Good morning to all of you, and good morning to those who may be watching online because this is a live stream event. I'm Vikram Nehru and I'll be your moderator this morning, and it's my pleasure to bring to you three excellent panelists, Bill Sweeney, who's from IFIS, which is the International Foundation for Electrical Systems.  So today we're going to be talking about what's going to happen, what's well, what happened in the Myanmar elections, and we're going to talk about what happened in the Myanmar elections, which was incidentally exactly a month ago, on November the 8th. So this is, I guess, an opportune time to look back, but as important, and perhaps even more important, to examine what's going to happen the next four months before the new administration actually takes charge in late March or early April, because Myanmar at this point is in uncharted waters. Now we're going to conduct this as a conversation. I'm going to ask, in fact, Bill Sweeney to begin, because he's got a PowerPoint presentation where he'll lay the groundwork, but then I'll immediately go into questioning our other two panelists, raise some issues, and then we'll open it up to the audience for a Q&A, and then I would like to ideally try and finish this within 60 minutes. We'll try and finish this within the hour, because we would like to make it sort of crisp and interesting. All right, so let's begin with Bill. Bill, close yours. Okay, good morning. First of all, I'll do my best to make it crisp and interesting, as well as a little fast-paced. My job is to lay the groundwork. And in these days of a democratic deficit and concerns about closing space, what we witnessed in Myanmar was a democratic tsunami. We saw opening space. We saw people, as they believed that the process was full, fair, free, transparent, and accountable, engage with their feet in line and engage with their voices in their vote to give you a sense of the wave that took place. On the left, you have what the parliament looked like before the election in the lower house on the right after the election. Red is NLD, same in the upper house. To give you an illustration which all politicians will understand, there were over 6,000 candidates for the parliament upper and lower house from 92 political parties. Between the time of filing and the actual day of election, two died of natural causes. Her dead guy won. Think about that. This was known in the community that they could not replace him because he died right before the election. And he won. Now, that doesn't happen very often. IFAS's success with our programs in Myanmar started with our partnership with the Union Election Commission. We have been engaged with the UEC for almost three years. That engagement was first of all to sort of outline the tasks ahead of them and then the process of public engagement as well as actual specific pick and shovel work of election administration that we could do together. We were supported in this effort by USAID, by DFID, by the Australian development, Australian development funds, Swiss development funds and Danish development funds with some help from time to time from the Canadian development funds. So this was a true basket effort trying to do great things with the Union Election Commission, a body which was completely appointed by the president and whose chairman at the end is a retired general and is considered one of the closest friends of the president. So this was a body that was used to giving orders in a military sense, very little public engagement. It was also a body that for legitimate reasons, other factions in Myanmar had great suspicions of, but they did a terrific job. It was a challenge over three years. First element was stakeholder engagement. That meant working with all political actors on an ongoing basis for over two years in terms of what was going to happen on election day, how polling places were going to be selected, which ones were going to be closed because of flooding or violence, how the ballot process was going to work, how it was going to be counted, where observers could be. All of that information came out of a strategic planning process, which for many people in Myanmar was the first time their government had ever asked their opinion about anything. So we had this process underway for well over two years and then followed through on it. Secondly was the national voter list. The voter list in Myanmar basically consisted of thousands of handwritten notebooks maintained by local governments and ministries. There was no national voter registry at all. IFIS in partnership with the UEC was able to digitize the entire list. Then running our civic education programs throughout civil society and political parties post the entire list and have millions of people go to their public polling stations and check their names. Not once, but twice. So that of a voter registry that ended up being 33.5 million people over the course of 60 days before the election, there were over 6.5 million corrections. Those corrections were then absorbed and on voting day the list worked. And from my perspective, this was one of the most nervous election days I ever had because the flash point in so many societies is you go walking in to vote. Your name's not on the list or there's a typo or and in Myanmar they had a very complex record and suddenly that becomes the start of disruption of the polls, election violence, arguments fist fights. You're trying to deny me the right to vote. No, that didn't happen. This list worked and this list worked because of the leadership of the UEC, particularly in drafting literally whole IT departments from other ministries to absorb 6.5 million corrections to a list in less than 60 days. Voter education was a constant part of this process, both as to how the process would work and then tasking throughout it so that it's to get people not just to attend a lecture but then to talk to their colleagues and friends and get them to check the list. And then get them to check the list again. In particular here with women's leadership, a program that IFAS started called She Leads. Each of the ladies around the table was one of our instructors. They, according to our numbers, touched about 2,500 people each. Angelina Jolie came to Myanmar to promote engagement. She came and what she's doing there is she's checking her name on the list. But culturally, this was a very big deal for women voters in rural villages to not merely go in to make sure their name was on the list but then if it had a correction to have the correction done in front of them. So they were asking the official, it's not just my name is wrong, but please correct it and then let me see it corrected. Very, very