence at the end, and so some of those bacteria are pseudomonas, singomonas, asynetovacter, etc, which are typical environmental bacteria, and some of them would be important by your mediation potential. What are the applications of this? This is a regular question that we got during the massive impact that we had in the media, and this is something that the journalists were asking most of the time. So there are basically like three main applications of your research. The first one is viral mediation, so even if the plastic core of the gum is very difficult to degrade, it beats, at least partial degradation can be carried out by those bacteria, because they are using the vast majority of the components of the gum as we have demonstrated. The second is forensics. So we demonstrated that you can identify the bacteria that are typical for a person in the chewing gum that has been chewed by that person, even if it has been left for weeks or even months on the floor. And it was done in Valencia in summer, you can imagine that. So it's extremely hot, and the degradation of the DNA is not high enough to make us not possible to identify those bacteria. So I explained bio-remediation, I explained forensic. And the other one is disease control. So if we were able to identify so easily those bacteria, I think it would be interesting to find out whether those pathogenic bacteria were viable or not. We didn't do that. And of course, there is also a very important research that should be done on viruses. We understand that viruses do not last a lot on the environment, but it would be nice to see how long they can be viable and whether they could be transmitted. I don't think so, but you never know from wasted chewing gum that is just lead there on the pavement. Anyhow, for obvious reasons, it's not a good reason to let your chewing gum stick on the floor, but you better put it in the wheelchair. So who did that? The first author and the one who was chewing gum for a long time was Leyla Satari. Alba Nguyen, she created all the very nice visualization work and also data analysis in collaboration with Angela Pidal and then myself. So we were surprised when I got a phone call by Marc-Abraham, who was the guy there on top, and he told us that we were awarded an ignoble prize. He didn't tell us what kind of prize it was. And then during the ceremony we knew that the prize that we were awarded was the ecology prize. And these are some pictures that we took or a print screen from the ceremony in which the awards were given to us. Impact. So the impact of that has been massive. This is the first tweet that I made, and you know that in Twitter you have this possibility of identifying a statistic of those tweets, so the statistics of the tweets. So as many as 150,000 people saw that tweet, that's a lot. And 12,000 of them were clicking on it, etc. So this is an amazing number of clicks and more than 1,000 likes, etc. So in terms of impact, this is an amazing event. Then most of you are familiar with Almetrics, which is a way to measure the popularity in the medium of scientific papers. So that paper of ours has a very, I wouldn't say low, but average, popularity was 45, I think. The day before we got the ignoble prize, and just a few days later it was 650. But look at the number there. So 447 people tweet there. That's a lot of tweets. So 46 news, different news. We were on Wikipedia, mainly blogs, etc. So this is a massive impact on the news. This is just a selection. They are not all there of the new newspapers that published our story, and this includes Liberation in France, New Scientist Biotechnics, National Geographic, and several times in El País, who even made an interview to me that was one page in the online version of the journal. So this is an amazing, amazing impact on the medium. Television and radio. We were in La Ventana, in California. We were also in CBS. That journalist there was giving the news of our chewing gum work from South Africa. We were in La Sexta. We were in Brad's. We were in almost every radio, newspaper, and television channel in Spain. And of course we made a song in our acceptance speech. If you haven't seen it, you should immediately see it and watch it. And also we had like 480 likes of this speech that some people have said very kindly that is the best acceptance speech ever. So I guess that the next acceptance speech that we're going to give is also going to be some, if of course my colleagues agree. So the wastey chewing gum bacterium. Lessons from the ignoble price. Novel versus ignoble. One of the most common questions that I got when journalists asked me is would you prefer to have a noble price? Do you think you're going to have a noble price? The second question is very easy to answer. No, I don't think I'm going to have a noble price. Would you prefer to have a noble price or ignoble price? I would prefer to have a noble price because of the money. So in the case of the ignoble price, not only there is no money, but they give you like 10,000 trillions of dollars of Zimbabwe. That means nothing. So there's no money. But I have