In Alhamdulillah, without a doubt, without a doubt. Every word that I say here is calculated. When I say without a doubt, it means without any doubt whatsoever. All praise and thanks are gratitude for Allah, the Almighty. Why do I say that? In Arabic, the word hamd is incredible. It touches two things, at least two things. Gratitude and praise. That's how we start our day. That's how we start our Khutbah. Without a doubt, all praise and gratitude belongs to Allah, the Almighty, and the Almighty. And for that reason, we praise Him. We thank Him. We show our gratitude to everything that He has bestowed upon us, to every single thing that He has given us. Think about it.  When I ask a question, everyone thinks of a grand thing.  You got up this morning, didn't you? You said Alhamdulillah. You were able, Allah actually gave you an opportunity to get up in good health and praise Him and thank Him and do your prayer. Alhamdulillah. Tuwanas da wa firohu. So here's how it works. Each time that we come, we fall short. We ask for forgiveness. Forgiveness from what? There are a lot of outings. There's a lot of awesomeness Allah has given you and I. Do we fulfill all that in the manner that has been given to us? Not necessarily. Not true. We ask for forgiveness for all the shortcomings. Ma'as dayainuhu. And ask for help. What do you mean ask for help? Well, there are things that are within our control. There are things that are outside of our control. Even that are in your, within your control, you always ask for help. We ask for forgiveness. We believe in Allah and we put our full trust. Unconditional trust in Him. Ma'audubillahi min shururi anfusina. We have two things within us. There are two things. There are all those outside factors that we think and we are quick to blame, say, hey, I did this because an outside factor, namely, at least, namely, shaitan, namely your number one enemy. Why your number one enemy? Because Allah said so. In His book He is your number one enemy. We're quick to blame Him because He did something. He made me do it. We say that. On the other side Allah says there's something within you that you need to control it. And that makes you do things that you don't want to do. You're not supposed to do. That's why we ask protection. Ma'audubillahi min shururi anfusina. Wa min sayi'ati an'amalina.  And you're asking Allah sallallahu alayhi wa sallam protection from that. What does that mean by product? Very simple example. One of the days I was sitting there doing khutbah and haqib was giving me an amazing khutbah. One of my brothers sitting next to me, I don't know who he is, I've never seen him before. And he was doing this, constantly checking social media stuff. Young man sitting next to him sees that, oh hey, that's a cool thing to do. Maybe I should do the same thing. He gets his handy-dandy device and he does the social media stuff too, taking picture, posting in Instagram and all that. That is a byproduct of something that the other gentleman did, the other brother did. He wasn't aware of it, he wasn't thinking about it, maybe he wasn't calculating it, he wasn't, whatever it was, subconsciously and consciously, he did something out of his actions, someone else was affected and did the same thing. And we're asking Subh'anaHu Wa Ta'ala, protect us from this, ya Allah. Within your control, you ask from, protect. We ask god without God and we askyou, Oh believers, all of you. We don't know. Our Iman is our next elevated stage. You have been granted that. Amen Allah for that. Allah Allah calls you Muslim I want to oh believers Allah protect yourselves often you hear that it says fear Allah and I had a tough time explaining that to my students everyone thinks everyone thinks that Allah is out there to get you that's not what Allah says that's not why Allah created Allah gifted you everything that you have here that means you protect yourself in a way that you do not this appoint Allah what is an example these days when you travel you have travel by plane you have to have an ID card with you passport or some government issue ID if you travel abroad you have to have a passport with you you have to have a visa that is protecting yourself can you come back with this damage you are protecting yourself you are exercising taqwa each time that you see I read the light you do not cross the light when you are sitting there with a gun in you you are exercising taqwa you are protecting yourself from getting a hefty ticket Allah is saying it taqwa protect yourself from this pleasing Allah from the things that this creator this master of yours and mine said and giving you make sure you do not do not cross that line the way he deserved it that's a big topic that's a huge topic what does that mean the way Allah deserves it and I should be protecting myself and the companions of Prophet sallallahu alayhi wa sallam asked Prophet sallallahu alayhi wa sallam and I immediately came according to your capacity just to leave it at that according to the capability Allah has given you make sure that you protect yourself if you understand Arabic this is a heavy word this is a heavy heavy don't you ever dare die that you forgot the rule we just explained to you that you depart this world without being Muslim that's a command from Allah a few days ago a week ago or two weeks ago or so we were blessed to have our prominent scholar Sheikh Sallallahu alayhi wa sallam and he gave a lecture so I was fortunate to be in his company one day and I asked a question opportunities are rare to actually see an amazing scholar and be able to ask a question so the question I asked is this that has been bothering me I've been pondering upon that for a long time the question is asking Allah the question was do I to ask Allah for something well I hope I wasn't rude the way I put it and I'm going to put it the same way to you guys so if you know in just any age you have this little thingy here we have instant gratification anything that we want we get it instantly as a matter of fact if something is slow if a wi-fi is slow you get aggravated if something takes 0.2 seconds to download you get really aggravated as a matter of fact I was in a tangent I was in a plane and they said wi-fi is complementary we just gave it to you I'm like oh cool so I'm like hey let me log on to wi-fi what I can do the guy next to me he already believed that he deserved to have the wi-fi so it didn't work for a period of time he was so upset he was using foul language and all that what kind of thing is this that wi-fi doesn't work we already as if we own this as if this is ours the gratification is there when you order something online today you order something online you get instantly a confirmation two days later it shows up by your doorstep for a free shipment unless you want it 24 hours we want everything that fast we treat our relationship with God with Allah the same way often when we make a dua we ask something from Allah we want it right away we want it immediately we want it like what is this I ask two days ago God what happened I haven't seen a response I didn't see the delivery I didn't come to my doorsteps and often when we ask something we ask at a time of the need when we really need it when I really want that aid and I didn't study I want that God please help me out with my chemistry so I could get an aid when we desperately when we didn't do our dua and we really want to get married and we looked at someone and said oh my God this is it she is it Allah please help me out I really want to buy this car I want this house we want instant instant answer for everything so that's what I asked my sheikh he said respectfully sheikh how do we understand this what does this mean when we ask Allah what does that mean to us and when you started as a company scholars every word is so profound his answer I was expecting a 15-20 minute lecture his answer was maybe 30 seconds maybe one minute but it's had so much in it it's so much in it so much meaning in it so I came across an ayah after talking about what his response was which I'm going to give it to you in a couple of minutes or so because I don't have a lot to talk about Allah says this Allah says the translation was like this oh my God my rub my massive indeed my bones have been weakened and my head has been filled with white white hair white ashes and I've never been and I've never been in my supplication to you oh my God and happy loose translation this is about what are the prophets Zakaria what are the righteous persons in Zakaria listen to what he is saying listen to what he is saying this is the da'a this is the supplication he is asking for Allah I have never ever been unhappy never been unhappy about unhappier calling you I'm calling you with my da'a even though my hair is like white ash and I have I see weaknesses in my bones I see weaknesses in everything I do including my supplication to you I've never been Shak'i never been Shak'iya you know what is Shak'i I've never been depressed I've never ever ever been unhappy I've never ever been disappointed with your response with your delivery with what you have given me what she has not said everything is trust in God trust in Allah have a good opinion of Allah come to that come to that level of understanding that Allah has given you everything here for your benefit he doesn't get anything from your praise he doesn't get anything from your charity he doesn't get anything from your time but he has given you all that to make you happy if you have that level of understanding then you have a good trust in Allah that when he says he's going to respond to your prayer he's going to respond to your prayer from prophetic knowledge that we know, whatever we ask whatever we ask in this world anything about this world our concept has been completely upside down whenever we ask about this world we go asking never specific we have changed that to a specific I really want this house I really want an A and this the interesting part for me was that when football was playing sitting there and constantly for one hour and a half making du'at for the team to win and I was shaking my head I asked what are you doing he's like I'm asking Allah to help us to win we are in that level of