significant empowerment across the country. Finally, inclusion. One of IFAS's signature efforts in terms of participation around the world is participation by people with disabilities. We have made this a central part of strategic planning with election commissions around the world. I am delighted to report that the Union Election Commission embraced that concept. We had trainings in their headquarters that laid out the polling stations so that people with wheelchairs, people with other disabilities could go to the front of the line, had space to vote, were treated with dignity and respect. And this was an important step forward and noted in all the observation reports. So, looking ahead, there are a few, not many, complaints about how the election happened. There are some that are close, a fault line in their process is that the Union Election Commission is judge and jury, but they are going through that process. We all will talk about formation of a new government and electing the next president. However, I'm going to point to the fact that the UEC, the Union Election Commission, is a completely appointed body by the president. And this is a lower tier decision, but we'll be being made probably next April, May, June. And if we want to talk about serious constitutional referenda and change in Myanmar, then we're going back to the polls. So this is an area for those of us committed to democracy in this country, to not lose sight of what will happen next spring after the big person politics are done, because Myanmar made enormous progress, enormous progress. And the voices of the people were heard and counted. And that's resulting in the changes we're going to talk about. But let's remember, just as we were reminded this election was only 30 days ago, in about six months, we've got to look at a new Union Election Commission and what its charter and capacity will be going forward. With that, thank you, sir. Thank you very much, Bill. I must say, IFIS has done a splendid job in Myanmar. You were basically based in the Union Election Commission. And it was a tough ask from the very beginning, but I think in the end, you came through. I was an observer for the Carter Center in the elections, in what's called the Golden Triangle up in Chengtong, which is the area where there's a lot of drug smuggling and warlords and so forth. But one of the things that was striking in the election observation that we did was that there were virtually no problems with the list, with the voter list, which was quite astonishing, given the fact that the place was really out in the boonies somewhere. Well, thanks a lot for that basis. I want to turn to Ong Dinh now. The question I want to pose to you is, well, now that we've had the election, Bill's laid out what happened there, but now that we've had the election, we've got four months of a transition process. How is this going to unfold? What's going to happen? What should we be looking out for? Today is certainly one month after the end of November 8th, also, about four months away from the new government taking over the office. So every people are wondering whether the military will really agree to transfer the power to the new civilian government or not. So we all remember the last night between the 1990 election, which was not recognized by the military government. So we don't want to see such a repeal of history again. So one week ago, on December 2nd, Daw San Suu Kyi held meetings with President Thaisingh and the Gomanai chief may online separately. So both the president and the Gomanai chief have pledged to cooperate hard for the transfer of power as smooth as possible and also according to the existing laws and regulations. And two days ago, Daw San Suu Kyi also met with former Gomanai senior general Thaisingh for two and a half hour at his residence on December 4th. So usually, we don't hear about such a high level of meetings from the Daw San Suu Kyi or never. But this time, we got something from someone we don't expect, who is initially three of, the grandson of senior general Thaisingh, who he himself met with Daw San Suu Kyi on November 19th. So he wrote a post at his Facebook stating that he was the one who facilitated the day's meeting and said that both Daw San Suu Kyi and senior general Thaisingh were very, with mutual respect and very friendly. And he also stated that senior general Thaisingh pledged to support for Daw San Suu Kyi if she was for the development of the country. So far, Daw San Suu Kyi hasn't denied or approved this post yet. So for me, I believe that the power transfer will be smooth. And then we are going to see the new government by already taking over the office in April 2016. Yeah, it's a funny thing that in preparation for the new rules in the upcoming parliament. Now, I know this will be a letter collecting rubbish on the streets, learning English, and studying the constitution and the history of the annuity as instructed by Daw San Suu Kyi. And she will set his ammunition for them before they take their seats in the parliament. Really? Thanks. Christina, so while all this is going on, we must remember that Myanmar has had the longest running civil war in modern history. 60 years of conflict. And there's been this parallel peace process that's been going on. It's not a nationwide ceasefire agreement really, only eight have signed on. So what's going to happen now? Is this peace process going to continue? Or is it going to start from square one? What's your assessment? Right, first I'd like to say thanks so much for inviting me today. And you have raised a very important issue because while we're thinking about all the meetings that Aung San Suu Kyi is having with various important people, this peace process is continuing on the one hand and the civil war is also continuing on the other hand. And for President Thane saying, he really wanted to make this one of his signature legacies of his administration achieving peace during his term. But that's been much more challenging for him than he initially expected, and there are several reasons for that. One is because of the number of ethnic armed groups and their different interests and positions. Another is because of the long history of mistrust between the ethnic armed groups and the government, particularly because ceasefires in the past have not led to a political resolution of the conflict. But a third reason is because the military and the President's peacemaking team have often not seen eye to eye on how to proceed. And the military has perceived that the peacemaking team has often made concessions to the ethnic armed groups that they felt were going too far. So the military has tended to pursue a military