Thank you to the organizers for the invitation to speak and I apologize, I have to speak in English out of necessity. So, and so while somebody remarked just after Michael's talk that so my job was now to just wrap everything up instead of explain how it all hangs together. And so somehow luckily I had decided from the beginning not to attempt to do this. And so instead I wanna give a talk which is maybe a little different again to some of the previous talks. There'll be some, the relation with history will just be my own naive view of history. So my view of history of mathematics is the heroic view where Galois are supposed to inspire us and we sort of derive maximal inspiration from him and from the work that followed. And at the same time I want to try and illustrate in some detail with some concrete examples some of the concepts that have been discussed in a way that I hope will be useful to at least some people here. So certainly not to any of the experts but maybe to some other people. So my own understanding which has sort of developed as I was thinking about this meeting is that the theory of Galois representations seems to begin with Galois himself. So Galois considers a polynomial of prime degree say P and he says that well we let G be the Galois group of F. I shouldn't say this is irreducible. And then he says that G is solvable and hence the polynomial is solvable by radicals if and only if we have an embedding of G into this group of matrices sitting inside Geo2FP where well this G acts on the P roots of F so this G naturally sits inside the symmetric group on P letters but this group acts on Fp, via affine linear transformations and this is also has P letters and so in fact this group sits inside Sp as well. And so this was Galois so-called Galois theorem and it produces an example of a Galois representation over a finite field. So something I didn't know until quite recently was that of course the many people he didn't know was that Galois also studied another example of or introduced another example of Galois representations into Geo2FP so again Galois and now we'll use the modern language says if we consider an elliptic curve and I have an example in mind so let me write down my example. So y squared, this is an example of an elliptic curve so that's a cubic equation in x and y and it has some graph in the xy plane and because it's a cubic curve we have a relation which is somewhat hard to draw. This is a somewhat realistic depiction of the graph but it's rather flat so it's a little hard to draw but when we draw a line a line will meet in three points a straight line will meet this cubic in three points. Now this cubic has one distinguished pointed infinity so all the way up here there's a pointed infinity and so there's a ternary relation on the points of this cubic and there's a pointed infinity and so we can define an operation an operation is a ternary relation we have to begin with two things and produce another but we can think of it as a three things being related and so the relation is that p plus q plus r equals zero so the pointed infinity will be the zero if and only if p, q and r are collinear. So the points of this elliptic curve form a group and so this has been explained in the lecture of Housel and in the lecture of Bost. Of course Gawar and his contemporaries at least in our modern view is probably for me easiest to say they labored under the language of elliptic integrals which made it harder for them to discuss this group law but they could certainly understand it and discuss it and what they found is that of course these points are, I've drawn a real curve but as most people or everyone here knows in fact if you plot the complex points of this curve you get a torus which we can describe for example a C modulo ellatus so in Bost notation you wrote gamma so this is a lattice in C and then it's easy to see the torsion points so the p torsion points in our elliptic curve well as a group this is as a space and as a group it's a product of two circles and so the p torsion points are just if you like there's even a pz plus even a pz or if you want a two dimensional vector space over fp but a typical thing that seems to happen in number theory is that rather simple objects get presented in rather interesting ways so that if you try to for example with this curve that's not so hard but already minimally painful to compute by hand the two torsion points if you try to compute the three torsion points you suffer more the four torsion points is as far as I was personally willing to go by hand it's not so easy to actually find the equations so the equations on this curve that describe the x's and y's that live in this set of order p squared these are the equations of multiplication that Jacoby and Abel and Galois were trying to find that Bost was discussing as he said they're these marvelous formulas one could also say horrendous formulas so it's not so it's not so easy to actually describe this rather simple group concretely in terms of these x and y and so one reflection of that is that so we write e p q bar for the points that are p torsion so the x and the y will be algebraic numbers and because the equation had coefficients in the rational numbers the Galois group acts we're solving an equation over q we have irrational solutions but they have the Galois symmetry and so this is another source of maps of the Galois group of q into g o 2 of f p so those are two ways in which Galois introduced representations of the Galois group of q into g o 2 of a finite field and so the title of my talk was Galois representations and so Galois deformations or deformations of Galois representations so what is the theory of deformations about? So primer-facie if we begin with some row bar from a homomorphism from g q into g o 2 of p what we mean by deforming this means lifting row bar to representations whose whether entries of the matrix live modular higher powers of p say modular instead of just being having matrices to find modular p try and find representation with matrices to find modular p to the n which when you reduce modular p recovers the original row bar so that's what I mean by lifting row bar to a row n and so we want to study these lists or these deformations and one thing we observe is they form a space what does this mean? Well what does it mean to have a space? You have a space if you can say whether two points in the set are close or not and if we have two if we have for example two lifts of row bar modular p to the 39 we could agree they were somewhat close if they agreed modular p to the 38 maybe still reasonably close but not quite as close if they agree modular p to the 20 primer-facie they have to agree modular p because they're both lift to a bar but we can so we can talk about how congruent different lifts are and hence our set of lifts is a space and the kind of basic goal given row bar understand the space of lifts and then an important point that I have to come back to is perhaps with conditions so we can put conditions on our lifts and the kind of conditions that we might want to put are related to the conditions that Michael described in the near the end of his talk ramification conditions so but to explain why we would do that I have to talk about the kind of true goal the more kind of verified goal of the theory is to establish the conjectured relationship between our representations and automorphic representations so that's so this theory of deforming our representations was introduced by Barry Mazer so the whole thing I have introduced introduced by Barry Mazer inspired by work of Hitta in part which Hitta's work had its origins in the theory of modular form to the relation with our representations and Mazer introduces theory as a way to try and understand what Hitta was doing but more generally to see more deeply how we would understand the relations between automorphic forms and Gaoua representations so that's sort of been the goal of the theory from the beginning and it's the goal of the practitioners currently so when I speak about Gaoua representations satisfying certain or lifting satisfying certain conditions I have conditions in mind which are going to be local conditions at various primes on the Gaoua side which is supposed to match in the sense of Michael's matching of row p's and pi p's that are supposed to match with conditions on the automorphic side but I think what I would like to do is to try and illustrate explain a Gaoua deformation problem an actual honest one which will illustrate some conditions some liftings, some conclusions and it's going to be in a very special case but I think it's sort of indicative of how the general theory goes so let me turn to a special Gaoua deformation problem or I should say a very particular one well in fact let me sort of as a so the problem I want to describe will be GL2 but let me begin with a preliminary with GL1 so this is an example that's been mentioned many times already because we can't hope to discuss it it's Gauss's theory of cyclotomy but let me describe it in a certain way it's not exactly how Gauss described it I think so I will use the language that Jean-Marc Fontaine introduced in his talk so P a can be any commutative dream and we have the following function that we can apply to a so mu P to the n of A we define to be the elements of A which are P to the n fruits of one and so there's a functorial construction in the ring A and we produce a group of course if this is a subgroup of the multiplicative units inside A so we have functorially construct the group from A and we construct the group by solving an equation in A so that's called a group scheme this is in fact a finite flat group scheme so this is an example well this symbol is mu P to the n is a finite flat group scheme so it's a group that depends functorially on A constructed by solving equations and if you have such an object you can apply it to Q bar we can apply it to the algebraic closure of Q and on the one hand it's a functor so we get an action of the Galois group of Q or more concretely we're solving equations with coefficients in Q even in Z with values in Q bar so we have an action of the Galois group of Q of course in this particular case it's not a mystery what the values are the P to the n fruits of unity form a cyclic group of order P so this is isomorphic to Z mod P to the n and so this action gives a representation maybe I'll call chi sub n because it's a character into G O 1 of Z mod P to the n and this is called the mod P to the n cyclotomic so we can look at the mod P cyclotomic character the chi 1 and then all these chi n's are deformations of that chi 1 so this is an example of a collection of compatible lifts of a one-dimensional mod P Galois representation and they have a property which is that they are finite flat they're all constructed by solving a finite flat group scheme so this finite flat is an example of a vermification condition so we've seen various vermification conditions occur in the previous talks we've seen unremifed away from S we've seen crystalline and deram at S so this is a very special a very special condition it's a special case of crystalline and it has a very concrete thing it just means you're solving some equations and so with this warm-up done now we can move to n equals 2 keep that we move to n equals 2 okay so now I want to begin with a row bar a two-dimensional row bar and then I'll write down some row n's and so well a good place to start is is a Galois theorem because that gave us some two-dimensional row bars so we just have to choose an f we have to choose a solvable polynomial with prime degrees so let me choose