Distinguished delegates, ladies and gentlemen, thank you very much for coming back in large numbers and on time. I'm particularly glad because this is one of the most important issues we're going to discuss in our four days together. We just had a fascinating lunch and conversation with our panelists here, and I certainly learned a lot. And above all else, I came away from our lunch today with a much greater sense of urgency than perhaps I've had or should have had in the past. And I think you will hear from the distinguished esteemed minister from France and our colleagues, the ambassador of Fiji here in Geneva and Mrs. Kiyama representing a major organization. You will hear from them as experts why we should be concerned and why we should be doing more, much more, even in IOM, which is just one of many players. So I will keep my remarks very brief because we only have something less than an hour, and you want to hear from these speakers, not from me. But I just wanted to underline the urgency of this. This continues to be a major area of IOM's agenda. We've been writing and reading and researching on the subject for about 20 years. We got started a bit late, but we're with it now. And I want to say that how much we need to try to integrate the thinking that you hear today into the global compact for migration because it's going to be a major driver of forced migration and irregular migration for some time to come. I'm extremely sorry that the convention executive secretary, Mrs. Patricia Espinosa, could not join us today. Something came up at the very last minute, and her statement will, however, be made available to all of you through our secretariat. So let me then say that let me just start by introducing the panel. We're very honored to have back, I think, it's probably our second or third time to press the minister into service, but we're extremely grateful to his excellency, Mr. Nicholas Ullo, who is the minister in the new government of President Macron for the ecological and inclusive transition of France. Great pleasure to introduce and have the honor to welcome you, sir, back to our council session. Over the past decade through the Nicholas Ullo Foundation, the minister has lobbied and received the unanimous approval of the charter for the environment through the challenge of the Earth. He proposed an ecological pact to the French presidential election candidates and urged them to put environment and climate concerns at the very heart of public policy. He also helped organize the what's called the Grinnell de l'Enfayeur-en-Am is a conference that brings together government, local authorities, trade unions, business, voluntary sectors to draw up practical green policies. So we're also proud that in his former capacity as envoy of the president of the republic in preparation of the Paris Agreement, his excellency, Minister Ullo, endorsed our Atlas of Environmental Migration, which is a great honor for us. I also want to introduce on my left someone well known to you who are here in Geneva, her excellency, Mrs. Najat Shamim Khan, the ambassador and chief negotiator for the 23rd Climate Conference of Parties, COP 23, under the Fiji presidency, ambassador and permanent representative of Fiji to the United Nations here in Geneva. Ambassador Khan has been with us for a while and now is going to be even more in view here in Geneva as the chief negotiator for the COP 23 presidency. She will oversee the formal negotiating process on behalf of the presidency of Fiji. Among other highlights in her impressive professional career, she holds the honor of being the first woman to be appointed a judge in Fiji. She served as a judge for a decade and later started her own consultancy and was appointed to her current ambassador or post by the prime minister in 2014, how time flies. Actually, it's an honor to have you in the 108th IOM Council Session. I want to introduce also Miss Keiko Kiyama, co-president of Japan Emergency NGO, acronym JEN, the executive director of Japan Platform Japan. She has been serving for refugees, working with refugees, internally displaced persons and survivors of natural disasters since she joined JEN in 1994, two decades ago. And from 94 to 2000, she worked as the regional representative of JEN's program for former Yugoslav countries where she and her teams supported self-reliance of refugees and IDPs through hundreds of projects in huge varieties of sectors. Miss Kiyama, it's an honor and pleasure to welcome you here today. So let me, first of all then, make just a few more comments, namely that contemporary migration policy and practice is not possible to shape it in the way we did 10 years ago or even five years ago.  I gave you my one personal example. When I first went to Africa, my first diplomatic assignment in 1963, 55 years ago, we flew over Lake Chad. I'd been asleep and I looked out and I thought we were over the ocean, so big. I came back in 1998, I guess it was, as ambassador to Nigeria. I did a fly low, fly slow trip over Lake Chad and permanent dwellings were being built in the bed of the lake. It's one example of what happens in a period of 25 years. Secondly is migration is inevitable, it's necessary, and it's even desirable if we manage it well and respect human rights, including helping people to prepare for the impact of climate change on their lives through a positive adaptation to be used later with mitigation efforts. And I do believe, third point, that the global compact that's gonna be negotiated next year is a historical opportunity to make sure that global migration governance efforts take into account, respond to, and respect the importance of environmental and climate change drivers of migration. So let me now, having welcomed our panelists, let me start by once again giving the floor to His Excellency, Mr. Nicolas Hulot, the Minister of Ecological and Solidary Transition of France. So you have the floor. Thank you. I suggest you take your headset because my English is not very good and it will be more comfortable for everybody. Monsieur le Direct. Dear Director-General, thank you very much for having welcomed me here. Thank you very much for all of these warm introductory words that you have just addressed. Thank you very much and also dear Executive Secretary, dear Ambassadors, dear Vice Chair, your Excellencies, dear friends. First of all, I would like to thank you, Mr. William Lacey Swing, for your invitation. I would also like to take this opportunity to underline the exceptional work that you have carried out at the helm of this organization. This organization is absolutely fundamental, this international organization for migration. Geologists have informed us very recently that we would have brutally gone from one geological era to another geological era. They have informed us that we are now in the Anthropocemic period, which means that we have entered into the era of humanity without even knowing this, which means that humanity has become its own factor, its own determinant for our future. And I am asking myself this question in front of you today, whether we, if this means that we are our own factor of change, is this good news or bad news? This is the question that I'm asking myself because a French philosopher used to say that I deplored that the fate of humanity was in such bad hands as his. And of course, we must prove him wrong because personally, I am very pleased that we still have our future in our hands. It is still up to us to decide our destiny, but everybody here understands that if we no longer control of this phenomena, we will no longer be able to control our own fate and we will go into a very decisive era. We will enter into this new era where the, where there was going to be a degradation of all sorts of phenomena that we can observe now. Therefore, I would say that if there is a skill that we should take on as soon as possible at the beginning of this 21st century, it is lucidity. We really need to look at today's realities, to face these realities straight, eye to eye. And I understand that these realities are sometimes very terrifying and very complex, but we should not to discard them and put them to one side or forget about them because personally, the one thing that I'm very afraid about is to let the future decide for us, our destiny. Sometimes we put things to one side saying that we are too busy, but this is extremely dangerous. And I am just mentioning all this because the subject that you are dealing with here in this organization is one of these subjects. There are certain experts here around the room, but often people dissimulate the severity of these topics and issues that you deal with here at the IOM. However, this topic that we are dealing with today is absolutely essential. We must carry out our duty, which is the duty of humanity. This topic of how to address migration and climate change in the global compact is not a future topic. It is a topic that is currently affecting hundreds of thousands of men, women, and children around the world. These are men, women, and children that are already living in situations of vulnerability. And I have often mentioned this. The climate change crisis is an excess injustice because it adds suffering to suffering and that it affects mostly the most vulnerable populations already. And you know this here, of course, already, but many people outside of this August, but he do not know about this. As you know, a climate change of phenomenons or desertification, natural disasters are already displacing twice as many people as conflicts. And we know of all the tragic consequences of these displacements. With your permission, please allow me to reiterate here our devotion to human rights of all migrants, regardless of their status. We also commit ourselves to the reinforcement of absolutely necessary cooperation between countries of origin, transit, and destination.  It is neighboring countries of affected zones that have been affected by climate change are welcoming with very few means of the first displaced migrants because of a climate related event. They are doing this out of humanity spontaneously, but we also have this duty. We have a duty of solidarity. The linkages that exist between migration, climate change, and environmental degradation have been proven. And at the same time, are very complex. They have been proven already. There are territories that are close to the coastline where we can see that desertification can be threatened in the long term and even in the short term. Extreme weather events, which this morning we have been reminded about, the WMO confirmed this morning that there are more and more extreme weather events. And they lead to displacements that are sometimes temporary, but more and more definitive displacements. Climate change also affects, in the long term, entire swaths of territories that increase poverty and misery. All migration, of course, are not because of a result of climate change. Often there are many different factors. However, everybody recognizes that climate change is one of the root causes for migratory flows. And once again, it adds injustice to injustice. We have, in fact, entered a new climate era that forces us to look at reality, to face reality and to not give up, but to find solutions. This is why it is absolutely essential to take action. The Paris Agreement is the first response and is the most important one. In this context, I would like to commend the chairmanship of Fiji at COP 23. The linkages between migration and climate change are also very complex. On one hand, climate change is not the only cause for migratory flows. There's also the degradation of land and ecosystems. However, we can see men and women's impact here directly, deforestation, pollution, overfishing, irrigation systems, and agricultural practices that are completely unsuitable. This all contributes to problems linked to migration. Now, what can we do to help fragile states that