So the next talk will be by Ricardo Zanfa and he will explain extending the topological pre-ship bandala junction to sites and toposes and this is joint work with Olivia Carmelo. Thank you. I hope everybody can see the slides. Yeah. So here I will be presenting to you a part of the joint project with and working on Olivia and I. And so basically what I will present to you today is this. So we have this known result in topology. When we have a topological space, X, we know that there is an adjunction between the pre-ships over the space X and the bundles over X. That is topological spaces over it. We wonder if we can do the same for an arbitrary small site and in fact we do. If there is a site, CJ, a small site, we can build an adjunction in the same way where instead of topological spaces, we'll have toposes of a certain kind over our base topos. And the properties of these adjunctions do reflect what happens in the topological case. So as I was telling you, this is an extract of my joint work with Professor Carmelo, which is Relative Topos Theorical Biostacks, which will be available in a few days. And in particular, I will recall briefly the topological pre-ship bundle adjunction. Those of you who are interested and want to see it again, you can find it, for instance, in Sheets in Geometry and Logic, though the result is quite ancient in topology, let's say. And I will also cite the local version of the same adjunction. This is somehow harder to find in literature. You can find it though, still in Sheets in Geometry and Logic, it's kind of implicit in some of the exercises. So I've written it here. So for those of you who haven't seen Olivia's lectures last week, I will recall how the topological pre-ship bundle adjunction works. So we know that we have this adjunction where X is a topological space, any topological space. The functor lambda is called the bundle of germs. And basically, it takes a pre-ship p. It computes this set. These are the stocks of germs of the pre-ship. We won't need to see the definition again. But basically, you take the germs of the elements of p in a point text, you glue all these sets together into this co-product. You have a canonical projection. And you can topologize this set so that this map becomes a continuous map. And this is called the bundle of germs of the pre-ship p. On the opposite direction, the right adjoint gamma is called the local section sphincter. It takes a bundle over X. So we have our continuous map p from it to X. And we call local sections the continuous maps from an open U inside X, such that they work as a section of our map p. So they are the local sections of p at the open U. This defines a pre-ship. And the properties of this adjunction are the following. First of all, we can calculate the fixed points of the adjunction. The fixed points in the pre-ships for our topological space are the ships for the topology. While the fixed points in the bundles are what are called the etal bundles over X, which are basically the local homeomorphisms with co-domain X. And they are the fixed points of the adjunction. So in particular, we get an equivalence at this level. The second important property of the pre-ship bundle adjunction is that when we start from a pre-ship, we compute its bundle of germs and then go back to the local sections, we end up getting the shiftification or the associated shift of our original pre-ship. So the composite gamma lambda is the shiftification factor. So you see the basic points in this result are that pre-ships and most importantly, ships over X can be thought as a category of spaces, because we are really seeing them as etal spaces over our base space X. And also that the shiftification factor gets a geometric interpretation in terms of local sections. And this is interesting because when you compute shiftification for a general grotendic topos, in the literature you almost invariably find just the one description which goes back to grotendic with a double plus construction, which is I mean it's a very nice construction, but it's very algebraic and very hard to use because when you compute that, you take the matching families for a pre-ship, you quotient them with respect to an equivalence relation and then you do the same process again. So it's kind of hard to manipulate it in a concrete case to do computations with it. While for instance, when you have topological spaces, you have this very nice description. So you know that shiftifying means taking the local sections of a particular bundle over your base topos. And at the beginning I told you that there is also a localic version. This basically happens because even though when you build the bundle of germs, you use the points in the space, you don't really need points. So you can do the same things point free and you get the pre-shift bundle of junction in the formalism of locales. So if L is a base local, you can consider the pre-shifts over L, its shifts, the locales over L and the et al, locales over L, et al map of locales is the natural generalization of the et al map of topological spaces, and you get all the same properties. So a junction, a joint equivalence at the level of shifts, and you can recover the shiftification. So it is natural to want. Ricardo, we don't see your video. Maybe you can switch it on. You don't see my video? Is it only my problem or someone else? I can see it. I see it myself. Okay, so maybe it's just me. Okay, sorry for the interruption. Okay. So we wonder if we can do the same for a generic site. So we have our topological space, and we want to substitute it with a site. So as the title of the slide suggests, we think of topos is a generalization of spaces. And so the generalization of continuous maps over a base topological space will generalize to geometric morphisms from any topos to our topos of shifts. This is the most unnatural generalization one can think of. There is, however, a size issue here. Because when we define the local sections of a topological space, we are considering home sets. If we want to do the same here, of course, we cannot speak of home sets, because the class of geometric morphisms between two toposes is in general not just a set. So we have to restrict that in a certain way. And we propose this restriction. We call a topos e over our base topos, small or relatively to the base. If for each x in the site, and in a moment I will tell you why we choose this, this category of geometric morphisms. So you see these are the geometric morphisms from this slice topos over the representable, given by x, to our topos e over the base topos, shifts Cj. We ask for this class of geometric morphisms to be a set after equivalence of geometric morphisms, of course. So why do we choose the elements in the site? Of course, we won't appreciate over the site. That's obvious. But the reasoning is in the topological case, the elements in the site are the opens. So in this case, we are really saying we are taking something from an open in the topological space to the space we are considering to calculate its local sections. So given the notion of topos small or relatively to the base, which mind is referred, I say topos, but the object of interest is actually the geometric morphism, because of course we may have the same topos with different geometric morphisms over the same days. And we call topos with this superscript s, topos over shift Cj, the full subcategory of the topos is over our base that are small, that are relatively small. And this will allow us to define local sections and have them being a set. So appreciate. In particular, we also want to generalize the notion of et al, topological space. And of course, we already have a notion here of et al topos. A topos over a base is said to be et al or equivalent to a local homomorphism, the terminologies are equivalent. If it is the topos is equivalent to one of these form. So it is equivalent of a slice of our base topos. And also this geometric morphism is the canonical geometric morphism to the base. So it's the one whose adjoins from the right adjoint to the essential image are the dependent product going this way, the pullback factor going this way and the dependent sum in this way. We denote the category of et al topos is over a base with et al over shifts. And in particular, all et al toposes are small relatively to the base. So we have this inclusion. And in a moment, I will tell you why.  Now to define the adjunction, the local sections functor at this point is straightforward with the generalization of what we have in the topological case. Given an essentially small topos e over shifts Cj, we consider its image by a gamma to be disparate shift. So you see it's the local sections of e at the elements of C. And we know that these are sets because he is small relatively to the base topos. So which we chose e to be sure that this lens in set and not somewhere else. The definition of the bundle of germs, the left adjoint is requires a bit more of work, not much. But basically, we start with a pre shift P. We consider it's grotendic construction, which is a vibration over C, discrete vibration in this case. And since C has a topology J, those of you who have followed the latest lectures last week already know this, we can endow this category with the smallest topology, which we call the Jp, making this functor of comorphism of sites. We call this topology Girod's topology for the pre shift P. We call the site Giro side and obviously the topos Giro topos for P. Since this is a comorphism of sites with this topology, it induces co-variantly a geometric morphism. So we have always this geometric morphism, which is furthermore in this case it's also an etal geometric morphism, but in general we have it and it's always essential. So this is the bundle of germs functor. And to prove the adjunction at this point, it's you will see it's quite easy to prove it because it's a couple of lemmas and the rest is pretty straightforward. The first lemma shows that the Giro topos for a pre shift P is a