Food is an issue obviously that's important to all of us, and ensuring food security is at the top of the leaders' agenda across the region. It is also one of the most complex and challenging items on that agenda. Let me just briefly run through some of the different aspects of that challenge that leaders face. Food security is, first of all, a production challenge, how to decide which crops to grow on which lands with which input and with which infrastructure to take product to market. Food security is a management challenge under the constant pressure to increase production and yields, how to maintain competitiveness, and also to keep up with rising demand. Food security is a multi-stakeholder and organizational challenge, with key important roles to be played by businesses, by government, by society, and by farmers, all of whom need to be involved in the policymaking process one way or another. Food security is a climate and environmental challenge as the push to increase production and to increase yields, also risk putting increased pressure on forests and to increase the use of perhaps unsustainable amounts of inputs such as pesticides and fertilizer. And finally, food security poses a regulatory challenge as governments need to protect consumers from big swings in food prices to keep a lid on food price inflation and also to protect consumers from contaminated or harmful foods. Now in the face of that daunting set of challenges, we are privileged to have an excellent and genuinely multi-stakeholder panel today with government, business, and society all represented. Let me briefly introduce the panel to you, and then we will begin our conversation. To my immediate left is the Deputy Prime Minister of Vietnam, His Excellency Guyens Huon Phuc. To his left is Peter Tercuve, the President for Southeast Asia and Australasia for Unilever. In the middle of our panel today is Excellency Samdech Huon Sen, the Prime Minister of the Kingdom of Cambodia. Welcome, sir. To his left we have Anna Chilzuk, the East Asia Regional Director of the International Development Organization, Mercy Corps. And finally, to my far left, RFP Rakhmat, the CEO of Triputra AgroPresada, a diversified agribusiness firm here in Indonesia. Thank you all for joining us today. To get us started, I'd like to give the floor first to Deputy Prime Minister Phuc for a few opening remarks. Deputy Prime Minister, Vietnam has been an emerging market success story in harnessing agricultural growth to drive overall economic growth and to reduce poverty. The agriculture sector employs more than 60 percent of Vietnamese and contributes more than a fifth of the country's GDP. What is the government's view of its own role, both as a policymaker and as an economic actor, in driving and pushing forward growth of the agricultural sector? Please. Excellency, ladies and gentlemen, first of all I wish to thank the Web for inviting me to this highly relevant session, because for security and farmers, it's the common interest of all countries, especially Asian countries. Agriculture is very important, it also creates the jobs for the people and the momentum for economic growth. So I want to share with you that in the last crisis, agriculture is a very important peel to help Vietnam's economy recover. In Vietnam agriculture, development has strategic importance as more than 70 percent of a population living in the rural area. In 2014, Vietnam exported 6.5 million tons of rice with the voluend total of 31 billion US dollars, and 11 lines of goods we have exported worth 11 billion US dollars. We have many export products such as cashew nuts, coffee, rice, rubber, and aquaculture products. And these results are brought about by our strong commitment for reforms. So I want to share with you some of the experience of Vietnam first. The government should make strong commitment to agricultural development. Agricultural development and food security must be put at top of the national development strategy agenda. In Vietnam, much effort has been invested into building a competitive and environmental-friendly agriculture and agriculture business. And second, we need good policies to help mobilize investment, especially from the private sector. Through the public-private partnership, in recent years, many multinational countries and FDA, FDI and local enterprises have made huge investments in agriculture business to form vast specialized farming zones with high value added in, for example, agriculture and dairy industry in Vietnam. And I would like to share with you that we have many preferential treatments for companies working in the agricultural sector because the productivity of agriculture is still lower compared to other sectors. So we have many incentives. And third, I think the cooperation in food security and agriculture is very essential. Vietnam has joined different global and regional initiatives on agriculture, including the new vision for agriculture initiated by WEF. Vietnam also cooperates with other make-home countries, including Cambodia and Laos, via bilateral, trilateral, and multilateral frameworks to form competitive agricultural value trains for such produce as rice, corn, coffee, rubber, among others. So I wish to take this opportunity to kindly thank His Excellency's prime minister, Hoon Sen of Cambodia, for his support in promoting Vietnam-Kambodia cooperation in this area. Vietnam and Cambodia enjoy very good cooperation, and fourth, it is essential to explore new export markets. In 2014, Vietnam concluded FTA negotiations with the Republic of Korea, the Customs Union of Russia, Belarus, and Kazakhstan. And then Vietnam is about to conclude the Trans-Pacific Partnership talks and also FTA with the EU. This FTA's promised expanded market for Vietnamese agricultural products. This also means more opportunities in the business in Vietnam for international investors. So on this occasion, I would like to call for foreign investors to seize the opportunities to invest in agricultural sector in Vietnam. Many countries, especially Japan, Republic of Korea, are investing successfully in this area in Vietnam. And fifth, it is critical to enhance cooperation for sustainable use and management of water resources, especially after the chance by the rivers in the regions. Businesses of large rivers, like the Mekong Functions, not only has green lungs, but also rice bowls of this region. Therefore, water cooperation will enable a better food-secure future by promoting economic development and environmental protection. And I'm sure that prime minister Hoon Sen shares the same thoughts with me. Thank you very much. Deputy Prime Minister, thank you very much for those opening remarks. Peter, if I may, let me turn to you for our next question. As you're one of the largest consumer products companies in the world, Unilever works across many countries almost always in collaboration with a broad range of stakeholders. And indeed, if we may follow on with sticking with Vietnam as our topic, in Vietnam, Unilever has many such partnerships, not just with government ministries, but with a broad range of industry and consumer organizations, including a very active partnership with the Vietnamese Women's Association. Perhaps you could share with us what Unilever looks to get from some of these partnerships, which one seems to work well and why. Thank you. Thank you, Adam. Food security for us has basically three elements that need to be enough food. It needs to be affordable and it needs to be of high quality. We believe that we can only achieve this when we unlock the potential of the smallholder farmers and help the small and medium-sized food industry to raise their quality level. Vietnam and the Minister Phat is sitting in the room has been excellent to work with us on a large number of partnerships to make sure that we raise quality standards in the industry. We have a fantastic partnership around tea. Vietnam historically has a good tea industry, but over time the quality had deteriorated and we want to make this a big tea export base again together with the ministry, training of farmers, organizing, financing for farmers and making sure that we get quality that is competitive on the world market. But it is not all. We have very good partnerships around hygiene, hand washing, bad hygiene still cost many lives and together with the Ministry of Health and with the Vietnamese Women's Organization we organize grass road programs in villages to work on health issues like basically making sure that they are good toilets, making sure that they are good hand washing facilities. And I truly believe that only by working with governments, with NGOs and getting companies involved, you can achieve rapid change at scale. Very good. Thank you. Anna, maybe I'll turn to you. Peter touched on the topic of sort of getting smallholder farmers engaged. You've worked in Indonesia for many years on the topic of agricultural inclusion. How to make sure that farmers and farmer interests don't get sidelined in this push for higher production and higher yields, but rather operate effectively in an ecosystem with larger players, be they private sector or state owned. What sort of, from your experience, what sort of inclusive business models have you seen work well, in particular those that lend themselves for being scaled up? Excellent. Thank you, Adam. So I represent Mercy Corps, which is an international nonprofit organization, and we work on both the humanitarian relief and the development side. And for us, really, we're looking at ways in which we can help people build or rebuild secure, productive, and just communities. And ensuring that agro systems are environmentally sound, efficient, and that they're benefiting and improving the livelihoods of those who are involved at the production side is critical for us. And I think if we step back and sort of look at the scale of the issue, I think it becomes obvious that this is not something that any one type of player can solve alone. I mean, sort of elevating the discussion up a bit, by 2050, the world is going to be feeding 9 billion people. And the calculations are that we need to be producing 70% more food than we're consuming right now. And I think if you sort of bring that back to the region, here to Asia, you know, perhaps chronic hunger isn't as acute an issue. However, the statistics say that two thirds of the world's undernourished population is living in Asia and the Pacific. And then if you sort of add on to that, the issues around climate change and the disruption to production patterns, if you add on to that, the effects of urbanization, we all know that cities are fantastic engines of economic growth, but they're also sort of disrupting the labor availability in urban areas, in food-producing areas. And I think the question of what's that happening to the choices that people in rural areas are making, a theme that has come up in the discussions around Croatia has been, you know, how do we make sure that being a smallholder is being a farmer by choice and not by necessity? And I think if you look at the complexity of these issues, it really becomes evident that we need to bring together these coalitions of different types of stakeholders and identify where everyone has a role to play. And that's why sort of if we look at inclusive business models, one thing that we're finding very exciting and