understanding but fit dunya hasana is not a bait hasana is not a car hasana is not marrying someone hasana is everything is general when the prophetic thing has taught us when you ask ask general and also ask because have that level of trust in God in Allah that he will give you the best when you ask for something has happened in my life multiple times when I ask for something specific that may or may not be good for me but you have to have the trust in God that he will give you something better than you're asking that is where the purpose of the du'a is that's where the purpose of supplication is you have to have that level of relationship built already with your master that you will get an every du'a in one way or another way some way it will get accepted you will get something and here's the level of trust we need to have in God if you don't see it here you ask for something specific you didn't get it you have to have the critical pillar of our belief is to be in the next life that is in the beginning it says whoever has iman is one of the things that they believe you should have that trust that you will get it by multitudes in the next life my sincere apology again because you're not here I just had to just put something here out of top of my head if I said anything that doesn't make sense or if anyone I sincerely apologize I say this to you I say this to you ask of God for forgiveness he is the one the only one who can forgive you the only one who can give you what you're asking for so make this 30 seconds and I'm going to sit here count and ask for something that is valuable that is to ask for forgiveness thank God peace and blessings of God peace and blessings of God please in part of the Quran is this about to recite it there is one act Allah says he does it only part in the Quran this is a completely different on his own one of these days we are going to talk about it and Allah is commanding all of you to do it and we are going to do it insha'Allah you salve on the Prophet yaa salve on him and salve on him Allah is commanding all of you to pray for him to pray for him And to age of praise You are the mostnehmen of the Majlil Allah is commanding to you repay your indebted gratitude And to alright your soul in prayer it is very important the Quran is explaining his special orders The Quran is here The teacher in me doesn't allow me not to do one thing, and I've done it all the times that I've stood here, and this time is not going to be an exception.  The way Qutbahs conclude every single Juma'ah, almost every Masjid, from the Ayat of Quran, from chapter 16 and 19, I believe. Allah is commanding you, each one of you, me and Chris, that you are three things to do. And avoid at all costs three things. Here's my homework to all of you. I'm not going to translate it. I give you the address. 1690, go look it up, make it a part of your learning this afternoon. What are the three things that you're supposed to do? Ponder upon it. Don't just look into shallow translation. Ponder upon it. Incredible wisdom, and avoid three things. If there has been my life struggle, if I guarantee that you have some level of understanding these three and three, that is the success that you need. You will earn success that you have never ever seen before.


Okay, thank you so much. So as the speakers before me, I would like to thank the organizers for putting together such a wonderful conference. So the goal of my talk today is to discuss a novel approach of how to extend frequencies of integrable PDs to spaces of functions of low regularity or spaces of distributions. But before I state the main results of, on this topic we have obtained, I would like to give an application to the well-posedness of MKDV2 and the modified KDV equation. And let me mention right away that all of what I talk about today is joint work with Jan Malnoll. Okay, so let me begin with the KDV2 equation. So we consider the KDV2 equation on the circles, period one. The KDV2 equation is an evolution equation, dispersive evolution equation of fifth order. It comes up in the long wave approximation of water wave equations. Of course, the coefficients chosen here written down here are of very specific nature and in the approximation, many more of these type of equations come up. But this specific choice of coefficients makes that this equation is actually an integrable PD. First it's a Hamiltonian PD and the specific choice of equations makes that it's actually in the KDV hierarchy. Therefore, it can be written in a Hamiltonian way. So DDTU is equal to DX, the L2 gradient of the Hamiltonian H2, that's the KDV2 Hamiltonian. It is given by this expression, so it involves the L2 norm of the second derivative of U. So H2 is well defined on the subolive space H2 and has some non-linear parts. DX is usually the Poisson structure introduced by Gartner. So I recall this is the second Hamiltonian in the KDV hierarchy. So the zeroes Hamiltonian usually referred to as H0 is the L2 norm and the first one is the famous KDV Hamiltonian. So the bell positeness result which comes from this analytic extension I was talking to at the beginning for the KDV equation two reads as follows. It's well posed on L2, despite the fact that it is fifth order and the Hamiltonian is of second order. So it's defined only in L2. So for the convenience, we restrict to the symplectic leaf of subolive spaces with average zeroes. So this is a cosimere of this Poisson bracket. The same results would be true on any of such leaves. Okay, and then also have to introduce many folds M as zero D. So these are the functions U in subolive space H with average zero, so that the L2 norm is constant. And because the L2 norm is the zeroes Hamiltonian in the KDV hierarchy, it is invariant under the KDV two flow. So this manifold is invariant under the KDV two flow. So the well-posedness results for the KDV two equation reads as follows. KDV two is globally in time, C zero well-posed in H as zero for any S bigger or equal to zero. It means that the solution map S continuously extends to, I mean, from more regular data where it is known that solutions exist, it extends continuously to a map of the following type. So initial data in H as zero goes to solution. These are continuous functions of the time interval minus TT for arbitrary T into H as zero. And this map is continuous. However, this map is nowhere locally uniformly continuous on H as zero. It means that if you give me any open non-empty set, U on H as zero, then if I restrict S to the set U, it's not uniformly continuous. In addition, if I take S bigger or equal to one half, and T is strictly positive, otherwise it consists just of one potential, the zero potential is uninteresting, then this map actually is uniformly continuous on this manifold. But on contrary, if S is in between zero and one half, then again, the solution map S is nowhere locally uniformly continuous, even on this manifold, even if I fix the L2 norm, it will be nowhere locally uniformly continuous. Okay, then the second group of results concerns ill-poseness. And to describe these results, I have to introduce a renormalized KDV equation, which I refer to as KDV2-sharp. So it is again a Hamiltonian equation, and I subtract this term here. This corresponds to the Hamiltonian H2-sharp, but I subtract 10 times H0 squared. So again, this is an integral PDE because this is the zero's Hamiltonian in the KDV-aharke. And therefore the difference, of course, is again integrable. So then the result on ill-poseness goes as follows. The modified, the renormalized KDV2 equation is globally in time, C0 well-posed on each subalpha space H as zero for any S strictly bigger than minus one. So for all distributional spaces H as zero, KDV2-sharp is still well-posed. Again, it means that the solution map S-sharp continuously extend from H as zero to the space of continuous function in the time interval minus dt to H as zero. As an immediate corollary, it says that KDV2 must be ill-posed below L2 due to blow-up of phase factor. So if I represent the Fourier series, the solution of KDV2-sharp in Fourier series, let's write it down like this. So this would be the N's coefficient of the solution at time t of KDV2-sharp with this initial data. Then these coefficients compare to the corresponding Fourier coefficients of the solution of the original KDV2 equation with the same initial data V as follows. The N's Fourier coefficient is obtained from the N's Fourier coefficient of the KDV2-sharp equation times this phase factor. And of course below L2, this phase factor blows up because H to the L2 non-gets infinite. Okay, so the results improve on earlier results on well-posedness on the circle. And there has not been so much results in the periodic case, but more recently, a lot of results on the line in particular by Gua-Kuan-Kuan and Kennegan-Pilo where they looked at solutions on the energy space contained in H2. Okay, so much about KDV2. Now corresponding results for the defocusing MKDV equation, we also have some results on the focusing one, but I don't wanna talk about right now. So the defocusing MKDV equation, everybody knows on the circle is given by this equation. So it differs from the KDV equation by the fact that instead of U, I have here U squared. Again, it's a Hamiltonian PDE. This is the symplectic gradient where DX again is a Poisson structure from Gartner and this is the L2 gradient. The MKDV Hamiltonian is given by this expression. It's DXU squared plus U to the fourth. So in KDV, you will have U to the three. Here you have U to the fourth. So here we have an ill-posentness result of the MKDV equation below L2 and this goes to state it again. I have to renormalize the MKDV equation. I call it MKDV-sharp.  