accumulate all sorts of different handicaps that are, for example, related to nature, economic, environmental, and social handicaps? What must be done? We can not deny another type of reality. The first victims of global warming, as I just mentioned, are the poorest populations, the most disadvantaged, but also paradoxically, the people that have less contributed to climate change and degradation. And this is why I've always thought that this was a major injustice, because these men, women, and children are subjected to the consequences of a phenomenon that is itself the result of a mode of development that they have not benefited from, and a phenomenon that they have not provoked. And they are going to be the biggest victims of this. And I am stating this here because history is never amnesic, and we always have to bear in mind these realities. This is really the heart of climate justice, which has been enshrined in the preamble of the Paris Agreement. We can take action in many different ways. First of all, climate issues must be integrated to all the work that is carried out in multilateral international organizations that have to do with human mobility challenges. The development of the global compact for safe, orderly, and regular migration, which results from the declaration that was made in New York on the 19th of September, 2016, represents an opportunity that we must take up. Thanks to its unique expertise, the IOM is providing very precious support. And here, once again, I would like to commend all of your work and efforts undertaken towards development of this compact. France will continue to participate actively, especially in a few days' time in Puerto Vallarta, and then, of course, during the entire phase of negotiation. France will contribute and will continue to re-affirm the respect for human rights of all migrants regardless of their status. We will also look at the need for reinforcement of cooperation between countries of origin, transit, and destination. Above and beyond this compact, we must take this opportunity to highlight the linkages that exist between climate change and migration. We also, of course, need to improve data and knowledge related to climate-induced migration and find as quickly as possible sustainable, concrete solutions for displaced people or at risk of being displaced. This issue of the protection of these people is absolutely essential. This is the raison d'être of the work of the platform on displacement linked to natural disasters, which was an outcome of the Nansen Initiative and which facilitated in 2015 the adoption of an agenda for the protection of displaced persons in the context of natural disasters and climate change. For all of these reasons, France, which has been a member of the steering committee, has supported actively this platform and has contributed to the projects of the IOM. At the same time, we need to work on prediction of environmental changes to be able to help societies avoid the worst and take the best decisions. Resilience strengthening must be an absolutely essential a key of any public policy to ensure the stability of human communities. The prevention of risks is also paramount. There are many different efforts that have been undertaken in this area. France has been carrying forward with other bilateral partners, as you know, but also with the WMO and the World Bank, an initiative that I commend here, which is the Initiative Cruise, which aims at improving preparedness and prevention for extreme climate events. And once again, I would like to highlight this terrible example, which is that recently, when there was a series of hurricanes in the Caribbean, when the entire world was observing on their screens these tragic events in certain areas in Haiti, some people were not even informed of the approach of these extreme weather events. We must work upstream through the implementation of the Paris Agreement, of course, but also by respecting the pledges that were made to benefit southern countries, also the improvement of agricultural practices of the preservation of land and ecosystems and putting an end as well to deforestation and to and start reforestation. Concrete answers are necessary and this will allow us to decrease the pressure on natural resources, especially in the most fragile areas. We must also support the development of strategies that place ecosystems at the heart of development. This presupposes everybody's mobilization. For the very first time, indeed, in the implementation of the Rio Convention, a decision was adopted on the topic of migration during the last to COP 13 on the notification which took place in China in Ordo last September. We must therefore foster all synergies that exist between different organizations on this subject and continue to mobilize all of our energy to protect our planet and, of course, to protect our humanity. Now to conclude, this is why the president of France, Mr. Emmanuel Macron, decided to organize on the 12th of December in a few days, a summit in Paris to be held in conjunction with the UN and the World Bank to be able to mobilize all actors that are fighting against climate change but also to help find solutions for adaptation and mitigation. France put forward at the General Assembly the United Nations in September, a global compact for the environment which aims to align all the great principles of international environmental law. This program, as you can imagine, is very extensive but the good news is that there is no fatality to all of these migratory floors that are more and more dramatic and tragic. We have all the means at our disposal if we choose to use them and work together. Thank you very much for your attention. I know that you would want me on your behalf and as well as myself to thank the minister for a very brilliant presentation of the urgency of the matter. That's something that has been too easy to ignore in recent times. He's put us before the reality that among other things, climate change is becoming, is already one of the great drivers of forced migration. He outlined several of the very, what I would call cruel ironies. Number one is that it's neighboring states or receiving states often have to carry much of the weight of the results of climate change. Secondly, it exacerbates people or poverty of people who are already in great need and then it affects the most vulnerable and often the most innocent who've done nothing to contribute to climate change. So I think it's very, very, very important for us to keep that all closely in mind. That many of the priorities that we have now will have to be changed if we're going to succeed in this. And I think he gave me a perfect transition to our next speaker by praising Fiji for its presidency of COP 23. So let me without further ado, who I've already introduced, but ask our Excellency Ambassador Khan, Madam, you have the floor, please. Thank you. Thank you very much indeed, Director General. And may I also commend the IOM for organizing this important high-level event. It is an event which allows us to discuss the synergies between climate change, the environment and migration. This is a very, very important subject indeed for us to focus on. May I also congratulate Mr. Ullo, his Excellency, on the important conversation that he's just had with us about the relationship between climate change and climate justice. And really at the crux of that is something that I would also like to talk about. And this is the importance of putting people first in relation to any solutions that we have relating to climate change, the environment and migration. May I say in relation to persons who are displaced as a result of the environment, as a result of climate change, that it is very clear that when they are displaced, that existing vulnerabilities become exacerbated and that when you move people from, and we know this very well in the Pacific, when you move people from the coastline where they're used to being fishing people onto higher ground where they suddenly expected to be farming people, that this already creates great disruption for their way of life and the way of life for the entire community. And it also exposes those who are already vulnerable to acts, for instance, of harassment, of violence and of lack of access to medical services, for instance, to further vulnerability. So we are very aware, particularly coming from the Pacific, of the very negative effects of climate change displacement if we are not careful to adopt approaches which we've heard could be well described as an approach of climate justice. So this is a very good way to start. May I say also that here in Geneva, we have seen important initiatives which show that any attempt to deal with climate change and displacement and migration should be one that reflects coherence in the various agencies which deal with such displacement. And we saw that very clearly in the adoption in the 35th session of the Human Rights Council of a resolution on human rights and climate change which recognized these linkages. So the linkages between human rights and the number of other policy areas which included the effect of displacement on loss and damage, on gender, and on the rights of persons who are indigenous. Following on from that resolution, we had the very useful intersessional panel which was organized on the 6th of October here in Geneva. It was a very good first step to understand those linkages and also it provided an opportunity for an initial exchange of breast practices. We are also looking forward to the OHCHR report next year on the gaps in human rights protections in the context of climate related migration and displacement. It was very timely that this year Fiji shared the chairmanship of the Oceans Conference in New York which looked at the importance of oceans and the environment and was instrumental in fact for the call for action which was adopted by the parties in New York as a result of the Oceans Conference. And that conference also drew very clear links between the oceans and people and sustainability and economic development, something that is very, very important especially for the Pacific. In addition to that of course, Fiji had the presidency of COP23. And really I want to take this opportunity to talk about some of the outcomes of COP23 which had people at their center. And as I've said before, it is really important that when we look at the entire area and the entire subject of how we deal with climate change and the effect of climate change in society and on social institutions that we put people first. So this was the first time that a small island developing state had the presidency of a COP. And it was natural that we would as a result of that presidency want to see a people centered COP. And we've now begun to call COP23 the people's COP because we saw a number of outcomes at COP23 that reflected people and the wishes of people as well as the involvement of people because you simply cannot impose ideas on people. It's very important that people participate in the processes of deciding what is best for them. And so quite unexpectedly, this year at this COP we had a result on agriculture. For those of you who are familiar with climate change and its processes, you will know that it's taken some time to get there. It's been a struggle, but for the first time agriculture was recognized as one which required priority. A work program called the Coronavial Work Program named after our agricultural research station in Fiji was launched and a consensus was reached in agriculture which is not only going to look at the emissions of the agricultural industry but is also going to look at small farmers so important in countries which are developing small farmers and their role in reducing emissions. So a very good result on agriculture. The gender action plan. It took 12 years of socialization for there to be a gender action plan. And at last at COP23, the gender action plan was launched which looks at the integration of women not only in national action plans and national strategies but in international climate change governance. Very important because sometimes when you look around the room at UNFCCC processes, you wonder whether women have become an endangered species. We had a result on long-term finance, also unexpected. We had the first ever open dialogue between states and observers. We had, and I'll pause here for a video, for the first time we had a child opening the high-level segment and really I mean for all of the extremely intelligent, knowledgeable and well qualified people in the room including with respect President Macron, this little boy really stole the show. So if I can pause there just to show a short excerpt of Timothée's speech to the high-level segment at COP. 2017 has really been the year underlining the relationship. 