very much aligned with the type of impact we want to have is partnerships like Grow Asia. I think that because they're trying to define very specific targets that look at both sort of managing this very delicate balance of the growth and the scale, the environmental sustainability and the inclusiveness. And if you have different types of actors coming together with that joint objective, in my mind, that's the way that you achieve that balance. And I think also this is, in my mind, sort of the next horizon of inclusive business models. To date, what we've seen I think is there's been many pilots, there's been many attempts. And I think that they're demonstrating good progress. But by definition, I think as long as you have been limiting it to one company engaging or one sector, you will always be limited in terms of the horizons of growth and the scaling out. And in my mind, what Grow Asia is now going to do is it's going to take these individual models and the individual sort of championed efforts and it's going to embed them in both national structures and regional structures. And in my mind, that's sort of the way to go because if you think about sort of, we all talk about scale and impact at scale, but if you really break it down and think about, so what are the pathways to that? I sort of, I'd see three areas. One of these is around replication. So basically having ways to look at what are best practices and take them, adapt them to a particular country setting, a particular sector setting. Another one is continuing to build out within the pilots that are already making good progress. And then a third one is sort of taking the lessons that come out of the individual inclusive business models, the individual pilots and feeding into systemic solutions. And I think this is where the role of government becomes so important because aligning on policy decisions, aligning on national and regional strategies is one of the ways in which we're going to achieve impact at scale. Great, thank you very much. Let me now perhaps turn to Prime Minister, Prime Minister Hun Sen to get some reflections from you from Cambodia's experience. In Cambodia, the agriculture sector employs almost 70% of Cambodians, most of them small holders, small farmers living in rural areas and contributes almost a third of Cambodia's GDP. As you have said, in fact, as you said yesterday, there are many opportunities to increase the role or increase the contribution of the agriculture sector to the economy generally, but also for reducing poverty and improving the livelihoods of farmers. What is your vision? What is Cambodia's vision for the agriculture sector and specifically how the government aims to increase and improve farmer livelihoods and welfare? Thank you, sir. Thank you that you allow me to talk about food security. Based on the experience not just in Cambodia, but in the region in the world, the food security, energy has been looked at as, but I should therefore highlight when you have no oil, you will not die.  So this issue is a concern of many in general in the world. The number of populations keep growing at the time. The land for agriculture is getting smaller and smaller through the growth population, the building of housings, on the land that needs to do the farming to feed the humankind. In addition to that, there is some wrong vision at the time of energies by going up. Some countries have been juicing the land that is do farming to feed the sum of other people to produce. They buy oil to feed the machinery. And I think that maybe we can avoid the past mistakes that committed during the world economic crisis the last few years. In Cambodia, for us, from a country that imports food, shortage of food, now become a country that has food for export, and a country who has been class number one, that the number one quality is right. The most delicious rice competition in Bali, Indonesia, competition in Hong Kong, and competition in Cambodia. So our rice can go to European markets comfortably because our rice has a very good taste. What we should think is that the numbers of population that keeps growing along with the limited land, Cambodian vision, especially since I started to hold the powers 30 years ago as the youngest prime minister of the world, in 1985, I have been carrying out land reforms to land reform that enables Cambodians to expand gradually the numbers of rice production. But in that perception, if we carry out the old plan, it means that through extensive cultivation, which is the tradition of Cambodia, we cannot afford it. The Cambodian habit is that let's say if the families of five people, we must have one hectare of land. So if the members of families increase to 10, you must have two hectares. So in this way, the environment would be cut down, the forest would be cut down. Therefore, we change from extensive cultivation to intensive cultivation. Through solving the irrigation problem, through intensive cultivation, selecting of seeds, it means that we have to increase the feeding capacities on the existing land rather than expense the farming. We can sell some of them. But if we expense too much, we cannot afford it. For Cambodia, the land, mostly we do only one crops. But we are able to export around 3 million tons of millet rice and in form of unmarried rice, some are more than 5 million tons. So if we can manage, expand it to do two crops per year, we might have capacities to export. I think even more than Vietnam, I think, in which today, you expand only 6 million or 6 or 7 million tons. But Cambodia, one crops, we are able to export 3 million tons. But if we could do twice to expand the irrigation system and the yield, then we can export even more, more than the amount of Vietnam export. Vietnam lands get tired already. I'm also grateful to Vietnam on two points. On one point is that Vietnam is also a country that have research on Vietnamese rice. But we will not still Vietnamese rice it. We should abuse the intellectual property. We have to do it ourselves. And our own produce food that we get number one three years successively. Second, I'm grateful to Vietnam that have buying Vietnam without paying tax. Because ladies, Vietnam is straight up buying rice from Cambodia. We consider having gold but have no package. We have rice but we have no proper meal rice, have no warehouse, have no money to buy the rice on the people. Now we are investing to promote, to stockpiling and buying from the people. That's a point I would like to share with you. And based on what the speakers have said, related to the farmers, we can form them to many means. Let's say they are their own means. They can form through the education system. They can live together, do farming together through the management of the same education system. And through them, we can form the farmers association and which give them the bargaining powers with the buyer. That's a point we see that there's still a potential between the farmers. And within that, the government have to provide the opportunity for them to know the price that with the market, in which we call, I mean, a grow business, in which we call a grow business. Even agriculture cannot export. But we use the word on-spot export. Tourists coming to Cambodia last year, it's 4.5 million. 4.5 million, all these people, they do not pick their food or bread or rice from their country. They come and eat the food in Cambodia. So we use the perception on the spot export. It meant that we export our rice, our farming, animal farming, our vegetables to the hotel. And when tourists eat, it's like they're exporting to. And we like to take this opportunity to talk about food security and energy security. Before, the farmers make no profit because the price of food, energy price, and OPEX expand, increase it, it will. But those who produce food has been affected. The farmers spend more funds, but not beneficial. Therefore, I need to change the idea repeatedly that there should be the rice export association within Edmeg, which includes Vietnam, Thailand, Laos, Myanmar, and Cambodia. We do not want to form such association of a rice export association to increase the price of rice to those who buy the rice. But we would like to coordinate. And it is also bringing powers for OPEX so that they cannot increase the oil price too much. But now the price of oil has been going down. And I hope that OPEX will not increase the price of oil. Another point I would like to request to the developing countries, the developing countries, we speak repeatedly about the framework of WTOA. We talk about non-subsidy, but you can ask the developed countries, the way they subsidize their farmers. Making the farmers of the developing countries cannot, we cannot export to their country. That's the problem we had to think universally, recommend it, not just the liberal countries because it's a problem of market. If the one market opens, one market closes, and then they are loaded out to export. But the barrier is on the sanitary. So that's an issue we need to have to solve it commonly, whether it's the developed countries and developing countries or the poor countries. We have to discuss with each other on this issue, in which a doha round should be concluded successfully. Thank you for your attention. Prime Minister, thank you very much for those remarks. Arif, if I may turn to you now, I want to follow up a little bit on the very important point the Prime Minister made on intensification. But let me preface that with another question, sort of turning our conversation back to Indonesia. Food security clearly, if not at the very top, certainly among the top priorities of the JAKOI administration here in Indonesia. Although there seem to be still a number of definitions of what food security means, and therefore, of course, how best to implement it. From a business perspective, how do you frame that challenge? Well, actually, I agree with Prime Minister Hun Sen said earlier. I think when we talk about food security, we really need to discuss it from the point of view of the policymaker. Because public policy affects everything that we do in the private sector. And based on my experience, talking to a lot of government officers, when we talk about food security, the first thing that comes into their mind is food sovereignty, that everything that consumes must be produced from within the country. Now, this way of thinking is actually fine, but with one condition. The productivity of that food sector has to be very high. The danger comes when the productivity is low, and the governments are tempted to mess the problem by creating artificially high price control, which, in effect, is a subsidy to inefficient industry, as Prime Minister Hun Sen has mentioned before. So I'm a firm believer on efficiency and free trade also is Vietnam and Cambodia as well. So in my view, the best way to tackle food security issues is by making sure that each country really focus on what they're best at and continuously promote for free trade. And in Indonesia, one good example of this is palm oil and sugar. We're really good at palm oil. In fact, we're the largest exporter of palm oil in the world. In terms of sugar, on the other hand, we are the largest importer of sugar. And if we take a look at sugar prices domestically, it's about 30% higher than international prices. And we do that because we want to protect