Again, this equation is Hamiltonian. H-sharp is its Hamiltonian. It's H minus six times H0 squared. And again, H0, the L2 norm, is conserved by the MKDV flow and therefore it will be easy to compare the two flows. And in order to state our ill-posentness results, I have also to introduce the Fourier-Lebesgue spaces, FLP, P between one and infinity. So this is a space of periodic distributions whose Fourier coefficients, the sequence of Fourier coefficients are in LP. So of course, due to Parseval's identity for P equals two, FL2 is just the usual L2 space, but for P stricter than bigger, this is a big space. It's a big space of distribution and it gets bigger and bigger as P goes to infinity. In particular for P bigger than two, this contains elements which are not even measures. Okay, so the result for the MKDV goes as follows. MKDV-sharp on FL, on Fourier-Lebesgue P is P between two and zero at the following properties. It's locally in time C0 well-posed, meaning that for any initial data V in LP that exists in neighborhood V and the time TV so that the solution map as sharp continuously extend in this way as before. In the case V is equal to zero, we can have a slightly stronger result, namely the equation is not only locally in time, a C0 well-posed, but actually globally in time well-posed on V0, so this would be true for any T bigger than zero. So again, as in the KDV two equation, we have an immediate corollary, saying that MKDV equation is ill-posed below L2 due to blow-up of the phase factor. So again, if I take the Fourier representation of a solution of MKDV-sharp and write it in this way with initial data V of X, then I can compare the Fourier coefficients of MKDV-sharp with the ones of MKDV in the following fashion. The N's Fourier coefficient of the corresponding MKDV solution is the one of the MKDV-sharp equation times this phase factor. So again, if I'm below L2, this phase factor gets infinite. So of course there has been many work on the MKDV, so maybe first a few comments. So we expect MKDV-sharp equation to be also globally in time zero and zero well-posed everywhere on FFP, but there is one thing we don't know to prove at the moment. And I also mentioned right away because I might not have time during this lecture to explain anything of this, that the key ingredient in the proof theorem two is to view the MKDV Hamiltonian as the corresponding Hamiltonian and in the NLS hierarchy. So it's the fourth Hamiltonian, so NLS is the third Hamiltonian in the NLS hierarchy and MKDV the fourth. So does this mean that your result is also valid for the complex version of the equations? Yeah, yes, very big yes, absolutely. Actually we do extend the frequencies to the system. We call it MKDV system because it's actually, of course we have to be in a neighborhood of the real case. It cannot be arbitrary far away because we probably have hyperbolic structures of the equation. So of course there has been many, many work on MKDV on the circle. Essentially it is well-posed for HS as big or equal to zero. So then there are also other works. So maybe I don't want to spend too much time on this but just mention maybe a little bit more in detail. One result by Luc Moline on ill-posedness of MKDV below L2. So he proves that MKDV is ill-posed in HS for S strictly bigger than zero in the following sense. The solution map is not continuous as a map from C0 infinity with the norm HS coming from the sub-left space with S strictly smaller than zero into C0 minus DT periodic distributions. So we can view corollary two as sharpening Luc's result saying that ill-posedness of Luc is really due to the fact that you have blow-up of phase factor.  So the method we will, we prove these results are the so-called non-linear Fourier transform or Birkhoff map or normal form transformation. So it makes, these are new coordinates which make that the equations when expressed in these coordinates are actually linear and the dynamics are described by frequencies omega n. So the crucial part in improving these well-posedness, ill-posedness results is by extending these frequencies in the corresponding spaces of functions of low-regularity or distributions. So as applications of these analysis of these extensions of these frequencies we have already mentioned or the well-posedness of the PDEs as stated but also that actually was the original motivation of why we started to do this is it applies to Hamiltonian perturbations of such PDEs. So it has important implications on the properties of the action to frequency map and also it allows to analytically extend the Hamiltonians and to discuss its convexity properties which are important for Nekoroshev type results for perturbations. So to keep the exposition simple I will explain the method actually for the proof for the KDV frequencies but even in this case actually we improve known results. At the end if I have time I will discuss very briefly the de-focusing and KDV equation to see how it connects with the NLS system. Okay, so to start I have to review quickly this non-linear Fourier transform or these normal coordinates for KDV. Actually these coordinates are good for the whole hierarchy for any Hamiltonian in the Poisson algebra generated by the KDV equation. So the setup is the scale of sub-alef spaces h, i, c stands for complex value these are periodic functions. We include s bigger or equal to minus one so some negative s's are included here. So as I said we have the Poisson bracket which was introduced by Gardner so these two functions f and g on this space is sufficiently regular L2 gradient have a Poisson bracket defined in this fashion. And note that the average is a cosimere meaning that for any functional if I put the average as the functional g then this is identically zero. So this cosimere leads to symplectic leafs and in the sequel I will only restrict to the zero leaf so average zero and again the z refers to the complex numbers. So then to state the results of normal coordinate cells I have to introduce sequence spaces so these are LPP sequences, complex values so this stays for c and they have weight s. So this is the weight and to the sp and zero stands for that the element of the sequence in the middle is actually zero has to do with the zero leaf. Okay and then we also introduce the real subspace of this consisting of all complex sequences which have the property like for Fourier sequences that z minus n is a complex conjugate of cn. And then to each of such a sequence we associate a sequence of actions for n bigger or equal to one they are obtained by multiplying zn with z minus n for all n bigger or equal to one. So just as an exercise because I will use this later we will consider sequences in LP spaces with weight s plus one half then the corresponding actions has double weight so this is two s plus one and p gets half because of the square. And as a special case if we are in the real subspace then this is a complex conjugate of this so i n is bigger or equal to zero and then the sequence of actions is actually in the positive quadrant of this LP two sequence space. Okay and then the integrability of the K-DV hierarchy can be formulated as follows. So as our base space we take h minus one zero so the real space of functions in sub less space with average zero in s equals minus one. We take then there exists a complex neighborhood of this space in this complex space and this complex sub less space and a map from this neighborhood into the corresponding sequence space associating to each potential the corresponding coordinates complex Birkhoff coordinates refer to as complex Birkhoff coordinates so that the following properties hold. When we restrict this map to the sub less space h s zero for any s bigger or equal to one then actually it's a real analytic diffeomorphism onto the sequence space there is a two missing here s plus one have two. Second fees canonical meaning that to pass on brackets of the coordinate functions or the standards one. Of course here we have complex coordinates so we don't have one but an i instead all other brackets vanish. And thirdly the most important property is that the Hamiltonians in the K-DV hierarchy are real analytic functions on the actions only. So it means that in H K-DV so this is the Hamiltonian is defined in H s so the corresponding sequence of actions is in weighted L one space with weight three so if my potential is positive then the actions are in the positive quadrant L three one and correspondingly if I have the K-DV two equation then I get this kind of real analytic map. And lastly actually fee of zero is zero on the differential of fee at q equal zero is essentially the Fourier transform up to this little weight which comes from the Poisson bracket. So as I said this map is usually referred to as pick-off map and the coordinates as complex pick-off coordinates. The principal property of fee is this three it means that it linearizes the PDEs in the K-DV hierarchy. So then we come to the frequencies the topic of my talk. So the frequencies of K-DV and K-DV two equations are given by, so we take the Hamiltonian and the ends frequent is obtained by the partial derivative of the Hamiltonian with respect to the nth action for any n bigger equal to one. And then the equation as I said linearizes in these coordinates and they read as follows. So the ends coordinate the time derivative of the ends coordinate is minus i this comes from the Poisson bracket omega n K-DV cn the omega n's K do not are invariance of the flow because the actions are invariant and hence the frequencies and hence these equations can be very easily integrated and the same for K-DV two. So key ingredients in the proof theorem one, theorem two are the extensions of these frequencies to spaces of functions of low regularity and distributions and in addition asymptotics of the frequencies as n goes to infinity. So the setup we choose to achieve this extension is as follows. So we write, so as I said I do this only for the K-DV frequencies just to save a little bit of time. So we write omega K-DV n as this is the frequency of the area equation sort of the linear part of the K-DV equation plus let's say a remainder which we call omega K-DV star n and of course it's enough to extend this omega K-DV star and in order to obtain asymptotics for omega n actually you want to extend not each frequency by itself but we want to extend it as a map. So we look at this as a sequence. So we have to determine from which space to which space this it's usually called the frequency map or the action to frequency map which in integrable systems and in perturbation theory plays an important role. Okay, so here is the main result. So for the K-DV star frequencies. So the