Assalamualaikum warahmatullahi wabarakatuh. Good afternoon, ladies and gentlemen. And once again, let me introduce myself. My name is Sarah Wayne and it's an honor for me to become your moderator for today's dialogue or talk show session. But first of all, please do allow me to take off my mask for this session, ladies and gentlemen. And once again, welcome and we'll be starting the talk show of the palm oil and environmental sustainability, the high level policy dialogue. But before we start, can I have first a big round of applause? Is everyone ready to start the talk show, ladies and gentlemen? And I would like to welcome everyone here who is at the venue at the Barabudur Hotel and also those of you who are joining online. Welcome and we'll be starting the talk show in just a moment. But before we do start, probably I would like to give an overview first, as we all know. And as we have also listened that palm oil is a very prominent vegetable oil commodity in the world and the global supply chain. And it's one of also one of the world's most controversial communities, ladies and gentlemen, as we all know. And of course, as we all know as well, palm oil is mostly produced here in Southeast Asia, namely Indonesia and also Malaysia. And palm oil contributes highly and is also one of Indonesia's key export commodities and also contributes significantly to the country's national development. And through this dialogue that we will be having in just a moment, we will be having three sessions today. We will be able and also we are aiming to bring together stakeholders and also experts to discuss more on the sustainability of palm oil itself, especially in light of the global crisis that we are all facing, ladies and gentlemen. So without further ado, please do allow me to welcome our speakers for the first session, ladies and gentlemen, where we will be discussing palm oil price fluctuation and also supply chain. So without further ado, please allow me to welcome our first speaker, Mr. Oke Nurwan, the special staff for expert improvement and foreign trade development, the Ministry of Trade Indonesia. Welcome, Mr. Nurwan, and I would like to invite you to please come up onto the stage and please kindly take a seat. You may sit wherever you like. As you may see, my phone is already at the very far right. Yes, please, sir. And next, ladies and gentlemen, please also welcome Mr. Agus Purnomo, the Senior Advisor on Sustainability for Golden Agri Resources Limited. Welcome, sir. And once again, please do take a seat. Any seats you'd like. And next, I would like to also invite onto the stage, Professor Bustano Arifin, the Professor at Lampung University. Welcome, Professor. Please once again come up on stage. And we also have Mr. Destrico Malayiputra, the Senior Policy Advisor for Sustainable District Association to please come up on stage. Please give her applause, ladies and gentlemen. Welcome, sir. Please come up onto the stage. And now, ladies and gentlemen, since we are having this discussion session both online and offline, we also have our speakers who are joining us virtually this afternoon. Please welcome onto the screen Ms. Goldamir McTanya, the Representative from Apcasindo. Once again, can we see if Ms. McTanya from Apcasindo has joined us? Good afternoon. Please give her applause for Ms. McTanya. Ms. McTanya, can you please say your short greeting? We would like to also check if we can be able to hear you for the talk show. Yes, absolutely. Thank you, Ms. Wayne, for introducing me and thank you for the opportunity to join the discussions. And honored to be here and honored to have the dialogue back to you. Thank you very much, Ms. McTanya. We can hear you clearly. Thank you also for joining us and we are hoping to have a wonderful session with you as well. And next, please also welcome onto the screen Mr. Nurhanuddin Ahmad Surambo, the Executive Director of SAWIT Watch. Hello, good morning. Good morning, Mr. Nurhanuddin. Thank you. And we can also hear you clearly. Now, ladies and gentlemen, let me just take my seat right here and we will be having the talk show, the first talk show session. But before we do, once again, I would like to remind everyone of you here that since this will be a talk show and dialogue, therefore, we'd like to invite everyone here to also please join in by asking your questions and presenting the questions to our speakers and by accessing the Slido. And how you can access the Slido is to access the link, which is trade hub, ask slash trade hub and also by scanning the barcode that is available on the screens of your application or gadget, ladies and gentlemen. And now without further ado, we would like to jump into the talk show and also ask and also dig into the insights from our speakers who are here this morning. So without further ado, I would like to start with Mr. Nurhan first. Mr. Nurhan, can you please tell us here in the audience about the condition of the global oil globally? Why are the prices right now is fluctuating? What is happening in the global scale? And committee, can we also have another microphone on the stage just in case? But here you can use my microphone first. Okay. Thank you. Thank you, Mr. Wing. Why? Okay. Thank you, Mr. Wing. Well, first of all, I think I don't have to mention everybody's here and everybody has been delivering in its opening ceremony. Well then, distinguished participants who are here and also online. First of all, while the invitation was not coming to me, it was coming to my director general for domestic trade. I was the director general, but I am on retirement since 1st of July this year. So I was asked by acting of director general for domestic trade to be here with you. And I would like also to extend his apology from Pak Sailendra. And I am here on behalf of him for this event. Secondly, I was informed by DMC just now. I would like also to benefit, to take the benefit, the facilitations that are coming from the committee who has kindly enough facilitating interpreter for me. So I would like to take this many to take the benefit of the facilitation so I will deliver my answers in Bahasa Indonesia. It will be more convenient for me. Thank you. So the answer to the questions. Sorry. This is May 2021. The government at that time predicts that this is a momentary incident. Because there is a conflict between the oil supply in NABATI. Among them is the oil production in Canada, about 6%. And then there is the oil supply in NABATI, which is based on palm oil from Malaysia. Where from Malaysia, it is estimated that the formal number is between 6% to 8%. At the beginning, there was only a flood in Malaysia that entered the market. Then after the pandemic, there was a reduction in the number of jobs that were returned. So the oil production in NABATI was reduced. What happened in Indonesia in 2021 was considered by the CPO and CPL. It will be produced above Rp. 51 million, based on the CPO and CPL. And the CPO must have a target of Rp. 49 million. The production is only Rp. 47 million. And of course, this is the cause of the oil supply in NABATI. The second, when the situation happened, it was also in America that the use of soya bean oil as a basic biofuel increased quite a bit. From 2070 to 17%, in 2021, it was already 35% for biofuel. And there is also a concern for the oil production. At that time, it was considered that the oil production would be better soon. Canola will also be better soon, so it will be considered again. The next concern, which is unpredictable, is the inflation from Russia to Ukraine. Even so, we have discussed before. Russia and Ukraine are like Tom and Jerry. But we have received a response from the large population of Ukraine that there will be no inflation. So, our opinion is still that NABATI oil will soon return to normal production. Canola oil will also return to normal. But it turns out that at that time, there was an inflation. So, there was a chance for a sunflower seed. And at that time, the condition of this oil price was a burden for the export of Indonesia, but it was not a burden for the mothers who used fried oil. It was not a burden. So, on the 3rd of January, Mr. President, Mr. President, I would like to tell you that the government is ready to pay the price of fried oil. So, the previous government did not pay the price of oil products or commodity.  Well, including fried oil, the base of this fried oil is the CPU. And the CPU is not controlled. It follows the market mechanism. So, the price of the CPU, fried oil, the production is rising. At that time, a dilemma was raised in the people as the biggest oil producer. Why is the price of fried oil so high? Well, from the point of view of the market mechanism, at the end of the president's government, we must immediately prepare the oil, so that the oil will be regulated by regulation. The regulation is based on the regulation of the oil and the preparation. Actually, why should this be regulated by the domestic market obligation? Because usually, because the margin is too big, between domestic prices and international prices. The government, through the Ministry of Trade, usually intervenes on the market mechanism as long as the fluctuation or change of the margin of the price is only 5-10%. Usually, we intervene on the market mechanism through the operation of the market and so on. But the margin is too high, there are too many companies that use this high margin. So, fried oil became the topic trend at the beginning of this year until seven months later, and now it has been under control. But until now, the government has been controlling it. It has not returned to the market mechanism, it has not been confirmed when it will happen. Because it turns out that the fluctuation of the price due to the lack of income is also due to the pandemic that is affected by high biologics. That is why it is affected. But the situation is now, the price has started to return to normal except for the high biologics. Because earlier, it was easy from the pandemic to increase the price of international biologics that has reached 4x the price of 4x the container. Even the supply of the container is not strong. The biologics has not returned as it was before. The price has started to be stable because earlier, the production delay was good. Even this October will be hot. In addition to the geopolitical, Russian-Ukrainian inflation that is still not certain about the oil. Thank you. Maybe Mr. Agus Purnomo would like to have any addition to your insights especially regarding the conditions on the multi-factor that has been explained by Mr. Nourwan. Thank you, Madam. I would like to follow the clue from Mr. Oke to use Indonesian language. In addition to what has been explained by Mr. Oke, which I agree with, the Chinese factor is very close to the productivity of the agricultural industry. And what has happened in the United States, with the dryness, with