our inefficient sugar industry. But again, the consumer have to pay for that. So if the government wants to reduce our reliance on sugar imports, the most important thing to do is to invest in long-term initiatives, such as irrigation, which our president has done a superb job in the last six months. And by doing so, we can gradually reduce the price of domestic sugar. So I think the essence of continuously driving productivity up and promoting free trade relentlessly has served Singapore really well. And if you look at Singapore, they really have no natural resources whatsoever. Let me then follow up with this point. And actually, I'd like to ask a number of members of the panel a version of the same theme, which is the point that the Prime Minister just read, which is intensification. With rising incomes and rising demand for food and rising population, as Anna mentioned, the onus falls on getting more out of currently cultivated land as opposed to opening up new land or new forest for agricultural use. That's a very difficult balancing act for governments. How to balance the very real and concrete need for higher agriculture production against the need to avoid environmental degradation or how to ensure a sustainable supply change, et cetera. Now again, from your perspective, as a large-scale commercial operation, what seems to work well in terms of increasing productivity? The larger-scale part of the sector already does well in this area. But what do you see working well in terms of how to improve productivity of the sector as a whole? What, in terms of kind of from a partnership or a use of technology or linkage programs, what's the large-scale part of the private sector doing to drive sector productivity up? I think there are two main things. As rightly said, I think there are many clashes between food security and climate change. And one of the ways to resolve that is through intensification. And one example that we have in our industry is by utilizing marginal soil, such as sandy soil. As you can imagine, sandy soil has very low nutrition and carbon storage. But in our industry, if we can somehow manipulate that soil to become more like mineral soil, it can be a breakthrough for the industry. So we've done so in the palm oil by reconditioning the sandy soil, utilizing empty fruit bunches from our palm oil meals, which is essentially waste. And by doing so, we can significantly increase the production. Now, the second ways to improve productivity is by looking at smallholders. Because no matter what kind of food products that you grow in Asia, most of them are still grown by smallholders. Now, even in the palm oil industry, where big players play a big role, half of them are still owned by smallholders. And the productivity of the smallholder is much lower than the big enterprises. And if we dig deeper, even on the smallholders group, you can actually see two distinct groups. One that's completely independent and the ones that are associated with the big enterprises. And guess which one has higher yield? The ones that are linked to big enterprises can have up to 50% to 100% higher productivity. And the reasons are two things. One is because of access to capital. The big enterprises can act as a guarantor for the smallholders to have long-term financing from the banks. And the other reason is because of transfer of technology from the big enterprises to the smallholders in terms of better planting materials, better fertilizers, and also better management. And I'll give you one example in the rice industry. In the rice industry, the old ways of the smallholders when they apply Urea fertilizer or nitrogen is through a broadcast application. This is a very inefficient process. With the introduction of Urea in the form of briquettes and plant them about 10 centimeters from the soil surface, the productivity can actually go up by 25% while reducing the dosage of the fertilizer by 25%. And in the process, reducing contamination to water and greenhouse gases. So these are so many things that we can do between these partnerships. Great. And if I just may now go kind of in reverse order, I'd like you to stay on the same topic, though, from your work at the community level and sort of from that perspective. What seems to work well in terms of that linkages with other parts of the value chain, other larger investors in terms of genuinely and sustainably, not to overuse that word, but sustainably bringing around change of agricultural practices and productivity at the smallholder level. I think a lot of it has to do, sort of building on Arif's point around ensuring access to information for smallholder farmers so that they can actually be empowered and make appropriate choices in the value chain. And I think that sort of then links to ensuring that there is access to the appropriate products and services. And I'd like to just share an example of an initiative we're undertaking in a number of countries, including in Indonesia, which is really around reducing information as symmetry for smallholder farmers by providing a bundled platform of agricultural information, of access to financial products and services. And this is something that's done in partnership with a number of different actors. It's done in partnership with universities, with input suppliers, with off-takers. It's done in partnership with the government. And what we're seeing is this is an efficient way of ensuring that we're able to sort of translate this into yield increases as well as ensure environmental sustainability. So for example, we have already reached 70,000 farmers in Indonesia through this platform and through the partnership for Indonesia Sustainable Agriculture, we're now starting to replicate and build it out across the country. And with a recent pilot that's undertaken with Sinjenta, we're working with 400 corn farmers looking at linking them to credit for agricultural inputs and seeing very rapidly significant yield increases around the range of 40%. Thank you. Let me sort of go from society back to government if I will, Deputy Prime Minister. Vietnam has placed a very high priority on increasing the industrialization and modernization of the agriculture sector in Vietnam. You have a target, I believe, of three and a half percent growth of the agriculture sector between now and 2020. So sticking with this theme of sort of balancing objectives and policy trade-offs, from your perspective, from Vietnam's perspective, what is that right balance between industrializing the agriculture sector in order to improve productivity on the one hand, with protecting farmer livelihoods and maintaining rural employment on the other hand? I think that the balance between industrializations and agriculture is very important. Therefore, the policies for agriculture and farmers is very important. We have policies on tax, policies on land, policies on the reductions of land-use fee and preferential incentives for investment in agriculture to increase the productivity and to add more values. In Vietnam, we set the target that 50 million Vietnam is down for every hectare of agricultural land. But we have come far beyond this target. We can even reach 500 million or even 2 billion Vietnamese down worth for hectares of agricultural land. And second, protection of the rights of farmers is very important. We should provide training, agricultural services to the farmers to facilitate them in the production of agricultural products. And most importantly, I think we should reduce the labor force in agriculture sector. However, we have to improve the efficiencies and the productivity. I totally agree with you that all the advancement of technology and agriculture is very important or agriculture of high quality is very important to further improve the productivity. So this is the way to balance between industrialization and the protection of farmers. We also have to better use the lands for agriculture development. Sort of a common theme on intensification versus extensification. Peter, let me bring you in on from the business perspective. Again, on that similar issue on intensification, smallholder productivity. And maybe if I could ask you to address specifically if you would this issue about access to capital. Oftentimes, we see in many countries in the region smallholder farmers constitute a big part of what we call the unbanked or those outside the form of financial system. What have you seen, what innovations have you seen that have been driven by the private sector to help address that issue? Yeah, very good point. As Unilever, we have a stated ambition to connect 500,000 smallholder farmers directly to the Unilever supply chain system. We believe we need the smallholder farmers because we need the capacity of the smallholder farmer. But obviously, when you then work on improving yield and improving quality, investments are needed. And the unlock we believe we can bring as a large client or as a supplier base for them is to make sure that we give contracts, long-term contracts that can be used to organize financing. And what we do at this moment in time is to work with cooperatives of farmers and give guarantees on volumes and go with those guarantees to financial institutions to make them bankable. And I believe that often the largest unlock of smallholder farmers is training, but maybe even more important capital to upgrade their lands and facilities. If I may follow on with a slightly different question. And again, food security is a little bit on the eye of the beholder, sort of how we define that. Let me ask you a little bit about the almost literal definition of food security, the security or safety of food. You've worked across Asia for the last decade, I think a number of years in China, the last five years across different countries of Southeast Asia. From that perspective or from your experience, where do you put that issue, that issue of food safety within the conversation around food security? Obviously, the first focus always is, is there enough food? Is there affordable food? But then the quality of food becomes the next big frontier. We all know that China over the years has been very, very successful in boosting the quantity, but they had massive issues with managing the quality from farm to processes. And when at a certain moment, consumers do not trust the food they can buy anymore, it leads to massive social issues. When people are afraid, it leads to social unrest, rich people are able to buy expensive imported food, poor people are not able to do that. So rebuilding and building trust in the whole food chain from farm, from processes, to retailer, to consumers is essential. And I think for us in Asia, it is really, really important that we keep current trust levels at a high level, because when we end up, and I hope not, with the same sort of issues that we were facing in China, this would be very, very bad. So it's not for me only about how can we upgrade the farm, but especially what can we do with the small and medium-sized enterprises and large enterprises who process food to make sure this is done at very high, reliable level. Ultimately, food is about trust, and we need to make sure that the peoples in our country can trust the food they buy, whether that is in the small stores, whether that's in the mini markets or in the big supermarkets. Great, thank you for that. Let me, I know we