omega K-DV star analytically extends as follows. So we can view the frequencies either on sub-left spaces or on the corresponding spaces of actions. So I wrote the two at the same place because this might be a little bit more difficult to decipher than just the sub-left space. So the extent to H minus one, zero. So on the level of actions this means we are in the positive quadrant of L1 sequences with weight minus one and it goes not quite to the same space for S equals minus one but a little bit larger space namely an LR space with weight minus one for any R strictly bigger than one. But if S is between in the open interval minus one, minus one half, then we go from the space L to S plus one one into the same space. And if S is bigger or equal to minus one half and then again we have somewhat a weaker space on this side, this has to do because this has asymptotic expansions in one over N and it appears at some point and you cannot improve. Okay, then we have asymptotics. So essentially the N's frequency or omega NKDV star is minus six IN. So this is the N's action variable plus an error term which can be estimated in this way. And this error term depends a little bit on the S. So I mean there are more precise estimates but just to keep it simple I stated in this way. So if S is between minus one and minus one three and this is the form of the error term we get and if S is bigger or equal to minus one three it actually doesn't improve. Again, due to asymptotics which you cannot change in one over N. Okay, certainly we have seen that if it's S between minus one and minus one half then omega KDV star is a map from the space to itself. And therefore I can look at its differential and we can prove that its differential is actually fragile. It's actually minus six identity plus compact. And then I mentioned also because for one application I need this that we have a special case. Actually we can also extend the frequencies to Fourier Lebesgue spaces but I just take one example. This would be Fourier Lebesgue S equals minus one half P equals four which leads to an action space of L2 plus. So also in this case, omega KDV star can extend as a real analytic map and the differential is flat on. Okay, so this is the essential result on the frequencies and I will discuss a little bit on the proof in the second half of my talk but first I want to give applications. So of course one application we have already discussed but I would like to go back a little bit. So first we can use these frequencies to analyze the PDE, the PDE is considered, the integral PDE is considered in Birkhoff coordinates. So it allows to analyze the dynamics of the angles in a very precise way. So we decompose any of such frequencies which come up in an integral PDE in the following fashion. A n plus B n plus omega n star. A n is a polynomial in n with constant coefficient. B n is a polynomial in n with flow invariant coefficients and then omega n star is of the form leading part plus remainder. So just to give an example, for the KDV frequencies the A n's would be the frequencies of the area equation. If I consider it not only on the zero leaf but on the whole sub-alive space actually I get a B n which is 12 times the average of q times n p and then omega n KDV star is minus 6 a n plus remainder. And similarly for the KDV2 equation this would be the frequency of the linearized equation at zero. B n would be this kind of expression and again omega n star would be linear and I n plus a remainder. So the B n's and the omega n's are possible cause for the PDE for not being uniformly C0 well-posed or not being locally uniformly C0 well-posed. The growth of these coefficients might create phase D coherence which will lead to these vicarious notions of well-posedness. And of course it will lead to imposedness in case of blow up. Okay then of course we can analyze this using these frequencies the PDE and the original sub-alive spaces. So if ST is a flow map in the sub-alive space Hs0 we denote by STv the corresponding flow map in the Birkhoff coordinates and then the flow map ST can be obtained from the one from the Birkhoff map by conjugation through this Birkhoff map due to the fact that V is in practice. So how can this be used? Let me illustrate this just for illustrative purposes for the KdV2 equation on Hs with S bigger or equal to 1. So one can prove that omega 2 star is actually a continuous map from the space of actions into L infinity which is uniformly continuous on bounded subsets. And so are the corresponding Birkhoff maps and its inverse. And because B and 2 is constant on the leaves with D equals constant the KdV2 uniformity is 0 well-posed on this sub-manifold MS0T. So by analyzing the frequencies in this way one gets these type of results. OK then just maybe as a remark let me mention from this analysis it suggests to think of a possible role of the critical sub-alive exponent Sc in the analysis of ill-posedness. So if I look at the Fourier if I write down the solution in Fourier space then I can write it in this way. So An of t is an amplitude exponential i omega t the phase factor and exponential i and 2 pi x. So a possible scenario for ill-posedness in Hs is and the possible role of the critical sub-alive exponent is if S is smaller than S0 we have ill-posedness due to the amplitude blow-up of the amplitudes. If we have already ill-posedness before Sc it might be due to the phases. So that's essentially true in the MKdV equation following our results I explained. OK so second application as I mentioned is the convexity of the KdV Hamiltonian. So to explain it I introduce so this is a KdV Hamiltonian and we re-normalize by subtracting a term which gets very large if I go into functions or spaces of distributions. Then because KdV Hamiltonian is defined on H1 therefore the corresponding spaces of actions is a positive quadrant of L1 sequences with weight 3 is real analytic. So there was a conjecture by Sergei saying that H star KdV analytical extends and is strictly concave on L2+. So the L2+, is the space of actions I was mentioning in Serum 3. That said I will use it later for applications. Here it is. Now in earlier results Big Bayef and Cooks improved that this Hamiltonian is actually concave. So they prove this for finite gap potentials and then by continuity show that it's concave once you know that you can extend it continuously. And then last year actually we proved together with collaborators that the H star KdV actually extends to L2+, and it's strictly concave near I equals zero so at the origin. And using our theorem 3 now with the property 4 actually the conjecture 3 is almost true in the following sense. So this renormalized KdV Hamiltonian is strictly concave on an open dense subset O of L2+, with the origin being an element of this open dense set. It means the following that if ever my action is in this open set then the Hessian of the KdV star, I mean this is the same actually as the Hessian of the original one because I just deducted the linear term. The Hessian of the renormalized KdV Hamiltonian is strictly concave in the sense that I can bound it from below by minus C, L2 norm of J, for any J in L2 where the constant C can be chosen locally uniformly around it. Yes, absolutely, thanks. Okay, so as I already mentioned, convexity property is relevant for stability results of the KdV type. Okay, so maybe there's also application to the action to frequency map, maybe I leave this in order to be able to explain a little bit. But Thomas, where it loses strict concavity, it is degenerate concavity, there are flats, is that how it loses it? So it's open dense, so we don't know. I mean, Sergei thinks it's everywhere but I don't see any reason why there should not be some zeros in between. Right, but that's the failure of strict concavity. Yeah, it's always concave, but strictly concave on this open dense subset. So for local perturbation theory, no local way is enough, of course. But, and the fact is we prove that the differential of the frequency map is fret home and that allows us to together with analyticity to have the open dense thing. Okay, so outline of theorem three. So I recall theorem three was the analytic extension of the frequencies. So I need first to introduce what are called the flow exponents. So on the real line, the corresponding notions would be probably the transmission coefficients. So these have been already introduced in the seminal paper by Peter Lex in the 75. So for Q in W, so W is this open neighborhood of H minus one zero. We look at the Schrodinger operator, so this would be a distribution. You can do spectral series still for this and the spectrum is discrete. The eigenvalues come in pair. Maybe I write them so if it is real. So this is the lowest and they are, if Q is real, then they are on the real line and they satisfy, they can be ordered in this way. So the pairs never coincide with another one but the two elements in the pair might coincide. Then we define the gaps. So this would be these intervals here and the gap lengths which would be the size of the length of these intervals. And then we have here another gap G zero which is to the left of L zero. Which is infinite. Okay, then I have to introduce the discriminant of the thing. So of course if Q is regular, the discriminant is given by the trace of the flow K matrix and one can show if Q is sufficiently regular, then actually it has a product, this product expansion involving the eigenvalues of the Schrodinger operator. And in case you're in low distribution, you use directly, you define the lambda by using this product expansion. Anyway, product expansion will be all over in the analysis of, in the estimates of all the quantities involved. And then we introduce a canonical root of delta squared minus four. This usually gives rise to the hyper elliptic surface associated to the spectral problem. And this is well defined on C minus the gaps. And for Q equals zero, just to give an example, it's sin times square root of lambda. Then the flow K exponents. So this are the, so we have the flow K multipliers would be the eigenvalues of the flow K matrix. And if you write them in exponential form, you get the flow K exponent. And one of them can be