the lack of water, because there are also floods, it caused less production. Indeed, for agricultural businesses, the climate change is actually a challenge that has been experienced today. It is no longer a question of theory. What I would like to add is other than the natural aspects and also the political uncertainty, there are also several market countries whose policies are changing and sometimes it is difficult to access the market. It depends on the country, there is a country in Asia that is similar to the country of production, and then it raises the import price for Soviet products. Later, if it is better, the price will be reduced. There are things that are out of the ability of the Soviet producers to influence the political aspects of the market, and now there are also several conditions that may later be affected towards access to Soviet products to the market in Europe, for example. In Japan, there has been a discussion, but in general, the aspect of sustainability is rising so for the next 10 years, there is a need for us who work in the field of the production of this Soviet product to show the energy from the aspect of sustainability of our production. Thank you, Mr. Agus. And once again, because today we can use two languages, if there is a question that you would like to ask, please do. If you would like to ask a question, you still can ask in English. We'll be more than happy to translate the question for you, ladies and gentlemen. Alright, we will continue to Mr. Mustanol Arifin. Is it? Do you want to use the same question? Yes, we would like to also ask the same question. Also, regarding the condition of the climate change as well, it has also been mentioned by Mr. Purnomo. What can be done to mitigate the condition that is being faced, especially by our farmers? Thank you. Ladies and gentlemen, the climate change is really a big challenge for us here. One of the strategies that you all understand, I think we apply certification. Of course, to follow all and the standards, both certification and standards. We have here RSPO, we have here ISPO, and somehow we have ISCC. But not all. This is one to make adaptation and mitigation. I just take note from the government's decision two days ago from Comra. Harry mentioned earlier that the volume or the one that has followed standard certification is only 19 percent. The land, the total land that has been certified is 4.6 million hectares. It's about how much? A third? Okay, 25 percent. 30 percent maximum. Ladies and gentlemen, to adapt to that, the government has per press. So there is a per press, there is a per press, in 2019, RAN-KSB, National Action Plan, the next step. National Action Plan for Sustainable Palm Oil. That's to to do both adaptation and mitigation. But there are not many that could translate into action, into programs and intervention in the field, especially the provincial and the local government. So the key is the responsibility of the private sectors and small holders. The question how to do partnership, I'm not talking about the monitoring values, it's too much. How to do the partnership of big companies such as companies by Mastagos, Papunki, and the partners. Ladies and gentlemen, the ones that really get impacted by the price fluctuation and probably the policies, at least small holders. What kind of small holders? Independent small holders. Ladies and gentlemen, in this private sector, Mr. Sarah, the most vulnerable are those that don't want to be partners. I think it's PR. It means big PR for us, independent small holders become one of the main tasks. I try to say if this talk show could have some suggestion, policy recommendation for any programs that create or at least have incentive for our small holders both in the partnership or any programs that could improve the productivity and implement the sustainable strategies of palm oil production. If that's all, I think we could contribute to the climate change. Now, who will start? I still remember the government back then, there was an incentive called an incentive for financing. Back then, we didn't have an incentive. That's where it's lightened up. Now, I think you can confirm it later with your friends. From the model, it's done to pay for the palm oil production. If you don't pay for it, they have to depend on the price that is fluctuating. Alhamdulillah, the price has started to rise. I saw it when I opened the site. For the site, it has started not bad. The FOB for the CPO has 904. Then for the TBS, 1,100, 1,900, even there is a lot of withdrawal. If you open the site, the first price is not 11,500. But there is no bigger price. The last price is 11,400, 11,300. It still looks good. It is not below 1,000. Maybe I raised the price fluctuation with the certification and adaptation of this model. Thank you Prof. Mr. Agus. Thank you Prof. Indul. So what can be done by the company to the dominant market? So the market gives opportunity to the company to help the farmers to find and guarantee the model to do the certification so that the productivity will increase twice or more. Then in the market, it will get the standard good agricultural practice. The second is in the market that often gives incentives for sustainability. There is a clause for special allocation or treatment for small holders. So it is a new opportunity that will be realized to sell products that are from small farmers. Small holders products can only be sold if there is a chance of failure. There will be traceability. The company where I work has a data of 110,000 small holders with geotech location and other information that can be used to make labeling that products that enter the market are products from small holders. Thank you. Thank you very much Mr. Agus for your answer. We also want to ask Mr. Destrico what are your views especially regarding the price fluctuation that has been explained earlier by our other speakers and also the governance the impact that it has and also the supply chain. Mr. President, I would like to answer the question of the moderator. We would like to reach 5 points in our view. Indonesia is a country that is affected by the CPO. So we can't distinguish between the CPO and the CPO for energy needs. So I have written some materials. So if this condition is not intervened then Indonesia will always be affected by the CPO scale. When the export is reduced then every customer is oriented to export and the government can forget what is in the domestic market. This has happened a few times ago where the different biodiesel is safe. On the other hand, frying oil is difficult to find and the price is also expensive. So this phenomenon is also caused by the activities of this commodity. First, the subsidiary for frying oil we can see the number. We can check it here but for verification it is around 7 trillion in 2020. Then the incentive for biodiesel is very high. Very high in 2021 or in 2002 and for farming in the previous sector that did the farming and plant management that is also minimal. So we think that if we increase the production process that is indeed intervened from the beginning. Second, our CPO scale for the need of food and biodiesel cannot be distinguished in terms of appearance. Where does the CPO scale for biodiesel whether from Sumatra or Kalimantan cannot be distinguished? Everyone, the CPO wants to do anything cannot be distinguished. In terms of the need for biodiesel it will always increase because there is a B10, B20, B30 and B100 program. On the other hand there is a need in the farming sector other than frying oil that also increases or does not plan the distribution agenda. So we will always be distracted from this interesting market system that is good for the needs of the country or international needs. Third, Indonesia is a country that is very resistant to market pressure or market pressure where in Indonesia as a result of the World War II in the country of buyers it already has a high sustainability commitment. For example, the EU as a region where selling aircraft products it does anti-defrostation. So far, Indonesia is able to convince the market to develop from the principles of sustainability through the certification RSPO or through the operating system at the level of the market. It must be exposed. It must be informed. It must be delivered to the EU that Indonesia has already started to the aspects of sustainability and to various policies that have been imposed. So they understand that we are currently aiming for the ideal sustainability but the process needs time and time. But there is progress. It must be informed. Fourth, Indonesia is also willing to offer supply from the CPO because from the area of the supply and production in Indonesia it has the potential to offer supply if it is not controlled by the operating system. With the potential of 14 million 14 million even 16 million and so on. And if the production is active the CPO product is extraordinary. Now the question is whether the domestic market is able to offer supply or the market is ready to make a transaction with this production. If not, Indonesia itself will be forced to offer supply because of the presence of supply. It cannot be stored anywhere and cannot be sold. This must also be something that we think about. And the fifth, I want to tell you in a different context in other questions we have the CPO fund in Indonesia. In our opinion it is still oriented to energy so it is a bit weak to pay attention to the length of the supply and production of the supply and production at the level of supply. So, just look at the incentive given. Is the gap very high between the needs of the biodiesel which is mandatory by the government with the need of sustainability in addition to the government. Connection is the demand of the government that the CPO likes or is not obligatory. So, honestly the government if it chooses not to reduce the supply it can only be done because there is no demand. But it must be admitted that the supply is growing in the field. That is the first thing I want to tell you about why there is a fluctuation in the price at any level. Thank you for your understanding. Next, because it has been discussed about the condition of the supply in the plantations we want to know more about the condition of the farmers itself. Therefore, I would like to ask Ms. McTania to please present yourself onto the screen. We'd like to ask and also dig in your views regarding the fluctuation the level of fluctuation at the farmer level. How has it impacted our farmers? Ms. McTania? Yes, please. Please use the English language. I would like to ask Ms. McTania I would like to follow the code and direction of the plantations that are located in the plantations. What do you think about the plantations? Good. First, I would like to tell you that this order can be reached to the farmers who cannot be left behind. So, please replace me. Then, another