wanna open up the conversation to the audience, but let me maybe ask one final question of Prime Minister Hun Sen. You spoke in your earlier remarks about a number of balancing goals for the government, intensification versus extensification or food security versus energy security. Let me ask you if you would address another aspect of the trade-off, which is increasing production versus environmental sustainability, how to make sure that production is increased in such a way as to limit the climate footprint of the agricultural sector. Thank you. The speakers I've been raising. I should talk to the private sectors. Private sectors has opportunities to play more roles. The expertise in the agriculture, it's not just the policies of the Raja government, but the private sectors is also a sector that brings the development of agriculture, especially for food security. I would like to add that private sectors can play a role to buy up the spotted farmers to a one place, bring them to one place through a contracted farming or through setting up the processing base in which all farmers that bring their product to supplies to the factories for processing. To call food, it does not that we plant it. We start from planting until it comes to the table that is called food security. It cannot just call only planting or harvesting. Processing is very important and it is a part of the market mechanism to help the farmers in relation to the pressures on the environment. The growing numbers of populations, for sure there will be pressures on the environment, including food, which will need rice on other crops, the problem of food and meat, but we can find a way to reduce the pressures on the environment, which cause the loss of the forage, which are brings to the bigger climate change. Climate change requires us to have more study. There's our seed, let's say that the resistant to 35, 38 degrees Celsius, what when the ball getting warmer and warmer, whether the seed today can stand that heat or not. We pose a question on the research institution, as well as those super users, the seed to keep up to the situation and to cut the middle red tab. We need to cut the red tab, which is among our officials. It means that from the research into the production of the farmer has to be the shortest way that bring us success in which we can create new seed and give to the farmers to grow it and then we can win in the competition and can bring to the environment market. We know that Europe, they selects rise so much about food so that they can guarantee the people safety. I will take this opportunity to send my blessing. No need to learn from anywhere else, but to pressures on environment, or this issue. We learn from Vietnam. Vietnam in the 80s, I know during that time, Vietnam is still have cooperative. Vietnam was free shortage of food, but Vietnam is the rising spot countries. Vietnam means the soil get very tired. There's two crops or three crops per year in Vietnam. So Vietnam can tie up their farmers with the production system, including supersizing and export. And this success also happen in China and in the Republic of Korea, South Korea. It means summer or dawn, new village movement of Popak Chung Hee President in which now his daughters is moving, continue this moving summer or dawn, new village movement. And that is a lesson it's good for developing countries and need to copy. I think my copy could be more than what you like to have. Let me now open up the floor to any questions that there may have. If I may ask of the audience to a couple of things, to identify yourself, to identify who you'd like to direct your question to, and if you would to keep your questions reasonably brief so we can take as many questions as we like. I'll take two questions to begin with and then we'll get some answers. Yes, sir, here in the second row. Good morning. My name is Jacob Robbins and I'm the chief executive of a company called Emitera, which is involved in making agribusiness investments in Asia Pacific and beyond, also representing Olympus Capital Private Equity Fund in the same area. My question is with respect to food security, one element of course is productivity, intensification, enhancing farmer practices to be able to achieve high yields and all of the above. But a critical element that I was not hearing any input on during the course of this discussion was the whole area of food storage and the infrastructure to be able to support that. It's one thing to grow, but there's a significant amount of wastage that takes place in the entire food chain because of inadequate storage facilities, elevation, cold chain, et cetera. So I guess my question would be directed to two members in the panel, Mr. Kulve of Unilever and also Prime Minister Hun Sen. What is the private sector doing to facilitate these investments and what is the government doing to be able to provide their share of the support to build the infrastructure for food storage and infrastructure to enable true food security? Thank you. For our second question, I may ask Esther Panunia of the Secretary General of the Asian Farmers Association to either comment or ask a question to particularly bring in the farmer's perspective here. Thank you. Thank you very much, Sir Chair. And I am Esther Panunia. I am from the Asian Farmers Association for Sustainable Rural Development and I would like to make two comments and one question. For the first comment, I like the phrase farmers by choice. But the reality is a large majority of the farmers in ASEAN countries are farmers by force, okay? So, but in terms of food security, if you want to have a food secure ASEAN, we have to contend with this reality that many of the small farmers are there farming, so we have to help them, okay? So that they can be maybe in five years time, in 10 years time farmers by choice and their sons and daughters can be also farmers by choice. So, because of this comment, I would like to also ask our panelists, especially from our governments and the CSUs and the business, how would you, how, what would be your programs and policies to attract the young into agriculture? The second comment is and question is on free trade, okay? You, maybe you will know that many of the farmers organizations are have very critical concerns about free trade because our experience is because of some free trade agreements, many of the farmers, small farmers have been seriously affected, their livelihoods has been displaced. So what we would like our question for the governments, our government especially is what would be your policies so that free trade agreements, especially involving agriculture, will not displace small holders and maybe put them in competition with others in the arena. Thank you. Thank you very much for both of those points. Let me, I think that's kind of actually three quite general questions that almost any of the panelists could tackle. Peter, let me ask you to begin, if you would on a thought on the food storage question and the supply chain more generally, and then I may turn to our government panelists on the question of farmers by choice. This is actually a really, really good question because the world doesn't really have a food problem. More than 50% of the food produced is wasted, thrown away by consumers in the rich world, full fridges, products not used in the waste basket, enormous waste during transportation, enormous waste during storage. So first priority for solving the food crisis or the upcoming food crisis is consumer change, making people more responsible to actually consume the food they buy in the rich world and making sure that we make a big investment in storage and transportation because indeed 25 to 30% of all food produced get lost during this stage. We believe that by linking up big consumers of agricultural products like ours with small holders, creating guaranteed demand will enable farmers and very importantly cooperatives of in farmers to make the necessary investment during the different stages of the chain. But for sure, stopping and holding, pushing back food waste is not only an economic opportunity, but also a major moral issue that we need to address. It is insane that there is so much undernourishment on one hand and on the other hand, we throw and lose so much food. Deputy Prime Minister Fook, let me turn the, actually go to the last question if I may, which was around free trade. Vietnam is not just an exporter nation, it's one of the largest agriculture exporters in Asia. Trade is very important for the sector and for Vietnam's economy more generally. To the question raised by Esther, how do you see that trade off? What is the right balance between maintaining open markets, growing exports, with ensuring, again, farmer livelihoods are protected at home? With this enchantment, why negotiating TPP, even the U.S. or Japan? Also so try hard to pretend that the agriculture sector, like other Asian countries, and in Vietnam also the most important thing is how to protect the rights of the farmers. But we cannot just try to protect domestic interests and skip and miss the integration opportunities. Therefore, Vietnam really wants to be part of TPP together with big partners like Republic of Korea, China, or EU to be part of TPP as the question raised by, from the floor, that we should have a transformation in agriculture sector, restructuring how to reduce the labor force in agriculture in the rural areas. Same in Cambodia, because 70% of the population is still working in the agriculture sector. Why in the U.S.? Only 1% of the population working that area and in Japan the figure is still lower. Reducing the number of the labor force working in the agriculture does not mean that reduction in the productivity or reduction in the number of products. Therefore, high productivities, high income, in line with industrialization of agriculture and high quality agriculture, high productivity agriculture, are very important. And every country is most sick, their own comparative advantages that other countries do not have. For example, the pharmaceutical, the medicine, herbs and plants, our strength that other countries do not have or with our seafood products, also one of our advantages. Therefore, I think that we should continue our negotiations for FTA, but we should have suitable roadmap to protect our families along the line of industrialization and modernizations. And we have to reduce the number of the labor force in agriculture with increasing productivity. Well... Minister, would you like to also address this question of the transition from farmers by force to farmers by choice? What allows that transition to happen? Maybe I cannot answer straightforward to that question, but I'm interested in the issues of liberalization of the trade that will lead to conflict. And this conflict is not between the developing countries exported to developed countries. And even the developed countries, they are also in conflict. Let's say, for example, in France and UK, they conflict on meat, cow meat. They choose about mad cows. And the left-wing message, you still remember that during the Spain export cucumber to Germany, the Germans say that the virus from cucumber to prohibit tomato. It means that it's very sensible issues because the farmers in each country, they would like the protection of their production and increase the price. South Korea, there