conical co-limit in the category of toposes over the base. So basically we have our category of elements here. You see every object in here is mapped to an etal topos, which is going to be shifts over the representable index by that element. And so what happens? Why do we want it to be a co-limit? Because we want lambda to be the left adjoint of a home functor, of a contravariant home functor. So it's going to behave like a co-limit. And this is in fact true. You can prove this, it's a computation. So you see if you start from an arrow, geometric morphism from lambda P2E over our base topos, since this is a co-limit, having an arrow here is the same as having a cocoon. The cocoon has legs starting from toposes of this kind, this etal toposes 2E. Each of these legs is indexed by elements in P. So for instance, you will have a geometric morphism, which is indexed by an element A in P of X. So a cocoon of this form is the same thing as a natural transformation from P to this set of geometric morphisms, which is gamma. And so lambda is the left adjoint of gamma. So we have the adjunction at the level of pre-shifts. We want to see what happens when we restrict to shifts. And for that, we can use these two lemmas on etal toposes. The first one tells you that if you work over a base topos, arrows between etal toposes can be presented directly with arrows inside the base topos. So any geometric morphism here above E is presented by an arrow in the base topos. The second lemma tells you that the gerotopos of a pre-shift P, which we described in this way, is actually equivalent to an etal topos, which is the etal topos over the shiftification of P. And with these two lemmas, you can prove all the nice consequences about the adjunction, the pre-shift bundle adjunction. Because, see, if you start with a etal topos, shifts Cj over F, and you compute its gamma, its image, the local sections are defined in this way. But using the first line, you can reduce these two arrows from this representable to F. You go from the etal toposes over the base to arrows inside the topos. And this is just F by unit a lemma. This equivalence allows you to conclude that fixed points in small toposes over the base are in fact the etal toposes, the fixed points for our adjunction. In the opposite direction, if you start with a pre-shift P and you consider its shiftification, again, we do the same thing in reverse. So we start from the shiftification, we use unit a lemma, we move to etal toposes. Arrows from here to here are the same as arrows from this etal topos to this etal topos. But this is just gamma of lambda of P, because we said here that lambda of P is precisely this last topos. So this again, this allows you to conclude that fixed points of the adjunction are the J-shifts and also that the composite of gamma and lambda is the shiftification factor. So we end up with the let's say the pre-shift bundle adjunction for general sites, which you see is really the same thing as what happens in the topological case. Pre-shifts with relatively small toposes restricts one equivalence between shifts and etal toposes, no longer spaces, and you can recover the shiftification by composing the two adjoints. Can you say at this point how you overcome this iteration twice for the shiftification in the topos case? Yes, I will tell you later how, in a certain sense, in a couple of slides. So let's say what is interesting about this adjunction is that you can move in different directions. You can go up, let's say go up and see it as a truncation or reduction of a wider phenomenon, two categorical phenomenon. You can also go down and describe the shiftification using sites and their morphisms or comorphisms, or you can cross the bridge, let's say. So in some cases, for instance, I will show you in pre-order sites, you can actually forget the topos theoretic information. So you end up with a description of the shiftification that is really topos-less, let's say. So for the two categorical adjunctions, I won't tell you much, Oliva's already told you about this on Saturday, but basically there is a two categorical adjunction which leaves at the level of pseudo-functors from our category two ket and the toposes over the base topos. We have these two adjunctions. The right adjoint is still a local sections functor. The bundle of germs left adjoint behaves in the same way as in the discrete case, so it takes a syntax category and builds its zero topos, which is the topos over its associated vibration. And when you take this adjunction and restrict it to the one-dimensional case, you get, again, our discrete adjunction. So for those of you who are interested, of course, you will find plenty more content on this on the forthcoming paper. Going down, what is interesting is that this provides a geometric interpretation of the shiftification as local sections, because you see the value of the shiftification of p-atex is set up to equivalence of geometric morphisms from this topos, which is the one indexed by our object to this topos. And of course, speaking about classes of geometric morphisms is not that simplifying, let's say. But at this point, since you have geometric morphisms, you can go to sites. You can reduce to sites in various ways. So one way is the most standard one is using flat J-continuous functors. So a geometric morphism from here to here will correspond to a flat J-continuous functor from this site to this topos, or equivalently to a morphism of sites from this site to the canonical site of the topos. Another way of seeing this, which is harder to see at first, but basically you can present this topos with this site. It's the slice category of the x. This is the gerotopology for this discrete vibration. And all the functors in here can be presented by comorphisms of sites from this site, which presents the first topos, to this site, which presents the second topos. Mind, it's not that all comorphisms of sites will give you geometric morphisms in here. Of course, they have to satisfy some conditions to give you something which leaves over the base. The third point, which somehow is connected to the question, is the following. It's hard to give you really a technical idea of why this happens. But if you think of elements in the shiftification, an element in the shiftification of P attacks is something which may not exist in P, but is given by gluing local information in P. In the same way, it happens that a geometric morphism in here may not be presented at the level of sites by a comorphism, but it is locally presented by a comorphism of sites, and even better by morphisms of vibrations. So what happens is that you can find for each geometric morphism in here, you can find a j covering the family of x, and a family of morphisms of vibrations from c over yi to the vibration of P. And this is really telling you, I'm taking elements of P, I'm seeing them locally. These are all comorphisms of sites, and these, let's say, jointly induce a geometric morphism over here. So we are saying you may not have a presentation at the level of sites in terms of comorphisms from the site presenting this topos to the site presenting this topos, but you can restrict to a j covering family so that you have this presentation. And this somehow connects with the double plus construction because when you do the double plus, what you have is at first you have matching families up to, let's say, the local equality, and then you do a matching family of locally matching families. So what you get, sorry, a matching family of matching families, modular local equality. So what you get is the information of a, it's hard to explain, but you see it's, you get basically a local information for which when you restrict nicely enough, you get the same geometric morphism. So the point in the plus construction is that you have your local information, but the local information doesn't induce something already at the level of the site. So not something from CJ to INTP, but at the level of toposis it does. That's where the double plus kind of strikes in. I know it's a bit foggy. I will try to be maybe clear later. I'll finish now. And for the last point, as I was telling you, there are some cases in which you can move away from toposis altogether. You can forget the toposteoretic information as it happens for pre-order sites. So I recall you this result of locales. So basically locales over a base include into toposis over the shifts for that local. This inclusion goes into essentially small toposis, sorry, relatively small toposis. And also, I recall you reminded that for a pre-order site, this happens, the shifts over that pre-order site. By pre-order I mean category in which between two elements there is at most one error. It's a locale, a locale topos, and it is represented by the locales of ideals of j ideals of the category. And you can do the same for every pre-shift over your category. The topos you get is locale, and you can see it as presented by the ideals of the vibration. Using this, if you consider in particular pre-shift over a locale, shiftification is described in this way. And this is what we said before. This is gamma of lambda. But then, since we are in toposis over a locale topos, this is locale, and this is locale, we reduce to locale. So this is the same as maps of locales from this locale, which presents this sliced topos to this locale. And you can plug this in in the adjunction. And basically, you get this for pre-orders. You get that your adjunction at the topos theoretic level already exists at the level of pre-shifts over your pre-order and the locales over the ideals. And again, this induces the equivalences we expect. In particular, we get the notion of, there is a notion of et al net of pre-orders. So you get the pre-shifts over a pre-order are the same thing as et al pre-orders over a pre-order, and shifts are j et al shifts, generalizing a result in this article by Hemme and Iro. And with this, I think, yes, you used all my time. So I thank you for your attention.