a famous one so I take f of x equals x squared plus one in Galois context and he produces for me a two-dimensional Galois representation I have the Galois group of q of course the roots of this we know they're plus or minus i so we factor through the Galois group of q a joint i over q which is a fairly simple group it has the identity it has complex conjugation which will embed into f2 star f2 1 0 but f2 stars are fairly simple groups which just will one goes to the identity and c goes to the only non-identity matrix which is one one zero one so that's an example of a two-dimensional Galois representation one thing I want to remark is that this two-dimensional Galois representation is again finite flat so this is an equation we can also obtain by solving equations of course we built it by solving an equation but that equation doesn't realize the representation as being finite flat if we think about how the Galois group acts on the roots of this equation we get a permutation representation on a set of order two I'm trying to make a linear representation on a vector space over f2 of dimension two but so this robot nevertheless it's finite flat and I can just write down the function for you so let me write it down so I'll call it g sub one in anticipation of having some g sub n's in a moment so g sub one is going through again be a functor that takes a ring and produces a group so I start with a ring and I'm going to produce a group and it has to have something to do with a square root of minus one and you'll see that it does so I take my ring and I adjoin a variable i so that i squared equals minus one and then I look for elements so not just in a but elements in a adjoin i such that a naught plus a one i squared equals one and also such that a naught times a one equals zero and now so these are square roots of unity but not inside a but they're square roots of unity inside a adjoin i so they're naturally multiplicative group and you can check the g1 of q bar this is for any a this is a group of order two which is constructed so all the elements have order two so when we plug in q bar we're going to get some f2 vector space and in fact uh... it's spanned by you just check it's spanned by minus one plus zero i and little i so this little i is the actual square root of minus one inside q bar and this capital i is a formal square root of minus one that we adjoin to q bar so it's uh... yes zero plus i times i so those two elements span g1 of q bar is an f2 vector space and you compute how gawa acts and it acts through the representation row bar and so that's for example what it means to realize this row bar as a finite flat representation and having done that we can deform it so deform it in a kind of obvious way if we had the second use of unity we could lift them to fourth and then eighth and sixteenth use of unity and so on so we can play the same kind of a game here so we define gn of a to b so i have a variable now zn so this is an element of a adjoin zn and i want to satisfy the equation that this element now to the uh... two to the nth power equals one i again ask that the the products of the distinct coefficients vanish and here this zn the formal variable satisfying the relation instead of just adjoining a square root of minus one we adjoin a two to the nth root of minus one and so again this is some very explicit group scheme that we can write down so again this is thought of as sitting inside this multiplicative group so it's a attaches a a group to every a we get a group the exponent is two to the n and we can map these groups one to the other by squaring so we we square and we set zn squared equals zn minus one and z one of course will be capital i you see that you get a map you get maps of these groups and so we've written some group schemes that form a kind of a group scheme of exponent two and that exponent four and exponent eight which are compatible we can take the q bar points and we get a family of representation so we set rho n to be g n of q bar this is a two dimensional representation of gq over now z mod two to the n and these rho n lift rho bar compatibility so so one reason I'm writing down these equations is just so in the uh... maybe the first day Howard Edwards in his talk commented that gawa's theory was in principle constructible constructive but in practice one couldn't write down the equations and this is certainly the feeling one has when one works with elliptic curves in the torsion elliptic curves so I think that somehow at least for me psychologically useful to see some family of finite flat group schemes some family of equations which is written down which you can just see by hand is is there is not a complicated thing as this concrete is more concrete than what gawa is writing in the premier memoir but it's somehow pointing at the same time to the general theory to the theory of schemes to the theory of deformations to the theory of gawa representations so what what can we say now about this family so is this family of any uh... is this family of any merit at all well this family has a very prescribed ramification because it's finite flat over as we say these group schemes of a flat over z so this is over z so this is a finite flat group scheme over z and that's a very very tight ramification and it's furthermore the only kind of prime that's getting into the action is a prime two and that's a very small prime so michael explained in his talk on the automorphic side that if you restrict ramification you get a final statements and he said that such things are less obvious on the gawa side but we should remember there are some final statements on the gawa side that we know well so we know minkowski's theory which tells us that there are no unamified extensions of q we know the finiteness of class groups and then by class field theory we know finiteness of abelian extensions if you restrict the ramification and so similarly this this set of group schemes kind of is witnessing a certain finiteness statement because the ramification is so tightly constrained and so what one can show is that the row n the unique list of row bar that a finite flat over z and so that's a typical example of a theorem in deformation theory you start with a row bar that's perhaps of interest you impose conditions that reflect ramification you have you hopefully have an example of gawa representations you'd like to understand and then you try to identify your you try to make your example exhaustive enough so make your examples are sufficiently exhaustive in relation to the conditions you imposed to see that all the examples you know is a draft from some all the examples you know coincide with all the possible examples that nature knows and so so of course the difficulty is if you can if you make your constraints too tight I mean you may get something a nice statement but perhaps not so much interest so so I want to push this example a little further make it a little more interesting by introducing an elliptic curve so well for me that's kind of interesting enough to have an elliptic curve hopefully for some other review as well and so which elliptic curve do I want to bring into the picture so I'll use that one so let me just recall it so we have x y squared plus x y plus x is equal to x cube minus x squared minus x minus fourteen now I guess thank you so so this is actually a rather interesting elliptic curve it's not sort of the first elliptic curve in nature but it's maybe the third so so Huzal and Burst both explained in their talks that the in the 1830s people were studying these modular equations and so this is the equation that relates all the elliptic curves with varying modulus and all the isogenous elliptic curves for some prime p so so the kind of modern notation for the kind of the modular equation for p isogenous so something we can do that was harder for for the ancients to do is we don't have to write an equation we can just give the object a name so our notation is x naught p and when we write x naught p so as Burst explained you have a choice of variables j and j prime k and k prime k to the one quarter and k prime to the one quarter when we write x naught of p we're not committed to any particular variables in fact we can choose them as we want so I'm going to choose these x and y and this is x naught seventeen so that's the curve x naught seventeen so it's describing the modular it's describing the relation between elliptic integrals and then seventeen times the elliptic integral although I couldn't tell you now how to compute x and y in terms of k and k prime but one could in principle even in practice with a little calculation so so it's a very natural curve and so as a and so as I described at the beginning its torsion gives rise to Galois representations and now what kind well there'll be to compute the torsion on this curve we have to solve equations we have to draw lines and figure out when we add something to itself so many times whether we get zero or not so we have to solve equations so we get a group scheme and what kind of a group scheme do we get well we almost get a finite flat group scheme except a world be finite flat over z in fact there's an a priori reason for this so there's a theorem of growth and dig which said I think it's due to growth and dig which says that if all the n torsion group schemes for an elliptic curve for every n a finite flat over z then the elliptic curve would have good deduction at every prime over z but this elliptic curve doesn't have good deduction as chronicle already knew at seventeen at seven so so most at most primes when you reduce it it looks like a nice cubic curve but at seventeen it has it has a node so this curve has a node at seventeen in fact I can even tell you the point so you can check so this has a node at the point seven thirteen mod seventeen you can just compute the derivatives there and you'll see they both derivatives finish and so what happens is if you take torsion points if you write down the group scheme of torsion points it will be finite flat away from seventeen but typically what happens so you'll see this first when you look at the fourth division of points is that when you reduce the module at seventeen some of the points hit this node when you reduce the module at seventeen and that means they escape from the group so this nodal curve is not a group the node is if you remove the node it's a group at the node there's no group law and so some of the torsion points escape into the node when you reduce mod seventeen so so it's a group scheme of a z but it's finite flat just away from seventeen what happens what happens is that at the prime seventeen when you look at say the the two to the n torsion and you have z mod two to the n cause z mod two to the n and you reduce mod seventeen it will turn out that exactly one of the two dimensions doesn't go to the node and everything else does so kind of so to speak only half of the dimension of the gawa representation sort of survives in character 617 so we say that semi-stable so this group scheme so this gawa representation on the torsion points here they are finite flat away from seventeen and semi-stable at seventeen and now but not that's not completely the case because there's a little mercy which is that if you look at just the two torsion points you can compute them there's the origin eleven over four and minus fifteen over eight there's minus one minus two i and then there's minus one plus two i minus i these two have to be conjugate and so the two torsions to find over q adjoint i so the gawa action on the two torsion it's not trivial but it factors through the the gawa group which is the