is a demonstration in this import of cow meat from America. So that's a point that we need to find a common solution. It's a package of issues of the world. Another issue in relation to stockpiling, in which so far no answer from any speaker. For ASEAN Plus 3, we have a stock facility. But in each country, I'm talking for the Cambodian style. Cambodians have the reserve stock of rice, rice and rice seeds. The state responsible for the stockpiling to the state company, which is public enterprises. At the time the reserve stock is expired, we push it into the market and then we buy the new one to distribute the seed and the food. And besides, we motivate the private sectors so that the private sectors can have their own stock in case of disaster, especially disasters which involve flooding or drought. I would like to recall a bit. In the year 2004, tsunami in Indonesia and a number of countries. In early 2005, they were submitting a jagata in the relationship to the tsunami. Then World Food Program stocks food in Cambodia, export from Cambodia to a number of countries. So it means that ASEAN Plus 3, we have a food stock facility. And Cambodia herself also has her own stock. Another point I would like to talk about, Excellencies, I'm in prison from Vietnam, talk about the tax of farming land. Cambodia, I object taking tax from farmland. Those who are after me, they tax on the farmlands, it's up to my time. Since until today, 36 years already. I've been holding the power more than 30 years. I do not limit tax on the farming land. I still have another three terms. I will be able to win the election. I will continue this policy. I will not tax on the farmland of the farmers. Because tax from the farmers, there is a financial need for the nation. But we should allow the farmers to benefit from the land, interact with them by their ancestors. And how to manage them? It leads to the generation. Maybe it cannot be prime ministers until we are 1,000 years old. And for the balance, the farmers by choice and by force. And this is, it's not a time that the farmer, of forced farmers or choice farmer. What we should see is that this is a time of goods production. It's not a traditional production system. Even in my ethnic minorities, before they produced rice only for their own consumption. But now, they produce to sell in the market. So the point of our success in relation to the volunteers farmer. This year, they can plant rice. When the price of rice go down, they can grow corn. And later, they do not grow this.  They grow the other agricultural products. So I think that do not stress too much on farmers by choice. The market mechanism, the private sectors have a big role to play. So that our farmers can change the attitude from farmers planning in traditional way to the farmers producing goods. If farmers producing goods, they can do the same. They can do the same, they can do the same. If farmers producing goods, it's a liberal farmers. They can have their own choice to the market mechanism. Thank you. We're running a little short time. If we have time for one or possibly two quick questions, if there are any other questions from the audience. Yes, in the third row there. Thank you. Use the microphone, please. It's an interesting panel. I'm Abhis Sulari from Pakistan. And in this whole discussion, I wanted to hear about drinking water as well. Of course, food security is not only about production, affordability and food quality. We can have best of the best lunch in this hotel and have a contaminated glass of water. The result would be food poisoning. So in order to be food secure, we need to think of drinking water. And what are the plans and public-private partnership on drinking water? And second as the region is going towards economic integration, are there any plans for ASEAN food bank? For those who would be the losers in the immediate to medium term. So are the governments, they are planning to have some sort of arrangement food bank for the nations of the government in need? Okay. Let me ask Anna to address the question on water and to the extent that that is figured into the Grow Asia partnership or other programs that Mercy Corps has been going on. And I might ask the deputy partners to very, very briefly because we're quite short of time, we're down to just two minutes. So Anna, very quickly to you on the water question. I think that's an excellent point and thank you for raising that. And I think it does feed into sort of the broader question of environmental sustainability. And if I look at sort of the targets that Grow Asia as a multi-country, multi-stakeholder platform is taking on, the question of targets around environmental sustainability is very real. And I think that this is something where we need to push ourselves even further and make sure that we're not just looking at targets around greenhouse gas emissions, but whether we're actually tailoring to questions around water usage, which I think, again, going back to the point around sort of what's happening with climate change, with access to water, with drought and rainfall patterns, that's becoming an ever-increasing priority. And Prime Minister, Deputy Prime Minister, very briefly on the question of the food bank and asking on stockpiling question, essentially. Currently in Vietnam, there's no national food bank yet, but we have many concrete policies to support the people for the food reserve, to promote the manufacturing of agriculture and food products. Particularly, we have a special program, the credit program, with high-professional rates to support to assist the development of agriculture. Prime Minister, we're very, very briefly, please. By some young clay, I would like to refer a bit. If you have to have a rice bank or food bank and managed by the state, I think it is disastrous and it is not a free market economy and it's the condition of WTU. What is important is the state has to pay attention, increasing, encouraging the private sectors to stop the food through the mechanism and the state support, like excellent delegation Vietnam mentioned. If the state manages it, we will lose. If the state advises it, we make no profit. Just get experience. Because I've been undergoing three forms of economy. After both, we manage a plenty of economy because we have no choice. But I became the prime minister. I started the economic reforms. It's a transition. It's a combined of plenty of economy and free market economy. From 1991 until today, it's purification of free market economy through the accession to WTU in 2000. This showed that if the state manages the rice bank or food bank, then there will be a loss. But on the contrary, the government needs to give encouragement to the private sectors to do it. Thank you. For that thought. We are unfortunately now out of time. Let me just very briefly recap two or three points or insights that I picked up from the conversation. One being that farmers need to be at the center of our discussion on food security. And in particular, smallholder farmers and the issue of increasing smallholder productivity may be the most difficult and the most important part of that challenge. Secondly, achieving food security requires a genuine multi-stakeholder approach. And that in turn probably requires some organizational innovation and a new way of thinking by both businesses and government.  And policies to promote higher yields and higher production also need to be mindful of the potential climate and environmental risks that come along with those policies. So with that, our session has come to a close. For those that are interested, there is a Grow Asia press conference. I believe it's next door in the exchange room. That starts at 10.25. And with that, I'd like to ask you all to join me in thanking our panelists for a very rich discussion.


During the summer, prior to Pearl Harbor with an eye on the Pacific and Japan's imperial ambitions there, the first Second Marine Aircraft Wing Marines and Sailors reacted swiftly after December 7th, 1941. Taking flight from its original stations in California, Second Marine Aircraft Wing provided air support for the seaborne armada of Marines and Sailors as they island-hop toward Japan. After three years of bloody combat, Japan surrendered and Second Marine Aircraft Wing returned state side to a new home along the Noose River, Cherry Point, North Carolina. From there and across the Crystal Coast, Second Marine Aircraft Wing has trained thousands of naval aviators for service across the globe. How's the Cherry Point, New River and Buford flying Leathernecks with Second Marine Aircraft Wing have deployed in support of nearly every U.S. conflict, operation, war, engagement and contingency since heading east in 1946. 2015 marks year 74 in Second Marine Aircraft Wing's history with aircraft that show evidence of the evolution of naval aviation. The Corsairs, Hellcats and F-4 Phantoms of yesterday have given way to the F-35s, MV-22s and C-130s of tomorrow. As the platforms have improved and evolved, so have the Marines and Sailors who fill the ranks of Second Marine Aircraft Wing. Deploying aboard Navy ships as an ever-ready force, joining partner nations to respond to regional crises and transporting ground troops belonging to Second Marine Expeditionary Force, Second Marine Aircraft Wing continues to provide the best combat and humanitarian response, air support available anywhere in the world and continues to be second to none. Operational excellence, standard-based, respect and concern for all. They are the tenants that define the Second Marine Aircraft Wing heading into the 75th year of existence. It's important that Marines understand the heritage and culture of the Marines and those that gave the ultimate sacrifice before them, that served before them. It's very important for Marines to understand that history so that they can continue the legacy of the greatest fighting force in the world. It's important to me because of people like my father. He served proudly in the Korean War with Second Marine Aircraft Wing and all those fathers of all those young Marines out there, they deserve our respect and our remembrance. History is important and 74 years ago we had some of the earlier aircrafts and 10, 15 years from now we'll look back at CH-46s for instance the same way and it's part of that history and I'm glad to be here and be able to celebrate the Second Marine Aircraft Wing 74th birthday. Not many people get to do what we do and if you stay motivated through it and just think about the positives every day and the bigger picture of what we're out there to do, supporting those pilots so they can do their job and just knowing that you're helping even if it's like a little thing.  We have a family that works together, they care about each other. Happy birthday Second Maul. Happy birthday Second Marine Aircraft Wing. Second Marine Aircraft Wing have a happy 74th birthday and we'll see you next year for 75.


It's a real conversation, and everything I said was short and sweet to the point with a question at the end. I'm not, and I'm reading them.  And then I can adjust my voice in my conversation and my questions accordingly. Because they're actually the director of the conversation, because you're asking questions and then seeing where it goes from there. It picks up two a day, in five years you're the number one guy or girl in the state.