interesting point is that in the discussion about the plantations discussed by Mr. Oke, it is interesting that Mr. Prof. Bustanul Arifin mentioned that what is most important about the plantations is the price. When it comes to sustainability or sustainability as mentioned by Prof. Robert Tasi there are three social, economic and environmental and certification we are talking about the focus of the plantations and the planting. But we are also talking about the fluctuation of the economic pillar. What happens is with the fluctuation the economic pillar from the next step to the next step is still a lot. We can say many rooms for improvement for the maintenance of the language. We are talking about the price fluctuation where if we look at Mr. Oke's explanation the price of the CTO of the world is spiking. Because it turns out that Indonesia can provide supplies to many countries that ask for it. In one of the most interesting and ironic of the plantations we are talking about free of charge. Even if we look at the news there are those who want to sell free of charge. Like the presentation where we try to see the growth of the CTO because from the plantations perspective we are talking about the new plantations or fresh fruit bunch when on the top of the global CTO it turns out that as we see it the plantations are free of charge. From this situation it turns out that there are other areas that should be the attention more from the plantations. There are two lines red and blue. What is the meaning of that, Mr. Ibu? There are two categories of plantations and non-nitra. As mentioned earlier from the rule of the government where the government tries to rule we can sit down and have a discussion in the Sawit industry and it turns out that the first rule is the Plasmas. Then it grows until the new rule in the first year of 2018 the change of the Dixie becomes Mitra and Non-Mitra. It turns out there are differences in the gap. This is what happens. So if we ask the market price fluctuation the world's oil if we ask a big and turbulent for the Sawit industry because it turns out it turns out that as mentioned earlier the system should be strengthened if we want traceability we want no deforestation actually there are many answers when this system we build it with power then it will be able to where the plants can really sit become a container that is protected protected by the market mechanism that can up and down, up and down back to the government authority because this is the one country the Indonesian public does the government want to change the authority about the continuation back to what Professor Nasi said actually the Sawit industry is a category of plants that is not like paddy because at the beginning of the year in Papua like this in the forest so if we want to say no deforestation there is an automatic answer according to me so according to us we ask and especially there is a signal that the price is still a lot showing a big impact to us farmers that can actually be a learning that can be further spread to become a material of discussion because this theme is for a high profile discussion to give insight what's next what's the take out and then what's the action plan so this is what I think can be a point point to protect us what is under this if there is a price above the lower price so when there is a price outside the lower price then there will be a sanction or there is a protection like what there is always a question and room for development thank you we will continue next we will be successful because at the same time we also want to get insight from Mr. Nurhanuddin from Kacamata Bapak regarding the price fluctuation how is the system and what should be done especially as said by Bumaria McTanya regarding the condition or how about our farmers thank you for a few thank you first of all I would like to say there is a group that people are interested this is a group in our community we have about 10 million people in my opinion once discussion after sustainability that should be done by the group other than me there is also a group next I would also like to mention we are also collecting a lot of data we have a lot of agraria in our community we have a lot of data in my opinion I think it should be done in the future back to the previous question about the fluctuation if the action is correct fluctuation is one of my opinion but how fluctuation does not have a lot of data this group we have to adapt we manage I think it is important how to move forward the people the people who say we have to adapt with the local conditions I imagine in this community the government should define who is one because the definition we have is still very complicated how to build the two buildings that is my opinion the government should clarify so that there is no a condition to make a better condition we can do it do not reach a wide range in comparison we have not yet reached there so it is still very complicated where the discussion was held earlier I think it is more detailed so that which is what I think next I think it is also interesting with the group situation that we have Mr. Agus, Mr. Pestanol but in this context it is important to define a condition the price earlier I there is an idea actually in this price range we also have a different price maybe we can use how we have a concept like there is a basic price maybe we can continue when we have this we can see that price which good that's the price will be applied although there is a lot of current conditions the price will also increase but the price will increase the speakers are not different but the small 2 ha for such a long time I think it is important for us to keep this in mind in the future if we really want to achieve something that we can do in the next 40 years. There will be a national action plan for the next generation. These are the things that should be answered. I understand that the government has a lot of good policy, but it may not implement it. The national action plan for the next generation has just been implemented in 9 provinces. There are 25 provinces that have a lot of good policy. There are 247 cities that have a lot of good policy. In the future, there will be less than 15 cities. 15 cities that have a lot of good policy. It has just been implemented. I imagine that the government should have a lot of good policy. The government should have a lot of good policy. And the government should have a lot of good policy. So that the government can understand the problem of the economy and the condition of the economy. But if that can be solved, I believe that it can be solved with the government. Because of the current situation. There are other conditions that I think are important. The situation here is also not only important. The consumer has also been affected. Where the consumer is in a position to accept and appreciate what is happening. In my opinion, Wall Street is in the middle of Oka. Now the situation is getting better. In my opinion, I don't think it's too late. Maybe I should thank you first. Thank you, Mr. Nurhanudin, for your additional questions. Ladies and gentlemen, ladies and gentlemen, we will now begin our question and answer session. For those of you. I just commented on the value fluctuation. It turns out that now it is connected to sustainability. So, I wonder why this is my point of view to comment. Because of my career path, I have been involved in sustainability. That is why I have been involved in a business in Belgium, in Brussels. With Europe and us, we have a lot of discussions about sustainability. With the current climate, especially the issue of climate change, we need, what is it called, mitigation, climate change. And that, in the journey, it is important for us to do mitigation towards climate change. And at this time, the answer is environmental sustainability. For sustainability, as I mentioned earlier, the word is certification. And the word certification becomes a specific challenge for the condition of Indonesia. Because previously, it was very significant to the presence of petanists in Indonesia. That is the first. But what is not clear is the sustainability itself. We are talking about sustainability, where is it going? This is the problem that has always been discussed. The answer is certification. But certification has aspects that become criteria in certification. That is also not clear. Because previously it was not clear for petanists who are only small, 1 or 2 hectares, if the big one is okay. The direction of sustainability, the direction of certification, where is it going? Is it a product sustainability or a trade sustainability? Sustainable trade? Sustainability supply? Sustainability demand? But all of this is related to environmental awareness. Isn't sustainability the definition of sustainability is too far? Mr. Haripurno, if I am not mistaken, sustainability is nothing because of employment and traceability. That is the main thing. Even though in Indonesia, with these challenges, even in G20, we are facing a sustainable development goal. Right? Where the key point is poverty alleviation. That is the way the word is. Poverty for Indonesia makes the meaning so that with poverty alleviation, this is a rural area. The one used by Koteca can now use a mobile phone. That is why poverty alleviation. Right? But why is it always directed to the employment? Employment must be used by the people. Only then can it be certified. There was a photo of it. It was not certified. It can be certified. Right? But is this suitable for Indonesia who used to be a farmer with a small farm? Right? Only one or two hectares. But it is filled with very challenging conditions for them. And they are difficult for them. Especially at different prices. Especially, the attention of the employment is still not optimal compared to what I have said about the farm. The plasm is okay. The farm with various reasons does not meet the standard of quality and so on. Meanwhile, they must follow the environmental sustainability in the climate change sector. This is the problem until now and it is challenging. And there is a difference between I am sorry that there is a difference between RSPO and ISPO. That the development of sustainability is more directed by the country that is more advanced and more this. I think for them it is related to unemployment sustainability is related to traceability is related to biodiversity and so on. Meanwhile, Mr. Forty-Elevation has never wanted it. That is important for us. That is the challenge for us over the elevation. Now talking about the farm level that was mentioned earlier this is the impact. Now for us the impact for the farm level is not because of the price. Because they are the price that happens because it is considered not sustainable. Not quality. Not worth it. Even there is a difference that is related to the environment especially the environment. This one. And not yet the owner and the owner of the farm. That is what happens. What is important for us. I have to comment because this farm is something that is strategic for us even for the international export to enter the division but one of the only because the farm is competitive so we have to environment sustainability for the farm.  