same gawa group that roba factors through and in fact you can check this is isomorphic to roba so this elliptic curve the two torsion doesn't know about this node in characteristics seventeen the two torsion is finite flat over z but as you look at if you were to compute the four and the eight and higher two-power torsion eventually it discovers the node and so uh... what do we have so we could look at we can consider deformations of roba that a finite flat over z seventeen inverted and semi-stable at seventeen and the determinant equals the cyclotomic character it was a member as uh... as both explained for an elliptic curve the determinant of the uh... the uh... the uh... the intersection pairing on homology gives you a pairing on the two to the n torsion but it takes values in roots of unity and so the determinant is cyclotomic character so we could look at that defamation problem and then we have two solutions so so the row n coming from my group scheme is gn a one solution to this defamation problem because they're even finite even at seventeen they're better than semi-stable and then i take the two to the m torsion points on this elliptic curve and those are another solution and again it turns out that these are the the unique for the only two solutions to that defamation problem and so that's just another example of a defamation problem and a solution but it's already a little more interesting because it involves an elliptic curve it involves the characterization of an elliptic curve purely in defamation theoretic terms and so and so that's that's one of the so this is sort of one of the goals in general defamation theory to characterize certain defamations of interest perhaps especially attached to interesting objects such as elliptic curves in some gawa theoretic purely gawa theoretic terms and how does this relate to automorphic forms well so now let me just be a little griffer but this elliptic curve E it was I mean it was x0 17 so it somehow thought logically relates to a modular form actually so it relates to a cuss form which well I can write down the q expansion anyone guess it's it's a certain form of level 17 and what about these are these finite flat row n well they relate to something as well they there's an there's another modular form of level 17 the eisenstein series as this q expansion and you can check that for example minus one and one a congruent mod two and minus one and three a congruent mod two these are congruent mod two in fact even if you forget the constant term they congruent mod four and that reflects the fact that this row n and this e were deforming the same row bar so so the fact that you had two different families of gawa two different kind of solutions to the gawa defamation problem coming from the same row bar on the automorphic side that reflects that two automorphic forms were congruent and so the theory of the theory of congruences of automorphic forms is sort of a tool on the automorphic side which is the kind of automorphic mirror of the theory of gawa deformations so we know there has to be in the postmodern formulation each side has to kind of answer a question of maybe pose a question to the other side and so to the theory the question to the theory of gawa deformations poses to automorphic forms is the theory of congruences of automorphic forms so okay so that's sort of supposed to be an illustrative example that shows the some of the kind of technical features of the theory but I hope give some sense that it's the same mathematics the same part of mathematics that was being studied by gawa and arbol and jacobi it's the same chronicle gawa it's in the same tradition it's the same kind of questions we've hopefully just moved a little further in our understanding and what I'd like to close within the last few minutes is just to say using this as some kind of illustration what what happens in the general case in the theory of deformations so well ultimately what happens is that some spectacular theorems have been proved so the modularity conjecture for elliptic curves the sato by wiles and taylor wiles the sato tate conjecture for elliptic curves by clausel and hyresonship of baron and taylor the uh... and then another important result very important is the caisse conjecture sold by carry and ventabagé well so kissen uh... and roughly okay so those are those are some theorems but where does gawa how did our deformations enter and so roughly to prove these sort of theorems one needs four steps and so we can just briefly describe the four steps and see how they relate to these examples so the first thing is you need to construct gawa representations attached to automorphic forms so in this case I had only two automorphic forms in the picture one was an eisenstein series and these correspond to some characters on the gawa side they're billion class field theory and we had a class form that was attached to an elliptic curve and so that problem was solved but in general this somehow this this is the problem of shimua varieties the general the the uh... developments arising from considering chronic as jogantram to misquote langlands is this part of the story then one has to having shown that they are gawa representations attached to automorphic forms one is going to try and show that they fill out certain deformation spaces so one has to show that there are enough such gawa representations which now the question of showing there are enough automorphic forms so one has to somehow count automorphic forms and be able to produce automorphic forms then one has to be able to bound the size of the gawa deformation space from above one's bounding it from below by exhibiting automorphic forms and hence exhibiting gawa representations and one must find some other way to bound it from above and with luck the two bounds meet and then one's proved that all gawa representations of a certain kind are attached to automorphic forms and there so there so one basic difficulty which has sort of been alighted here is you don't know what gawa deformation space you have to consider a pro because the gawa deformation space depends on the row bar and if suppose i have a an elliptic curve that i'd like to prove is modular and i look at its p division points and that's the row bar and i'm going to look at the deformation space for that row bar and i'm going to try and fill it up with automorphic points we'll have to know there's some any automorphic points at all and the conjecture that they are such points was was ses conjecture and that's been proved but the exhibiting for a fixed row bar to say especially dimension greater than two to exhibit any automorphic forms at all that give rise to this row bar that live in its deformation space seems to be one of the hardest problems and maybe it's one of the row blocks to further progress at the moment so the generalization of ses conjecture is a fundamental issue once that's dealt with there's a question of exhibiting enough automorphic forms to fill out the deformation space and that has to be coupled so that's and then there's a problem of bounding the deformation space so it turns out those two problems become coupled in an amazing method of tailor and wiles and so the substance of the method roughly is that you have a very very complicated space and you can compute its tangent space you can compute the tangent space your deformation space at row bar but it will turn out to be very high dimensional typically and when that happens you don't know whether it's high dimensional because the space is high dimensional or does because the space is highly singular and in fact what you want is a space to be low dimensional you want it to be as low as possible so you can fill it up with all the automorphic forms you know but your so your hope is that it's highly singular and low dimensional but your fear is that it's quite smooth but huge dimensional but so what what happens in the theory of tailor and wiles is that they choose carefully certain directions in which to relax the deformation problem and so it's as if that's as if you were in the following situation as as if you had this variety and you computed the tangent space at the origin and saw that it was two-dimensional but you didn't know that whether the variety was a surface or a curve I mean it looks like it should be a curve but perhaps there's a surface you know perhaps this is you know perhaps there's something strange happening it would be probably better if I added more variables but let me just keep it as it is and so the the argument of tailor and wiles is the following that you you eliminate this equation f1 you see what happens when you remove that equation but you carefully chose that f1 among all the possible elements in the ideal so that the tangent space did not enlarge so the tangent space is still two dimensional but now there's only one equation so we must have a smooth surface and then our original variety must have been obtained by imposing a non-trivial equation in a smooth surface so our original variety must have been a curve so that's the argument of tailor and wiles but you have to choose this equation very carefully to not change the tangent space and at the same time they want to fill up with automorphic points so at the same time you as you remove that equation you get more space now there are more points that solve the equation they choose these primes so that they can make sure there are a lot of automorphic points there and I'll just close by saying that I was struck by again something I saw in boss talk today that well in the end in the tailor wiles method you choose is relaxing the conditions the equations you choose are the equations that say finite flat at 17 so when I relax you know in my two deformation problems I did I relaxed the condition at 17 from finite flat to semi-stable this is the kind of thing they do they relax the condition by allowing ramification at a prime but very interesting that you sort of have x naught one you have x naught q this modular equation and then as both said you have x one q which looks at the the actual q torsion points on the elliptic curve and we saw in the letter of jacobi that this is unsolvable but this is abelian and this abelian extension is what makes it the tailor wiles method work and in the end they can argue they're doing non-abelian class field theory but in the end they can use the principles of abelian class field theory as they're captured in the theory of gala chronology and so I mean somehow I found that a very kind of inspiring thing to see that the most advanced method in the current technique is somehow echoed being you know discussed in some sense maybe in a very ephemeral sense but appearing in some way back in the first practitioners of the theory of equations that gives me a good sense of continuity in the field you know optimism for the future so I'll stop there the question the case you discussed at the end it's complicated enough but it's it's still the case where finally you prove that you have the isomorphism and you have a complete intersection right yes so it's even more complicated in the general case and in particular in those well well in the most I would say like the sort of there's a there's a more recent form of the tailor wiles method which one will call the tailor wiles kissing method which deals with an additional phenomena which is that when you when you relax the conditions at a prime to add automorphic forms you count how many automorphic forms are added and the number of automorphic forms you have new forms you obtain is linear in the level and that's enough to see that the dimension of the automorphic if you