2016, we were hit by one of the strongest cyclone ever struck Fiji, the strongest in the southern hemisphere. My home, my school, as as a food, water, money was totally destroyed. My life was in chaos. I asked myself, why is it happening? Why is the cyclone getting stronger? What am I going to do? I walked along one supplantation searching for what to take home for dinner. Fishing the river for fissure prawns. Walked amongst once a dense forest only to be filled with despair and frustration. My once-beautiful village I once called home is now a barren and empty wasteland. Months that follow, summer temperatures continue rising, production of soil moisture turning our land into a tile. Tree is not bearing fruits and ages was seasoned. Water bodies getting dry each day. Fishes, streams, prawns, eels, dead on lakes and river. I feel the pain, the remorse, the anger, the loss, the terror, the insecurity, worthless and useless as I watched everything around me turning from green to yellow then brown. I stress sign that we are dying. That's indicated. Thank you very much indeed. And that was Timor the talking at the high level segment as the very first speaker. And I understand that he has been invited by President Macron to also speak at the Paris Summit. Also an important outcome at COP23 was a work program on education under the Paris Agreement and a workshop on education is going to be held in May 2018. Also launched at COP23, the Suva Expert Panel on Loss and Damage to look at the sharing of best practices not only in relation to what's happened but also to discuss support for loss and damage. The Fiji Clearinghouse for Risk Transfer, a recognition that insurance has an important role for dealing with loss and damage and five high level events aimed at coherence in relation to climate policy. We have for the first time the recognition in a COP decision that the Adaptation Fund shall serve the Paris Agreement. And in addition to that, considerable input into the Adaptation Fund by developed countries. But of course, COP23 was intended fundamentally to move progress towards the Paris Agreement work program and to introduce the design of the Talanoa Dialogue. What we could now call the Talanoa Dialogue which was of course originally called the Facilitative Dialogue. And it is in relation to the Talanoa Dialogue that I have to say that there was a strong degree of support from observers as well as parties and that as a result of that support and as a result of the discussion around expectations for the Talanoa Dialogue, we will have a degree of observer input throughout 2018 in a process which is guided by the methodology of Talanoa, a form of dialogue in the Pacific which is inclusive, participatory and non-judgmental. And the aim of the Talanoa Dialogue is to enhance ambition in relation to the informing of the next round of NDCs. So again, a very important process. We announced the design at COP23 and of course the process of Talanoa will be unrolled during 2018. I do want to say in addition to the outcomes of COP23 that the Pacific is going to see an unprecedented level of displacement in the coming years and that is because of rising sea levels. Fiji has already offered its own land and its own country to some of the countries of the Pacific specifically Tuvalu and Kiribati. But in order for us to ensure that that is a humane and dignified process, it's very important that we adopt a regional solution to ensure that this is a process which is consensual, which is dignified and as I've said before, based on human rights. And it is very important that Fiji, whose constitution includes a right to a clean environment, very important that in relation to any solution that we have for the Pacific, that we have one that is inclusive and participatory and one that reflects the Pacific spirit of welcome and bullet. And I'll stop there, Director General, thank you. Madam Ambassador, as with the minister, you've given us exactly what we had hoped for and I thank you for that. I'm not gonna make any effort now further to summarize because we're run out of time. I have two more speakers and I know that the minister needs to leave promptly at four. I wanna make sure that it gets you out on time as much as we'd like to keep you. And if we don't have time for a lot of statements or questions, we will ask that you share these statements written form later and some of the remarks you wanna make on this could be even be included in the next session of the general debate. So let me move immediately to the video that we have with Eric Solheim, the head of the United Nations Environmental Program in Nairobi. 2017 has really been the year underlining the relationship between natural catastrophes and environment on one side and migration and conflicts on the other side. We have had the horrible cyclones in the Caribbean as well as in the United States. We have seen the drought in Somalia, landslides in Sierra Leone and great flooding in Bangladesh and India. So many people have been suffering from the enormous impact on natural catastrophes. That's why we need to make the link between what we are doing in the International Organization for Migration and what we are doing in UN environment. UN environment just one year ago joined the UN Global Migration Group. We are very encouraged by the open process you have put in place, the inclusion of environment and climate issues in the broad thinking around migration and conflicts. And the preparations for the global compact for safe, orderly and regular migration, which I hope we will be able to finalize in 2018. This work highlights the role of the environment in either creating stable and prosperous societies or driving migration and displacement. Just as it demonstrates the potential impact on the environment of failing to adapt to climate change or reduce the risk of disaster in the first place. Take the quarter of a million people in the Caribbean affected by the hurricanes Irma and Maria, which was so devastating this year. In Puerto Rico alone, nearly 80,000 people were evacuated. Half the power grid remains offline and for vulnerable people like Jorge Lopez Ortiz in Puerto Rico, that means being a virtual prisoner. It's impossible for her to cook and too dangerous to go outside after dark. Her only lifeline is a rope passed through security bars to aid groups delivering food and water. So the media headlines have gone, but the problems have not. These are the kind of far-reaching consequences we need to remember than taking decisions on land use, on energy, on infrastructure and in so many other areas. Decision that we are looked into for decades, what we decide to do in 2017, have implications for maybe 50 years to come. And that have the potential to create either virtues or vicious cycles. That's why it's so important that the work of the global compact should be linked to the work to tackle climate change, to protect biodiversity, to fight poverty, health destruction, to fight for equality, security and decent work. I very much hope this will be reflected in the discussions today and I really look forward to hearing the outcome. Let's work together to make the link between environment and migration so that we can serve the planet and its people. Thank you, Mr. Chairperson. I'm honored and humbled to this opportunity to give a presentation at this high level panel. The comments I will be making today are based on my humanitarian background. As Mr. Chairperson have introduced, I have been working in the field of humanitarian assistance for over 23 years. One of my early day missions was in the former Yugoslav countries. It was early 90s and we were serving for refugees and displaced persons. What we learned there was the dignity and strength. Surely exist within those who seemingly vulnerable. We also saw how easily one careless distribution of unified materials could take their dignity away and discourage them to take initiative of their own lives. Therefore, we have been emphasizing the importance of supporting self-reliance from the very early stage of emergency. Many people have criticized the self-reliance is for the phase of development or at the earliest in the transitional phase. However, from our experiences, we also learned that the earlier they are involved, the earlier they will become self-reliant. So there are four points I'd like to make sure that to make sure to be included in the global compact of safe order and the regular migration. Some of these may have already been thoroughly discussed, but it is always better to emphasize important things repeatedly. The first one is mainstreaming environment and climate change in promoting safe orderly and regular migration. I'd like to express my deep appreciation to IOM's efforts on this. Disasters affect those who are vulnerable more severely. Thus, it will require more resources for them to recover from the damage. In such resources, if such resources will be allocated for the vulnerable people before disasters hit them, they might be able to become providers of assistance rather than recipients once disaster occurs. Second point is to tackle with root causes and prevention. I also highly appreciate that IOM has been emphasizing the importance of peace and development. It also aligns with one of the conclusions of the World Humanitarian Summit, prevent and or end conflict. Each individual in disaster affected areas are no less capable of supporting themselves if such a disaster did not occur. It is extremely important for the damage, damage of disasters to be minimized so that they will not be forced to migrate due to adverse drivers. The third point is migrants and potential migrants are the first stakeholders. Tackling root causes requires local knowledge. Therefore, it is totally natural for them to be included in not only implementation of projects, but also in all the processes including strategy-making, planning, monitoring, evaluation and researches. Since they are the owner of their own lives, when they are included in all the phases, the project will be more efficient and productive and the result will be to the point and sustainable. Because their background varies, we must make special efforts to include people with various backgrounds such as women, minorities, physically and mentally challenged. Needless to mention, they are the owner of their problems as well as precious resources. The fourth point is nexus beyond collaboration is the key for innovation. All the stakeholders must come together and produce innovative solutions for fundamental issues. Currently, humanitarian need is the largest since World War II. In 2015, UN was able to raise only 55% of funds against it appealed for humanitarian needs. And unfortunately, the number of people in need is not decreasing. Insufficient funds may not affect quality, but definitely the quantity of assistance that unfortunately increases the vulnerability of those who had been already vulnerable. The ongoing way of humanitarian assistance will not be able to fulfill the objective of assisting to satisfy basic