Sustainable for Kanolawin. Sustainable for Kedelay. Sustainable for the environment. Even earlier the farm was contributing to the emission of CO2. Right? But earlier the competitive aspect until because I was a diplomat doing the operation is because the competitive is disturbing the products of other types of oil and oil. I remember this story very disturbing disturbing. And earlier at the level I now the government is improving at the farm level the farmers that not the mother-in-law but the family the farmers I agree at the level of the price but at the time the the farmers is because there is a lack of commitment from the businessmen the government at that time needs to stop the businessmen from doing the export ban. At that time we need to disturb so the businessmen do not ensure the direction of the president to provide fried oil with affordable price even earlier because the margin that is too much a lot that benefits this situation for self-interest needs to be appreciated by the government. The government does not refuse to take the policy no matter they are not cooperative with the export ban. The impact is immediately affected by the CPO price and disconnected because the international price has always been the CPO in Indonesia depends on the price of the CPO as long as the price of the CPO is not relevant with the international price there is no problem with the farmers there is an export ban disconnected between the international CPO with the KPBN price the international CPO price while the KPBN price is far away we are improving and it is easy and good the target of the president is above 2,000 now the price of the CPO is 2,000 or above 2,000 but the price is not too far as before the price of the CPO can be doubled the price of the CPO what we do is the must be the price of the CPO is connected to the international CPO not to the KPBN because the KPBN the contribution is small the price of the reference price that is spent is followed by the international price because it will be continued but this is the market mechanism that the CPO depends on the KPBN that the transaction is only for 3 million so that is the effect so we are improving now the price is getting better the international price is getting better it is not yet it will always reach the farmers especially with the inflation rate that is rising in several countries Indonesia is estimated at the end of the year so that it is big enough even though it is better than other countries we estimate the inflation rate at 7% and this will reach the farmers the price will rise the price will rise especially if the inflation rate will rise the inflation rate will rise this will affect everything but we still estimate here is sustainable the palm oil is the one that is related to the farmers not sustainable that is related to climate change but at this time it is also important sustainable for the farmers so the definition of sustainable and the criteria of sustainable is not the focus that is developed by the country but I agree we have to develop our own definition about sustainable palm oil and offer television thank you this is a more comprehensive explanation for all of us and because we are tired many of you have started to think about lunch it is 12 o'clock please ask to open the slide are there any questions that have been submitted through Slido and for those of you who are here maybe we will start with the Slido first if there is still time please prepare one more microphone because there are questions directly on the screen I will read this is the first question I cannot see the screen the first question is for Agus Purnomo is there any implementation of sustainability for example international certification or ISPO has an impact on the value of the CPO in return for sales to market mechanisms to get a better domestic value please Agus if the question regarding international standardization with domestic value I cannot answer and I will answer for domestic value but if the impact of certification on the value the impact is there and that gives what was mentioned by Prof. Inul is the premium price so things that have sustainability it will be bought with a higher price the problem is indeed there is still a little bit of certification so that the premium price can be minimized also not much and the premium is also different there is a segregated or identity preserved from trees to products that are sold to foreign countries the sumber is known clearly the oil is clear if still mixed in tanking for example there is a mass balance then the premium will be lower and that is what we often see as premium price for sustainability as long as the premium price is there sustainability cost can be covered the problem that wants to prepare a little more that is just a little and the market is there that is also the most important market while the larger market wants to find the cheapest price and not so concerned with sustainability so sustainability becomes a burden for the producers in the company because consumers are willing to contribute they still want the cheapest but sustainable that cannot be sustainable there is a limit thank you Mr. Agus and please can you answer Mr. Oke please the answer is actually the question is the implementation of sustainability such as certification or expo has an impact on the price of the company and so on I may see from the other side because the problem of sustainability as mentioned is the problem of environmental sustainability linked to climate change so there is no limit this is our importance to take care of the global environment but this will impact all areas to that well there is a premium price in the land because the company only takes a sustainable certificate that is why the market doesn't do the certificate the standard price is sustainable in returning to the market to get a good domestic price I have an experience that that our product there is a development from Europe must be traceable and so on there is a difference from us that if the product is traceable the premium price doesn't happen there is no there is the market that environmental friendly it is getting as long as the people in Indonesia not yet I am sorry I am talking about sustainability there is a difference with the oil market which is more hygienic for the people 42 percent of the oil market is dirty the only thing left in the world is that is it responsible for sustainability for Indonesia the oil market is still needed right so is the oil market getting a premium price it doesn't happen because the people still choose the market thank you we will continue to the next question father and mother for Panitia will we open the slide or can we directly please father Panitia will prepare the microphone please thank you from Gabki maybe we don't ask to give an additional explanation regarding the information especially about the ISEPU certification because a lot of people asked so now there are 895 certificates with total area 5.187 million hectares from 895 Angkota Gabki 560 or 64 percent there is also a cooperation 26 cooperation throughout 2020 so the cooperation is already on the track to the ISEPU certification because in the new ISEPU system in 2024 in 2028 in 2025 the ISEPU certification will be required to get the incentive for the ISEPU audit to be carried out by BPDKS and also at this time the ISEPU certification has been carried out for socialization for sustainability and in 2025 all the certificates can be made by ISEPU especially now total certificates for the certificates is 41 percent 12 million hectares then there is a question I want to explain between ISEPU and MSBO 3 certificates 3 are the dominance actually for principles and criteria the 33 certificates are identical only the heading is different but the content is similar indeed in the ISEPU it is still voluntary but if ISEPU and NSBO are mandatory then the difference is useful if in the ISEPU there is a premium price and I have several times mentioned that there is a premium price but if in the ISEPU MSBO there is no incentive for TBS or CPO for ISEPU that's a bit of a joke thank you thank you thank you and as I said there is a next question from one of the speakers thank you for the information please please please my name is ISEPU from the POPSI Association of Tani Sawit from Tani Suwada yes because it is enough for cooking oil that is expensive in Tani if we look the production of the oil is from year to year and if we look the biodiesel is rising until now it is 12 million millions of liters if cooking oil is a bit only 3 million cooking oil is needed by the people not by the industry because in that area the business of Sawit is destroyed this is a dilemma for us all of that is a lesson for us especially in the government or in the business in the business itself there are fairs there are fairs for the TBS of Tani there are some permanent in 2018 but it is not used as writing writing this is what we need to discuss later this will be changed in the RPC the 0.1.2 we will discuss about this change about sustainable we have followed RANS-KSB the one in there is sustainable we will follow in the future the PSR will be launched in 2024 it will be a bomb stock it will happen because in the past the TANAM was not good with the PSR it will be a production because the government is hoping to control the COOKING OIL the biodiesel or the export the government then from the business we have criticized the business we have tried to train the TANAM for good agricultural we have tried to accept there is no no sanction this is what we hope what from the business what the business for the business we have done we follow the RANS-KSB follow the RSVU so that the business this is what we need in the future from the 2015 we have used the TANAM certification this is what we ask the question is what from the government especially what what the DMO for Indonesia because Indonesia is one of the biggest CPU for the domestic needs thank you I would like to answer or comment the question is this is starting from the question that the government in supply chain the problem starting from the community they take the margin because they take the benefit then sell it then I am a copy team in the trade hub it is worse so I am tired I have been trained to take the red card so that the quality of the coffee is good they mix it again they take the function in grading the sustainability there is also a question the question what to do it is true one of the because the price is wrong maybe Bumaria can confirm Mas Rambu can