close up the automorphic forms the dimension of the space that they fill out is the right dimension but these spaces could have multiple irreducible components and so then one has to investigate the question of whether all the components are filled out by automorphic forms in fact it's there's a slightly naive rendition of what really happens but at that point the commutative algebra and the geometry become more sophisticated the complete intersection drops away a little bit but still this I think this is a kind of reasonable mental model for what's happening in the tailor wiles method so I have a non-mathematical question so if I understood correctly you explained that a major open problem was to describe more or less explicitly on the representations that lift a given one and for me this question has a eugntrum like flavors flavors so is this a delusion or is there I don't think so and in fact so I mean I maybe gave a slightly wrong impression that I mean not only it says conjecture be improved for n equals two but there's a potential says conjecture for a kind of high-dimensional Gal representations which is of vital importance in the progress inside to take in everything else but also of vital importance in the proof of the full says conjecture so and but that's an argument that uses geometry to construct the the lifts and so I mean if we can interpret eugntrum to mean the interaction between Gal representations and geometry I mean it's exactly seems to be that sort of a question not too difficult but eugntrum doesn't have a precise formula in fact maybe depends on the dreamer I don't know if there are questions in the answer to the question I don't know if you hear me or if there is someone in the meantime I would like to remind you that there is a cocktail at 19 hours at 45 products at the school Normal Superior in the historical room of the library of letters


Income Tax 2021-2022 Excel Worksheet. Create a tax formula worksheet using Excel part number three. Get ready to get refunds to the max. Diving into Income Tax 2021-2022. We are in our Excel worksheet in prior presentations. We started putting together the income tax formula starting from a blank worksheet within Excel. If you missed those presentations, you might wanna go back and take a look at them. The idea being that we're gonna be putting together the income tax formula in somewhat of a more simplistic type of form, helping us to visualize the formula and also helping us possibly to kind of make a double check as we do data input into tax software. So we're gonna be continuing on here. So we have the outline of the formula. We have in essence the income statement, the top half of it, income minus the adjustments to income or above the line deductions, schedule one deductions you could call them. That gives us the AGI or adjusted gross income. And then we subtract the greater of the itemized or standard deductions, which we have some fancy formulas here to pick that stuff up with the if formulas and so on. And then we've got the qualified business income deduction, which would only be applicable in certain instances, possibly if for example, having a schedule C, that gives us our taxable income. And then we jump down to the bottom and we pick up the actual tax from the tax software because we're not gonna calculate the tax into the system, but instead we're gonna rely on software to do that. That's why it's gonna be blue here because we're gonna be showing blue items as the items that we're gonna be populating in this form, basically manually putting that number into the system.  And then we're gonna be subtracting out the refundable credits and the payments. Now we wanna add some more information to it including the sub schedules. And you'll recall that this outline in essence, you can think of it as basically the first page of the 1040, although the 1040 is a little bit more expanded than that. And then all other schedules feed into some line item in general on the form 1040, the kind of summary page. That's in essence what we have here. So now let's just add some of the other items that we might expect in another tab that will then feed in to the first page so we can see how that will work. So the income line item, we already added for example, the income line item for the W-2, even though that was on the first page of the 1040, some of that stuff will be here like the W-2 income. We put it on a separate tab on our formula because I think that it's easier to basically visualize. We also could have some other stuff that will feed in here, such as a schedule B for example. So if I went down to the schedule B, this is interest and ordinary dividends. And it would only be used if your interest and dividends were over a certain amount. But for example, that's another area that you can see adding into this income line item. So we might have multiple tabs, for example, that are going into the same line item. You could try to put some of those stuff on the same page right here and say it's all income items or you might have another tab. It could be a little bit more clear to have more tabs. So I'm gonna say let's have another tab. I'm gonna double click on it. This is gonna be an income tab and I'm gonna call it interest and dividends or an S schedule B, schedule B tab. So we're gonna say that. Let's go ahead and format it. I'm gonna select the whole tab. Like we have seen in the past, right click and format it. Format all the cells, formatting the cells to currency. I'm gonna make the negative numbers bracketed, get rid of the dollar sign, get rid of the pennies and then I'm gonna say okay and then hold down control. I'm gonna scroll up a bit and so there we have it. And I'm not gonna put a lot of detail in here at this point in time. I'm just gonna just to get an idea of these sub tabs and then when we get into these line items as we go through the practice problems we'll build up this Excel worksheet as we go. But in general, you're gonna have interest and they might be coming from the 1099. So I'm gonna say interest. I'm gonna select the whole thing again and make it bold. So we might have interest and then they could come from like 1099. So this would be big, 1099 interest. This one might be indented now and then we could have a few spaces. So I wanna have, we could have multiple places that we're getting 1099 income. So I'm gonna give it a little bit of space and I'm gonna make this whole thing blue to indicate this is where my data input will be. So I'm gonna put my bucket here and if you don't have that blue it's gonna be in the more colors and the standard here and then that blue right there that's the one, that's the Excel is fun guy blue. And then font here hit the dropdown we're gonna go down to the all borders. And so there we have it. So if we had interest of say, you know, $100 then I'm gonna total that up at the bottom. So we'll say total interest, total interest and I'll sum it up on the outside with the trustee sum formula, sum of these items. And then I'm gonna add dividends here too because this form has dividends in interest typically. So you got dividends down here. So I'm gonna have another category part B. I might even sub-categorize it as part A and part B. So I might say this is interest or part A, part A or part one, was it? Part one, part I, part one, right? Isn't that how they say it? Part one and part B. So then I'm gonna put dividends down here, dividends. Part two, not B, two. We're doing Roman numerals, not letters, Roman numerals. So this could be bank, this would be a form 1099 whatever data input that we're imagining here. I'm gonna indent it. I'm gonna make this whole thing blue. We'll give it a few spaces down here to give it enough room. So that looks good. I'm gonna make it blue, put brackets around it and this will be the total, total dividends, put that on the outer column equals the sum of these two. And dividends can be a little tricky because you might have, I'll put like $50 in here, you might have dividends that are taxed at different rates. So we'll talk more about that later, but just to give a general idea. And then if I was to take total interest and dividends equals the outer column here, the outer column, I'm gonna sum up the outer column. There it is. That number is what I wanna pull into the line item, the first line item on the 1040. Going back to the 1040. So what I'm gonna do is double click on this 100, go to the end of it and say plus, go back to this tab and pick out that 150. So that's where we can see now we're at the 100 and 150 in the income line item. And we can continue on with that with different income line items. You can see here that this schedule B feeds into the 1040 on line one or on page one into the interest and dividends that are gonna be on page one. So here we've got the dividends, dividends, we've got different areas of ordinary dividends versus qualified, we'll talk about those later and the interest. And also you might not have schedule B if it's below a certain threshold. We'll talk about that later, but you can see how that kind of feeds into page one. So there is that. So let's move away from income. There's a lot of other things that will be fitting into the income line item. But that's the general idea. We'll just keep on adding tabs as we need them, feed them into the income. Other tabs might be schedule C, schedule D, schedule E and so on. And then adjustments. So adjustments we could go over here and say, okay, how does that work on the tax return? If I entered an adjustment that would be typically on schedule one and page two, this would be adjustments to income like educator expenses, certain business expenses of reservists, health insurance moving. So you might then say, okay, I'll just make another tab here that includes all this stuff or at least a lot of this stuff in it in my worksheet. So I'm gonna say, okay, let's make another tab. I'm gonna say, let's make another tab. And I'm gonna put this, I'm gonna drag it, grab it and drag it, grabbed it and dragged it. Get over here thing, drag it did over there. And then I'm gonna double click on this and I'm gonna copy that. It's gonna be adjustments to income. Adjustments to income schedule one. So double click on it, call it schedule one adjustments to income. So there it is. And this time I put the schedule first, maybe I should be doing that all the time like schedule B before this part. So maybe I should be saying schedule B cut and put that up front, maybe. Is that better schedule B? And then the income form 1040 income. I'll leave that the way it is because it's the 1040. Okay, so I'm gonna go back on over here.  So I'm gonna format the sales and I'm gonna make it currency, dollars, brackets, negative and get rid of the dollar sign. No pennies because it's a tax return. I'm gonna increase the size, holding control scrolling up to 190 for me. Select the whole thing. I'm gonna make it boldened. I'm gonna emboldened it. The whole sheet has been emboldened. And then I could add basically all of these in place. I'm not gonna add them all right now. So if you wanna do this at one time, you could. I'll just add the IRA for now. That's one of the more common ones you're gonna see. So let's just add an IRA. So we'll say IRA. I could name it up top. Let's say adjustments to income. It might not be in the same order. It won't be because I'm gonna just add the IRA here. IRA, IRA, I'm gonna indent. Now you could have multiple different components for the IRA because you could have the married couple IRA for the husband and spouse. So you might want a couple of spaces even within the IRA. So you might say IRA and then you might have a couple of spaces down here for the IRA. And then you could have the total IRA possibly. So let's do that. Let's give it a couple of spaces. Like one, two, three, four. I'll make that blue and bordered. And I'll call this total IRA. That's not the IRS. What are you doing, IRS? IRA, IRA, IRA. Not IRS. And then I'll say the totals on the outside. I'll put this in the outer column equals the sum of these items in the outer column. And so if I had an IRA of like $1,000 for example, there it is. And let's pick up just one more just for another example, student loan interest. Okay, let's say, okay, student loan interest. Maybe I should skip a line. Student loan interest.  