Hello and welcome to NewsClick. The recent surge in the COVID-19 cases has struck hard on India. The daily cases have doubled in a matter of 10 days and in Tamil Nadu it touched an unprecedented 7,819 cases in 24 hours as per the government report on April 14th. We have Dr. Sundaraman with us, the global coordinator of the People's Health Movement, to tell us where the state is headed in the coming days. On March 1st the daily count was 470 in the state but now we are touching anywhere around 8,000 cases a day. So in 45 days there has been a 17 times spike in cases. Why and how is the virus spreading in such a pace? So it's always a bit difficult to answer why but we do know that we are seeing a very rapid acceleration of the cases, more than three to four times the rate of acceleration that we saw in July, August. And though case fatality rate may be low in absolute number of deaths are also rising very fast. Now one of the important reasons for this is a wave is actually when you have a number of outbreaks, smaller outbreaks in a number of sites which go unnoticed and they rise a certain amount of transmission starts in place and then they snowball into a wave. So preceding wave is number of discrete outbreaks. If it is just one outbreak then it will clearly be focused in one place but we find that it is across the state and across the country. So what you can reasonably presume is that between January and March, there have been a number of outbreaks which have snowballed. Remember that there are number of countries which have either seen no second wave or seen very small well-contained second waves. New Zealand, Australia was well-contained, New Zealand had no second wave, South Korea was well-contained, Taiwan, Chinese themselves have not had a second wave. The Japanese have had discrete waves. These are outbreaks. Vietnam had a major outbreak in Danang. They went after it, controlled it and that was the end of it. But here you have had actually a number of outbreaks that have grown unnoticed and reached a certain size. So the question to ask is why did it go unnoticed? In my understanding, there are two or three reasons. One major reason is the lack of an effective contact tracing and disease surveillance system, where you pick up the case loads when they are moved. A second thing and this in Tamil Nadu, I want to emphasize is a major problem and has not been there as part of the discourse. There is a very high degree of both stigma and denial. There is a strong sense in the village when you go, there is no such thing. This is a made up story and even when there are deaths, because there is so much shame attached to confessing that one has stigma or confessing that one has had COVID-19 or confessing that the village has had COVID-19 outbreak that they would go into denial. People will say things like, oh, there is no COVID-19 in our village. These two people got knows what happened to them when they got tested and it became positive. So as if the testing made it positive. So there is a high degree of denial and that's why Tamil Nadu is even struggling to reach its vaccination targets on that. Because at some point, this denial is a big phenomenon. That means that people don't come forward and the state has created so much of a shame and guilt complex about having COVID-19 that you can't locate it until the hospital start flooding. And we are better off than Gujarat and Madhya Pradesh where the crematoriums have started flooding. And that's one reason why is because between the last wave and this wave, we have really improved our organization of hospital care in Tamil Nadu. So therefore, we are in a much better situation in terms of getting people to hospitals and treating them there. But we haven't been just as successful in preventing spread because our engagement with the community, our contact tracing, the degree of health seeking behavior changes and whether we need is very low. All of our attention has been in only towards physical distancing and masking. While that is important, there are limitations to how far you can go with that social distancing also. But what is very important is that we have never addressed the issue of stigma and denial and how much that is acting as a barrier in our content. I don't think there is a single commentary that touches it. I do think this is a major phenomenon here. And in the same time when we have elections along with this stigma and denial, I mean, we saw massive gatherings during the elections in the rallies, in the campaigns and so on. So what has been the contribution of the election period and should we have not had elections in such a pandemic in such a time? So there are two questions here. What is the impact of the elections and should we not have elections? The elections must have acted as an amplifier. It does because there are more people out there, more contacts, more likelihood of transmission. Maybe not even so much outdoor rallies, but even if the rate of transmission is low, the numbers are so huge that the transmission would have definitely happened. And we would have also so many meetings that have happened in house, people meeting with their party workers, party workers meeting, going house to house. So definitely it has acted as an amplifier. But I would hesitate to put the blame entirely on elections. And I think that, for example, there are many states which did not have elections. Shatishgarh is seeing its largest outbreak. It did not have a single major gathering at this period. It did have in the November period when the cases actually went down. And it did have in Maharashtra, for example, has not faced elections. So to put it completely on is making it too simplistic an explanation for it. But in the middle of an outbreak, certainly we could have done much better in the use of social distinctions and restrictions when we were doing much greater self-awareness and much greater monitored awareness of how basically COVID-appropriate behaviors could have been followed. We could have done better. But come to your second question. Should we not have elections? I would actually say that's a very dangerous statement to me. Anything that undermines democracy is a serious threat in the face of abandonment. So whether you may extend tomorrow the same argument to street protests, you may extend that same argument to large gatherings of any sort which are able to respond to a highly authoritarian state. And at some point you do need people's participation. So whereas it is important and I do think that in the election queues and in the booths, it was better. It could have been even better. It was reasonably well managed. But I don't think the normal work of democracy should be interfered with. Because there are greater dangers on authoritarianism than on the sort of outbreak. There is a huge way and you need people along with you. You need a legitimate government to be able to mobilize it. So no, I don't think the election should have been postponed. It could have been done with greater caution and restraint. But at some point it should not be postponed. And that I think is a point that we need to strongly make because this will be used tomorrow against all democratic mobilization. And we should I think be on record not