confirm one of the because the customer doesn't want to buy they ask a good question there is no place where they are full they are still waiting but the price is right if there is access there is Mas Bungi said the price is added so that there is a combination so that the government from supply chain to the end there is a place if only certification first but they don't get a good price I I just asked I am a coffee team in the trade hub later the wildlife team more parallel we will make the discussion the context if there is additional access maybe there is incentive to the income or to the farmers who have city the income is added then they don't have to be afraid but there is one more we haven't discussed if the CPO or the TBS is in the in the team then there is a question about the fatty acid that there is a question about the health that we haven't discussed but if the capacity of supply chain is very high maybe there is a benefit maybe Mr. Atos can add please Mr. Deserico I share the experience we have in the TKL we are a secret team association of the government to try to answer such questions so first we have to admit the space in the area then with the presence of the mill the game is high so the high production is a little so don't tell the other this capacity has never been educated that we have offered supply we have supplied so the supply chain the area the supply chain what is the name the province this is one question that we have to do every farmer in the supply chain must be educated so that the expansion is not happening every day because of the price they have a certain capacity to do so what is done by the TKL so this is the 8th we are in Sanggao province with the government in an agreement between the government and the Sawit company especially the mills to do the best for farmers who have reached through the STDB to do the certification especially to get DO so if we talk about the difference the sustainability price and the non-sustainability price so we try to gather the farmers who already have this high commitment get the premium price in case they get special DO especially in the area what is the area that has been verified in the area first of all the green area the STDB principle and the company have a commitment to do the best for them so first of all we get open access to get the best price so the price can be 2100 maybe by adding 100 or 2200 or 2300 we can achieve sustainability in Kabupaten that is what we are trying to do in Kabupaten it turns out we do it in Kabupaten so the LTKL is only in Angkota we try to gather the commitment there are unilever, PepsiCo there are Musimas we try to invite them we inform the government this is the area your source that already have the STDB roughly with our commitment to do the best to take care of the STDB what is your response to them so there is a dialogue between the government and the company the government move with the standard price but on the other hand the special price should be paid to them that is the experience that we have put in Kabupaten thank you share your experience how are you answering the questions because of the limited time because of the time maybe because of the discussion there are a lot of questions I don't think it's possible but after the talk show there is a microphone it's okay after the talk show is it okay? are you ready or do you want to ask about the time keeping okay because of the limited time please excuse me after the talk show thank you thank you awesome all the insight and experiences thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you ladies and gentlemen thank you


So it's a real great pleasure to start the afternoon session with Andromeda Chiodi from Warwick who will tell us about the polarization of surfaces with particles in the land. OK, thank you. And also, especially thanks to all the organizers for inviting me here. I mean, I'm really pleased to also have finally met Eugenio Calabi, so I'm very excited. So it's really, for me, a great opportunity to screw up a seminar. OK, so I would like to talk about some sort of long term project jointly with the different people. So Daniele Bartolucci, Alessandro Carlotto, who is here, Francesca de Marquis, and David Ruiz. OK, so let me start, as we saw yesterday, with the uniformization problem. So I will consider a compact surface sigma with metric g and no boundary. So a classical problem in geometry is to find somehow the best possible metric on the surface. So for example, whether you can deform the metric so that you get constant Gaussian curvature. OK, so due to the uniformization theorem, this is the case. And the sign of the curvature depends on the topology of sigma. So if g stands for the genus, for genus 0, you can get positive curvature. For genus equal to 1, 0 curvature. And for genus greater than 1, negative curvature. So this is an if and only if. And this is somehow how far I can keep up with Donaldson's talk. So I will stick to two dimensions. And I will consider this problem, which is kind of, sorry? Real dimensions. Real dimensions, too. Yeah, it's really, OK, I'll do my best anyway. So I consider a problem of fixing the surface and m points, p1 pm on sigma, some angles, positive angles, t1 and tm. And the question would be to deform conformally the metric to get constant Gaussian curvature on such an object, keeping somehow prescribing the conical structure at these points. So that would be my notation. So if you choose a conformal metric in normal coordinates near a given point, pI. So I call theta i the opening angle of this cone. And I call theta i, I write it as 2 pi times 1 plus alpha i. And alpha i will be greater than minus 1, so that we get positive angles, which can exceed 2 pi. So with this notation, somehow the singular structure is encoded in a divisor, which is just a collection of the singular points with the singular weights alpha i. OK, so this comes somehow to a PDE, a L'Uville equation. So in the smooth case, if you deform the metric conformally, and if you write the conformal factor conveniently as e to the 2w times g, then that's the transformation law for the Gaussian curvature. So it comes with the L'Uville equation. And kg tilde will be the new Gaussian curvature after the conformal transformation. So the problem is reduced to a PDE. And in the presence of a divisor, you get this singular version. So you simply subtract off some Dirac deltas with the weights alpha j. So I have a slightly more complicated expression for writing down the angles, but you get a cleaner equation here. And you get some Dirac deltas at the singular points. So if you take a standard cone, then you can get it just by folding a nicely piece of paper. So the Gaussian curvature will be 0 on the smooth part. While you get a Dirac delta at the tip with weight minus 2 pi times alpha. So in particular, for alpha negative, so this would be a standard cone. And for alpha positive, then you get an orbit fold with angle greater than 2 pi. All right, so there is a constraint on somehow the function to be prescribed by the Gaussian formula. So if we want the new curvature to become constant, then kg tilde has to be equal to some constant rho. And rho is assigned prescribed basically by the Gaussian formula, which you can get basically by smoothing out the singularities.  So a useful example to keep in mind is the American football. So I will actually use this several times. And the integral of the Gaussian curvature over the smooth part amounts with this notation to 4 pi 1 plus alpha. Because in the Gaussian formula, you have to compensate the curvature of the two conical singularities, each of them carrying an amount of curvature minus 2 pi alpha. So you have to add the 4 pi alpha to the smooth part. OK, actually, other values of rho can also be interesting for actually physical reasons. In fact, singularly equation, so even regular ones, appear in physical models like Tron-Simon's theory, a little weak theory, and also as a mean field equation stationary flows. So in this case, basically there is no particular constraint on the parameter rho. So for those problems, it just plays the role of a physical parameter. But for the geometric problem, there is a constraint given by the Gaussian formula. All right, so this is a problem with the variational structure. You can somehow desingularize the equation by a change of variables. So first of all, you solve for the Laplace equation equal to Dirac delta. So you get the Green's function on the surface, which has a logarithmic singularity near the point. And if you just make a change of variables, then the new equation you get somehow is more regular. So the singularities are gone.  And so I'll write down the equation, so which is a problem total equivalent to the previous one, minus delta u equal to rho h of x e to the 2u, say, minus 1. And the weight function h of x is positive and behaves like the distance from the singularities to the power 2 alpha i. So it might blow up or vanish depending on the sign of alpha. And OK, so here's the variational structure. So you can find solutions as critical points of this functional, which has the Dirac-Leh energy. So we saw this function in various fashions in these days. 2 rho, so then there is a linear term. And then a tricky term which involves a logarithm of the integral of h of x times e to the 2u. And somehow, this is the most tricky term to understand. All right, and you do it using the Moser-Tüdinger inequality. So maybe differently from Boo's talk, I mean I will read the correct constant here, so I will really care very much about it. So that's the Moser-Tüdinger inequality. So with my notation, the constant is 1 over 4 pi. So I'm putting e to the 2u. And u bar is the average. I'm sorry? I forgot the logarithm. OK, well, it doesn't matter anyway. So you cared about finiteness, but yeah. OK. And u bar is the average of the function u on the surface, which makes somehow inequality consistent. And so the constant 1 over 4 pi is sharp, because you can insert into the inequality bubble functions, which have this form. So you fix a point x on the surface, and you are basically developing a spherical metric near the point x. So when the parameter lambda tends to infinity, they become more and more concentrated. And in fact, the conformal volume converges to 4 pi times the direct delta at the point x you consider. And the metric is becoming more and more round. OK, so with this choice, both sides of the equation diverge at the same rate. All right, so but here there is a weight function, which behaves in this way. And the best constant was found by Chen and Trianov. And there is also some rated work by Chen and Yang in, say, domains of R2. So here's the best constant. So it depends on the weight alpha j in front of the singular points. OK, so let me comment on this. When alpha is negative, which means, say, when you have locally like a