So maybe I'd make these black and white. Depends on your preference. Just to note that this is like a new section maybe. Black and white student loan interest. And again, you could have multiple people that have like student loans depending on husband, wife, that are coming on different forms. So you could have a few of those actually. So let's give it a little bit of space here and give it brackets and we'll make it then blue. So there it is. And say, let's say we had one of these forms and let's say it was a big $200 student loan interest. And so then that would give us the total, not the teetle, total student loan interest. Tap it out, tab, tab, or one tab and then I'll sum it up, summing it up. And so there we have that. And so this is just a rough draft. We'll keep on adding these as we go, but you can see kind of the pattern here that we have.  And then we'll sum up the outer column, the outer column, there it is. And then I can bring that over to the first page. So this first page, I'm not just gonna have a zero there. I'm gonna say this equals whatever I come up to in my subschedule, which is right here, 1200. That will match in essence what we do on the tax return when we populate items into this schedule A and then it will feed into page one. So for example, if I went into the IRA here, say IRA, let's go into the IRA, sorry, I got hiccup. And then I'm gonna say this is $1,000 and I'm gonna bring that on over. Now schedule one is populated as you can see and we're on page two, so there it is. And then it sums up down here and it pulls it over to page one, back to page one. And so now it pulls it into two page one. Now it pulls it into two page one on that line item that's pulling from schedule one. That's kind of how it's built in a similar fashion as it is with our formula here. Let's go and simplify it back. Let's bring it back to our starting point. Let's get rid of the other income, no dividends. Let's get rid of the dividends. Let's get rid of the interest and let's get rid of these items too. And I left a couple of spaces up here on accident. I'm gonna delete a couple rows from one to three, highlighting from one to three, right click and delete those back to the first tab. Okay, so then we have the greater of the itemized or the standard deduction.  The standard deduction is gonna be something that I'm gonna draw from down here. So this is something I'm gonna say is a blue item that I'm gonna data input it right into the first page. So I'm gonna make that blue. This one, however, is gonna draw from a sub-schedule, which will be equivalent or similar to me recalculating a schedule A. So it's called the schedule A itemized deductions. So I'm gonna say, okay, let's make that one. I'm gonna make a new tab, pull it to the right, grab it, left click on it and drag it, get over here, go right there, thing, dragged it over. And then you could have just asked it, right? If you asked it nicely, you wouldn't have had to drag it. Anyway, I'm gonna double click on it. This is gonna be a schedule A, itemized deductions. If I, when I spell anything wrong, because I will, it's not an if thing, then bear with me, I'm gonna count. I'm gonna select the whole worksheet and right click on it and format this thing. Let's format it, currency, put some brackets and some red on the negatives, drop down, none on the sign and take down the decimals. Let's make it the whole thing bolden and bolden the whole thing, hold down control, scroll up a bit and this will be the schedule A. Again, we'll get into more detail on the schedule A because it's a pretty in-depth schedule but you could go line by line and say, okay, I got the medical, the medical has some components to it that we'll have to talk about it. Taxes, we can add the different tax line items. So this one's gonna get a little bit more detail. So let's just, but let's just add like a summary for now. Medical and dental expenses. I'm gonna say, all right, medical. I'll call this a schedule A, itemized deductions. And then I'm gonna say medical and dental. Medical and dental. Okay, let's make this black and white, maybe make these black and white. And then there's gonna be some other kind of subcalculations we'll have in here. So I'll get into that later. There's like an AGI limitation possibly that you can see as they apply 7.5. And so we'll talk more about that later. It'll be a little bit more complex, but not right now, because that's not where we're at. Right now I'm just gonna say, let's make it all blue, put some brackets and let's just imagine, let's just leave it at that for now. And then the next one, the next one's gonna be taxes you pay. So taxes, so it's, and this will be total, total. I can put the total, total, medic, total, medical and dental.  Is that what they called it? Taxes you paid past tense. Okay, let's make that black and white, black and white. And this includes different kinds of taxes. So you could have like state tax, local, local tax, property tax. So we'll get into more of this in a future presentation, but let's just add something here for now and we'll say, let's say this is like 500. On this one, I'll add a couple more lines just to give it some space, brackets around it. Let's put some blue here and this is gonna be total taxes you paid. Bringing that on out to the outside, summing it up. So there's one. Let's do another one. I'm gonna say, okay. What else we got? Interest you paid. Let's stop it at that one for now. Interest you paid. So I'm gonna say, interest, interest you paid. And so let's make that one black and white, black and white. We've got mortgage interest, mortgage interest. And there could be like multiple different, different mortgage interests. So we might even wanna get a little bit more detailed on that because you could have multiple different forms that from different banks, even if you have one home. So you might say, okay. Maybe I need a couple different line items here. Maybe four just to be, just in case I've got someone who has a few different ones here. And I'm gonna say, and then if we start to populate this, let's start to populate this one at like 6,000, let's say. So they could have a 6,000 and a second, let's say, of 1,000. So there we have that. And then I'm gonna sum this up to the outside. Total mortgage, total, mortgage, interest. And we'll bring that out to the outside equals the sum. Actually, now let's sum it up. Let's sum it up right here. I can sum that up right here. Equals the sum of these items. And then we could have other interest, right? Other interest. And we might apply that out. We might have some other interest that we would deal with. And that would give us then the total, total interest you paid, which I'm gonna say now it's gonna be equal to the sum of these two. Not summing these up because I already got a total down here. So there it is. Now, this is just a basic format. We'll go into more of this later, but I'm gonna go ahead and say this is, stop this for now. This is gonna be the total, total itemized deductions. Now we'll get more detail into it as we start making stuff, but I'm gonna sum this up for now outside just so we can see how this is getting built. So we'll just sum this up. And then when I go over to the first page, first page, let's make this a little smaller, on the form 1040, this is not gonna be hard-coded as zero, but it's gonna equal what is on my itemized deductions. So it equals, in this case, that's seven five. So there's the seven five. And in that case, I can kind of go through what happens on the tax return, tie it out to what we had as we recreate the schedule A and basically see, okay, does that make sense to me? Does it make sense? Can I build it myself in Excel? If I can, at least I'm more likely to get some idea of what it's doing. So there it is. Now notice that due to our formula, the if then formulas, because this is lower than that, we're not gonna have itemized, we're gonna take the standard. If we were to increase something on the itemized, and this is usually gonna be like the mortgage interest, that's why most people that itemize are mostly more well off, possibly not just having a home right now these days, but having an expensive home with a large mortgage on it, most likely living in a high cost of living area. So we're gonna say like, what if this was 15,000? Then we're gonna say, okay, then that's usually the kind of thing that'll push you over. And we'll talk more about that later, but now you're taking the itemized. So if you had like a home, and that would increase the property taxes that you'd be paying on a more expensive home and a high cost of living area, then that could significantly increase your itemized deductions and push you into an itemizing kind of capacity. So now you're itemizing instead of taking the standard. So there is that. So I'm gonna go back on over, go back to the simplified one. I'm just gonna delete this for now. Just get an idea of this. And so that's back down to zero. And you can see how you go back into these every time you do a new tax return, clean it back out and then work it again so that you could basically reconstruct what is happening for whatever tax return you're working on. Now we're to the standard deductions. The standard deduction we're pulling from down below. I might wanna pull this worksheet up a little bit so I can see it. So I'm gonna put my cursor on 18 and drag down till I get to 27 and right click and delete. So I pull it up a bit. Maybe I'm like one more row. I'm gonna put my cursor on 18 and insert so it's not right next to it maybe. Insert so it's down a little bit. So there it is. It's down there. You could also put it maybe on this side but I kinda like reconstructing when I have to do calculations over here. If there's anything I wanna recalculate based on this information. So I don't like having it on the left or on the right. That's right. That's on the right. So this is pulling in from the standard deduction which means it's not like you're hard coding it directly but you're pulling it in. You're gonna have to adjust that from this sheet by basically doing some data input. Not hard coding or typing in the number but you're doing activity. That's why I'm gonna make that blue. And then we've got the, this one we'll talk about later the qualified business income deduction. Possibly we would want another worksheet for that as well but we'll get into that later. That's gonna give us our taxable income. So that's our taxable income. This is obviously a formula.  It should calculate properly if everything's set up right. And then this one I'm not gonna do anything to either. That's gonna give us the tax before our credits. Now this one is something that we would pull from the actual tax return. That's why it's blue. Now next time we'll get into the bottom half which is talking about the credits and the other taxes and so on. And we'll add a couple more schedules that we'll show you how we're gonna tie these out in a similar way to other schedules.