human needs. Therefore, innovative solutions are in desperate needs. The actors on the ground are also diversifying. Therefore, closer tie amongst all the stakeholders need to be developed and innovation are eagerly sought for. For closing, I'd like to share our experience of the great eastern Japan earthquake. The earthquake hit large areas. Due to tsunami, huge area was damaged. Many depopulated towns and villages were included. Those villages had already had various problems in relation to depopulation. The tsunami even more expedited depopulation. Therefore, it was obvious that even if they recovered all the materials they lost, they would not have been able to rebuild the same lives they had. Without tackling the fundamental problems they had from before the earthquake and tsunami. In other words, the earthquake and tsunami forced them to face the existing problems. Innovation was desperately in need. Japan platform is a consortium of 47 Japanese NGOs where I served as a co-president from the time of the earthquake. The majority of member NGOs of JPF was scattered through the earthquake, tsunami affected area and worked with local communities. We faced the same agenda, innovation. Therefore, starting from 2014, JPF held Humanitarian Innovation Forum involving various stakeholders, including local people. This undertaking had been adopted by Asian Disaster Reduction and Response Network. And now, many innovation workshops are held in various parts of Asia, including earthquake affected Nepal. Without innovation, we are not able to serve for the need of various vulnerable people. And I believe that we can make innovation together. Thank you. As with the other speakers, I wish to thank Ms. Kiyama most sincerely for very good presentation, giving some idea of more from a practical level of what it's like on the ground where we do work on climate change matters. I'm afraid that we have about two minutes left. I'm not sure that's time enough for 10 minutes. 10 minutes. Okay, okay, good. All right, did I have a series of speakers here? I have the speakers of S speak Madagascar, Costa Rica, Germany and the European Union with others perhaps to follow. But let's start with Madagascar. You have the floor. Mr. Finimon. Thank you very much, Chairman. First of all, I'd like to thank you for the organization of this panel. I'd also like to thank the panelists for their excellent presentations. Mr. Director General, looking at the factors and the root causes for migration in the context of the New York Declaration of 19 September 2017, the members have looked at all the notions that gave rise to forced displacement and irregular migration. They looked at the multifaceted nature of causes mentioned and their complex interdependence with the example of combating extreme poverty, climate environmental factors, basically the objective of the global compact is to come up with solutions at a global level by adopting integrated approaches of commitments which would be feasible. One of the proposals to this regard was to establish partnerships in a global context of shared responsibility, taking account of flexibility and adaptability that we'd like to insert into this global compact. And I would like to ask the following question and I'm asking it of the three panelists, what are the areas and the types of cooperation which you consider decisive to reconcile climate change adaptation and mitigation while including the cross-cutting issues of sustainable development and economic growth? In other words, the solution, should it take account the fundamental aspects inherent to the social, cultural and economic aspects? Thank you very much. Merci. Etna Costa Rica. Senor Director. Thank you very much Director General and thank you very much to the panelists for the interesting talks they gave today. The minister certainly talked about something which today seems a fact which is the importance of the environment and the global agenda and this is a major gain but it has been a fairly difficult combat for many countries in this global agenda and I'd like to refer to this because although he was referring to certain dates or deadlines, I recall that in the 62nd United Nations General Assembly where this was in 2007, the Chancellor Costance said at that time that we could not say better late than never. At that time the General Assembly had decided that the central issue was climate change but 20 years before in 1987, President Mahmoud Abdul-Gayun of the Republic of Maldives had come to the General Assembly to warn us all that he was not going to talk about policies but rather he was coming to talk about the death of a nation and this because from his standpoint and his appeal for help, he said his nation whose 1900, some 1900 islands were gonna be submerged by the sea level rise 30 years ago, we had that warning, that presentation from the President of the Republic of Maldives and finally today we're taking action and moving forward, certainly the global compact for safe, regular and orderly migration is a unique opportunity for us to be able to have this link between migration, human rights and climate change and I could say that it's a virtuous cycle because it has these three elements but at the same time they move or gravitate around the sustainable development goals and I think the global compact is a major opportunity for us to assert this extremely strong and solid link and in addition, it will be with a perspective of sustainability, this was very well said by the representative of Maddes Gaskar, he was talking about problems of economic development for countries who are developing. How can we look at climate change, migration and human rights if this is going to prevent our development but it shouldn't be seen as a perspective of sustainability in facing this problem of human mobility. I simply also wanted like to stress certain initiatives that are also been created in parallel frameworks and all of these have to be linked up and I'm thinking of the Geneva Pledge which is an appeal for negotiators on climate change to sit down with the human rights negotiators and to have an exchange and I think this would be a possibility including people from the migrant population to have a holistic approach. Thank you very much, Mr. Director General. Harmony, you have the floor. Thank you Director General for giving me the floor. I asked for it because Germany is the current chair of the platform of disaster displacement and I will keep it very short in order you can take maybe another speaker. We of course, we find it essential that the GCM addresses human mobility in the context of disaster and the adverse effects of climate change goes without saying and we have elaborated key messages, valuable key messages as we think how this can be integrated in the GCM text and you can find them on the PPD website which is disasterdisplacement.org. So, thank you. Thank you very much, European Union. Thank you Director General. Honorable Minister Excellencies, thanks for the rich panel and for putting this important issue of climate change on the agenda of today's meeting and of the GCM. I'll try to cut myself, my comments short in the interest of time. I speak on behalf of the European Union and its member states. Climate change is creating complex humanitarian and development challenges. It has devastating effects on people, communities and their livelihoods. According to the ICMC, 24 million new displacements by disaster happened in 2016. Many more are displaced by less spectacular but more permanent slow onset impact of climate change like sea level rise or desertification. Better evidence is needed here for us to understand how many IDPs cross borders and become migrants or refugees and why. Left unchecked, climate change can become a leading driver of migration and forced displacement worldwide. Migration and disaster displacement in the context of climate change is not primarily a cross border problem. Thousands of internally displaced persons also need protection assistance following disasters and the adverse effects of climate change. The EU sees it as our shared global responsibility to tackle climate change and climate-induced displacement. Our global strategy approaches the nexus between climate migration and security in a joined up way from prevention to managing the impacts. This global strategy also emphasizes the role of building resilience to promote security. Effective and timely adaptation work also helps us address underlying causes of forced displacement. It can prevent, minimize and respond to disruptive impacts. This is why the EU is engaged right now with the most vulnerable countries to increase their resilience. With the 2.9 billion Euro EU Emergency Trust Fund for Africa which was created to address the root causes of instability, forced displacement to stem irregular migration and to contribute to better migration management. We in the EU decided to work in unison and to join forces with the private sector. This joining of forces finds its latest manifestation in our external investment plan to help boost investment, growth and decent job creation in partner countries. The EU will provide 3.35 billion Euros with the aim of mobilizing up to 44 billion Euros in investments to help create opportunities and tackle the root causes of forced displacement. Finally, Mr. Chair, the EU's member of the steering group of the Platform on Disaster Displacement and supports the implementation of the protection agenda resulting from the Nansen Initiative in close cooperation with IOM. I thank you very much. Thank you very much. In the interest of keeping the minister on schedule, I'll stop the questions here. I hope you'll submit statements and in the respect of the other delegates that perhaps let the minister respond first if you have anything. Merci beaucoup. Thank you very much, Mr. Director General. I apologize for not being able to stay here for longer but I will give you more time in the next few days, months and years to come because the subject is so important to me. And I would like to say to the representative of Costa Rica that I am outraged, I am very surprised and frightened that it has taken us 30 years to understand the reality in front of us. If we take another 30 years to go from this reality to the implementation of our objectives, if there is really a 30-year gap, I don't know if humanity will, should keep the word, the term humanity. I want to be an optimist, of course, but we are going to have to change how we do things. Money will not to do everything but money will facilitate a lot of things. We can't ignore that. In 2008, when there was the financial crisis, we showed such creativity to be able to save the banking sector. And without being demagogic here, it did not take eternity to avoid a collective bankruptcy. And I have to say that I hope that we will be able to have the same amount of creativity to help our fellow citizens and to help humanity as a whole. Now, to respond to Madagascar's question, we must say, we must, and for the future, and this is really the purpose of the event that we will be organizing in France, but I'm saying this very cautiously, of course, because I can't presuppose of state's intentions. But of course, we will have to completely put on an equal footing attenuation and mitigation because up until now, the phenomenon that we have been seeing, and this has shown us already that climate change is already underway. This is a true tragedy for hundreds of thousands of people around the world, and I remembered that the number two million was mentioned earlier. I think there are a certain number of priorities that should have an influence, of course, on donors' activities, especially when it comes to the most vulnerable populations. We must allow them to protect or rehabilitate, restore their ecosystem, especially arable land. I completely agree with the analysis of Monique Barbu, who is the executive secretary of the UN Convention to combat dissertification. If we undertake a worldwide movement to allow certain countries, and here I'm thinking about African states, and more particularly the Sahel region, if we pledge all of these different means to rehabilitate dissertified lands, and we know how to do this, thanks to agroecology, this would allow us three things. First of all, avoid people leaving their territories. Secondly, for people to come back to their land. And thirdly, it would make sure that this land was arable once again, and therefore they would be able to fight against climate change, because these people would then be able to stock carbon dioxide and, of course, participate to mitigating the migratory phenomenon that we have been observing here. I also believe that we must do everything at our disposal, because the technologies are available. We need to render them economically accessible to all of these countries for renewable energies to become an accessible common public good for all of humanity. So this is just what I wanted to say very briefly. Once again, France will, of course, be at your side, Mr. Director General, and we will be an tireless ally. Thank you very much for your attention, and I would like to also thank the other panelists for this event. I have been discovered since I became minister that the formula agenda for a minister was not just a legend, and indeed, I am very, very busy and very booked up. Thank you very much. Thank you.