written in this way. So for any Q, again, even if flow K series doesn't make sense, because delta makes sense, you can define this in a perfect way. It's well defined, also it doesn't, even if there is a little singularity here, this is integrable. Okay, so these are a list of important properties of the flow K exponent. So f of lambda is analytic away from the gaps which are open. So if the two eigenvalues here coincide, actually this flow K, the f of lambda extends analytically into this double eigenvalue. And we have specific values at the periodic eigenvalues at lambda zero, by definition it's zero, because we start integrating at lambda zero plus. And here one can show you the fact that the potential is periodic, I get here minus i and pi. And then we introduce a version of this flow K exponent by normalizing it differently, fn of lambda, so that at lambda equals plus, lambda plus minus n, this is actually zero. Then one can prove that fn changes sign across the gaps. So here we have different signs, but there are limits as we approach the two sides of the gap, and hence the square of fn actually analytically extends in the neighborhood of gn. We have estimates, we have an explicit formula of the gradient, and the fn's are related to the actions by this contour integral. So gamma n would be a contour around the gaps. Okay, and then most importantly, there is an asymptotic expansion of f of lambda. So actually we use later on only f for of lambda, so I write down the expansion right for this. And of course we have a little problem if we do this for distributions, it's enough to do it for real finite gap potentials. Finite gap potential means that only finitely many of these eigenvalues are simple and the rest are all closed, and it means that they'll potentially see infinite. Okay, then one can show that there is an expansion as l goes to infinity of this form. So it's actually a meromorphic function, has a pole at infinity of order two. Similarly, so we see at the point of the residue, the Kdv Hamiltonian is involved. Similarly, for the Kdv two equation, we use instead of f to the four, f to the six, and this makes that the Kdv two Hamiltonian appears again at the place of the residue. So later on if you do contour integration, it's a way of picking up the Hamiltonian. Okay, now contour integral of four around simple eigenvalues because we know outside this is an even power, so we know it's analytic. In particular, it's analytic here, so because I have finitely many gaps open, I know that outside the big disk this is analytic and therefore I can use contour integration to pick up the residue here, and on the right hand side, I will have by contour deformation just integral of our contours on the pairs of eigenvalues. So S is a set of Ks where the eigenvalues lambda K minus lambda K plus are simple, meaning that gamma K is different from zero. Okay, so this gives us the corresponding formula for the Kdv two equation. And then the idea is to develop these expressions further in order to get the formula for the Kdv two equation. Now let me explain this a little bit in more detail. Now here is the crucial idea. So from Hamiltonian formalism, we know that when I express the equation action and angles, then the ends frequency is nothing else than the derivative in time with respect to the ends angle. And this is equal to the Poisson bracket of the HKdv Hamiltonian with theta n. So of course, in order to have the angles defined, I need that the ends gap is not collapsed. So this goes only for simple eigenvalues. Okay, so this allows us to get a formula for the omega for the ends Kdv frequency in the case where n corresponds to an open gap. So it is equal to this expression. I substitute our expression we got from the residue calculus for HKdv. This is the expression. By the property F5, I know how to compute the gradient. I insert it here in the Poisson bracket and I get this. Now we use a very important identity from our book, saying that the Poisson bracket of delta. Okay, so this is where Pcn has this product expansion. These are actually related to holomorphic differentials on the Riemann surface. So these are very well known quantities and play anyway a very important role. They come here a little bit out of the sky, but they are not. Okay, so here sigma and K are the zeros. These zeros are completely determined by this equation. So this is a normalization of the holomorphic differentials. And they can be easily shown in case the potential is real, they have to be within the gap for N different K, for K different N. Okay, so we insert and we get this expression here. And now we expand F of three as Fk minus ak by cubed and get formulas for, get in this way a formula for MKd, for the N's Kdv frequency. So for this to express this, we introduce the M's moment of the, of the Fkl's. And these M, now we use sort of important symmetry properties of these moments. And that is actually why we can succeed in extending to such low regularity. So first of all, for all M's, these moments are identically zero. And this has, so I don't wanna explain because I'm running out of time. So also if gamma K is equal to zero, then these moments for all M and N are zero, for this specific K. And finally, the zero's moment is nothing else than the integral of this holomorphic differentials over the gap scheme, gamma K, which is nothing else than Dirac delta times two pi. So using all this, we get the following formula for any real finite gap potential of average zero. We have this formula. Omega NKdv is two and pi cubed. So actually this comes from expanding, from this, if I expand this expression, I get this term and this actually gives precisely this. And correspondingly, the frequency of the Kdv to Hamiltonian, the N's, has a formula of the four omega Np to the fifth. This is a linear part plus this part, which we already came up with when we discussed frequencies plus omega N2 star, where omega Nster can be expressed of the moments of F and K of the moments two and four. Okay, so the strategy for proving theorem three is we use formulas of theorem six to analytically extend omega NKdv and omega N2 by analyzing in detail these moments by showing that this series, by showing that they individually, they analytically extend to H minus one, first of all. Second, by showing convergence of the series by deriving asymptotics of these quantities. And for this we use sort of quite involved estimates for product expansions of terms, which involve in these moments. Okay, so maybe I leave this and then just maybe one last little thing. So coming back to the NLS system and the MKdv equation. So I said at the very end, if I have time, I would briefly say something, how this can be, how MKdv comes up in the NLS system. So I recall the NLS system is a system of Hamiltonian PDs for phi plus phi minus in HSHS, complex valued, given by this expression. It's a Hamiltonian PD where the Hamiltonian is given essentially by the NLS Hamiltonian, but with these two components. And the Poisson bracket is the usual one with this factor minus i because I'm in the complex version. So if I restrict this system to a real invariant subspaces I get actually the defocusing NLS and the focusing NLS equation. So if I restrict to phi plus equals phi minus complex conjugate I get the defocusing NLS. And if I restrict to phi plus equals minus phi minus complex conjugate, then I get the focusing NLS. And this NLS system has the NLS hierarchy. It starts with H0, H1, this is the moment. And then H3 is the NLS. And as I said, H4 is related to the MKDV equation. We call it the MKDV system. So this would be the first equation, one of the two for this Hamiltonian. And then this Hamiltonian system has also invariant real subspaces, namely in the case where in addition to phi plus being the complex conjugate of phi minus, they are equal. So u is actually real. Then we obtain the defocusing MKDV equation. And if phi plus phi minus is real but they differ by a sign, then we obtain the focusing MKDV equation. So then the idea is to look at the Hamiltonian H4 we actually expand the Birkhoff normal form theory to Fourier Lebesgue spaces. FLP with P negative, with P between two and infinity to these spaces of distributions and then extend the frequencies of the MKDV system to these Fourier Lebesgue spaces. And then of course we have to make a little analysis because it's a subspace we are looking at for MKDV, how the Birkhoff coordinates restrict in this case of these real subspaces. So maybe I leave the details here. We stop. Another question? Yes, you showed us how to extend these frequencies to wider spaces for Fourier Lebesgue. Yes. FLP for P bigger than two. Yes. What about P smaller than two? This is easier. This is probably easier. Yes, because it's contained in L2 so that the series is essentially made. Yes, but you get additional. Yes, yes, you can. Yes, there was a little bit less of interest but can be done. Yes, for instance you can do everything on the venous space. Yes, absolutely, absolutely. Absolutely. Nice space. Yeah, I agree, I agree. More questions? There's recent interest in well-behaved space, quasi-periodic or even space almost periodic solutions. And that involves then, for KDV, other ones too but I just heard of the KDV. And that of course involves some important spectral theory of that. So you have to do the good reflectionless ones but then the time evolution seems to be, at least this sounds like this is machinery that would work for that. So this is a question, is that a possibility? I think so, yes, I think so. Meaning gaps are no longer ordered but doesn't really matter. I must admit I did not look into it but I think the machinery should be extendable to this case, yes, absolutely. So, but we were more thinking of by looking at the action to frequency map in infinite dimension so there we can also show that this, but this is in the periodic setup that the map is actually a local defilmophism. So that means potentially you can do KM theory with infinitely many, at the total of infinite dimension because you can control the infinitely many frequencies through the action, you can go back and forth. All right, if not, let's thank Thomas again. Thank you.