All right, so we will now decouple this long-range Coulomb interaction by Habat-Stratonovich. And there are various types of Habat-Stratonovich transformations for fermions, bosons, real periodic fields. And so the density is real and better periodic. So we will use the corresponding transformation, which is the following. This is some kind of general interaction written with some matrix A. That can be decoupled as follows, one over square root of a determinant, and then the integral over all the Habat-Stratonovich fields. So capital N is the number of sites in the lattice. And we have as many Habat-Stratonovich fields as lattice sites. Now we have a term which is quadratic in these fields. And we have a coupling between the density and the Habat-Stratonovich field, where in this notation somehow the summation is implied by a kind of matrix vector notation. And these fields, phi, they are also real and beta periodic. And here this A is, of course, just the non-local interaction v tilde. So if we apply this transformation to our lattice action, we obtain the following transformed action. So the hopping part, now from the Habat-Stratonovich transformation, quadratic part in the Habat-Stratonovich field phi i tau v tilde r minus 1 ij, ij of tau, plus then a local coupling between the Habat-Stratonovich fields and the electrons. And here in these curly brackets, we recognize the non-interacting or the inverse of the non-interacting Green's function of the lattice. So this we can write as G0 minus 1 component ij, where G0 is the non-interacting lattice Green's function. And if we use this notation, then we see sort of an analogy now between the fermionic part, which has this quadratic term with the non-interacting lattice Green's function, and the bosonic part, which has a quadratic term with this inverse Coulomb interaction. And so this then motivates us to map this system in the extended DMFT approximation to an impurity problem, where we have a fermionic vice field, which describes this hopping of electrons into the bath and back.  So then if we just let's just write down the form of this action. So we map it now to the following impurity action in this e DMFT formalism, namely a quadratic term with the fermionic vice field and the retarded sort of hopping of the electrons. That's the usual term, which we have in DMFT, where this is the inverse of this non-interacting impurity Green's function. And then in analogy to this, we have a similar retarded term for the Habat-Stratonovich fields with some non-local interaction, which I call curly u inverse, which now couples these fields at different times tau and tau prime. And that is sort of now the bosonic vice field. And this is the fermionic vice field. And then we still have the local interaction between this bosonic field and the electrons like this. So this thing here would then be our fermionic vice field. And this curly u would be our bosonic vice. And these need to be fixed by a self-consistency condition in such a way that this impurity action somehow reproduces the properties of this lattice model, at least the local properties. So the fermionic vice field is just kind of Green's function. So this has sort of the properties of a Green's function in imaginary time. It's beta-antipariotic, for example. It looks like this. This is g of tau, where this is beta, 0. Whereas this curly u of tau is more or less of the form of the dynamical interaction, which we have discussed before. It's sort of a beta-teriotic function. It looks like this, this kind of general structure. And both of these functions now have to be fixed in a self-consistent way. Now, it's somehow not very convenient to work with these Haberstra-Donovich fields. But once we have done this mapping onto the signicide problem of this form, we notice that it's quadratic action in the phi fields. So we can sort of undo our Haberstra-Donovich transformation now for the impurity problem and integrate out, again, the phi fields and go back to a purely electronic action.  So in the following, we can, after sort of undoing our Haberstra-Donovich transformation, we find the following action impurity system. The usual fermionic part, which is unchanged. Well, this quadratic phi term, after the Haberstra-Donovich transformation, is replaced by a quadratic term in the density. And with the u, instead of the u inverse, and this part here disappears. So we have one half integral 0 beta theta theta prime. And now n of tau currently u tau minus tau prime, n of tau prime. And also from these determinants, which appear in the Haberstra-Donovich formula, we get another term, which is minus logarithm of square root of determinant of u. Now you see that we have end up with an action, which is exactly of the form which we have sort of studied in the last lecture. Some impurity system with a general retarded interaction. But now this interaction has to be computed in a self-consistent way by a self-consistency condition, which I still need to explain. And so this term with the logarithm of the square root of the determinant, we can rewrite a little bit as, for example, one half logarithm of the determinant of u. And then we use a formula which says that the determinant of u can be written as the exponential of the trace of logarithm of u. So this is exponential of trace log u. And then the exponential cancels with this logarithm. And then we find this is one half trace log u. So this is the action, which we really want to use then in the calculations. This is the action with the Haberstra-Donovich field, which was useful to derive the single side action. Now we need to derive two self-consistency equations, one for the thermionic-wise field and one for the bosonic-wise field. Basically, this will be, again, based on the identification of the local laggis-greens function and the impurity-greens functions. And both the thermionic and the bosonic-greens functions. So now we have to compute the thermionic and the bosonic-greens function of the impurity or problem. So how are they defined? Thermionic-greens function is just, as usual, the expectation value, or maybe with minus sign of C, C dagger, that you should be familiar with. That's the impurity-greens function, where this expectation value means now the expectation value evaluated with this impurity action. And the bosonic-greens function, we call w, is the corresponding correlation function for the phi field. So that is the expectation value, phi tau phi of 0. So now we want to work with this action in which we have integrated out the phi field. So it's a little bit non-trivial how we can get this phi-phi correlator from this action. So we need to do a little manipulation to see how we can get this from such a purely electronic action. And so first we start with this action here, which I call star. So from this action with this Harbott-Stratonovich field, we can easily see that this correlation function is simply the derivative of the logarithm of the partition function with respect to u minus 1. So if we take the derivative with respect to this bosonic-wise field here, we get the phi-phi correlation function. Bosonic-greens function can be written as 2 times d ln z d u minus 1. So that follows immediately from this expression here. And now we can manipulate this a little bit and see that this is the same as 2 times d ln z d u times d u d u minus 1.  So this we can write as minus 2 u d ln z d u times u. And now we go to this action here, with the phi field integrated out here.  So we can easily take the derivative of the logarithm of the partition function with respect to u. Now we evaluate this term from this action here. And we find d ln z d u is nothing else than, well, from this term we get the density-density correlation function. If we take the derivative with respect to u, so 1 1⁄2 times n of tau every time ordering. And now if it matters n of tau, 10 of 0. And now we have to be a little careful. So we have another factor of u here, 1⁄2 log u. And so if we take the derivative of this one, we get another contribution, which is minus 1⁄2 1 over u. Now we plug this into here. We find the following expression that the bosonic impurity grains function can be expressed as u minus u chi local u with chi local density-density correlation function. And this is something which can be very easily measured with the algorithm that I explained in the previous lecture. So we calculate this with say Monte Carlo. And we know u. And then we can compute the screen interaction. So that's how we can do it. Maybe a little practical remark. Usually it's better to define the interaction term with respect to the density fluctuations. So we subtract the average density from these densities here. And then this chi local becomes sort of the connected charge correlation function. So OK. Now I think we have everything to set up these two self-consistency loops. First loop is the fermionic self-consistency loop, which is completely identical to the one for usual dynamical mean field theory. Let's rewrite it as follows. We have calculated our impurity grains function by the Monte Carlo technique, which I described. Then we compute next the impurity self-energy by using the impurity Dyson equation. And then we say that the lattice self-energy, the fermionic one, should be this impurity self-energy. So we approximate sigma of k i omega n by sigma impurity of i omega n. Where here i omega n are the fermionic Matsubara frequency. And then we use this approximate self-energy to compute the lattice grains function. So we write gk i omega n, which I mean the exact expression from the Dyson equation would be the non-interacting lattice grains function inverse minus sigma k i omega n. And this whole thing inverse, that's the exact expression. And this we approximate now with the impurity self-energy here. We have a lattice grains function. And next we compute the local lattice grains function by averaging over momentum. And now we use the dynamical mean field self-consistency and say this should be the same as the impurity grains function. So this is the DMFT self-consistency. If we do this, then we can use, again, the impurity Dyson equation and the impurity self-energy to obtain our new Weiss field, g inverse nu, which is now g local, inverse plus the old impurity self-energy. And then we use our Monte Carlo or whatever impurity solver to solve the impurity problem with this new Weiss field. And that gives us the grains function. So that's the fermionic. Now in complete analogy to this fermionic loop, we have a second loop for the bosonic. G grains function and the bosonic Weiss field. So let's assume we have computed our bosonic impurity grains function. Then we define the self-energy, bosonic self-energy, which is nothing else than the impurity polarisation function, which I call here pi. And that is defined as the bosonic Weiss field minus the inverse of the impurity grains function. Next step is that we approximate the bosonic lattice self-energy by this impurity