tell me doctor where are we going this time i don't know what that song is sure you do gotta get back in time bum bum bum gotta get back in time give me the chorus that was the chorus oh no i don't know it back to the future it's hui luis and the news is back in time from from back to the future it's in the credits yeah it's in the credits yeah you know don't recognize that one you're young yeah i know welcome back to our stupid or xcv it's up corvin i'm hui luis happy independence day rock and roll giant yeah what what year uh independence is it for india this time uh 47 right so oh i'm 73 because my dad was born the year they had independence so it should be 73 74 74 this year 74 should be 74 independence day india obviously you've seen the title so we are doing a movie we wanted to use something to celebrate uh independence day and this one has been on the list for quite some time we've seen we say i think every song did we see every song i think we've seen every song i know like the first one was like the first like one of the first rithic things we ever saw and i think that was the thing that remember when we were like that was rithic right i think it was that song but it was a different reaction that we looked back and we're like that was rithic and yeah i was going to say something but i'll wait till we get into the review anyway i'll say it but yeah so we've seen uh i think every song i believe i believe it was every song i'm really trying to think if it wasn't there's only one we didn't see yeah anyways but obviously it came out i believe in 2004 the film is laxia uh and it's directed by far far our well it's the first directorial film of his we saw good question because we've seen one other uh i don't remember really yeah why did i think that was his sister uh no that's uh that's farhan he wasn't he didn't just produce that he did he directed that he did produce it he did produce it as well i i uh man but anyways yes so they were directed by farhan octar uh starring and i'm gonna talk about john with a very special appearance by ompori ompori and actually a few others uh including um i'm reshpory yeah as well and our dose pankaj yeah but he was edited out which i'm very upset about why would you ever do that i heard a story though that like this was like his first role because it was right right first role and so he took all of his family oh no he didn't know he was cut out of the film that's i think that happened in oise too awful i think we heard a story about that happening to nois at the beginning but that is that is so at least let him know i get it i don't actually if i see that clip i don't know how you could cut pankaj honestly seriously but that is the absolute worst that is terrible anyways uh this could be a hundred and four that came out 2004 uh almost 20 years ago yeah uh so i think mostly you've seen it and in fact i think it's more of a cult classic because at first a lot of people it wasn't a big success did but didn't was it rithika success rithika at the time was already a success yeah but the film itself okay was not like a huge box office so it's kind of like a lot of films obviously until later and then it obviously people uh more appreciated after that anyway so once again hundred cents for a review they have a watch they'll watch it it's on netflix for us i don't know if it is for you rank your initial thoughts please well and that is really kind of a test of a film as if it stands the test of time if you remember a film 20 30 40 years later i think it was a success yeah um i i my basic overall takeaway from the film is that it's a predictable yet thoroughly enjoyable film that shows that farhan octar can act and boy can he get sound people around i mean can direct and get sound people around him uh and it i really appreciated rithik um it now that we're used to indian films going because you you wouldn't see a serious military film have like some of the musical numbers in here especially that one where he's doing the yeah right the thing we saw at the beginning almost two and a half but i'm really beginning more and more to appreciate that style of indian cinema for what it was and what it has meant as a thumbprint of the dna of indian cinema so it's not an award worthy film but it's still to me the biggest part of it that i think is really nice is it was a great choice for us to watch because i think anybody watching this while they wouldn't be moved like they would some like saving private ryan yeah i still think this is enough to make even a non-indian say jai hind and it's predictable but i still enjoyed it yeah absolutely i did as well uh there were i think it's probably the same part for you the the the flashback was probably it was definitely my least favorite part right um but and like i'll compare it to almost still chaha the coach will die even though it's nowhere near as gz nowhere near as over the top and i'm not saying it's like that no there's no cheese but obviously they did the thing where obviously these people who look like they're 35 tried to be basically teenagers again right and then they did some you know weird corky teenager stuff so in that aspect it was a little similar but uh the rest of it like it started off great really assuming is what your your tweet or whatever it was about yeah just as it got started because i tweeted this and i put it on instagram i was just it started and the credits were rolling and we're going and i'm seeing the the titans that you know directed by farhan on like i know we're getting into this military movie and it's independence day and i was just overcome with emotion it's like i'm so grateful that these names farhan octar amitabh bhakjhan rithik roshan and predi and all the other people in it it's like this has so enriched my life and i was anticipating it to be good because of the players involved yeah um so it started off real real good uh like the scene with him amitabh bhakjhan talking to him obviously big b's big b um and then when it transferred over it's not that it was bad it's just it wasn't as engaging to me and i know why they did it obviously the story's about a a guy who has no direction or objective right this is the objective is the word uh in his life and he's kind of just like a slacker comes from a well-to-do family right that can if you want it he could go get a job with his dad if you wanted to i get i get all that it's just some of the stuff was a little cheesy like when he's in the military and he's just off looking he's like you don't have to be that on the nose with it that's what i'm gonna buy the other word i had in addition to predictable was simplistic so like for example later on when priti and her fiancee would you knew they were gonna break up the way that they did at the dinner table was so simplistic and so easy in the writing yeah i did i did love that scene for her priti though for her yeah absolutely and but it was again it was forgivable even though it was predictable it was forgivable but yeah so it started off great and then it got into that but uh my favorite parts were when it actually got back to him in the military that's my that was and then obviously the great i think um battle scene at the end expression for 2004 yeah agree i thought farhan did a fantastic job with that so let's just get into this yeah uh rithic i think there's one of his strongest performances outside of the maybe the the little cheesiness from the from the flashbacks i think this jota akbar i mean i think he did well on super 30 as well um but there's one of his strongest performances i believe i agree this is one for me where i i i i already liked rithic and already was rooting for rithic right um but watching him here this is like you see all the potential inside of this guy for being a solid actor and a hero fully believable on the character obviously a great dancer a great dancer very believable with all the military training he had to do and all the military ops he had to do yeah um and the moments where and even in the the songs but also in moments where he's just being pensive like one of his best moments that could have been so bad with an actor that's not as good was when he's standing looking at the ridge and she's there and he's like i have an objective now and he points up to the peak it was a beautiful moment for him i thought where a lot of other actors would have it wouldn't have been there and i felt like he was fully invested and it it raises the bar for me for another another great scene i think with him and predy was actually when she came to the the base and the song was going on and they were just staring at each other from that song from opposite sides even though i think we saw that it obviously meant more here because we were more attached yeah i was watching it and i was like oh yeah the guy sitting next to her that's not a way but they were just for a while just staring at each other once again one of the hardest things to do uh even though it looks so simple but to look like you're actually engaged and to look like what you're you can tell what they're thinking about in their brain like commercial acting yes it's at which commercial acting is one of the hardest things you'll ever have to do man it's one of the worst audition things it's awful where all you're doing is sitting there and you don't have the track playing to give you the emotional context what you've got as a director saying okay now be seemed too long for her even more okay and you're looking for a motivation you're yeah you're just everything about it is so hard to be real and they were both great yeah i thought she i thought did very well like i said i love that scene even though the like i said the film is a little predictable but obviously at the time in bollywood yeah maybe not right but obviously we're in 2001 i mean 2021 i think the graphic nature was pretty shocking yes for for that time but the her scene where she was actually a strong independent woman yes but she was like hold on what the what the fuck you trying to say to me right now right you're trying to say i can't i can't do what i do because you're gonna be my husband right okay okay well thanks thanks see you later bye not gonna do that so i love that because obviously if people are mistreated like that i never want them to stay in those awkward relationships so and you you don't get to see that often because obviously i think it was a very good scene because with indian culture