to oppose that. That is true. So I think I'll shift the focus now. I'll ask about the vaccine. So we are already, there's been a shortage of vaccines. But at the same time, we also see there's been wastage of existing vaccines. So what do you say about that? How can, why is this happening? So in the public health field, we know this wastage has a certain root. For reasons of cost and efficiency, usually the vaccine comes in vials where 10 to 15 are packed to a dose. And once you open the vial, then you must exhaust that vial within that time. Now, when you go to centers which have low turnout and you have one or two people trickling in, when you open a vial, then some doses are used and some are left unused. And then you can't keep them even in a refrigerator. You have to throw them out. So therefore the wastage occurs because unless you have a collection of people, you can't do. But people come in all through the day and therefore it is difficult to secure that collection of people. Now, one of the major ways in which this has been solved in public health is to actually mobilize and give appointments together so that you give appointment for 100 people together and then you can be sure that at least 90 people will be there or 70 will be there and you need to open one batch of vials at a time. So this is essentially a bit of efficient logistics mobilization that needs to be coordinated. It's a delivery issue. It is not an utter issue of lack of demand. But lack of demand is also there because in the beginning, when you did not make this logistic arrangement, you had the assumption that the moment you open up for vaccination, there'll be a flood of people there. That's not happening because the really most vulnerable people have required a far greater public outreach than what has been available now. And in fact, remember what I was telling you earlier, the issue of denial, the issue of that there is a pandemic at all. People will say things like, oh, those people are paid monetary incentive, so they come and report test positive. But it's not really test positive. So in this situation that to actually build the case for the role of vaccination is a very important step that you need to do. They also have experience of many people recovering etc. So you need to actually explain this much better. So the nature of public outreach that is required, especially to vulnerable sections. I had a long discussion on a TV show with representatives of the Coimbedo Vegetable Park. They had a lot of demands relating to lockdown and prevention of restrictions and management of restrictions. They didn't raise the demand of saying that all of us must be vaccinated. Yet these are traders and vegetables who are retailers and vegetables, which each day meet over 100 people. To prevent them from being super spreaders, you need them all vaccinated. Yet this was not one of their demands and yet they had very well articulated demands. So my sense is that you have to work with workers' associations. You have to work with working people, with different sections of the community to actually sensitize them to this and that prevents wastage incidentally. But its main thing is it is able to speed up your wastage. The state is imposing a demand that everybody below 45 be vaccinated by 25th. It's a difficult demand to meet but it is meant to stimulate their public outreach in workers. But why are they facing such a situation when world over there is actually a problem of a queue? People getting their vaccination dates too long. And that again goes back to what I am saying, the phenomenon of the day. So much has been said about blaming people. People are to blame for this particular second wave. People are to blame. You did not wear a mask. You did not do this. So everybody when they get the disease are ashamed about it, ashamed even about the need for protection. We have to break and that complex builds up. So I think in achieving vaccination preventing these public awareness and sensitization, we just fine-tune to address the real problem not there. Not the general message that you are giving across the country or world. Specifically in Tamil Nadu, respond to the ways stigmatization has promoted. It started with the tabligi jamaat. But in different forms and then the way the police repress us, the way they beat up people, all of this creates an association of criminalization with infection. And therefore, good honest people deny having the infection at all. So I think that there is a much more complex issue over here. And the point about the logistic management is a small part amenable to management, especially if you are able to have a better outreach system. See, my next question is in connection to this question and what you have answered. So the Tamil Nadu Chief Minister at Apari Paranisamy, he has said that within the next two days, two days back, he said, within the next two weeks, all the government officials and government employees have to be vaccinated. There are two kinds of responses to this, that the government should not force people, should not force anybody to get vaccinated and other response being that only coerced and mandated efforts can ensure that the vaccine is controlled. So what is your take? How do we go about this? I think that this is a difficult question. I have gone on writing to say that you cannot blame a person, you cannot insist that anybody taking a ride on a bus or a train should be vaccinated. But you can insist that the bus driver and conductor should be vaccinated. The balance of risk and proportion is different. And you are on a public service, for example, we used to insist and I think it would have been put if India also did it, that people who are in hotels or managing the hospital kitchens are examined for carrier states of certain disease that can be food-borne and water-borne. This is important for us to actually say that people who are in these services will face a number of people. I still, therefore, there is a case for making certain occupations where the risk of spreading to others is much higher, much more mandatory. For example, airline pilots, a cardiac checkup is mandatory. You cannot make that mandatory for everybody. It's a balance of risk and the public good which you are facing on that. Now, I don't see the merit in every government servant being forced to do that. But to the extent that it is persuasion, it is welcome. In fact, I would have actually worried the other way around that in some sense it is denying much more people at much more risk outside the priority to get the vaccine. Whereas a person in a backroom clock within a government office will be much less susceptible and at risk for the disease and can work at home meanwhile. So I think that there is a requirement for this. Bottom line, I think they should be using persuasion as their main means. But there are certain categories of workers where we can insist that that particular task must be performed only by a person who is vaccinated. Otherwise, the danger of others getting infection from a person who can become a potentially infected person becomes too high. That part of it is there. I think we've covered a lot of things. I think we can end it here. Thanks a lot, Tappas and Ramas. Thank you.