standard cone with opening angle less than 2 pi, h of x is a singular term. OK, so you expect a worse constant because you have a diverging weight function here. OK, but when alpha is negative, you don't get a better constant because somehow you can consider one of those bubbling functions I showed before. And you let it concentrate at a point where h of x is not vanishing. OK, so you don't see any, say, advantage from the vanishing of h at the singular points. OK, you concentrate volume elsewhere. And so you get exactly the same constant as before. OK, so that's the reason why you see that constant there. And you pick up somehow the most negative weight among all the ones you have. Because that's where you pay the most price of having a singular weight. OK, so what's the consequence of this inequality? Is that when rho is sufficiently small, then you can easily control the logarithmic term by means of the Dirichlet energy. And therefore, your functional has a global minimum. So just apply the direct methods of the calculus of variations. All right, so then there are three geometric cases. So that's the value of rho constrained by the gas-monet formula. And there are three cases. So there's a subcritical case, which is the one I described before. So you have a nice coercive function which you can minimize. OK, coercive means that it goes to infinity when you diverges in norm. Then there is a critical case when you have exactly equality. So the functional is bound below, but not coercive anymore. So this can be sort of tricky. And the supercritical case when rho exceeds that chain trion of constant. So in this case, the functional is unbounded below. And there is no hope of minimizing. So if you compare to the classical uniformization problem, the subcritical case corresponds to k less or equal to 0. And by the way, when you are on S2, and if all the weights are negative, the subcriticality is also necessary. And the classical counterparts of the critical case is actually the sphere. So of course, for the classical uniformization problem, you can solve always. But in general, the picture of the functional could be something like this. So you might have a lower bound, but you're not guaranteed to be able to minimize, because you might have some kind of asymptotes. And the supercritical case, in fact, does not have a classical counterpart. And in fact, in some cases, you cannot solve for this problem. So one example, which is well known, is the field drop. So take the sphere with only one singular point. Then there is no constant curvature metric on such an object. And in general, if you take two singularities, then the weights have to be the same. So these results, you prove basically exploiting the Möbius transformations. And it's a sort of Kazan Warner type of abstraction. And in a paper by Shannon Lee, it was shown that if all the weights are negative, and if you are in the supercritical case, then necessarily the surface has to be an American football, if you can solve. And in a paper by Remenko, the case of three singularities on S2 was studied. And he derived the necessary and sufficient conditions for existence using basically monodromy methods. So patching somehow pieces of spheres together. OK. So I said, in general, when you are in the supercritical case, there is no chance of minimizing, but still you may hope to be able to find settled points. So I would like to describe a general variational strategy to attack the problem using variational methods. And that's, say, the general strategy you use in an abstract setting. So you're given a functional on some Hilbert space with values into R, so smooth. And a classical strategy to find the critical points of a functional is to look at the structure of the sub-levels of this functional. So here's one, maybe a simple example, just x squared minus y squared in R2. And in fact, you see there is a change in topology from positive sub-levels into negative sub-levels. So the sub-level transforms from connected to disconnected. So eventually, this is a complicated proof to show that the origin actually is a settled point for this function. And the general idea is the following. So if you're given two values a and b, a less than b, if there are no critical points in between these two values, then you can use a gradient flow to deform the higher sub-level into the lower sub-level. So you never get stuck in a sense. This is called the deformation lemma. And the consequence is that if you observe a change in topology between the two sub-levels, then there should be a critical point. So I would like to apply actually this general strategy, which is more theory to this functional, showing two properties that for this specific functional, high sub-levels are topologically trivial, contractible, while low sub-levels inherit somehow topological structure from a finite dimensional CW complex, which I call sigma rho alpha, which depends on the topology of sigma and the divisor alpha. So I will tell you exactly what this object is. So the idea is to show that by the deformation lemma, if this object, which describes the topology of low sub-levels, is non-contractable, then you should get existence, because high sub-levels have trivial topology. But you should be careful in making such statements, because asymptotes can give you trouble. So this is one example in which you have an asymptote and no critical point between C minus epsilon and C plus epsilon. And still, you're not able to deform the higher sub-level, which is disconnected to the lower one. So you need some kind of compactness criterion. The problem here is that if you follow a gradient flow for this functional, that will bring it to infinity. You lose compactness. And so you need some kind of compactness criterion to be able to apply such a statement. And this is done by blow-up analysis. So let me discuss compactness of solutions of the problem. And this is done using blow-up analysis. So as people usually do in geometry, so you rescale solutions and try to get some standard profiles. So here they are simple and only of two kinds. So we have the sphere with total curvature for pi and the American football. So I already remarked that with this notation, the integral of k over the American football is 4 pi 1 plus alpha. So when alpha is integer, indeed the American football is not the only profile. So there are also some sort of wiggly versions. But that doesn't affect the quantization of the curvature. Okay. So there was a result, indeed, about blow-up of solutions for this problem. So in the smooth case, there are results from the early 90s by Beziz and Merle, Lee and Shafir, mostly. And for the singular case, the analysis has been done by Bertolucci and Tarantello about 10 years ago. So you consider a sequence, Rhoyne, which is bounded, and a sequence of solutions of this equation. Okay. Then you have an alternative. Either you have uniform boundedness of the solutions, or if there is blow-up, solutions would blow up k spheres, plus possibly American footballs at the singular points. And this concentration phenomenon leads to some quantization, because the limit curvature somehow should be given by 4k pi, so which is the total curvature of k spheres, plus the curvatures you get from the American footballs. Okay. So you will blow up at some regular points, possibly, and at some subset of the singular points. All right. So if blow-up occurs, there is a quantization of curvature. So necessarily the limit value of rho must belong to a family of elements of this form, so which you can write down as sums of this type. Okay. So there is a quantization of the limit curvature in case of blow-up. And an immediate consequence of this result, which has been also refined by Chen Lin and Zhang, okay, but I will care about the quantization mostly, is that if you avoid those critical values for the curvature, then you stay compact. Okay. So if rho doesn't belong to this set, then you have compartments of solutions, so they will stay uniformly bounded. And also, in fact, the deformation lemma holds true. Okay. So in fact, if you can pick up some difference in topology between different sub-levels, then there will be a critical point in between. So the second statement is actually non-completely trivial and relies on some entropy inequality proved by Struve at the end of the 80s. Okay. So topology of high sub-levels, I claimed that it's trivial. Okay. So how do you show it? Well, if you have compactness of solutions, then you can basically deform by gradient flow the full functional space you're working with, so which is a vector space and therefore contractible, onto some high sub-level. Okay. So you have something like this. So for the saddle function, which I showed before, so you can deform the whole plane into the interior of two hyperbolas. Okay. So you would obtain some contractible set. And therefore, being high sub-levels, the formation retracts of vector spaces, they both have trivial topology. What about low sub-levels? So let me recall the quantization property of blowing up solutions. Okay. So if you blow up at a regular point, you get an amount four pi of curvature. While if you blow up at a singular point, you get an amount four pi one plus alpha. Okay. Somehow the main tool in our analysis is that we can prove a similar result basically for arbitrary functions. Okay. So the principle is the following. So if you concentrate any finite amount of conformal volume near a regular point, then you get an amount at least four pi of curvature. While if you concentrate near a singular point, then you get an amount four pi one plus alpha of curvature. Okay. So somehow you wait the points differently. And the general principle is the following. So the total curvature which is available is rho, so dictated by the Gaussian formula. And if you keep adding volume at those regular or singular points, eventually you will exhaust all the available curvature. And you have to stick to finitely many concentration points. So that's the general principle which I will try to illustrate. Okay. So based on the principle, you can consider a waiter cardinality as follows. So you wait a regular point four pi and you wait a singular point four pi one plus alpha. Okay. Depending on the weight at that point. And then you extend this cardinality to finite set just by additivity. Okay. And the set of say admissible configurations you would expect would be somehow the unit measures supported on finite sets for which the waiter cardinality is less than rho. Okay. So you allow concentrations which do not exhaust all the possible curvature. Otherwise it would be too much. Okay. So elements in this family can be written as formal sums of direct deltas with some weights and which are called the formal body centers of the surface. So the points Xi are in Sigma and the weights Ti are positive. And you can normalize so that it becomes