We'll come back everybody. So let's continue with the second talk of today's program. Luke Stahauer will tell us about invertible topological field theory with fermionic symmetries. Please. All right. Thanks for the introduction and thanks for the opportunity to speak here. Thanks to the organizers for this organizing this interesting topic. So I'm not sure I hope that the blackboard is sort of readable. I try and write very large and if the general opinion is that it's totally unreadable, let me know then I'll switch to my iPad instead. All right. So my talk is going to be about mainly about work in progress of my advisor and collaborators of Kekstotz-Tajche and their work is very is inspired very strongly by the famous work I would say by now of Frieden Hopkins and I'll tie it a little bit together in my own formulation and I will combine it with some work that's joined with Luke Stahauer. Okay. So the plan for the talk is the first half will be a blackboard talk and the second half will be slides on my iPad. And the first half I'll mostly explain one point of view on how to include fermionic symmetries, how to describe symmetries of fermionic systems in topological, maybe topological quantum field theories. And I will also go into, it means in a similar spirit to the last talk, I'll go into like these topological actions, I will call them topological partition functions, very similar to the last talk. And then in the second part I'll focus more on topological field theories themselves and I'll also discuss unitarity and if there's time I'll discuss spin statistics as well. So but for now my goal is going to be describing one mathematical framework for symmetries of systems with fermions. And there was already a very nice motivation in the last talk for invertible topological field theories coming from anomalies, we're mostly discussing anomalies and one other big amplification of invertible field theories is symmetry-protected topological phasers. So I'll start with a Nobel Prize, which should be well known, the Nobel Prize from 2016 on topological insulators. And I'll not really discuss what a topological insulator is at all. The only thing I want to do, oh I have to write large, large, large question, I want to extract the information of what kind of symmetry the system has. So if I ask a physicist they will tell me there's a tiny reversal symmetry. So this is the symmetry protecting the topological order and then there's the electromagnetic U1 charge symmetry. And they satisfy a couple of commutation relations. Like we have been told that time reversing symmetries should be anti-unitary. So you should have a relation that looks something like this. And in particular there should be also a relation that looks something like this. e to the i a q, so that's my U1 element corresponding to charge. So a some real parameter here. It doesn't quite commute with t because t is anti-unitary but there's a little sign change in the experiment. And then there's another thing that's important for me on existence and that's that t squared is not equal to 1 but it's equal to minus 1 to the n. And what do I write down when I was a mathematician? I want to know what the symmetry group is. My conclusion from this is that g is U1 that's the charge part. And I have a Z mod 4 coming from the time reversal part. But they are not quite a direct product but it's a semi-direct product. And the action of Z mod 4 on U1 is given by the surjection to Z mod 2 and Z mod 2 acts by inverse like that. And then there's one additional thing that you could demand in this situation if you like, which is called the spin charge relation. It says that there's a relation between spin and charge. And one way to formulate it is minus 1 to the q is minus 1 to the f. So physically it just says that the particle has on charge if and only if it is a fermion. And this leads me to if I assume this then I have to require that this minus 1 to the q which is in here is identified with the minus 1 to the f which is an element in here. And I have to quotient by a diagonal Z mod 2 group here. And this allows me to identify the symmetry group in this specific example. So what are some particular properties of this symmetry group? I want to formalize it in a definition. And the definition is the following. I define a fermion symmetry group, a fermion group to be a collection of a couple of things. So I have my compact V group which is like the symmetry itself. Then I have a continuous homomorphism which measures for me which symmetries are time-reversing and which are time-preserving. And I think I'll try to write Z mod 2 additively in this presentation. And please excuse me if I'm making mistakes with that. So for V Z mod 2 it's going to be 0 and 1.  So that's fermion parity. That's some element in the group. And it satisfies well clearly I want to have that squares to 1 if the notation makes any sense. And I also want to demand that it's time-preserving. So that's my definition of what the symmetry of a fermion system should be. We've seen already a very physical example. Here's a very mathematical example. If I start with a finite dimensional superalgebra. So Z2 graded algebra respecting the multiplication, the gradient is respecting a multiplication. And I want to think of this as the on-card being time-reversing and the even part being time-preserving. So it's not really super in a sense of fermions versus bosons. Then I define the following group. It's the collection of homogeneous and invertible elements inside A. And this comes with an obvious map to Z mod 2 given by theta of A is just the degree of A. And this is not compact because it contains all these scalars, scalar multiple of the identity. So I'll just take a quotient by only positive scalars just to get rid of the scalars to make it into a complex group. And now I define my minus 1 to the f to be the class of minus 1 in here. And this gives me an example of a fermionic group. Yes. Do you allow the central elements to be the identity, or do you want to have exact order? Oh, I really was afraid that I would get this question. Like maybe at some point in my life I will be able to make this decision, but at the moment it's very hard, but I think for this presentation I allow it to be one. But I mean, I agree that then it's not really very fermionic, but it's a very good question. So related to the example I just gave, you have this relevant theorem, I think, by Wolf, which says that there are only, or there are exactly 10 so-called super division algebras. So those are super algebras over the universe, for which all homogeneous elements are already invertible. And in particular, using the last construction, this gives us a condition, a sort of, this gives us a list of 10 very special fermionic groups. And this is related to so-called tenfold way in common matter physics. So this gives a collection of 10 internal symmetry groups that one could describe as internal symmetry groups of so-called 10 symmetry classes that occur for symmetry protected double-digital phase. So one example which goes back to the example that I just raised is if I take the super algeba to be the clippard algeba with two negative squares, then G of A is going to be a thing to minus. And in fact, you can show that it's isomorphic to the class A2 tuple algeba insulator example that I just started the lecture with. So these are fermionic groups. I want to go on to describing quantum field theories. Well, I don't know what a quantum field theory is, but at least starting with describing what fermionic symmetries should be, topological field theories. For that, I need first some notation. So I will denote group will be the grading involution of a fermionic group, which is the map that it's a polymorphism of a fermionic group that maps a group element to minus 1 to the f is if the element is off, or sorry, if the element is time reversing, sometimes I'll say off, since it's a z2 variable, I should say time reversing. So if it's time reversing, it's not to minus 1 to the f times itself, and otherwise it's just sent to itself. So that's some automorphism of the group of order two. And now this will be the main construction that I will use to describe quantum symmetries on spacetime. So if I have two fermionic groups, then their fermionic tensor product is defined as the following semi direct product. G semi direct H mod commons in two. I'm at a z2f. So every time I write z2f, it means 1 minus 1 to the f, group z mod 2, in which one of the two is permanent parity, in which H acts on G by first its gradient and then the z2x by the gradient homomorphism on G. And this looks very abstract, but you can make it super concrete by just writing out the formula, what this means. So very concretely, if I write two elements of this group, then the multiplication is just sort of, it's sort of tangent products over the z mod 2f with the coso sign. So it is, well, there's a sign, a coso sign, but it will just be G1, G2, or H1, H2. But then there's a sign, which depends on how much elements you, all the elements you switch with each other. Is there a good chunk? Okay, so this is like similar to what the tensor product would be of super algebras, that's the ID. And the resulting thing here, just like if you take the tensor product of two super algebras, is z2 cross z2 graded, like there are now sort of two gradings. I want to use them both.  