Good day, fellow investors. Welcome to the Value Investing School, Episode 1. How to quickly say no to stocks? How to quickly assess whether you should look deeper into a stock or not? In this video, we're going to learn how investing is a game of mostly exclusion. We're going to focus on the business yield, current or future, and that is what makes things easy. And then we're going to discuss how you shouldn't be a relative investor but an absolute investor. This is what makes the difference and this is what makes things easy. And I'll discuss all of these topics by analyzing a stock market example, Lossitan and Provence as a company. It's a company that has beauty skin related brands all around the world in 90 countries with more than 3,000 retail stores. You probably see that brand when you travel around the world. So during a week, I usually look at a dozen, more than a dozen of stocks and how do I know whether I should put more time into one or another? Well, the easiest separator is and Warren Buffett usually says that he can see a good stock from a bad one or a potential one from a not interesting one in just 5 minutes. And I'm going to give you the three key things you have to look at when looking at stocks and then simply say no, no, no, no to all those that don't pass the initial criteria when it comes to stock market research. I'm currently researching a stock list from an Asian Value Investment Fund and one of the stocks on that list is Lossitan and Provence. And the things I want to explain by looking at Lossitan and Provence are the risks of not focusing on the business yield, the risks of being a relative versus an absolute investor and then how easy it is to say no to an investment. So let's start with the first thing and that is the business yield. What is the business yield?  You invest in businesses, not stocks that go up and down on a daily basis on an hourly basis. You invest in businesses. So when you invest in businesses, the key components are the price you're paying versus the yield of that business. What is the business delivering in earnings, cash flows, whatever you are measuring for a specific business? So when you find those two components, everything else becomes less important. You have to see what is the price you're paying for current or even better perhaps future potential earnings of such a business. Warren Buffett always likes to focus on businesses that will be here 10, 20, 30 years from now and that he knows will be better businesses in the future. For example, Lossitan is a growing company which revenues line one that have been growing since ever practically. So practically tripling over the last 10 years earnings have done well two over the last 10 years doubling a little bit less than double. But they had some peaks a few years ago. Now it has been slowing down. So what would be a price that you would pay for these kind of earnings? We see an average earnings of about 100 million euros. So if you want a yield, a business yield of 10%, you have to pay 1 billion euros and then you get 100 billion in earnings. If you want 5%, then 2 billion is great. If you want 4%, then 2 billion 5 is okay. If you want 20%, then 500 million is okay for this company. If we look at the market cap of Lossitan, it's 20.6 billion Hong Kong dollars or 2.6 billion euros. That means that the business yield the company currently provides is 3.84% given the price earnings ratio of 26. You say, okay, price earnings ratio of 26 earnings yield just below 4%, that's not a great investment. But then you have to always look, okay, is there the future? What is the company promising? We have seen a really good growth line, growth company tripling revenues over the past 10 years. If they do that again over the next 10 years and they even triple or quadruple earnings, then it's a completely different story. So let's see at the growth potential. You can see here that same-store sales growth are 1.8% in 2019, 1.7%. That's okay, but they're really growing by enhancing the number of stores. They made some acquisitions. But then when you read the company's transcript, you always look for those things and then you see that they are in the midst of a strategic review. The group has new management because we have seen, let's say, the declining earnings over the past few years. So adopting omnichannel, mobile, digital approach. So the environment where they operate has really changed. Just to note on this, Lossitan and Provence is a product that my mother-in-law gets excited about. So not really targeted to the millennials, Instagram buyers out there. So they are changing, they're trying to change, plus on top of changing, they just did a $900 million acquisition buying a company that has $40 million in EBITDA earnings before interest, taxes, depreciation and amortization. So they paid 22.6 times EBITDA for skin care, whatever brand, hoping that the brand will grow 30% per year in the future and that they can scale this business in China where the brand enemies is completely unknown. So they have here some new products, mostly targeted for, of course, millennials that I think Lossitan might be losing the game there. But when it comes to investing, what this tells us?  Not that it's potential and maybe. I don't know whether the management will turn around the company. The management doesn't know it. They don't know what will be the result of this acquisition. What will be the Chinese market reflection on the new brand that they have acquired? Who knows, especially with tariffs, trades and anti-US politics there. So it's very risky. You don't know what will happen and that's something not that a value investor does not do. So we have an earnings yield of 4%, less than 4%. Slow growth, if we exclude acquisitions and higher new investments, earnings haven't gone anywhere over the last 10 years. And the risk, everything, the concept of the company is based on future potential growth based on a turnaround. All red flags for value investors. So it's not something I would invest in. Perhaps the brand Lossitan is valuable, someone might acquire it. But that's a risk I'm not going to run. So this makes things easy. We looked at the business yield potential or current. We've seen that the current is too low, the future is too risky and we simply say no. And now comes the second question. The stock market is buying this stock. The stock market is giving it a 26 valuation for an earnings yield of 4%. Why are they doing that? And here comes the notion of being a relative versus an absolute investor. If you're an absolute investor like Warren Buffett is, you focus on the business yield you want to buy. 99% of the market are relative investors because they care about how their performance will be in this quarter, in the next two quarters over the year and they just want to beat anybody else so to get more money to manage more fees, etc. So you have to separate that and being an absolute investor makes things really, really easy. So relative investors simply think that Lossitan is a good brand, it's growing fast, it just made a transformational acquisition and if it continues to grow at 10%, 15%, perhaps even faster thanks to the acquisition in the future, it deserves a multiple not a 26 but of 40. And then you see that this stock would be 30% undervalued. And this is the problem with relative investing, comparing to something else, comparing to Amazon, comparing to other brands, who cares what the others are doing. You have to care what's the business yield because that is what delivers long-term investing, investing not speculative returns. If we look at the market we see that the stock didn't perform well since the earnings declined but also we have these peaks, it never really took off. The stock is where it was since it was public, so even lower probably. So nothing special there, the company didn't manage to leverage the brand, do really, really good, except for the good earnings. So how to say no to a stock? Look at the business yield, look at the promises. Simply say no, no because there are what 70,000 traded names around the world. You just need a few for your portfolio for a great investment life. You don't need more than that. And that's why we just eliminate, we look bottom up at as many companies as possible but it usually takes three to five minutes to say no to something somewhere 10%, 15%, if you really dig deeper into a sector or something. And then that's it. If you find one of 50 is interesting then you start looking at it, look at the history, okay, what are the completely other components when it comes to really making a decision which we will discuss in other episodes. So please subscribe to the channel.  Don't look what others are doing and simply say no until it really hits all your investment criteria. And number five, subscribe as I said. Looking forward to your comments, any questions please share them in the comment section below so that I can structure this value investing school so that it better fits your investment environment. Thank you for watching, looking forward to your comments as I said and I'll see you in the next video.