to say honestly, the ignoble price, getting that was an amazing and very, very funny experience. And having a noble price might be great, of course, for many reasons, of course. But it's a bit too serious, maybe for my character, at least. So research, serious versus funny, this is very important. There is a bad thing about ignoble price is that some people think, and that was my perception at the beginning, that it's associated with bad research. But I was very surprised to see that 99% of the comments that we got and on the comments that were posted on the news that appeared about this were positive. So I think that most of the people are able to make a separation between something that is funny and something which is not good. But it's also true that as the third one highlights the impact on the media and opportunity for communication, every time that I was interviewed, and I have events like dozens and dozens of interviews in the last weeks, I took it an opportunity in order to make some fun at the beginning with the ignoble price, but then explaining to people that in our society, they are bakers, they are, I don't know, teachers, but they are also microbiologists, people who travel with a falcon tube in the luggage in order to try to identify the next unexpore microbial environment. And I think that for common public it's very nice to know, because there are things that they are discovering now within the COVID pandemics, which is the word PCR. So everybody knows about PCR now. But PCR wouldn't have been possible without the extremophilic bacteria living in Yellowstone in thermophilic conditions, from which attack polymerase was isolated and is currently as you all know used today. And this is a very interesting story that people understand, regardless of the information, that looking at something strange like Yellowstone or Westerchillingan can have very practical implications. And then TPI's, so quantitative data that changed after that, and I am talking here as a very personal point of view, my Twitter account is mine and the other office could of course give their numbers. I got like 300 more followers in Twitter, my LinkedIn explodes, I have so many, let's say friends in LinkedIn now are interested in contact with us. Almetrics, it just went from 45 to 650. Media coverage was, as I mentioned, massive. All friends, some people that I knew for a while that were in touch with me and from everywhere in the world, so this means that that information reached every corner in the world. And phone contacts, and what I mean phone contacts means that now in my smartphone I have like dozens of contacts of very well-known journalists to whom I can be in touch in the future if we have something important to communicate. So always I think in terms of communication, this is not science, we all know that, but in terms of communication of science, it's simply priceless. Anything that does take home message can stick to this. So thank you very much for your attention.


Item Number SCP-744 Object Class Euclid Special Containment Procedures Due to SCP-744's immobility, containment facility 744A has been built around it. A 2 km perimeter surrounding the area is blocked off with a concrete wall topped with concertina wire and is monitored by security cameras. Guard posts located on the perimeter are to be manned by security personnel armed with standard field gear. Any items produced by SCP-744 are to be retained until they can be used. Description SCP-744 is a large abandoned factory covering approximately 30 acres located in West Virginia. SCP-744 is only semi-operational, with most of the manufacturing equipment having either degraded to the point where it no longer functions or having been deliberately damaged by an unknown party at some point prior to SCP-744's containment. The portions of SCP-744 that are normally functional contain many types of manufacturing equipment that would normally not be associated with one another, including large industrial looms, automobile manufacturing equipment, and large pistons that do not seem to serve any purpose whatsoever. Current research at containment facility 744A is dedicated to studying possible connections between these machines. SCP-744's anomalous properties manifest once every 56 hours. During this time period, SCP-744 will activate its manufacturing equipment. While SCP-744 is active, it will actively use its manufacturing equipment to produce items. For a partial list of these items, see the log of items produced by SCP-744. All items manufactured by SCP-744 are moved via conveyor belt into a large anti-chamber, which appears to have been designed to assemble them into one machine. This chamber is no longer functional. It is unknown where SCP-744 obtains the materials it uses to manufacture these items. SCP-744-1 is a voice calling itself... SCP-744-1 claims to be a production manager for SCP-744 and that it is in an undisclosed location within SCP-744. SCP-744-1 will attempt to communicate with any person who enters SCP-744 through the use of speakers, which are located throughout SCP-744. These