we see that a lot in films another thing with indian culture that was represented that i this is one of my favorite parts of the film was his relationship with his dad and the way that that was depicted because great scene on the phone yeah the two scenes so well there's several scenes but the first thing you get relationally is the challenge the the quintessential challenge but the dad with the balance of the mom he didn't come off as an asshole you kind of understood where he was coming from he was being a bit of a hard on about things but you kind of when he when he was explaining to him my dad did this and i did this and now we had hopes for you he wasn't being the quintessential jerk you kind of had some empathy for the dad but that phone call yeah yeah when he says i love you dad great scene with both of them and the dad says i love you too i believed it and loved it and i i felt for a for a culture who has consistently talked about how in film you don't see a lot of emotionally available men and especially dads and sons that's probably one of my favorite dad and son moments in indian yeah film i thought i thought it did very well and that speaks to um farhan and i will get into him in just a second i want just a few more people um i would talk about son he's exactly what you want he's just so good he's exactly what you want yeah and it's i i think this is the first time we've seen him in a military and i 100 believed him in this kind of um officer or was he an officer was he a he was a commanding officer yeah sir uh in the army and he but he carries this this weight with him that you you just believe and he's never he's just never bad the dude is so good yep and i love the the appearance of pori i love the uh him and and you gotta go i think one scene from umresh pori as well um and that was that was great to see but i i thought i'm gonna talk about you did a great job as did all the other supporting guys that were soldiers with them because a lot of the times you'll have something like this and some of the other supporting folks around you weaken it and i didn't think they did i'd like for example when i forgot his name but he's the guy that comes back um who was supposed to put the flag up and he's just all torn up and the buddy who's trying to sell him up and telling him you're gonna put the flag up when he dies his response to him dying was believable and oftentimes when you have an actor in a smaller role like that they are cliche or they're uncomfortable and you can see it because the camera doesn't lie but i felt like everybody that was in there yeah did a very solid commanding officers that were trying to attack with them that was some of them that died once again this is part of the movie um i thought did really good job me too so i liked them all farhan is i think he's obviously we loved him as an actor yeah i think that's where we first fell in love with farhan yeah he's a he's a really good actor the man that's out of direct he sure does i think this is even though we enjoyed the chahattai i think this is even more impressive this one this one he got to flex his muscles and i actually thought to myself i'd like to know if mel Gibson saw this film for your hacksaw for hacksaw man because i mean granted hacksaw is a true story but there were a lot of things sound wise um image wise the way they were shot that were so hacksaw reminiscent that i thought i wonder if this is one of the military films that mel watched that gave him inspiration because it reminded me so much of hacksaw yeah so i don't know how much he's directed i know he's directing the new uh god olympia and adia green up film that zoe is writing yes that's very exciting one exciting development that we're gonna get next year hopefully the whole scaling the wall thing was so good i couldn't tell if we were looking at green screen or we were looking at a construction that was done with optical illusions or if they really found a cliff yeah and and you said sound at the beginning one of the biggest points of a war film is the sound editing and the sound mixing um and so i thought it did a fantastic job and freaking testing yeah the the as far as like the the caliber that's like we don't get to talk about the top the sound in this was just absolutely it was it was whoa so harry get out of here it was oh crap it's alexis uh i'll call her back when we're done because she's in new york okay um harry get out of here again going back to hacksaw the team that did the sound for hacksaw was the team that also did all the sound for the lord of the rings films so they won oscars for lord of the rings then i went to a screening of of hacksaw where mel was there and the the team of sound and i wanted them to win and they did hacksaw got sound mixing and sound editing the sound in this was as good as hacksaw rich yeah the sound was unbelievably good yeah and usually you don't get to talk about sound unless you're watching a war film or i guess at least a big action film big action film because that's where it's most noticeable or or like last year the sound oscar went to sound of metal because of yeah the nuances of what they were doing to portray his deafness yeah so most of the time it's going to be a big sci-fi action yeah film um but yeah i thought with all of that i thought farhan did a fantastic job weaving the story and also especially for this time everybody for the most part outside of some times in flashbacks was very grounded in their performances absolutely uh outside of the a few times when it not at least once again it's not like kuch kuch alt ahai srk and kajol in in the beginning over the top but there was a few times that it was just a little over the top uh by they're trying to show that they're teenage yeah yeah yeah all that kind of stuff but outside of that like especially 2004 in bollywood it's a it's a credit to nandini scherkent the casting director with with farhan i think it's a lot of foreign because this is his style yeah well the director has a final say yeah and he's like casting i don't want he's like garen johar right right and even even the really smaller roles like toward the end when they're going up the hill and we actually go and we see the pakistani soldiers at the top yeah they were actually quite grounded and quite believable a lot of times actually until the end a lot of the pakistani actors you didn't they didn't get faces no that's a choice by farhan an excellent choice to uh depersonalize depersonalize it and it's it's just it's a people that that they're fighting against i do have a question um not that this is a little small thing and it's not a problem i have at all i just noticed this that when he got to the top and maybe it is when he took the flag out it may just be an american thing i know for like american soldiers in america hit on the ground don't let the flag touch the ground i don't know what their flag code is yeah so i i'm assuming it's not the same code but i wanted to know because that would be something to just but also that's that's often when it's just um like like putting it up and down in very particular places obviously if they're in battle they're they're not really as concerned yeah and it didn't in any way bother me or distract me i'm assuming it just was a thought i had when he did it i'm assuming their code is probably similar a lot of military codes with flags yeah they're very honoring of their flag yeah um so i'm assuming it's pretty simple i noticed that as well um because my dad when i was younger he taught me how to fold in everything yeah it's always been a foregone to just doesn't touch the ground but i understand in that situation you know he's he's limping we didn't talk about the songs but we'd seen most of the songs and they're right they're great songs um it's it's super interesting to see that first one where he's like i have why am i like this song that we saw almost two and a half years ago i know no context i had forgotten it was in this film and when it happened i thought okay this is one of the things about this is what people who love like bollywood Indian cinema love because no one else does this where else would you see a movie that's this mixture of like hacksaw ridge and a quirky mtv video only here yep and it it was great uh i enjoyed it his proposal song and then yes i thought he i thought he was an idiot like she was all multiple times in this thing she was like hey i want to get back to you he's like no let's wait that's wait okay idiot yeah yeah but you know you got uh i think he it's because one had one point he thought she was engaged or she was she was engaged oh she was engaged i guess i found that out yeah um but i didn't like that engaged guy i'll tell you that yeah i didn't like him yeah me too uh as an actor or as a person you know but other than that i think i i think i mostly i like everybody in this that's it for the most part him i was one and then i can't think of another one that all everybody the whole military was great anytime they were there and it was a clear the one time the corkiness did make me laugh though in the in the flashback was when he fell off the thing when he was climbing up the thing and he's like this is gonna be so easy yes he just he called me up garden i was like i laughed yeah it made me laugh anyways uh so yeah there you go we enjoyed it if uh let us know what we don't know i guess yeah and why we're or what we missed what why we're dumb i know we i know we probably missed a lot of different things because one of the things we didn't talk about is not just we talked about all the technical and the artistic but we're learning more and more about the loc the tensions between pakistan and india as well as other countries like china the the complexity of kajmir and all those things what i appreciated is that this didn't get too into that it was more about just this one area and i think this is a good film for a lot of reasons if you wanted people to really get a taste of like a a bollywood film and i know a lot of people like that term but it's its own kind of thing this falls into that category and i think it's a serious thing it's got serious this it's got the great musical numbers and it really does give you an introduction because most people in the west are clueless us included about what the military history has been in the region over there between india and the powers of the in that whole area and i think this would give people enough interest to go wow i should learn more about that what's what's the line of control and what i've heard about kajmir before and i think would cause them to have interest yeah absolutely so let us know what's the next farhan film and pretty as well um but rithik let us know what should be our next rithik roshan film what's your favorite rithik roshan film i always forget he's in left by chance even though i was pleasantly surprised he was in left by chance yeah it's but it's still gonna be deborah for me still deborah yeah yeah this is this is a real this is really close up there yeah uh thankfully there isn't a a rithik film i don't like there are some performances of him i like better than others about gersen that's that's the one that you did that's the i like the film i felt like we said in the review there were certain aspects of the performance i would i would genuinely love to talk to him because he may help me clarify you know his process and what he was doing but at first at first glance that's the only performance of his where i had some questions all the other ones i've enjoyed yeah yeah same i like joe dachmar that's still my i think my favorite of that it's just an easy watch it's so good anyways let us know what the next one should be and happy independence day jay hi sir okay dang