Good morning, everyone. I'd like to thank the organizers for the opportunity, truly, to present this work here. It's really truly, for me, it's quite remarkable. So I'd like to talk about some work that we developed in the group of Professor Ernst Maia during the past years. And this work is actually a collaboration between many different research groups. And lots of people contributed very substantially. But these three stand out. I mean, for, well, not only in experiments, but also for the numerous discussions that we had to gather, Alexis and Ernst for teaching me how to bridge the simulations with these quite complex experiments that they're performing there. And yeah, so I have recently moved to the Universidad Autónoma de Madrid, where I have started, as a junior group leader, a five-year tenure. And so my talk will concern about the role of flexibility in different tribological aspects, particularly friction and adhesion. And I'm not so much worried in upscaling this. Instead, the interest here is focused in understanding how flexibility at single molecule level plays out in different dissipation processes. And, well, this taps into fundamental questions as we have heard from this beautiful talk this morning of Urwak on how rigid sliders now allow us realizing a wide range of superconducting interface, sorry, superlubric interfaces as the rigidity of the sliders prevents interlocking. And so one question that stands is if superlubricity and flexibility are compatible. And the other thing that it's perhaps more in the long run is from the tribology community to try to tackle some issues emerging in other fields, such as the burgeoning fields of molecular machines, where this single flexible molecules, where you have bonds rotating around a single CC bond, allow to produce work and transmit it into the media, and also to understand how molecules move over surfaces, which is super important for supermolecular devices, for example. And I realized how difficult it is when talking with Remy. And you might have heard about this first nano car race, where five world leading groups had to propel their molecules over surface for a finite amount of time. And only two out of these five groups were able to do it. And well, actually, they got the first prize for this. And well, so I'd like to discuss, then, the role of flexibility in different processes, in distortion, the friction, and then, say, in a more collective effect, so the motion of an ensemble of molecules. So these works have been published in various publications. You can find the references here. And I will leave at the end of the line the references. So the methods that we used were very closely interconnected experiments and simulations. I was responsible for the simulations part. And so the main workhorse is molecular dynamics simulations. The thing was that we're interested in this very delicate, say, a bending, a specific bending or a torsion. And whereas general force fields allow us to describe, say, even the dynamics of DNA, or proteins, or many other complex systems, here we really needed something with a bit more precision. So what we did is we compute the infrared spectra, so the vibration or the dynamic matrix of our molecule at the QM level. And then we fit it to a common form for which this is called the force field, or a common force field where you have, say, a stretching term, stretching, bending, torsions, and so forth. And then when you compare in red the quantum mechanical data of the different vibration frequencies of different normal modes with the classical data, you see that we have really good overlap. So this allows us to describe with the spectroscopic accuracy vibrations of molecules. But not only that, it also opens the possibility to tackle any other molecule we wish. So we're not bound by the available force fields. And then these are going together with cryophore spectroscopy experiments to manipulate the molecules as already described by Hemi. These experiments were performed by Hemi, and also Philip Dostofo, PhD student, that has just finished his PhD thesis. So the systems that I'm going to consider, the first bulk of the talk, will deal with the torsion and friction. And they, in both cases, will use the same molecule. And this is the one that Hemi already mentioned yesterday. And we could call it as a flexible graphene nano-reven. As we have, say, this polyurematic structure that is interlinked by a single carbon bond where you have this bending and this torsion. This, in the torsion alone, already has some effects. So for example, we see that the molecules, they absorb along bent conformations. And then another thing is that, contrary to graphene nano-revens that align along compact directions, we observed that these molecules oriented along non-compact directions. So first, the torsion, this will be very brief, as Hemi already mentioned, a substantial part. So we have a molecule that is deposited over the surface, as you can see here. And then we started lifting it up. You can measure the gradient of the normal force while you do so. And then when you look, which we call contact stiffness, and then when you look to the contact stiffness, you observe short and long detachment units. This is quite surprising, considering that it's a chain composed of identical units. And this repeats throughout the whole lifting process, and the simulations, and experiments. And to understand this, there are two basic ingredients. The first is symmetry breaking of the chain as you lift it. So you might remember the talk from Andrea Silva this Monday, where he lifted this graphene nano-revens, and you saw how they followed along, say, the line that they were originally oriented. Here it's not this case, because the molecules absorbed along a non-compact direction. And so in order to go forward, this was already discussed by Roberto Guerra and also Niccoli Manini that there is this compact directions, along which this graffitic structure nano-revens have much lower friction. And this also happens here for this flexible chain. So since he doesn't want to go along this high friction direction, it rotates, and this leads to spontaneous symmetry breaking. The other ingredient is the torsion between consecutive units. And this torsion, ultimately combined with this rotation, is what explains the two detachment lengths. So if one unit once detaches, it rotates anti-clockwise as this screen. It moves away from the sliding axis, whereas if it rotates clockwise, it moves towards the sliding axis. You can see this quite nicely. The green units are moving away. The purple ones are moving towards the sliding axis. And in this motion, led by the torsion of these units, you have different forces to detach each unit. So this internal degree of freedom, this additional flexibility, allow to basically differentiate these two kinds of detachments. So the second part is friction. The same molecule absorbed over cold surface along these non-compact directions, we lift it up, and then we manipulate it. As we manipulate the molecule, we can measure the contact stiffness, which is, again, the gradient of the normal force. And this contact stiffness, you can see that it has some modulation. And this has been shown before that when it increases, it relates to a stick event. And when it decreases, it's related to slip event. So the same stick slip behavior is seen also in our simulations. But what's puzzling is the distances. So the distance between the stick slip events is not the lattice distance along this non-compact direction. So in experiments and simulations, we get something around 0.25 nanometers. As compared to 0.5 nanometers, which is the periodicity along the sliding direction, or 0.29, which is the distance between the gold atoms. And the reason what's happening here, behind this kind of sub lattice stick slip motion, is because as we manipulate the molecule, we have this non-trivial, sine-winding, zigzag motion of the molecule, which is essentially composed by three elements. And here it's quite important to note that this is observed for regardless of the chain length. For example, you can get it for chains as small as three units. So the first thing that happens is there is the tail rotation. Second is that each individual unit, instead of going from one lattice position to the next, it jumps into an intermediate position. So this allows the unit to always go along compact directions. You can see it goes from here to here. And therefore, you break a motion of 0.5 nanometers into two of 0.25. And another interesting thing is when you look at the trajectory of these units, for example, this unit 2, the first that is in contact. And in gray, we represent the gold atoms. And you can see how it zigzags. The center of mass goes from one gold atom to the other. But as you go along the chain, you see that not all motion is coordinated. You see, for example, this unit U5 is moving in anti-phase with respect to this U2. So as this one goes away from the sliding axis and then approaches, the other does exactly the opposite. And this gives rise to this undulation that we see on the chain. So the other thing is what happens to this dynamics as we lift slightly more the molecule. And so to make it short, it changes.  