communications usually consist of SCP-744-1, attempting to convince the person that SCP-744 is a highly advanced manufacturing facility in need of minor repairs, and to convince the person that they should assist it in restoring SCP-744 so it can resume working towards its purpose. Attempts to receive further explanation of this purpose from SCP-744-1 have failed. The entity is either unable or unwilling to provide further details on this subject. SCP-744 was discovered on... 1954, when reports of a haunted factory reached agents embedded in the local military base. Agents dispatched to investigate SCP-744 were able to establish communications with SCP-744-1 and confirm its anomalous nature. Containment procedures were enacted on... 1955, with the construction of containment facility 744A. Persons known to have reported the haunted factory story were issued Class-C amnestics. Containment was successfully completed by agents of MTF-SI-7. Home improvement. As of... 1961, SCP-744 has been classified as Euclid. Log of items produced by SCP-744. Manufacturing Port Phi. Manufacturing 3 cm galvanized nails at a rate of 100 every hour. Nails are of low quality and most appear to be heavily degraded with rust in age. Manufacturing Port Zeta. Manufactures large steel beach umbrellas. Umbrellas are made of a variety of low quality metals and are usually heavily degraded. Produced at a rate of 1 every 11 hours. Manufacturing Port Aida. Manufactures 0.3 x 0.5 x 0.3 m blocks of steel. Steel is usually of high quality and appears polished. Produced at a rate of 15 blocks per hour. Manufacturing Port Kappa. Manufacturing 15 cm iron bolts. Assembly line appears to have been damaged as the bolts have severe manufacturing defects that render them unusable. Manufacturing Port Lambda. Badly damaged. Produces a constant stream of metal scrap. Scrap composition varies with samples ranging from bronze alloys matching the plating of SCP-2406 to grey metals matching the blocks forming SCP-1139. Manufacturing Port Psi. Produces steel washers. 2 cm wide and 0.01 cm thick at a rate of 200 per hour. Manufacturing Port Epsilon. Produces high explosive anti-tank artillery shells at a rate of 300 per hour. Personnel should note that these shells are highly unstable due to manufacturing defects. Addendum 744A. Log of communications with SCP-741. Interviews granted by SCP-744 have been very brief. Due to SCP-7441's uncooperative nature. Interview 7441A. Interviewed SCP-7441. Interviewer Dr. B. Forward. This interview was taken shortly after SCP-744's initial containment. Begin log. Dr. B. Can you please identify yourself? SCP-7441. I'm the production manager.  I can't find one of my so-called workers to help me finish this thing. Dr. B. Finish what? SCP-7441.  What you should know is that it must be done. And we have to get it done soon to meet the production schedule. Dr. B. I see. SCP-7441. So are you gonna get to work or what? Dr. B. Beg your pardon. SCP-7441. These machines ain't gonna fix themselves son. You have to get to work. End log. Interview 7441B. Interviewed SCP-7441. Interviewer. Dr. B. Forward. This interview was taken several months after interview 744A. Begin log. Dr. B. Hello SCP-7441. How are you today? SCP-7441. Fine, fine. When are you bastards going to get to work? It's been months and you barely made a dent in this place. Dr. B. Your facility is very degraded. And you have refused to give us any assistance in discerning the machine's composition. Perhaps if you told us more. SCP-7441. Don't talk nonsense. I've told you everything you need to know. Any more information would compromise the nature of the purpose. Dr. B. And that's another thing. You have yet to tell us what this purpose is. Can you elaborate? SCP-7441. You know I can't tell you that doctor. Just fix this place already. End log. Interview. 7441C. Interviewed. SCP-7441. Interviewer. Dr. B. Forward. This interview was taken two years after interview 744B. Begin log. Dr. B. Look, we've told you again and again. We don't know when the facility will be operational again. We have people working day and night. SCP-7441. Bullsh** you do. I see your people working. They don't do sh**. You and your people have been lying to me, doctor. I don't appreciate being lied to. Dr. B. Nobody is lying to you. We want to have this facility operational as much as you do. SCP-7441. Don't think of me as a simpleton. I see how you react to the purpose. You don't know what it is and it scares you. Dr. B. Now if you could just tell us what the purpose is. Maybe. SCP-7441. No, let me tell you something, mister.  If you see something that you don't get, you try to lock it away. The world deserves to see the purpose, doctor. And you are impeding it. I would think you of all people understand the futility of standing in the way of progress. Dr. B. Why can't you tell us? SCP-7441. That defeats the real, awful truth of it all. You'll just have to help me so we can see it. End log. Lesson complete. If you missed the previous orientation, go watch SCP-743. A chocolate fountain. Right now. Or for the complete course, watch this playlist.