self-energy. So we approximate the p of k and i nu n. So nu n is now a bosonic Matsubara frequency. We approximate by this impurity polarisation. And then we compute with this approximate self-energy or polarisation the screened interaction in the lattice. And so the exact expression would be the following, that w of k and Matsubara frequency i nu n would be, well, the bare interaction, the inverse of the bare interaction, 1 half v tilde minus 1 minus this momentum dependent polarisation function. And this inverse. But this we now approximate by this impurity polarisation. So we find 1 half v minus 1 minus impurity polarisation. That's now our approximation for the lattice grains function, bosonic one. And now we sum this over k, or average over k, to get the local grains function or the local screen interaction, supposed to be the same thing as our impurity fully screened interaction. That's the bosonic self-consistency condition. And if we use this, we can now use the impurity Dyson equation again for the bosonic version of the Dyson equation to extract a new bosonic vice field curly u. And as follows, we get the new curly u minus 1, which is from the bosonic Dyson equation, this w local minus 1 plus the impurity i. Now, in principle, we can solve our impurity problem to get new impurity bosonic grains function, or screened interaction. But we need this additional step. So the solver basically gives us, first, the chi local, this density-density correlation function. And from the density-density correlation function, we can then, and this curly u, we can get the impurity w. So that's the bosonic loop. And so now you see the complete analogy between these two loops, which has to sort of replace the vice field chi by u, curly u, the self-energy by the polarization pi, and the grains function by the sort of screened interaction w. And then there are two completely analogous loops, which fix both the hybridization function, or this curly chi, and the retarded interaction u in a self-consistent way.  I think you do it at the same time. I mean, you compute w and chi in the same simulation, and then you go through both loops at the same time. You update both the curly u and the curly g. So it's sort of simultaneously the same. You update both. And the solution of the impurity problem gives you both the w and the g. Yeah, it's one loop. Yes, yeah, yeah, it's one loop. Yeah, in principle, each step contains both. You do it simultaneously. So then maybe as a last topic, I can say a few words about combining the so-called GW method with this extended dynamical mean field formalism. Of course, up to now, I mean, what is very nice about this formalism is that we now self-consistently compute the interaction u. So we sort of create the screening effects in the system in a self-consistent way. And that gives us the dynamical u. But we still have a completely local self-energy. So this pi and this sigma is completely local. And in a real system, of course, we have some momentum dependence in these self-energies, sigma and pi. So one idea to build in some momentum dependence into this scheme is to combine this DMFT or extended DMFT self-energy with the momentum dependent self-energy of some weak coupling perturbation theory. And one obvious weak coupling perturbation theory is the GW method. So GW method is sort of the lowest order self-energy approximation in a systematic expansion in the screen interaction w. What does the GW method? So in the GW method, we approximate the self-energy, sigma, by the product of the interacting Green's function G, and sort of the fully screened interaction w. That's why it's called GW. And we approximate the polarization pi simply by the bubble of interacting Green's function like this. But this is now momentum dependent. So there can be different sites, i and j, here. So these are non-local interactions. And so one idea, which is actively sort of explored in this Abinishio and DMFT community, is to apply this method, which is widely used sort of in the Abinishio world with dynamical mean field theory. And the idea is just to basically take this perturbation theory and replace the local contribution from these diagrams by the DMFT analog, which sort of corresponds then to a different subset of diagrams. So DMFTs believe sort of supposed to sum up all the local diagrams. And now in addition to these local diagrams, we can add the non-local GW diagrams. So that's the idea. So written as a formula, we now construct a self-energy sigma GW plus EDMFT, which depends on momentum and frequency. As follows, we take the EDMFT self-energy, which is only frequency dependent. We add to it the momentum dependent GW self-energy. Now to avoid the double counting between these two, we subtract all the local GW self-energy diagrams.  And the same thing for the polarization. So we can define a polarization i in GW plus EDMFT, which depends on momentum and on sonic frequencies. That is the polarization function from EDMFT. We add to it this non-local polarization bubble from GW. And now to avoid double counting, we have to subtract all the local GW diagrams. So that's how we can construct some momentum dependent self-energy. And so how does the scheme look like now in this version? Well, we start, for example, from a converged EDMFT calculation. So this converged EDMFT calculation. This gives us the impurity self-energy and the impurity polarization. Now we construct a momentum dependent Green's function and polarization in the usual extended DMFT spirit. So we compute the G of i omega n, which is approximated as G0 minus 1 minus sigma impurity minus 1.  And then we compute the local Green's functions and from this device field. So that's all the same as before. So we compute G local i omega n by summing over k. And then we define the nu vice field using the impurity Dyson equation as G local minus 1 plus impurity self-energy. And the analogous thing, we have our impurity problem defined. And so we solve this impurity problem. So this gives us a nu impurity Green's function and a nu impurity w. And then we can define a nu self-energy. So the sigma impurity is the vice field minus the inverse of the impurity Green's function and the high impurity, the same with the bosonic vice field and the bosonic Green's function. OK. So up to now, everything is as before. And now comes basically this GW plus DMFT step. Do we? Yeah? OK. This one? Yes. Yeah, in principle, yeah. I mean, that's just a GW self-energy, which is non-local. I mean, in this diagram, the Green's function and W are non-local quantities. So it's, in principle, a k-dependent object. Yeah, all the local GW diagrams. So if we write this out, say a local GW diagram would mean something like this from i to i. And now the interaction sort of contains all kinds of doubles like this. And here, in principle, we can have i, k, l, i. So basically, all diagrams which go from i back to i will be eliminated. And all the diagrams which go from i to j different from i, we keep. Yeah? Yeah, that's the idea of this double counting. First, remove all local GW diagrams. Yeah, that's right. So that's what I'm just going to write again. So now we do the GW calculation. Now, as we evaluate the GW self-energy, so pi of GW. So I write it here now in tau space is sum over q. Green's function, q of tau. Green's function, q minus k of minus tau. So that's what I drew as a kind of bubble. And the self-energy, the only one, is the product of the Green's function and the screen interaction of this diagram. So that's the calculation of the GW diagrams. And then we extract a non-local part of these diagrams by subtracting the local contribution. So we calculate pi GW non-local. That's a usual GW diagram minus all the local GW diagrams. This really is just subtracting all the local polarization bubbles. And similarly for the self-energy, we combine this non-local part with these local impurity self-energies. Right now, the momentum-dependent polarization has the sum of the impurity polarization plus this non-local part of the GW polarization. And we write the self-energy fermionic one in the same way. This is impurity like this. And then we go back to this step two until convergence is reached. So now we have a new estimate of a momentum-dependent self-energy. With this, we can compute the local Green's functions and new wise fields. And we write this a couple of times until a converged solution is found. And so in principle, this is nice because if we now want to combine this with our initial calculations, where if we start from this GW, GW band structure, then we know exactly what are in a diplomatic form, what are the correlation effects included in this GW band structure. And then we can properly do the double counting if we add the DMFT self-energy. And that's not the case if we start from a LDA band structure where we don't know what the correlation effects are in a sort of diagrammatic language. So this is now an area of active sort of research to implement this scheme really in a material context. Good. So now, in principle, I have prepared some exercises. But I think we are running a bit late to start exercises. So maybe I'll just discuss one of the interesting things, which was also part of the exercises on the board here. Yeah? Yeah. If you want to do it for materials, yes. That's right. You get sort of, yeah, you get the orbitals to define your kind of hubbub model for the correlated orbitals. And a single band model. Few band models, yeah. That's in practice, you can of course only treat a few correlated bands. So then you define some, again, some low energy subspace for just a few orbitals. And you get the interaction from GW for these orbitals. And then you start this loop within this low energy subspace, and you recompute the interaction in a self-consistent way. The GW, you also, but yeah, I mean, yeah. In principle, there would be a feedback even from this low energy subspace to the high energy bands. And I think this, at the moment, is not realistic to do this. But what we can do and already do now is if you stay, if you do one GW calculation, then you restrict yourself to the low energy space. Then you can update the GW and the DMFT calculation self-consistently within this small subspace. And I hope that on a slightly longer time scale of maybe one year or so, we can maybe define an intermediate energy window where we really feedback the DMFT self-energy sort of into the GW part and self-consistently update the GW in a larger window of maybe 20 electron volts or something, but not the 100 electron or 200 electron volts for which the initial GW calculation is done. I think that's not realistic. Because nowadays, I mean, the GW calculation for this very large energy window is much more expensive than the DMFT calculation. So yeah, I think we can only really self-consistently do it within a small space. But that's what we do now. And it will be interesting to see if it's really an improvement over previous schemes. But. Yeah, this has