And in particular, you have the sort of diagonal gradient, and I want to take the even part with respect to that. So very concretely, I could take H, G tensor H, and what's the even part, so zero for the kernel of sort of the matrix of two. Well, it's G0 tensor, so very schematic. It's this, and I just throw away all the parts that contain something in the form G0 times H1, or the other one. Okay, so now I get to what's, this is what's related to the last topic, I guess. If you're given an internal symmetry group, how do you make the fermionic group that of course that you should put on spacetime? So given an internal fermionic group, I will define the spacetime structure group. So this is where the Lorentz symmetry comes in as well, and let's fix some spacetime dimension. And what is it? It is the fermionic tensor product of the internal symmetry group with sort of the Euclidean plus fermionic version plus allowing reversing orientations of the Lorentz group, and then I take the even part of that. So I only allow symmetries that combine, for example, a time reversing symmetry with a symmetry that, a Lorentz symmetry that reverses the orientation of spacetime. Okay, so let's do maybe some examples. So a simple case is, well maybe a very general case. It's the case in which there are no time reversing symmetries. And then what you recover is you take the internal symmetry group and you just take the product with spin. And the only thing you have to do is you have to mod i about a common z-mount 2 right here. So in particular, we can get back to the situation. And this is the reason that I answered Fiat-Johnson-Crete's question, as I did. So in particular, if I take minus one to the f to be one, which is a little bit weird, I'm allowing it now in the presentation. So this is, I take it to be one inside G. Then the thing that I recover is going to be G-Mod, sort of G cross SOD. So that's going to be the structured group of a bosonic theory that a time-reversing symmetry. Maybe one case with time reversing symmetries. So let's take G to be in minus one, which is an extremely complicated way to say Z-Mod 4. But I write the Z-Mod 4 as one minus one to the f t minus one to the f t. So t squares to minus one to the f. And then you can check that HD is going to be, confusingly, it's going to be in plus B actually, even though you might have expected it to be minus. But that's the thing that should agree with the physics, if I'm not mistaken. And what's now the point of this whole part, the point is that I claim that what we should do is we should endow, if we have an internal symmetry, we should, I guess, I should say, I want to couple the symmetry to a background gauge field. So endow the spacetime with an HD structure. I don't really have time to explain exactly when an H structure is on a manifold, which I apologize. But at least if H is thin, then it's a spin structure. If it's by SO, it's something like an orientation. And I'm very topological field theory focused here, I should say. So if you're not doing topological field theory, you should probably endow differential HD structures. So you also include gauge connections and stuff like that. But I will discuss topological field theories for you. And in fact, I will start with not even doing topological field theories, but just homomorphism sort of out of boredism groups. So just partition functions for simplicity. And those will be related to the invertible topological field theories with permanent symmetries. And for that, since I want to also consider non-unitary invertible field theories, I will need a little bit more complicated version of a boredism group. If you know any type of boredism groups, this might be one that you're not very used to. And if you're from the Max Planck Institute in Bonn, then you know this as the S K K group. If you grew up somewhere else, you might know it as Reinhardt boredism, I think, or vector field boredism if I'm not mistaken. But what is it? I take closed H-manifolds. And I, so those form a monoid under this joint union, then I take the growth group associated to that, portioned out by the S K K relations. And I decided to risk my career and make a picture of the S K K relations on the Blackboard. So there we go. So the relations goes follow. It's a four termination. So I take two manifolds like this, and I could take two sort of hyper surfaces that are diffeomorphic here. And then I'm allowed to switch them. So this is equivalent to, and now I just flip the two pictures around. And now it should look slightly similar if my drawing skills are reasonable. See, I flipped the upper parts. So it looks something like this, I guess. This is the S K relation. And this will give me some of the group under this joint union. And then what is going to be a sort of invertible field theory? Well, I don't want to do topological field theories just yet, but a invertible topological partition function, maybe I should have called it a topological action, because it's closely related to that notion that we had in the last talk. And what is it? The partition function is a homomorphism from the S K K group. There you go. To C cross. So this can represent some possibly non-unitary invertible topological field theory. And we get the partition function for that. And maybe this is the right time to remark and comparison to the last presentation that I'm considering discrete invertible field theories here. So I'm not doing the physically correct thing of considering this Anderson dual and doing all the nice things that we've seen in the last presentation. So in particular, things like terms, silence terms and stuff like that will not be contained in here. So that's unfortunate. But let's do an example at least, an example that is different from examples that we've seen in the last presentation. So what I could do is, I mean, this is, I'm going to fix the complex number. This is sort of my phase angle, if you will, though it's not quite that. And my partition function, my manifold is just going to be pulled up to the boiler characteristics. So these are just boiler theories that were also sort of briefly mentioned in the last talk. So this is one example. And in fact, in general, this is not unitary invertible efficient function. Okay, so I'm going to tell you a couple of facts. So you might know another borders group. And in fact, this STK group, there is a map from the STK group to that border. The border group is usually written like this. So that's the monoid of HD manifolds of the border. And this is not always an isomorphism, but it's always subjective. So here's one interesting example, which is the case that I mentioned to and the structure of this O in that case, the exact, I'm making a mistake, sequences like this, it turns out that the degree to the dimension to borders and group is isomorphic to see not to. And this extension is actually not split. So this is a non split extension. But this is sort of the most general non split that can happen in this kind of invertible theories. So you can prove the following, which classifies basically invertible theories, if you know the, if you know the unitary ones, but we'll discuss that later. So in the even case, you can show that the SKK group is isomorphic to a pullback of the ordinary borders and group. It's a little diagram like this. It's this pullback. I can map the borders and group always to Zmont to by taking the other characteristic modulo modulo two, that's always the borders are invariant because it's an integral over the topstiff Whitney class. And here it's just the Zmont to map. So this is indeed even. What happens for the odd? I don't quite know. It doesn't seem to be well known. But something has been proven by Matthias Trek and others. This is again a theorem of Kretschfeld's Titian. For the odd, there is a exact sequence. It's always surjective on the right, as I just told you, but it's not always surjective in the beginning. And in fact, this map is exactly injective if HP plus one manifold, so in one dimension higher, has even more characteristic sounds like a great condition. But in practice, it's actually really hard to determine whether every every manifold has even other characteristics. That's a super hard question. And I'm also not aware of any non split examples. So that would be interesting to know. Incredible. This was exactly how the matter is. I now wanted to switch to the second part of my presentation. So now go to share my screen. So the next part is going to be more about actually topological field theories. I will not just consider the invertible case, but also some non invertible things. I hope that's not too confusing. So let's get to it. So I will discuss like the main two things I want to discuss about topological field theories are reflection positivity and the space statistics here. So for that, I will start with first explaining what reflection structures are on manifolds, a little bit reflection structures on topological field theories. And next, I will get to reflection positive topological field figures and touch upon the relation with dagger filters. And if there's time, I hope there will be time. And I will also discuss the statistics theorem for topological field theories, in particular for invertible topological field theories. Oh, and I should say that when I say topological field theory here, I always mean the TSC style functorial definition of topological field theory, mostly just the non extended version. And if you're fancy, I sometimes do once extended. And mostly just the classical definition of topological field. So first, what are invertible topological field theories? I already mentioned that word a lot of times. So basically invertible topological field theories are one to one correspondence with these invertible topological partition functions that I wrote down. One very mathematical way to say that is that if you have an invertible partition function, like I just like I wrote on the board, then you can with appropriate target category, you can extend it further and further downwards to make a extended topological field theory out of it. So what does that mean in practice? So for example, just the ordinary TSC definition, you can just consider topological field theories with as a target, the group boy of super lines. So you just consider one dimensional z two graded vector spaces. And so in other words, it's just a normal topological field theory, but the super vector space is very important. We need those, we need those fermionic state spaces as well. And to make this a one to one correspondence. And yeah, so it's the usual thing that you demand for invertible things need all state spaces are one dimensional all partition functions are non zero things like that. And you can also do something like that once extended and one example of such an appropriate target would be the category of super algebras, which objects are super algebras, one morphisms are by modules, and two morphisms are interfiners. But for most of the talk, we'll just focus on this on the second point, just normal topological field theories, you know, to see the sense. Okay, so to motivate reflection structures and reflection positivity a little bit, I wanted to mention this little proposition about what do topological field theories with fermionic symmetry in dimension one look like. And this proposition here is pretty is not very hard to prove, and it takes a bit of work, but it's not very hard to prove once you have the borders of my boxes, you know, but the main point of this that I want to show this proposition is to show you the general structure of such such a one dimensional topological field theory. So, as you might have expected, you get some kind of representation. And it's a representation of this only at the time of preserving symmetries. But what did the time reversing symmetries do? Well, you get all these weird by linear forms and how so you get a whole collection of non degenerate by reforms. Oh, I forgot to include here. It's very important that it should be discreet. So let's assume that it's fine symmetry here. So you get all these non degenerate by linear forms and they satisfy this this, yeah, bunch of relations that relates different by the new forms to each other together with these representations. So that tells us somehow how the representations are adjoined to each other or something like that in this unreleased by the new forms and they have an even worse equation with this expression. And it's just both mathematically bad, and it's physically not really clear what this means. But once you assume reflection positivity, and I don't think I already mentioned that the reflection positivity is just the the Euclidean version of uniterity. So it's just if you have a Lorentzian theory, which is unitary, we rotate it and people usually call the Euclidean version reflection positive. So what do those look like? Well, it's much easier and it's much it's much closer to what you expect from the physics. So one dimensional reflection positive