And when you look at traces, you see that these jumps are almost one nanometer long. And this is also reproducing in our simulations. And actually, you can have, say, a more better understanding if you look to how this contact stiffness changes with the height. So here we have the displacement. And then in the y-axis, we have the height of the molecule. And in colored, we put the contact stiffness. Say black is the peak, so a stick event. White would be a slip event. And you can see that at low heights, we have this high periodicity of stick events. And as soon as we start lifting the molecule, they start to fade away and give rise to these longer slip events. So it's quite, and actually when you look to the trajectory, you also see that it changes very dramatically. Not only the contact stiffness. This only reflects that there's a different dynamics of the chain. And so it's quite remarkable that by changing, say, 0.1 nanometer in the chain height, you can change the dynamics of a nanometer long chain. And the reason for this is, once again, the torsion between the units. As the chain is absorbed, it remains flat. So the angle between consecutive units is 0. When you have this strong contact regime where the molecule is the one that is in contact is essentially flat, you will see that distortion visits values around plus minus 1 degrees. So you're essentially here at the maximum. However, as soon as you start lifting the molecule, even by a small amount, you enter into this purple region where the angle between consecutive units changes from 4 to 12 or 10 degrees. And most importantly, you have a substantial energy change in this case, which gives rise to a net torque to this front unit and then changes very much the dynamics of this molecule. So by lifting a little bit more, the molecule what you're doing is switching on or off the relevance of this degree of freedom. The other thing was how this zigzag motion endures a backwards scan. And you know that Shige Kika-Wai and Andre Benassi showed that this was possible to realize and graphene and revans. And this was associated with the superlubricity effect. And so we got curious if a flexible chain like this one could also sustain this. And the answer is yes. You can drag the molecule backwards. And it still continues to do in this zigzag motion. But now we're not at an angle, but essentially straight with respect to the sliding axis. But when you look at the trajectories of the individual units, so in black is the trajectory of this first unit in the forward manipulation and in blue in the backward. And you can see they are essentially overlapping. And moreover, you see it's very smooth transition from here to here. There's no stick and slip. Everything happens smoothly. And this actually relates to the fact that the forward and backward traces also seen experimentally have essentially no hysteresis, which we also saw in our simulations. And what's funny is when you contrast it with these results for the graphene and revans, where you saw much bigger hysteresis. And this kind of indicated that, well, these chains, they have really low friction so that you can actually manipulate them quite easily. And here we show the lateral sliding forces obtained from our simulations. And you can see that the static force is about 40 piconewtons for a ribbon of about 10 nanometers long, which is about the same value that Sigeiki and Andrea saw for these graphene and revans. And moreover, here we're sliding in a non-compact direction, in a higher friction direction. So this flexible design is possible to achieve this ultra-low superluricity. And then this was actually prompted by Alexis. We look at how this friction changed as we increased the chain length. And you can see here on the right-hand side, the lateral force for two different chains. One is about 13 nanometers, and the other is 21. So you can see it's almost double the size. However, the force is essentially the same. And this leads to this vanishing friction per contact area. When you plot the static force or the average force, whatever component you wish to pay, you will see that as you increase the chain length, this decreases. And this is quite surprising because the molecule, as you can see here, it's improving its registry in every slip event. So it's not structural superluricity because you're improving your registry as you go along. So we call it this flexible superluricity. However, they emanate from the very same source. And that is the incommensurability between the chain and the gold. So you know that the distance between this, say, hollow sides of graphene are 0.24 nanometers compared to 0.29 and gold. And what this makes is this induces a bending in the chain. And you can see here this bending angle between consecutive units in black as we slide the molecule. You can see how it oscillates. And in gray, we show this bending angle for another unit further down the chain. And you can see that as you enter into this, when you begin the onset of the slip event here, indicated by this dashed line, you see how this angle drops to zero in both cases. So the chain is bent, and then when it begins to slip, it straightens, and then it recovers a new bent configuration. And so in this way, this mechanical energy is being transferred and released from the chain into the slip and vice versa. And you could think that, well, if you, this doesn't scale, because if you have sufficiently long chain, then you need to synchronize this bending event, and this will cost more and more energy. The funny thing is that they are never synchronized. Here you show this angle for the different units, for, we take, I think, 10, and you can see that they are never perfectly synchronized because this incommensurability between the graphite, this poly-aromatic carbons and the gold leads to this asynchronous excitation of this internal degree of freedom. So in a way, you have this incommensurability between these two systems that permeates into a spatially incoherent bending. Kind of similar to this structural superlubricity, but in a more dynamic fashion. Here I was comparing, I compare some results for a rigid and flexible chain, and the results are quite obvious. The first thing in blue is the rigid, and in blacks the flexible is that you can see that the flexible can obviously split an event, a slip event of zero, five nanometers in two, and that the energy barrier or the static friction for us is lower for this behavior for the reasons already mentioned and also because you need to impede a smaller amount of atoms. So now I will very briefly mention on this assembly. Mostly because it's quite entertaining, I think. So you have this hard aromatic core. This was work done by Sebastian Scherb, Antoine Nino, and also Chemie Pavlac, and they had this aromatic core, and they were wondering what was the role of this flexible chains. If you add this flexible chains to this rigid core, what would happen? And in particular they were interested in molecular assemblies. Here you can see the molecular assembly at 5K. These bright dots correspond to the center of each molecule, so you can measure the distance between the bright dots and you get the distance between the molecules. You do it at five Kelvin and at 300 Kelvin and you can get a thermal expansion coefficient, which is 1,000 larger than conventional materials and 10,000 larger than any other material. So this already tells us there is a major anharmonic effect playing a role here. And well, that is actually the flexibility of the chains. When you're at low temperature, the system compacts to increase the interaction between the molecules. However, when you increase the temperature, this changes. So this is the molecular 300 Kelvin and you can see that although you have energy to move the chains, you still cannot diffuse the molecule. However, the assembly, when you're together these fluctuations, they lead to this thermal expansion of the chain, this anharmonic fluctuations of this flexible side chains allow us to reach this giant thermal expansion. So to come at the end, so we've shown how this flexibility allows us to tune the absorption, how it gives rise to this flexible superlubricity and how we can use it to create materials with giant thermal expansion. I'd like to thank all the people involved in this work, the group of Ernst and thank you for all the funding agents and thank you all for your attention. The question is for Robert. Thank you very interesting results. I was wondering whether you have some benchmark about the role of the interaction potential that you use between the molecule and the sub straight because I expected so that the subtle detail that you find might be influenced by particular by this potential. So have you tried the robustness of these results against this? Thank you. It's a very good point. I did try this. In particular, the one that I'm using for these simulations is the potential from Stefan O'Courtney, the scope force field. And I tried with others like this interface and other linear drones parameterization. I just saw your recent publication New Gold Force Field. And this one, the scope force field was the one that was able to reproduce better the distortion energies of these individual units. And well, as you can see, it captures very nicely the dynamics also of the chain. And so, yeah, so I did test it. And I found out that the scope, it's quite, or it served quite well this purpose, especially for aromatic compounds. Thanks. Very intriguing phenomenon issue. I was wondering, these chains are oriented along against a specific direction of the gold substrate along the reconstruction of the ribbon. Do you know what is the relative size of the moire pattern in this direction and the unit cell of your chain? Like, are these the unit of your chain like sub moire space, sub moire tile? A good question. So I did look at this because this is one analysis that Roberto and Nikola and Andrea, I think they also did for the ribbons. But in this case, the molecule is really so thin that, I mean, and then it bends to commensurate. And so I don't know by hand what would be the size of the moire. It's along the non-compact direction. So I cannot recall. But it would be interesting to see how it scales with the area of this. If you can link like a unit of different area and connect them with these bridges, how it will scale with the area of those. But yeah, we can discuss later. Okay, thank you. So I think we should move on to the next talk, which will be given by Olivier Nouvelle.