The House of Representatives has urged the Independent National Electoral Commission, INEG, to develop a mechanism that will ensure that dead and fictitious registered voters are eliminated. The motion was adopted after passing through a heated debate by members on Thursday at plenary. Honorable Leke Abujide made this call during plenary in a motion of urgent public importance noting that the last general election, fictitious names and names of people who are long dead were displayed on the voter's register while citing an example of his deceased father who passed on long ago and still has his name displayed on the voter's register. Know that in the last general election, it was glaring and crystal clear that people that were long dead had their names displayed on the voter's register. Even my own deceased father, who passed on long ago, still has his name displayed on the voter's register. Father knows that apart from dead voters, there are millions of fictitious voters who do not exist anywhere in this planet's earth, but have their names on any registered voters. It is believed that this came to being as a result of double or multiple registration by Nigerians, who had all half-intentioned of reading the elections, but the advent of by-mother voters accreditation system bevers, these faceless individuals can no longer vote. And for us to bring this matter as a matter of urgent public importance to delist in Nigeria, who have unveiled himself to register, it's unconstitutional, and it's not meritorious. Why I say it's not meritorious, Mr Speaker, because it's going to injure our cities, and it's going to put on the right of our cities to vote and be voted for. That you travel from here, from Nigeria to abroad, and you can convey yourself on the time the election is going on, and you want such a person to be delisted. Mr Speaker, I think such opinion and such assertion is not meritorious. However, not everyone bought into the proposal as Honourable Nicholas Osai countered the motion stating that it does not merit being urgent, as it remains a fundamental right for everyone to register for an election, irrespective of whether they voted or not, due to circumstances beyond them. I think that wake-up call on INAG is a germane reason for him to call INAG to look into these issues. INAG should develop more sophisticated software that can remove these names. Because elections can be challenged in court because of these things. Remember, Kwege is about to go into elections in Edo and other states. Kwege, Bayelsa, and some states. Nothing bad to say enhance the system. Who is very good? I think anything that will improve on the electoral process, we should go for that. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Over the last decades, the number of obese people has more than quadrupled. Nowadays, more than 200 million men and 350 million women in the world are obese. And the increase in obesity prevalence does not seem to slow down to date. Obesity is associated with severe medical consequences. It predisposes to non-communicable diseases such as type 2 diabetes, cardiovascular disease, as well as cancer. And the impact of those comorbidities on our healthcare systems, as well as on our societies, is enormous. As a scientist and passionate sportswoman, I've always found these data very intriguing, because the best treatment for obesity and its related disorder has been known since many years. Whether it's running or cycling or just taking the stairs instead of the elevators, any type of exercise protects against disease and promotes health. The concept that exercise is medicine has been put forward some years ago. Yet, while a lot of effort is put on trying to understand specific disease mechanisms, we still do not understand how exercise promotes health. In other words, how muscle contraction can start up a cascade of events that ultimately lead to health is poorly understood. And what I would like to propose here is to use exercise as a model to study health. Would it not be better to prevent disease rather than treating it? Or what can we learn from studying health? And perhaps instead of restricting our research focus only on searching for novel or understanding disease mechanisms, perhaps we can find novel therapies to fight disease by understanding how exercise promotes health. But this might be more difficult than initially anticipated, because exercise does not only increase health inside the active muscles. No, the muscle also secretes factors that circulate through the body and might have impact on other organs. Exercise makes you healthy, but also happy and smart. Moreover, the muscle is not, while much research has been focusing on the muscle fiber itself, the muscle in fact contains many other cell types, which all together form the so-called muscle microenvironment. During exercise, those cell types closely interact and they coordinate adaptations to training. And one particularly interesting is the role of the blood vessels. Blood vessels deliver oxygen and nutrients, but also remove waste products. And at the same time, they provide the niche where other cell types, including muscle stem cells, like to reside. Now, one of the very early adaptations to exercise is the expansion of the vascular network. My lab studies how blood vessels grow inside the muscle and how blood vessels interact with other cell types within this muscle microenvironment. And we study in great detail how blood vessels grow inside the muscle. In fact, the activation of one single vascular cell can initiate the formation of a completely new blood vessel where every cell instructs its neighboring cell to take up a specific and specialized role. But the muscle has also developed a distinct way to increase its vascular bed. The coordinated growth of vascular cells can lead to the splitting of the vessel and the formation of a parallel vascular structure. Whenever those blood vessels grow, we think that this, the increase in blood vessel growth instructs other cells to also reshape and optimize the muscle microenvironment. In fact, we believe that those newly growing blood vessels can actually sense the nutrient requirements of the adjacent muscle fibers and can adapt themselves to promote optimal oxygen and nutrient delivery to the fiber. We hypothesize that the increase in vascular growth in the muscle therefore leads to a complete reshaping of the muscle microenvironment, which ensures long-term training adaptations but also provides a platform for the delivery of health-promoting effects through the rest of the body. By understanding the key steps that control vascular growth in the muscle and the molecular mechanisms underlying the communication between the muscle fibers and its microenvironment, we think that we can discover innovative and unexplored therapies for the treatment of disease and the promotion of health. Thank you.


Welcome to the Engagement Hub for this year's Central Bank of the Future Conference. We've designed the Engagement Hub to help you make the most of your digital conference experience. Here you'll be able to check out videos and papers, submit questions in advance, and register for breakout sessions. When you log into the Engagement Hub, you'll land on the homepage. Here you'll be able to see the sessions coming up for the day. All welcome remarks and wrap-ups, keynotes, and panels will be broadcast from the same daily livestream from 9 a.m. to 1 p.m. Pacific Time. To watch these events, click on the livestream link and select Join Session. If you want to check out more of the agenda, you can click on View All Sessions or head over to our All Sessions tab. Keep in mind our agenda is set to Pacific Time. We recommend that you set the agenda to your device time. That way you won't miss any of the day's great sessions. Now, one great feature of our Engagement Hub is the ability to submit questions in advance to any panel session. To submit your question, just click on the panel session title and head over to this box on the right where you'll be able to submit questions in advance. After panels conclude at 1 p.m. each day, it'll be time for breakout sessions. In this All Sessions page, you'll be able to register for breakout sessions. We recommend that you register early. Keep in mind that each day's sessions run from 1 to 2 p.m. Pacific Time and you'll only be able to register for one breakout session per day. If you register for a breakout session and later change your mind, just click on Register. You'll now be free to select another breakout session for that same day. Another great way to get ready for the conference is to dive into our Additional Resources. In this Additional Resources page, you'll find papers and videos organized by session. Click on the session card where you'll be able to see the creators of the papers and videos associated with that session. You'll also find sessions organized by documents and by videos and great bonus content from contributors around the world. This concludes our tour. We hope you enjoy exploring the Engagement Hub and we look forward to seeing you at this year's Central Bank of the Future conference.