topological field theory, they're all isomorphic to basically your representation on a complex Hilbert space. And it's topological field theory. So it's kind of dimensional. But it's not quite a complex representation. So the time preserving elements act unitary, but the time reversing elements don't even act complex linearly, but they do act anti unitary. And that's exactly what you would expect from things like for example, witness here. So this would make more sense to if this is I would guess. Okay, so this is a motivation to define reflection positive theories. So let's get to I will briefly go through reflection structural manifolds. So given an HD manifold, I didn't define what an HD structure is. But I claim you can define its reflection, which is so it's a kind of generalization of orientation reversal in the case that manifold only has an orientation. And in particular an HD structure does. Yeah, I didn't say what it was, but it also includes an HD principle bundle. And I just wanted to highlight what the reflection does to this HD principle bundle. So coming back to the part I did on the blackboard, I defined this, this even part of the Spermian tensor product as the space time structure HD, responding to the internal symmetry group. But I mean, I define it as the even part of this. So by definition of HD, there's a short exact sequence of this form. And what I can do if I have a principle HD bundle, I can always enlarge it to make it twice as big by just taking a product like this with each hat. And then I have P sitting inside it. And I sort of take the other product, take not P, but I take the other sheet in this, in this enlarged P. And this will give me P bar, which is the HD structure. Sorry, it's the principle HD bundle corresponding to the reflective manifold. And you can continue playing with this. And eventually, you can show that this reflection actually extends to a whole Z2 action on the bordered category. I seem to have included a G here. I'm sorry. So I just mean HD here. But by HD of G, I just mean that it's the HD corresponding to the internal symmetry group G. So that's a little notation issue. Anyhow, so it acts on this whole bordered category, like that. And that's a symmetric model action. And now what is a TFT? Well, I always want to consider topological field theories with target super vector spaces, because I'm also doing fermions. So a topological field theory with internal fermionic symmetry G is a symmetric model function like this. What is a reflection structure on this? So a reflection structure is a way to make this into a Z2 equilibrium function under this Z2 action. And that actually turns out to be data, so it's Z2 equilibrium data for these two actions. So extremely, I mean, this is all very abstract. So very concretely what this means is we just have a bunch of isomorphisms like this. So get where M is like a spatial manifold.  Okay, so that's a reflection TFT. Now I want to get to reflection positivity. But first I want to make a brief detour to the connection with that dagger categories here. So what's a dagger category? Dagger categories have been used in several reformulations of quantum mechanical systems. And maybe it's not super surprising that they might also come up in this situation. So what's a dagger category? It's a category which is equipped with a contra variant functor from from itself to itself, which squares to the identity. And it is also the identity on objects. And you can extend this definition if you work hard enough to be compatible with symmetric motive structures which we need to make sense of topological theories. And the main example you should keep in mind here, which is also main motivation I guess for defining dagger categories, is the category of vector spaces with Hermitian inner products. So here I take S Herm, which is I want to take a complex super vector spaces. And they're equipped with Hermitian inner products. So they're like Hilbert space inner products, but they don't have to be positive definite. That's my definition of Hermitian vector space. It doesn't have to be positive definite. So in particular, there's the collection of super Hilbert spaces is contained in that. That's another example. But now it turns out that you can also with some work, you can make the borders of the category in the dagger category. But then you need to make some choices. And what are those choices? Those choices are Hermitian structures. And what does an Hermitian structure? So it's a little bit abstract definition again. So why does this make sense? Hermitian structure on a spatial manifold is a diphthermorphism which is compatible with the HD structure from the reflected manifold to the dual objects in the borders of the category. The borders of the category has a dual. And it satisfies this relation. And why does this relation make sense? Why does this make sense? If you would not write n here, but if you would write a vector space v, and it would be a map from v bar to v star, then you can check for yourself that if you have such a map like this, that's exactly the same as a Hermitian inner product on the vector space. Sorry, it's good to know that as well. All right, so what's the statement? So the statement is that you need to choose some Hermitian structures to make the borders of the category. So suppose that h is a choice of Hermitian structures on every object of the borders of the category simultaneously, which is compatible with this strong union. Then using this, you can make the borders of the category into a symmetric amount of dagger category. And the crucial formula is this very trivial looking expression, which is just basically what you would do to a matrix algebra. If you wanted to find the Hermitian adjoint, you would do bar transpose. So I'm doing bar transpose here. And then on objects, we have chosen a Hermitian structure, which allows us to identify Bono, which allows us to identify m bar star with m, so that it becomes the identity on objects after this identification with h m. So then the dagger is the identity on objects, but it could be not the identity on morphisms. Okay. Now additionally, if you have a topological field theory, which is associated with re-variant with respect to the reflections, then you will, using this choice, you will get a symmetric monoidal dagger function from this dagger category of borders to super emission vector spaces. So I should explain some notation here. So this, I don't know if I, this, the symmetric monoidal dagger category that follows from this construction, but I put a little upper h here to remind myself that this construction depends on the choice of Hermitian structures, possibly very strongly. Yes. And this will land not actually in super vector spaces, but in super emission vector spaces. As it turns out, I will go into that in a moment. And why is this nice? Well, I mean, it's nice because now our state spaces are suddenly, they have been approached, like you would expect from physics. And also because now we can require them to be positive definite, which would be something like reasonably reasonable to ask, because then there would be Hilbert spaces being finite dimensional. So that's the next step. If you have a topological field theory, which is C2 vector variance, then we say that it's reflection positive with respect to a choice of Hermitian structures. If the induced Hermitian inner products that I just talked about on all state spaces are all positive definite. So we had this induced symmetric monoidal dagger from here. And we require it to land in super Hilbert spaces, not just in super Hermitian vector spaces. And here I wrote a little equation to tell you that it's, it's pretty concrete. If you want to know using all the data that I just gave you, what's the, what the Hermitian inner product is on all the, on all the state spaces, it goes like this. So we want to identify the dual with the bar, that's the Hermitian structure on the on the vector space in the super vector space. And the first thing we do is remove the star inside using the fact that Z is a monoidal functor. And then we had this very special choice of Hermitian structures on every object, HM, and we apply Z to that to get here. And then we use the Z2 equivalence of the functor to find the inner theorem. This gives us an inner product. We require it to be positive definite. And note that, yeah, again, that this all depends on this, on this choice. The choice is really important. If I would compose somehow HM with some function F. And it would still be a Hermitian structure. And I would use that for let's say that F is like an automorphism M. And this will still be a Hermitian structure and say just for the sake of argument that C of F is maybe like minus the identity or something like that. Then the resulting, the resulting Hermitian inner product on the state space will be different by a sign. It will just be minus the thing from before. And therefore, if you start with something positive definite, and you change the Hermitian structure to something different, it will actually be negative definite. So you cannot just demand it for all Hermitian structures. You have to pick a choice of Hermitian structures. And this, you can also see this in, oh, I thought that something else. Okay, so this is first. Okay, so we get back to the invertible case. So what happens in the invertible case? So first thing I should say is that there turns out to be a somewhat canonical choice of Hermitian structure on the boredom category for any internal fermionic symmetry group as I gave. And from now on, we'll use that. And then you can prove this theorem, which I mean, I'm not sure who I should cite here. So I cited everyone. I guess the original statement is due to free op gates. They have the great reformulation of Unicura for non-extended field theories and also actual types now using these dagger categories. So what's the statement? So we start with this invertible topological partition function, which is the same as an invertible topological field theory. Then there's a distinction again between odd and even. In odd, it's a little bit nicer. So for odd dimensions, partition function has a reflection positive lift exactly when it factors through a homomorphism from the boredom group to U1. So that's very nice. And it's also unique. So there can be many different reflection structures on a different topological field theory. But somehow, if it exists, then the reflection positive lift is unique. And as a consequence, you get an isomorphism, something like this, which is closer to something you would find in the physics literature. Often they're closer to homomorphisms from the actual boredom group. And maybe I could mention here again what I already mentioned before, that I'm doing the street invertible topological field theories here. So I'm not getting this Anderson dual thing that we had in the last presentation. This is a little bit of a simpler situation than that. And for the even, it's a similar situation, but we only have this additional example of Euler theories that you take. You took this laptop and you took it to the power of order characteristic. And that gives you a theory, invertible topological field theory. And if you take that, if you take that to be a real number, then it turns out to be still in this definition still reflection positive. So you have this extra weird factor of our positive hang around. But otherwise it's very similar. Okay, then I hope that now is the example. Yeah, exactly. So this is a subtle example that I wanted to idolize. It's nice to ponder about. So what's the difference between the internal symmetry group Z mod 2 and the internal symmetry group Z mod 2? I mean mathematicians, I guess would say the same. But for me, this one contains minus one to the F as a non trivial element. And here, minus one to the F is equal to one. So that makes them different. But otherwise they're extremely similar as internal symmetry groups. So what happens?  