Everybody, my name is Joy Mochacha, as you all know. Welcome very much to Tuesday Entrepreneurship at Y in the Morning. Remember that you can reach us and talk, sorry, and actually fill in your thoughts and your views about the discussion that we're about to have. Let me leave you with our handles first before we begin and before I introduce our guests. Remember, those handles are Facebook Y254 channel and also on YouTube. You can watch this interview much, much more on Y254 underscore channel. And you can also find us on Instagram at Y254 underscore channel. I'm always at Joy underscore Mochacha. Today is Tuesday Entrepreneurship and we focus on different people who are doing different things, both for the families and for the communities, mostly in business manners. And who we've got on the, who we've got on stage today is Mr. John Coonrod. Hello, Joy, thanks for having me. Welcome on stage. Thank you. And we hear that you are into community development and community empowerment. Yes. Yes. And so your title would then be? Well, I coordinate the movement for community led development, which is a global civil society initiative of organizations that really believe strongly in empowering grassroots people to take charge of their own lives and destiny. Okay. Oh, to empower grassroots people to take charge of their own lives and destinies. Correct. That's amazing work. It's exciting work. Yes. And your program, well, you first came to Kenya in 1989. Yes. Is that the first time that you decided to start working with community development or did it come later on? I started working with community development in the 70s. So it's been a lifelong passion of mine to, you know, one of my heroes was Mahatma Gandhi. And on, tomorrow is his death anniversary and he left behind on his desk, one little slip of paper.  He didn't say make sure they're fed or clothed or housed. He said, make sure that they are in charge, that they have real voice, decision-making power in their own lives. Because that's what human beings want and need, it's the dignity that comes from being able to affect the issues that you care about. Yes, that's very true. And so what you're doing is important work. I'd like to know the name of your organization so that, because I don't know if our viewers are aware. Okay, well, I work for The Hunger Project, which is one NGO. And there's several. Yeah, there's thousands, millions of NGOs. I didn't know which one to start with. Mine is called The Hunger Project, but why I'm here is because we are providing the secretariat for this global movement of NGOs. So there are 10 NGOs here in Kenya, such as the Africa Capacity Alliance, FHI 360, Global Communities, Heifer International, Newer International, the Johnator, Vecocap and VAP to local groups and PACT. And these groups have been working for the last year to launch a Kenya chapter of the movement for community-led development. I see. And when it comes to The Hunger Project, how was it formed? How did you first start off? Well, The Hunger Project was started in the wake of the mid-70s famine in Bangladesh and the first World Food Conference. And we, like a lot of other people at that time, felt that traditional charity models weren't gonna solve the world's problems. We needed more of an empowerment model that would really recognize that the solutions to the challenges lie in the creativity of every human being, of young people, of women and men, and everyone can make a contribution. And so how can you transform those top-down models of development into a real bottom-up empowerment process that, as Gandhi said, puts people in charge? Oh, of course. And that's what's exciting about Kenya, because Kenya, under its new constitution, has moved real power and real resources down to the county level. Almost no other African country has done that. And so I and others around the world have been rooting for the success of Kenya's county government system because in other parts of the world, this is what has succeeded in places like Korea and Brazil and Indonesia and the Philippines. Rapid, broad-based progress has been achieved through community-led development. So seeing Kenya go this route has been really inspiring around the world. Okay, and I've noticed you've said something that I think will pique the interests of people who are listening.  No, especially the youth. And we'll touch on that a little bit later on. And also another thing you've said is that Kenyan counties have actually made, put measures in place for people to be able to find development in all sectors. And so I think that's part of what we call the SDG goals that are coming. I'm wondering whether you are also incorporated into that. Yes, I have my little SDG pin on. There it is, the 17 goals of the Sustainable Development Goals. And we launched this movement on the day that the SDGs were launched in New York in September 25th, 2015. So we seized that opportunity of the launching to remind the world community and everyone that the challenges of this era can only be solved through people taking charge of their own lives. And that women, youth, every marginalized group has to be empowered to solve these problems. And so that has gotten real traction. There are now more than 60 NGOs that are members of this movement around the world. We've launched seven chapters, national chapters so far in Africa and some in Latin America, Asia. So we really see that this is the only way to achieve the SDGs is by mobilizing the energy of every citizen in partnership with their local government for a sustainable solution. That's true. And so let's look a little bit at the future. Now that we've looked at the present, when it comes to Kenya as a whole, you've said that these measures that have been put in place by county officials that this is a good area to start with. And so what do you foresee for Kenya if you're looking at community development, how can I say, community development, the focus on it. And you're seeing that it's going to be a success in conjunction with the SDG goals. What do you find or what do you see for Kenya in the next few years? Well, I think the big four push that's going on, these that the president has stated of working for food security, working for affordable health, affordable housing, for increasing manufacturing, these are things that touch everybody's life. We all have to eat, we all have to be housed. This is something that, but solving those in every village is going to be different. That's true. What will secure food security in this county or that county is going to be very different. So the creativity of people, the engagement of youth are going to be the pathway to solutions. All right. And when it comes to the youth, what are your plans for them? When it comes to the hunger project, is there something that they can do to maybe assist if they're interested in it and as well as what will the hunger project do for our youth people? Well, the movement members in Kenya, a lot of them have a lot of experience mobilizing youth and creating space within communities for the voice of youth to be heard. Heifer International, for example, has a big youth entrepreneurship development program. And they're one of the key members of the movement here in Kenya. The other groups, FHI 360, the Africa Capacity Alliance, global communities all have been working with youth. So there's really two parts. One is to develop the leadership of youth and develop their own organizations. And the other is really get us non-youth. I'm a non-youth to listen and respect and support the initiatives of youth.  That's true. You know, I have enormous faith in the creativity of youth, but everything we can do to create more space for their voices to be heard and decision-making for them to organize their own spaces, their own organizations, set their own priorities in partnership with local government. That can go a long ways. And you will be launching the sea-elding movement. On January the 30th, here in Kenya. And what are some of the areas or gaps you find that the CLD will address when it comes to advancing development, community development?  