a unit measure. Okay. So you obtain a finite dimensional object. Okay. So what's the structure of this object? Well, it's a family of measures. So somehow the natural topology to be used should be the weak topology of distributions. Okay. So which by the way induces a metric on this object. So what's the structure of this set? Well, it's a finite dimension but it's not smooth indeed. Okay. And it's a stratified set. So union of many faults with or without boundary of different dimensions. And the problem is, okay, you can write down elements of this set, Sigma Rho Alpha in this way. Okay. So they seem to depend smoothly on parameters. But there are first of all equivalence relations because somehow different combinations of this type can represent the same element. And also there are rules dictated by the weight of cardinality. Okay. So we want that the sum of the weight of cardinalities should be less than rho. All right. So take this example. Okay. When four pi is less than four pi times the sum of alpha one and alpha two. So on the torus with two singularities which is less than rho and less than four pi two plus alpha one. Okay. So what is happening here is that you can consider these combinations and you're allowed to count one regular point. You can count two singular points. So take a combination of the two but not a regular point and a singular point. Okay. So what you get in this case is the surface you started with with a one dimensional handle. Okay. And in the case of three points, for example, if the weights are negative you can combine the three of them to obtain say a torus with some sort of sale attached at three points. Okay. So this set sigma rho alpha looks like this. So this was the case for say negative weights. For positive weights, usually you are allowed to take less points because the weight would be greater than four pi. So they're more easily forbidden in a sense. And as say a row increases and as the number of singular point increases somehow the structure of this set becomes really very complicated. So it could be a complete mess. So that's our result in terms of this set sigma rho alpha. Okay. So let me recall the set, the values of the possible blowups for the curvature. Okay. So which can be written in this way. And so that's a theory which is actually work in progress but somehow close to completion. So if a row does not belong to this say critical set lambda alpha and if sigma rho alpha. So this family of measures is not a contractible set as for example in the pictures we saw before then you can solve for the problem. Okay. The proof as I said uses most theory. Okay. And there are two assumptions here. So row shouldn't belong to this set lambda alpha. So that's used to apply the formation lemma. Okay. And as I said, high energy sub levels are contractible while I claim that the structure of low sub levels has to do with this family of measures sigma rho alpha. Okay. So I would like to mostly explain that in the rest of the talk. And since we are assuming that this set is not contractible then okay we apply most theory as I said. All right. So some comparison to some more recent results. So using this approach, we were able to prove this result in some special cases. So still with Alessandro Carlotto in the case of negative alphas, in the case of positive weights and positive genus with Daniela Bartolucci and Francesca de Marquis and for say positive alphas, but low values of the total curvature in two other joint papers with the roots and Bartolucci. And none of these results actually dealt with the weights with different signs with the exception of the result by Aromenco who studied three singularities on the sphere. Okay. And there is indeed a program by two people in Taiwan, Chen and Lin, to compute the degree of the equation. So they have a paper appeared in 2010 for the case of integer weights and this was actually done for the regular case so with no singularities in 2003, still by time. And I would like to say that in general, you would expect to get stronger results using most theory because most theory can detect solutions even when the total ratio of the degree of the equation is zero. Okay. So you would expect to get more general results with this approach. So in the rest of the talk, I would like to persuade you that somehow considering this weird object, sigma or alpha, is actually maybe the right thing to do for when studying this problem. And I will give you a couple of reasons. So we showed that the non-contractability of this set of measures is sufficient to obtain solutions of the equation. And you may wonder whether it might be also possibly necessary. Okay. So which is not known. However, there is an interesting result by Alessandro Carlotto, which is the following. So if you fix any surface with a metric G and some points P1PM, then you can find weights for which the problem is not solvable. Okay. So previous non-contractability results, which are the ones I mentioned before, were only available on S2 with at most three singularities. So mostly using the Möbius action. But here there is no restriction either on the genus or on the conformal class. So these are the first non-existent results in for say positive genus. And so they're inspired, in fact by this characterization. Okay. So in these cases, in fact this set of measures would be contractible and you would sort of tend to believe that there might be non-existence. Okay. And so in this paper, he also gives necessary and sufficient conditions for the non-contractability of this set of measures when all the weights are negative. Okay. So in general, it's hard to find optimal conditions for the topological characterization of this set. And especially on skiers. So on Torai you can play somehow with the first fundamental group, say. And I mean, it would be really nice to get help from some topologists to be able to find clean conditions for the non-contractability of this set. So this is another persuasion attempt. So to try to convince you that this set is natural. So as I said, you can write elements of sigma, alpha in this form. So as weighted sums of direct deltas. Okay, which are normalized. And I justified this set looking basically at the quantization results for blowing up solutions. Okay. So you know that a blow up of solution at a regular or singular point carries a fixed amount of curvature. While here, we're putting some real weights in front of these direct deltas. So I'm taking the weights to be arbitrary. But in fact, I'm not claiming these holds for solutions, but only for functions with low energy in a sense. Okay. So there should be more flexibility. And in fact, it is possible to find some test functions which are parametrized on this element which somehow destroy well the low energy sub levels. Okay. So they're parametrized on this family of elements. And if you consider the formal, sorry, the conformal volume associated to such test functions, okay. So this converge weekly to the elements in the space of measures you started with. And also they have the property that the energy goes to minus infinity uniformly for the choice of sigma in this set, sigma or alpha. Okay, so what you can do is to embed copies of this topological space into arbitrarily low sub levels of the function. Okay. So I would like to see also somehow a sort of converse characterization. So I saw that you can pass from these family of measures into low sub levels. And I would like to show actually the opposite characterization in a sense. Okay. And so this is done. So I saw that I can embed copies of this object into low sub levels. Okay. I would like to somehow give an opposite characterization. And I would like to show the following that for energy sufficiently low, okay, then the conformal volume has to look like one of these objects. So it has to be close to an element of sigma or alpha in the distributional sense. Okay. So that would be a sort of optimal characterization of low energy levels. Okay. And to do this, the general philosophy is that say a spreading of conformal volume of the surface gives indeed a better constant in the weighted MOSF2-inger inequality. Okay. And then you proceed in this way. Okay. So you use a contradiction argument as follows. Suppose you have spreading of conformal volume. I claim that you get a better constant in the MOSF2-inger inequality. And if you get a better constant, it means that you can more easily control the logarithmic term in the functional. So the tricky term. Okay. So that will give you a lower bound on the energy functional. Okay. So you can somehow use this chain of implications in the opposite way. So suppose that the energy is low. So namely that the lower bound on the functional fails. That means that you don't get a better constant in the MOSF2-inger inequality. Which means that you cannot have spreading on volume. So this will favor concentration of conformal volume. Okay. So I would like to give an idea of how this works more precisely. And this is done actually using some improved MOSF2-inger inequalities. Okay. So this is the MOSF2-inger inequality in the classical case. So when there is no weight and the constant you get is one over four pi. Okay. So this holds for your arbitrary. But the idea is that if you satisfy some extra assumptions then you can maybe get a better value here. Okay. So here are a couple of very well known examples. So one by Moser back to 1973. So if you consider even functions on the sphere with the round metric, then in fact you can push the constant from one over four pi to one over eight pi. Okay. And another well known example is due to a band still on the standard sphere. So you can push the constant up to almost one over eight pi provided the function u is balanced. So what does this mean? That if you embed the sphere into a tree and if you look at the conformal volume given by u so which is e to the two u. Okay. Then the center of mass has to be at the origin of S3. Okay. So this is another case in which you can push down the constant here. All right. So actually this theorem of a band relies on say a more general principle which was exploited by Chen and Li basically by localizing the Moser to the Injuring Equality. So that's the statement. So if you are able to spread the conformal volume over a certain number of subsets of the surface. Okay. So if you find say L plus one sets each of them containing a finite portion of the total volume and assuming that they have positive mutual distance. Okay. So then you can push down the constant from one over four pi to one over four pi times the number of regions you're considering here. Okay. Up to an epsilon. All right. So what is the consequence? Is that somehow spreading of conformal volume gives you a better constant here. All right. Which means a lower bound on the functional. On the contrary. So if the energy is low then you should expect concentration