already been done. Basically, you do GW, and then you do DMFT. Maybe you just combine the results at the end. Yeah, I mean, that you can do. And it's not that clear whether the self-consistent procedure is giving you better results. I mean, usually in the GW community, it's known that one shouldn't do GW self-consistently because the results are just not good. And the hope was that if you combine it with DMFT, if you have sort of a local vertex from the DMFT, that you can really do it self-consistently. Because this kind of one-shot philosophy of GW, that's really a bit.hoc and unsatisfactory. And maybe if one combines GW with the local part of the self-composure from DMFT, maybe one can really do a meaningful self-consistent calculation. That's the hope. At least on the model level, it works. And we now are trying to see what it gives for materials. So then maybe in the last 15 minutes, we can just touch a sort of interesting little topic, which is the relationship between this hybridization expansion, which I have described, and a very simple sort of semi-analytical scheme, which is called a non-crossing approximation. So that's maybe some people in the audience may be familiar with non-crossing approximation. And so maybe let's briefly discuss the relationship. And so let's look again at the simple case of a spinless fermion model. The partition function is the one we had on the board yesterday, trace time ordered product of e to chemical potential term u and the hybridization term. That's our non-interacting electron, which is hybridized with some non-interacting bath. And now let's expand this partition function in powers of the hybridization function. Then we get our partition function expressed in terms of these segment configurations, which we had on the board yesterday. We have these right simplicity like this. So here we have a C dagger on C, also the other way around like this, C, C dagger, and so forth, and many, many more. So in second order, we have this kind of diagram, of course, also this kind, and also this one, and also this one. And now finally, at third order, we find a diagram which has crossing hybridization lines. The first one with crossing hybridization lines looks like this, and many, many more, OK? What's the weight of these diagrams? So basically here we had 1. Here we had e to the beta mu. Here we had e to the mu times tau 2 minus tau 1, some times delta, tau 2 minus tau 1, and so forth. Now the point is that we can generate the whole subset of diagrams without crossing hybridization lines in an elegant way with some kind of Dyson equation. So all diagrams, except for this one on this board, we can generate in a sort of iterative manner by defining so-called pseudoparticle Green's functions. So let me explain what this is. Important point, those which do not have crossing hybridization lines, we can generate by introducing so-called pseudoparticle propagators. We have two in this system. We have two states. We have the empty state, and we have the full state. And for each of these two states, we now introduce such a propagator. For the empty state, we call it G0. And this sort of bare propagator has the following form. It's minus e to the minus energy of the empty state times tau, the energy of the empty state in this problem. I mean, I'm talking now about the empty atomic state. It's just 0. So if you have no electron on the impurity, the energy is 0. Similarly, we can define sort of a bare pseudoparticle propagator for the singly occupied state minus e to the minus energy of the singly occupied state, which in this model is just mu. Singly occupied electrons have energy mu. And you can see that in these diagrams, we basically always have these atomic energies appearing in the weight factor. But we can really sort of produce these weights by considering such pseudoparticle propagators which have the atomic energies, eigen energies, in the exponential here. And so how do we do this? We now define the following pseudoparticle Dyson equations, the Dyson equation for the empty state as follows. So we have an interacting pseudoparticle Green's function for the empty state. This is the bare pseudoparticle Green's function for the empty state, which is defined here, plus the particle Green's function for the empty state. And now comes a kind of self-energy insertion, which is of the following form, the interacting Green's function for the singly occupied state times the hybridization function. Then comes the bare and the full pseudoparticle Green's function for the empty state again. So this is a usual kind of Dyson equation where this is our self-energy. So this thing here is now like a self-energy, this pseudoparticle Green's function. So we have a sigma 0 in this non-crossing approximation, which is of the form interacting with the pseudoparticle Green's function 1 times hybridization function beta. This would be delta of minus tau, and this would be the self-energy tau. And in the same way, we can write down Dyson equation for our singly occupied state. That's the bare pseudoparticle Green's function for the singly occupied state plus bare times some other self-energy for now the singly occupied state, which has the form interacting Green's function for the empty state times the hybridization function, which goes in the opposite direction like this, and then G1. And so here we have another self-energy now for the singly occupied state, which is sigma 1 NCA equals G0 and delta. There may be some sign from the arrow which goes to the right. If you think about it for a little while, you will find that if you iterate, these are now two coupled equations which you can iterate starting from these pair propagators. You will generate exactly the subset of diagrams without these crossing hybridization lines. Because in the first iteration, you will have one hybridization function like this. Then you replace this interacting Green's function here by the expression here that will generate you further insertions of hybridization functions that you will never have a crossing between hybridization functions if you iterate this. And so it's a very simple calculation. So if we write down these Dyson equations explicitly, look as follows. So on the time imaginary time axis, these two Dyson equations can be written like this, from 0 now to tau, from 0 to tau 2. So that's the first one. And similarly for the G1, where you have two coupled differential equations. Here, you have the definition of G0 and G1. And basically, you have to solve this with the initial condition that G alpha of 0 is minus 1. Similar to this, their friends functions for alpha of 1 and 2. And then you get these interacting pseudo-particle Green's functions. And that's a very, very simple problem. Then you can easily see that the partition function is nothing else than the sum of these interacting 0-particle Green's function evaluated at beta and the interacting 1-particle Green's function also evaluated at beta. And why is this the case? This is because this G0 evaluated at beta is the sum of all diagrams without crossing hybridization lines, which start in an empty state and end in an empty state. And this expression here is nothing else than the sum of all diagrams which start in an occupied state and end in an occupied state. So these two give you all the diagrams without crossing hybridization lines from 0 to beta. So this is basically the contribution of the empty state, basically this contribution to the trace. And this is the contribution of the occupied state. And similarly, you can easily see, so just one minute, I have to maybe say how we get the Green's function. Now, the physical one, these are sort of auxiliary type Green's functions. So we need to say how we get the physical Green's function. And so what is the physical Green's function? Well, the physical Green's function is this. Within the NCA approximation, now the physical Green's function is 1. It's basically 1 over the partition function in NCA, which we have just written down here. And then graphically, say we have here a C dagger. So here's our time interval. Here's a C dagger. And here's a C operator. And this is time 0. And this is time beta. So we want to measure the Green's function where we create a particle at 0. And we annihilate it at time tau. Now we can obtain all the diagrams consistent with C dagger here and C here by just taking here the modified Pseudoparticle Green's function, G1, because here we start with occupied state. So it's a G1. And then here we annihilate an electron. So here we are in the empty state. So we continue with G0. That gives us all the diagrams, which are consistent with a creation operator here and an annihilation operator here. And that we can write as 1 over C NCA times a bubble of Pseudoparticle Green's functions like this. Now this is G of 1. And this is G of 0. So we basically take the product of G1 of tau and G0 of minus tau. And that gives us the physical Green's function. So that's a very simple calculation. And a few years ago, when I gave this as a kind of exercise to implement this NCA calculation, and one student basically solved this in less than 10 minutes. So he programmed the whole thing. And so it's very, very simple and fast impurity solver for the MFT, which works at least qualitatively in the strongly interacting regime. Basically multi-insulating regime. This is a good method. In the metallic regime, it's not very good, because this restriction to non-crossing diagrams is not really a good approximation in the metallic regime. But if you have time, and are interested in these methods, maybe it's fun to implement these coupled equations and solve them and see what it is. Yes? Something like these diagrams with cross denials. Well, it's somehow the result is always too insulating. Basically, the hybridization function in a metal is decaying slowly. So in an insulator, your G of tau is going like exponential, decaying exponentially with time. Whereas in a metal, your G of tau is basically going like 1 over tau. So it's decaying slowly at long times. And the hybridization function is behaving in the same way as the Green's function. So the hybridization function in an insulator is decaying very fast. The hybridization function in a metal is decaying slowly. So that's how one can understand why in an insulator maybe crossing hybridization functions are not so relevant. But in a metal where your hybridization function is not decaying fast, of course the crossing diagrams are important. And that's why this approximation is not working well in the metallic phase. It even becomes unphysical. If you do this approximation at low energies, at low temperature in the metallic phase, you'll get unphysical results, like causality violations in the spectral function and things like this. But in the mod insulator, where electrons don't hop very much, basically this approximation works rather well. OK, I guess if there are no further questions, we can stop here. Thank you for your attention.