So some of the counties have, and the Constitution also calls for directness and engagement in county government. So some of the counties have been very successful in that. McQuainey County, for example, is this week hosting thousands of village-level meetings to develop local plans and bubble those up through the clusters and wards to the county level. Other counties are still learning how to do that. So it's, you know, it's a bright new day in Kenya with these counties, but they're quite new. So how can we help them? How can the diverse local organizations in Kenya really support counties in achieving those goals of mobilizing communities? This is the community mobilization is the special expertise of civil society. You know, that's, we have a lot of experience in mobilizing communities and in working in partnership with governments to really create sustainable solutions at the local level. Right, okay, and another important thing is also allowing people or encouraging them to be in charge of the destinies, as you said. Right, and that requires a change in mindset. Yeah, I was going to ask because this is not about putting something in somebody's hand, okay, in some areas, yes. This is something that has to do with actually changing people's mindsets. And that is something that's quite difficult to do. Yes, you don't teach a man to fish. You actually cut the barb wire off the pond, removing the obstacles to people's creativity, removing the obstacles to people's full participation and development. But it's what everybody wants. Yeah. Everybody wants voice in the decisions that affect their lives. Everybody wants to move forward. Everybody wants to learn how to take charge of their destinies in fact. And to contribute. Everyone wants to contribute. That's true, but they don't know how in some cases. But this is the time to learn. Yes. If we're gonna achieve the future we want in the villages, in the wards, in the counties, then this is the time for people to really step forward. Change, stop waiting. Stop thinking someone else is gonna solve this and step forward and make it happen. Stop expecting someone else to do it for you. Yeah. And so moving on, I noticed you had mentioned that in some African countries, this kind of community development movement has not necessarily been successful, maybe because county governments have not included these measures in place. Well, first of all, they don't have money. So in most of the budgeting of most African countries, you know, here 20% is reserved for the counties. In a lot, in other countries, it might be only two or 3%. In Ghana, which is one of the more decentralized, it's 7.5%. But we think 20% is the absolute minimum share of a fair share of public resources that local government should have. Because even if you get everybody all mobilized, if they don't have any public resources, they're not gonna get much done. Exactly. So this devolution of public resources, a fair share of public resources into local communities is really what's needed. Oh, I see an image. Yes, there you are. What was happening here? Well, this is the International Food Policy Research Institute. They're a member of this movement. And so this was one of the introductory presentations of the movement. We had, at that movement, we had Relief International Speaking. We had Heifer International Speaking. We had a number of groups that are really committed to this approach. Coming together, the Aga Khan Foundation is there. The Aga Khan Foundation. Care International is there. All right. So this was a launching event at IFPRI in Washington. In Washington. Investing in communities, key to the Sustainable Development Goals, SDGs, movement for community-led development. That was in 2016. Right. And as you're going to launch the movement for community-led development in Kenya on the 20th, sorry, on the 30th of January, since you've already mentioned that in other African countries, the percentage that is allocated for such ventures is quite low, what is the next chapter after Kenya? Great question. We want every country to have one. And Heifer International, for instance, has a young woman who's very passionate about this in Rwanda. So she's coming to this launching to see how to launch a chapter in Rwanda. So I would bet that'll probably be the next chapter. Rwanda. Yes, but Tanzania, we would love to have a chapter there. We have a chapter in Uganda. They're going to be represented at the launch tomorrow. My colleagues from Ethiopia are going to be there. We really think that this is the pathway for everyone. And since everyone, there's lots of groups already working in every country. So if they could just come together, meet with their government, really just start the conversation. Because this has moved slowly. Governments change slowly. That's very true. We need to get going on this. We need to take some time. And so winding up our discussion, I'd like to know for anyone who is interested in joining your movement, what is their criteria? How do they go about doing it? Because someone may be watching and thinking, I'm really interested in this. I would really love to. And especially because we focus on youth, this is a good chance to get the youth in. Exactly. So let's say there's a young person watching. What is the criteria they have to follow to get to work with your movement? Very good. So the movement is made up of organizations, civil society organizations. So you have to first join one of those. There are individual members. They're organizational members. They have to be a legitimate registered organization in Kenya. They have to have a public commitment to community-led development. And they have to be willing to work together. You know, it's been a very competitive environment for civil society groups, but we are calling for them to really work together. So the groups have to be willing to work together. Those three things, legitimate, committed, and willing to work together. Legitimate organization, committed to that organization, and willing to work together with your movement. Right. Oh, that's amazing. And if you go to the website, community-leddev.org, slash Kenya, you'll see the first 10 organizations that have joined. So that would be a good starting place for anyone who wants to get involved. Okay. So a good starting place for anyone is to visit the website. I would like for you to repeat it again, actually. So community-leddev.org, all one word, community-leddev.org slash Kenya. Community-leddev.org slash Kenya is where you're going to find a list of organizations in which you can join and start off with when it comes to community-led development. So we've had a wonderful guest, Mr. John Coonrod, who is a community development leader, and he has come to launch his program here in Kenya, his chapter here in Kenya, and we wish him all the best from Y254 Kenya. Remember, this has been Tuesday's entrepreneurship, why in the morning to be exact, if there's any views and any thoughts you have on Mr. John Coonrod and what he has to say and the work he has to do, you can always reach him or you can reach this channel and also we'll find a way to tag him because unless you're comfortable sharing your social media handles. Oh, absolutely. Okay. At community-leddev, we're on Twitter, we're on Facebook, community-leddev, you can find us anywhere. Community-leddev on Twitter, on Facebook, everywhere. So all you have to do is hashtag, why in the morning, hashtag Tuesday entrepreneurship and speak to this wonderful man if you're interested in working with his movement. My name is Joy Mochache, this is Y254 channel, and remember you can reach me on joy underscore mochache. Thank you so much, Mr. Coonrod. Thank you, Joy, for having me. Thank you.