Australia pays Washington swamp monsters for war advice. Australia has been paying insiders of the U.S. war machine for consultation on how to run the nation's military, a massive conflict of interest giving that Washington has been grooming Australia for a role in its war agendas against China. In an article titled Retired U.S. Admirals Charging Australian Taxpayers Thousands of Dollars Per Day as Defense Consultants, ABC reports that according to documents which were provided by the Pentagon to Congress last month, dozens of retired U.S. military officials have been granted approval to work for Australia since 2012. For those who don't speak imperialist, retired U.S. military figure generally means someone who used to be paid by the U.S. government to advance the interests of the U.S. empire and is now paid by corporations and or foreign governments to advance the interests of the U.S. empire. These corrupt war mongers rotate in and out of the revolving door of the D.C. swamp, from government to war industry jobs to punditry gigs to influential think tanks and then back again into government, advancing the interests of the U.S. empire the entire time and growing wealthy in the process. This dynamic allows a permanent constellation of reliable empire managers to continually exert influence around the world in support of the U.S. empire regardless of who gets voted into or out of office in the performative display of electoral politics. It's a big part of why U.S. foreign policy remains the same regardless of who's officially running the elected government in Washington and it's a big part of why the media and arms industry which support the U.S. war machine keep playing the same tune as well. Among the American swamp monsters Australia paid for consulting work is the Obama administration's spy chief James Clapper who has an established track record of lying and manipulating to advance the interests of the U.S. empire. In 2013 Clapper committed perjury by telling the Senate under oath that the NSA does not knowingly collect data on millions of Americans only to have that lie exposed by the Edward Snowden leaks a few months later. In 2016 Clapper played a foundational role in fomenting public hysteria about Russia with the flimsy ODNI report on alleged Russian election interference which remains riddled with massive plot holes. He would later go on to repeatedly voice the opinion that Russians are almost genetically driven toward nefarious and subversive behavior. In 2020 Clapper signed the infamous and now fully discredited letter from former intelligence insiders saying the Hunter Biden laptop story was likely a Russian disinfo op falsely telling CNN that the story was textbook Soviet Russian tradecraft at work and that the emails on the laptop had no metadata on them. Also among the American military consultants paid by Australia is a man we just discussed the other day, William Hillerides, who will be telling Australia how to reconfigure its navy because apparently no Australians are available for that job. We now know that according to the released Pentagon documents Canberra has already paid Hillerides almost $2.5 million since 2016 for his consulting work. This information was originally reported by the Washington Post's Craig Whitlock and Nate Jones who last year broke the remarkable story that a former U.S. Navy admiral named Stephen Johnson had actually served as Australia's deputy navy secretary. A position which needless to say is not normally open to foreigners. This is just one of the many, many ways that Australia is being interwoven into the U.S. war machine. From our 2023 defense strategic review which further enshrines our position as a U.S. military asset to our Secretary of Defense Richard Marles saying that the Australian Defense Force is moving quote beyond interoperability to interchangeability with the U.S. military and being suspiciously secretive about who his golfing buddies were in his last trip to the U.S. To Australian officials angrily dismissing attempts to find out if the U.S. has been bringing nuclear weapons into Australia to the Australian media pounding Australian consciousness with anti-China hysteria to such an extent that we are now seeing hate crimes perpetrated against Asian Australians. I've always wondered what it would be like to witness the information environment of Washington's next military proxy from the inside. What it would be like to be a Ukrainian with an ear to the ground during the lead-up to the 2014 coup or whatever. Well, now I know. Now all Australians with an ear to the ground know. I have been generally dismissive of Australian affairs throughout most of my commentary career despite living here since my focus is on resisting the disasters that humanity as a whole is headed toward and Australia has always seemed like a fairly irrelevant player on the world stage because of its impotent subservience to Washington. But it's becoming clearer and clearer that it is exactly because of Australia's blind subservience to Washington that Australia is worth paying attention to since that relationship may well end up giving our nation a front row seat to World War III. Australians are going to have to wake up to what's being done to us and the abominable agendas our nation is being exploited to advance. We are being groomed for a military confrontation of unimaginable horror, one which absolutely does not need to take place, all in the name of something as trivial as securing US planetary hegemony. We've got to start saying no to this. And we've got to start right now.


Hello, in this short video, those who are interested in point cloud data for the Netherlands, I'll show how to download AHN4 data from this very nice website GeoTiles. Someone pointed it out today in the comments on a post on LinkedIn. And through this website, you can download colored AHN point clouds from the different versions of AHN. So you can zoom in on the area of interest, and when you're sufficiently zoomed in, it will show you the sub-tiles of the original AHN tiles. And you can click on a tile, and it will show you what is available for download. Choose it on OpenTopo, and it shows it in the files that you can download, and here you can download the LAZ file to be further used in QGIS, for example. It also gives the license information. Because the tiles are much smaller than the original tiles downloaded from PDOK, you can much faster load them into QGIS, while thus the conversion to the COPC format. And then it's time to fly around in the 3D view. You see that there are spots with voids, no data, and you can also maximize the screen of the 3D view. And to get rid of the voids, I have here added an aerial photograph from PDOK to cover up for the no data areas. So time to fly around.


Hello, everyone. This is Srinatharan. I'm a fifth year PhD student at IIT Bombay. As part of the Student Express Award, we are participating as a team called SAS IITB. So I'll just introduce our research topic in a few just a minute. So our study deals with utilizing the BEX technology, which is bioenergy with carbon capture and sequestration for large scale CO2 removal and its safe and permanent sequestration. Biomass based power plants and other industries which utilize biomass are sources of both CO2 as well as alkaline waste rich in calcium oxide or magnesium oxide. CO2 emissions from these industries could be captured using different solvents or solvents and the CO2 rich solvent could then be reacted with alkaline waste to generate permanently sequestered mineral carbohydrates simultaneously also regenerating the solvent. In an integrated CO2 absorption mineralization come regeneration of solvent which is IAMR process. Also the mineral carbohydrates generated could be utilized as alternative materials thereby avoiding indirect CO2 emissions. Currently the generation of highly concentrated stream of CO2 and its subsequent storage is an energy intensive and costly process. Also management of huge quantity of waste generated from different industries is a huge problem. By using the IAMR process in biomass based industries it would help in large scale CO2 removal thus resulting in net negative emissions on a life cycle basis. And the process would be the IAMR process is an energy efficient and a cost effective process which results in permanent sequestration in the form of stable mineral carbonates even in areas with low or no storage potential. Now I will quickly introduce my team members Anvesha, Srishti and Shubham. Hi, I am Anvesha Banerjee. I am a first year PhD student from the department of chemistry. Hello everyone, I am Srishti Bhambay. I am third year undergraduate at department of energy science engineering by IIT Bombay. Hello, my name is Shubham Kumar. I am a junior research fellow in the department of science IIT Bombay. And moreover I would like to add something to Srinatha here. Basically we are developing or working on the process that have been sustainable, scalable and we are trying to make a geo mesh technology and with this we are going to participate and hope we are going to be successful. Thank you. Hopefully we will definitely win the student experts award. Hope for the best. Thank you. Yeah, thank you all.