But the funny thing is in dimension one, they're actually equal. They're just equal on the nose. They're both Z mod 2. Additionally, you also have this isomorphism. They're both Z mod 2. However, there is one subtlety, which is that in one of the cases, the generator is the anti periodic circle and the other is periodic circle. What do I mean by that? So there are not many connected one dimensional manifolds with these structure groups. And there are just two. You have the circle with periodic boundary conditions and anti-periodic boundary conditions. And maybe you know that for the spin case, it is actually the anti-periodic boundary condition that's bounding. But for the SOD cross Z mod 2, it's the other way around. It's a little bit unexpected, maybe if you've never seen it before. And as a consequence, if the theorem that I put on the last page is true, then, well, the only, in both cases, you said have a single non-trivial reflection positive preferable topological field theory. But I mean, it should be a homomorphism from the border group. But in one case, it should map the periodic circle to minus one. On the other case, it should map the anti-periodic circle to minus one. So it's the other theory that's reflection positive if you take the other symmetry group. And there's only one way, in my opinion, that you can make these two different notions of reflection positivity happen. Namely, you have to choose a different Hermitian structure on the borders of the category. So there's a different Hermitian structure associated to it in which you have to put an additional spin flip on one of the two points. Okay, so that's a subtle example. So let's see, I'm a little bit out of time right now. And I don't want to rush too much. So let's see. I think I'll just mention this in a few words. So I just wanted to say that it's not very well known, but you can make spin statistics also very precise for topological field theories. And I don't know if due to who this is, but I learned this from a nice paper by Theodos Preet. And basically, the arguments, the argument goes as follows. So physically, the spin statistics theorem just says that if a particle has happened to your spin, then it's a fermion on the other way around. And it's actually a theorem for, as far as I understand, for unitary reflection positive theories, or it should be. But otherwise, it's a definition you can require topological theory to satisfy this. And how do you make this physics definition precise? Well, you have to make the observation that basically, a representation of a spin group has integral spin, if and only if, well, if it's like factors to SOD. So if the element of the kernel to the amount to SOD acts trivially. And then you can make a definition that's roughly the following form and has several generalizations, but this is the simplest one, that if you have a super representation of spin, then it satisfies the statistics exactly when this element is exactly the gradient operator. And this formulation has several generalizations to topological field theories and including internal symmetry groups. And let's see what I want to do. Maybe I just want to at least highlight that it's known. I'm not sure how alone it is, but you can show which of the invertible topological field theories satisfies spin statistics. So all of the reflection positive ones do, all of them in even dimensions do, even the non-reflection positive ones. And again, in other dimensions, there's a weird condition that it depends on the Euler characteristic of age manifolds. And I don't know how to say it's more simply than this, unfortunately. Okay. Yeah. And then I had some results finally, and I'm working on together with Lucas Miller in which we explored two-dimensional extended topological field theories with target super algebras. And we've classified all topological field theories with internal fermionic symmetry group satisfying spin statistics, at least in time-preserving case. And we're working on the case without time-preserving and still in progress. So this is not really a conclusion, but this is more of like a happy ramble. Let's get the physics closer to the math. When physicists talk about unitary and statistics, we can actually say what it is. And that's fun, I think. So thank you for your attention. Yeah. Thank you very much, Luc, for this very interesting talk.


Okay, okay. So my name is Luca. I work at CoroS in Berlin and I'm actually the leader of the containers team and Today we are going to talk about something which is the topic in here containers And especially like you have a cluster Kubernetes cluster, and you have your containers And what do you want to do with that running it? Fine. We're gonna touch into the details the internal stuff. So how Kubernetes is actually running your containers So first things a step back In Kubernetes, you're not actually running row containers. You're running pods pods are the basic unique of Execution and they tie together multiple containers in a single service Then Kubernetes stays care of basically scheduling them and doing some other task around like How to recover from failure and how to scale your containers your pods in your cluster Cool. How does this work? There are basically three main entities here First you have a cluster of course and there is a schedule in this cluster Which is the source of trot of trot which is taking care of scheduling your pods around Then you have workers and on each of these workers There is one entity called the cubelet which is a long-running demon a service Which is there and it takes care of receiving order from the scheduler And then there is another entity which is the container runtime, which is kind of an abstract concept Which is the one that is really running things. So whenever you say Kubernetes I want to run this pod Kubernetes goes the scheduler takes some decision and then delegates to the cubelet Cubelet is running on some specific node and then the cubelet goes and say look container runtime Which is typically Docker I want to run this container all together and then Docker goes and it runs actually your containers So it's pretty pretty easy To visualize it a bit better it works in this way there is always Some distributed key value store which typically it's at CD and there that's where the logic where the Scheduling part is happening then there are components which take care of Forwarding and propagating this information to other components in this case There are the scheduler and the API service and then you have multiple workers with these cubelets Which receive this kind of order and just execute the container and the pod We didn't start the timer, but it's okay Same seeing it as a hierarchy Actually, you have a cubelet on whatever node. Let's say it on node one and then You actually have this container runtime running for example Docker and then your pod get executed with all the resources inside of it So in this case, let's say that you have your service in there Which contains two application application one, which is the main application and some side car fine I think it's pretty clear up to a year From here on we go more into the technical part In reality when you are running your Kubernetes node, you have all these entities which are in there Typically you run it with Docker which means that you have a cubelet which is receiving some order and then Forwarding this order to the Docker demo the Docker engine Which then in terms as some internal components for example container D which take care of some other part of its execution And then internally delegates to something else for example to run C in order to run containers And then there is some magic going around it in order to group this container together This is let's say historically Kubernetes Then a chorus we had some kind of troubles Let's say and we also had some kind of opinions those opinions were There are too many components in here some of them until recently were not supporting auto blades checkpointing and restoring and most of those are like long-running services And they are tied to the lifetime of your container of your pods So we come up with an alternative which is like, okay Let's write a different container runtime So we keep everything the scheduler and the cubelet as it is and we just swap the bottom layer of it And that's where we are the rocket we implemented rocket and then we integrated it with Kubernetes All we did it is basically with a single runtime a single process instead of long-running demon and We also found out another Interesting point which is what do you have already on your system system D? Maybe you don't like it Maybe you like it is there it has interesting feature. So let's use it instead of re-implementing and demons So this is the usual configuration of a Kubernetes cluster running with rocket and then at that point we had some problem like okay But there are some tools that really wants to work with some kind of demon and we don't have any more a demon to provide this information so we also have some kind of Lateral components we just provide this kind of read-only information if you want to query into that Which is fine and then at that point we had like okay already to implementation It's getting the code is getting a bit dirty and messy to follow because there are different logic and different code path fine Let's sit down and have a discussion and this discussion resulting in CRI which is the new container runtime interface Which is being developed right now in Kubernetes the idea is the cubelet really wants some kind of fine-grain controlled on What is going to be executed on every single node and we want to move away more or less to the previous Paradigm where there was just this big sync pod logic routine into something Which is more granular like cubelet tell me which image you want to fetch from where and which container you want to schedule to run in which in which pod which Which resources you want in it and that's it and then we already have like some kind of protocol a standard Standard specification in order to that this component talks together, which is gRPC, which is an RPC mechanism based on protobuf And this is how CRI came to life It is currently experimental, so don't run it in production right now It is targeted for some kind of alpha beta feature in 1.6 1.6 and it will definitely happen probably this year Definitely probably Again trying to visualize it a bit better the idea now is we don't have any more or the services talking together We don't have different code path. There is a single way of talking From the cubelet to the runtime service and actually there are another part which is splitting up the image fetching from the Container running part. All of this is going through gRPC You just have to implement endpoints and being able to speak this gRPC protocol And then something in this case the runtime service will take care of scheduling your pods. This comes with some Other benefits, which is if you really don't like Docker or if you really don't like rocket That's fine. Just build your own implement your own. There are already several implementation for that and they cover different specific Topic, let's say So for example with rocket that was our design that was our approach But then you have like hyper hyper which is taking care of I want to really schedule pods Which are virtual machine and that's it How do you how do you find more about what I just told you? Well, you go online and you join the Kubernetes community that we are part of or you grab me outside So just go on github check the Kubernetes code This is done as part of sig node, which is the special interest group inside the Kubernetes community taking care of all these low-level details We have mailing lists. We have slack channel We have video calls and that's it and chorus is also hiring in Berlin, New York, San Francisco. So grab us