of volume. So suppose that the constant rho so the total curvature is less than four k plus one pi. Okay. So then this lemma tells you the following. So give me an epsilon and an R. So I can find an energy sufficiently low so that almost all the volume up to an epsilon will be contained in k balls centered of radius R centered at some points of the surface. So this means that if rho is less than this number here so four k plus one pi and if the energy is sufficiently low then the conformal volume has to concentrate near at most k points of the surface. So it will look like a sum of direct deltas. Okay. From the point of view of measures say in the distributional sense. Right. So using a covering argument so this is kind of easy to explain heuristically. So if the volume cannot be spread into say k plus one regions then it should be concentrated near at most k regions. Okay. So this I hope this sounds kind of reasonable. All right. So what is the roles of the role of singularities which I haven't treated so far. Okay. So let me recall the chain trial of inequality in the presence of a weight. So the constant you get is the minimum between four pi and four pi one plus alpha j. So in a first paper with the callot we extended the channel ease inequality to the case of negative weights still using some kind of localization argument. Okay. But for positive weights so you might hope that still if the volume measure is concentrated near the singular points then you might have some might see some effects of the vanishing of the weights near these points. Okay. So I recall that h of x behaves like the distance from the singularity to the power to alpha. Okay. So you might expect that if the volume gets close to there so e to the two u then you might see some effects. Okay. But you should be careful in such a statement because you might still concentrate a bubble arbitrary close to a singular point and have the energy go to minus infinity. Okay. So you would need to pick up some sort of more refined or microscopic structure of the conformal volume near these singular points. Okay. So you want to be more careful. So you might expect that something like a center of mass condition could be the right one. So that's somehow a nice guess but it's actually more subtle than just that. And here is actually one version of the improved inequality using sometimes kind of angular moments on condition on the volume measure. So we proved this proposition. So to simplify things, consider just the unit disk over two. Okay. With one singularity at the origin. So just the simplest possible case. Okay. With positive weight. So the proposition is the following. So suppose the weight is positive and fix any positive epsilon. Okay. Suppose the conformal volume satisfies this vanishing moment condition. Okay. So you look at the conformal volume times x to the two alpha which plays the role of H of x. And you assume that if you multiply it by say some Fourier mode. Okay. This product is vanishing in C for J running from one to K. Okay. So the center of mass condition would be just J equal to one. Okay. So suppose you're given this extra conditions. Okay. So then you can actually improve the constant from Chen and Li's which is one over four pi to almost the American football one. Okay. So you can get very close actually to four pi one plus alpha. So precisely you get one over four pi times the minimum between one plus alpha and one plus K. So for K large enough, you get in fact the American football constant. So you can think of this as a sort of non-linear Fourier improvement. So if this were a linear problem, so if you had say the two normal view here and the Dirichlet norm here, then you would just use Fourier. Okay. But this is a sort of non-linear version. So I think I really no time to say anything about the proof of this result. So which takes mostly a lot of pain. And yeah, I like to continue. So some comments. So the main new feature of this inequality is that in fact these are scaling invariant assumptions on the conformal volume. Okay. So somehow if you take your conformal factor and you dilate it, say close to the origin. So it might look very much like a Dirac delta. So it's very much concentrated microscopically. But still you might get an improvement in the inequality here. Okay. And so the scaling invariance is the main new feature of the inequality because you might allow, say, any rate of concentration. And the result is kind of sharp. Okay. So you find counter examples if in fact one of these conditions fails. And this also recovers some improved versions of the inequality, which were given by McCowen back to the 80s and Du Bois de Vantagantello. So McCowen was creating the case of functions with zk symmetry. So some discrete symmetry group. And they were treating the case of radial functions. Okay. So adding symmetry somehow helps to get bounce from below on this kind of functionals, as usual. And so the main comment is that in fact those assumptions are just say two k constraints. Okay. I'm assuming the vanishing of say k numbers in C. Okay. So these are two real, two k real constraints. Okay. So, I mean the improved inequality would be satisfied in the function space in a set of finite co-dimension. And the sets of finite co-dimensions you can intersect using transversality arguments or say degree theory. Okay. So you can apply the min-max machinery once you have attained such a condition. Okay. So if you require symmetry, of course, everything is gone because it's just infinitely many constraints. But these are finally many constraints. Okay. And you can actually apply min-max theory to prove existence of critical points. And let me say that in general, so I just treated one example, but in general, so if you really want to see the structure of the full set of measures, sigma or alpha, you might need to improve the constant even more. So you have some how to interpolate between microscopic and macroscopic structures, in a sense, regimes. Okay. So I would like to conclude with some open problems. So as I said, it would be very nice to have a clean algebraic condition in terms of the divisor and of the genus of the surface to guarantee actually the non-triviality of this set of measures, okay, which bioactive relates to existence. And as well, it would be nice to find somehow general non-existent results. Okay, so ideally, I mean, it would be great to prove that maybe this might be a necessary and sufficient condition. But maybe the non-existence result would be even harder, I guess. And in fact, in many situations, the parameter rho, so which is the integral of the curvature of the smooth part, might actually belong to the critical set lambda alpha. So we were avoiding those values for compactness reasons. And you might see that this set belongs to lambda alpha just by the Gauss-Bohne formula, okay. And in this case, so if you still want to attack the problem variationally, you might need some more refined blow-up analysis with some sort of refined geometric information on the blown-up manifold. So like a sort of positive mass theorem, for example. And in a spectacular work by Lin and Wang, so the case of flat-tor-i with one singularity with weight equal to one is treated, okay. So what you're doing here, so you're considering the, say, a flat-torus, okay, not necessarily the square-torus, and you're concentrating somehow all the positive curvature on the smooth part while the negative curvature will be concentrated at the singular point, okay. So what they prove, and this is really spectacular, is that you have existence even only if the Green's function of the Laplacian of the torus, so depending on the geometry of the flat-torus, has five or three critical points. So if you have five critical points, you get existence, otherwise, nonexistence. And they use a really deep theory of elliptic functions, and I mean, it's a theorem which I find really spectacular and astonishing. So I mean, it would be also very nice to somehow interpret this theorem, so to find a good explanation. And well, as I said, these equations also rise from physics, and the scalar case would arise from abelian models, and when you have non-abelian models, then you're led to some coupled systems of the equation, so-called Todda systems, which also have a geometric interpretation because they describe holomorphic curves in CPN. And in general, this system is actually quite challenging, so it would be nice to find generally existence results, so in this case. All right, so I stop here, and thank you for the attention. And also one more, say, happy birthday to Eugenio. So what was the wiggly American football on page 14? Oh yeah, so you can get it, I cannot draw it, in fact, but I can write it as a conformal deformation of the Euclidean metric, okay? So the standard bubble would be something like this, so you have one positive parameter, lambda, and you consider the logarithm of lambda divided by, so in this notation, I guess it's, I might scrub the exponents, but it's something like this, mod x squared, and maybe everything is squared. Okay, so this would be you. The American football metric would have a one plus alpha here and a one plus alpha here, okay? So it's a nice radial function. In fact, when alpha is integer, so this depends basically on only one parameter, which is lambda. When alpha is integer, you somehow get a different polynomial of x here, I can draw a picture of the solution. So this would somehow be like solitons, okay? And when alpha is integer, then you would get sort of two peaks, okay? When alpha is equal to one, you get two peaks, and when alpha is integer, you get, say, K peaks, which are distributed along the vertices of a polygon. Okay, and this somehow matches very well with our condition, so on, on vanishing moment. So in a sense, if you have enough symmetry, then somehow this condition is automatically satisfied, in a sense, and somehow if you, if you fail to get zero kth momentum, then you start plugging one of those functions to show that you do not get improved inequality. So that's somehow why I believe this improvement is almost optimal. But you don't have a picture of the solution? No, no, unfortunately not, yeah. But I carry the same total curvature, so, yeah. Do you think there could be a rigid approach? Yeah, in fact, I discussed this with Peter Topping, and as I said, okay, there are cases in which you shouldn't expect existence of constant curvature metrics, but he would suspect that there should be possibly always a richly soliton, with some maybe nice, say, asymptotic conditions in their singularity. And if that is the case, maybe it might be a way to prove a non-existence of constant curvature, maybe. Yeah, but it's a very interesting question, yeah. By the way, I wanna talk back in, someone correctly, just say North America. North America. Yeah. North America. North America. North America.