I have been brutally attacked by the government, I don't know I have been pleading condition to talk, I have been brutally beaten up. Now basically an administration which runs without consulting any of its stakeholders including the students. So to restore the statutory functioning of the universities and to address the fears which is known to the people. Now as the meeting ended, there was a dialogue at the meeting with the students and the teachers. The meeting ended roughly around six and there was some tension on the campus. There was some talk that you know lots is going to happen and there was something about unease in the air. And at 6.15, 6.20, 35, 40 of us were standing in front. 300 teachers, students were behind us and we saw these 70 masked men approaching us. And again as the tradition has been in JNU, we thought that we will be able to talk to these people who are approaching us and see what their concerns are. But they didn't come up, they were about 30 to 40 meters away and we could see their faces covered. They were carrying things in their hands and they started pelting stones of this big size. And the stones were not one, two or five, they were in large numbers and that led to the people started running as a result of the stone pelting. And one student started running and teachers started running, they chased. They chased us in the bushes, they chased us in the rooms and then it went on.  Women who were just walking or trying to be on the side were not left and the language was very abusive. And then it went on. And for the next one and a half hours, even when the national media had reported that JNU campus is going through this, the mayhem continued. And that is what is to be underlined that even when the news had come out that the violence continued on campus. And it was only after 8.30 or 9 o'clock that things declined. We don't know the situation right now who is inside, how many people have been injured. We have SMS messages from students saying they are inside rooms, they don't know where to go. They have injuries but they don't want to come out. So it's really, really panic and turmoil on campus and this administration has not come out. The administration will not come out even now to express any concern. My colleagues are injured, they are in the trauma center. There is not a word from the Vice Chancellor saying that his teachers and students are injured and he's concerned about them. And I dare to say that even if some of us had died, this Vice Chancellor would not even express his sympathy that his teachers have died. So it seems that this administration has no sensitivity, concern or anything to do with the students and teachers and the Karamcharis of this university. The rest of you all understand that what is it that lets Vice Chancellor go on and carry on with this violence and mayhem on this campus for the last 4 years in other ways and now literally by the use of non-students as a way to do this. I tried entering JNU through the east gate that's a small gate towards the east side of the campus because the main road to the campus was barricaded. When I reached the gate the guard, despite me telling him I was a media person did not let me enter the campus. A few minutes later an SUV with a BJP flag on it came near the gate and it was allowed entry inside. When I asked the guard why was this being done he didn't have a proper answer. So I entered the campus through the IIMC gate and when I reached the second T point near the Sabarmathi hostel a group of students at 2-3 of them on the road told me not to go further ahead. They told that a group of 70-80 men with batons and sticks are wandering around the campus beating up whoever they are seeing. So I stopped my vehicle and I was there on the road waiting for these people to leave. I could see after a few minutes around 70-80 men again with the lattes and batons walking around. So once when they left I went to meet our newsletter reporter Ravi at T Point. By then there was an event that was happening I mean an event was happening there which was stopped by the Goons. A JNU teacher's association had called for a peace demonstration which was organized near the Sabarmathi hostel. I could see chairs broken down, banners torn and even the cars of professors were all destroyed. Glasses were shattered, windshields broken etc. So I tried shooting something there but then again the group of people came and we had to disperse. Once when the group left again we came back to Sabarmathi and then by then someone told our reporter that they had also caused ruckus inside the hostels. So we went inside the Sabarmathi hostel and in room number 156 was the room on the first floor. There was a Kashmiri students staying and this room was dilapidated. Basically it is somewhat an isolated room in the wing and only this room was nitpicked and was attacked. Later we also got to know that there was another room downstairs also that was attacked. That was the room of a Muslim student again. So it is clear that the violence is being inflicted on Muslim students especially Kashmiris in the hostel. Once we spoke to the Kashmiri student and he told us that a group of men came and they broke open the door with the fire extinguisher that was on the wing. They threw flower pots inside and the room is a mess actually right now. So once when we came out of the Sabarmathi hostel around 100 student activists had already gathered at Sabarmathi hostel and they were expecting a few more to come. By then students from the Brahmavutra hostel, I mean by then there was another call given to the students of Brahmavutra hostel to march to Sabarmathi in solidarity with the students who are at the Sabarmathi hostel. So this grew in numbers eventually over time and after a point there was around 500 to 600 students and then they decided to march towards the main gate to break open the gate so that people who are in solidarity who have come from outside etc can enter the campus. 5th of January the time is 8.39pm. I am outside the gate of New Delhi Bay Jalanero University which just around the evening time saw a massive right wing violence by ABVP who brutally thrashed student leaders and students including the JNSU president Aishik Hosh who was hit on the head and she was severely bleeding. I am outside now and the situation is quite tense. There are around 100 ABVP members armed with cricket bats, lathis and they are chanting Bharat Mata ki Jai Sri Ram and it's a quite aggressive situation. There are around 200 police personnel but there seems to be just a spectator here. Just now ambulance was stopped by the ABVP protesters. They are not allowing any ambulance to go inside. One ambulance attempted to go inside and the ABVP protesters stopped it and they deflated the tyres, abused those doctors or nurses who were inside it and they also deflated the tyres and broke the glass panels of the ambulance. The situation is quite tense. Luckily the ambulance was able to get out of the whole hostile situation and that's the update till 9.15pm. 10.45pm, Yogendra Yadav and 4-5 people along with him who were gathered here were brutally beaten up. Two women who were with him were brutally dragged, their heads were pulled, they were manhandled. During all these violence what was happening when the women were being beaten up by the ABVP, the police didn't even intervene. They didn't even bother to intervene. The situation is better now outside and more than 500 civil society members, students of JNU, former students of JNU have gathered here and they have pushed back the ABVP people and formed a human chain around the gate. Thank you.


Australia has ramped up cooperation with ASEAN to support shared recovery from the pandemic. Because better health and economic growth is what we all want. Building on existing programs, our new cooperation spans ASEAN's three pillars. Within the socio-cultural pillar, Australia stands for access to safe, effective vaccines. We're flying in doses, starting with Vietnam and Indonesia. And through UNICEF, we're procuring vaccines for up to 9 million people in Southeast Asia. In addition to our contributions to COVAX and the ASEAN COVID Response Fund, and we're assisting with cold chain, training of health workers and information to address vaccine hesitancy. We're supporting ASEAN's Centre for Public Health Emergencies and Emerging Diseases and new ASEAN Health scholarships. Building capacity against disease spread from animals and increasing mental health cooperation. Within the economic pillar, we're backing the ASEAN Comprehensive Recovery Framework, expanding our work on digital trade standards, connectivity and sustainable infrastructure, partnering with Mekong countries on economic, trade, environment and cyber. And updating our regional free trade agreement with ASEAN and New Zealand. We look forward to supporting ASEAP implementation. And within the political security pillar, a new program is advancing cooperation on cyber and women, peace and security. And we've pivoted our counter-human trafficking work to deal with COVID impacts. We'll continue to support an open, inclusive, resilient region with ASEAN at its centre, in line with the ASEAN Outlook on the Indo-Pacific. A region where Australia, ASEAN's oldest dialogue partner, works even more closely with our friends, neighbours and partners to support recovery. Australia will be with ASEAN every step of the way.