strategy on the ground by continuing to advance into the areas that are held by the ethnic armed groups. While the President's peacemaking team has been trying to convince these same ethnic armed groups that were really interested in working out a political resolution to this conflict with you. So there's really been mixed messages from the military and the President's team. Aung San Suu Kyi has pretty much stayed out of the ceasefire process so far, and she has not commented very much on the impact on civilians in the ethnic conflict areas. Both the 100,000 Kichin who've been displaced in Kichin State and more recently, Shan people who've been displaced in Shan State. The ethnic minority representatives, both the armed groups and the ethnic political parties, have been disappointed that she has really kind of taken a standoffish attitude toward the peace process so far. However, her party platform says that the NLD is committed to instituting a federal union, and she herself has hinted in the last year that she would give a better deal to the ethnic groups than perhaps the thane-sane government was prepared to offer. So there is some hope there, but also concern. She has said that she will lead the peace process once her government takes power. The text of the nationwide ceasefire agreement was basically agreed to in March this year, but the signing didn't actually happen until October. And one of the big sticking points was the fact that the Army wasn't willing to allow three of the ethnic armed groups that it's fighting against to participate in signing the ceasefire agreement. And some of the other armed groups said if this is not an inclusive process with all the ethnic armed groups signing, then we're not going to sign either. We don't want to be part of this divide and rule strategy of the military. So in fact, as Vikram noted, only eight of the ethnic armed groups signed this deal. And I would just note that it was actually approved by the parliament two days ago, yesterday, sorry, yesterday. But the process is stipulated that after the agreement was reached within 60 days, framework would need to be drawn up for the political dialogue. And then 30 days after that, the political dialogue would need to begin. And this process is actually going forward during this transition period. And so in late November, representatives were chosen to develop this framework. And that framework is supposed to be approved on December 14. Now one of the sticking issues in developing this framework has been the representation of the NLD within this body that's developing it. So political parties were allotted eight out of the 24 seats with the government and the ethnic armed groups getting the other seats. But in those eight seats, the NLD were only given two seats, even though they won the election by a landslide. And so that was something that they didn't feel comfortable with. But ultimately, a bigger issue for them is the amount of decision making power they will have in this political convention that is supposed to meet after the framework has been finalized. And that body and the composition of that body is one of the current sticking issues in this process of finalizing the framework. It's expected that there will be over 500 people in this political convention. And that they will be grouped. So there will be military representation. There will be government representation, which is separate from the military. There will be political party representation that will include the ethnic political parties, but also other parties like the USDP. And then there will be ethnic armed group participation. And also a certain number of seats reserved for other people who should also be there, which would include lawyers and representatives of civil society. So Aung San Suu Kyi and the NLD are very concerned that they would have a leading role in this body. And presumably, if things go forward as they're supposed to, this body would meet for the first time in January, which is over two and a half months before the NLD government actually comes into power. And this sets up a challenge because the NLD presumably has a position that's different from the military in terms of the political dialogue. Given that the NLD has said that they stand for federalism, while the military has been more reticent to adopt that position. And the military is continuing its offensives on the ground. Nevertheless, Aung San Suu Kyi said to ethnic political party representatives in parliament earlier this week that she would like the ethnic minorities to think more about what they can give to the union rather than what they can get from the union. So there is a question about really to what extent Aung San Suu Kyi is going to advance the rights of the ethnic minorities and how this process is going to play out during the transition and then going forward once her government comes to power. And she will have to balance not only the interests of the ethnic groups or the ethnic people as a whole, but also the military within this peace process. But then thinking more broadly of the peace process within the broader context of all of the political and economic reforms that she would like to make. So this is something that the NLD is going to have to handle with great skill and sensitivity if they are to be successful. Thank you. Christina, one of the outcomes of this election is that the ethnic political parties were essentially routed by the NLD. The NLD did not enter into a coalition with them or into an agreement with them in all the ethnic states. So that's bound to affect the dynamic in this peace process. How will it affect it? Will it hurt it or will it help it? Well, I think there are a number of factors to consider. One is that Aung San Suu Kyi has said that she will include ethnic minority representation in her cabinet. So it depends who those people are in the cabinet and what kinds of positions of power they are given and if they are given a certain degree of responsibility over the peace process or not. The other key factor is within this body that's going to develop a national accord that would resolve the political conflict between the ethnic minorities and the government. How much decision making power will the ethnic representatives actually have? And that includes both the ethnic armed groups and the ethnic political parties. And I would note that there is a question of who really represents the ethnic minority people. Is it the ethnic armed groups or is it the political parties? And then even among the political parties, there are the political parties, the ethnic minority political parties who are currently in the thane sane parliament. But there are other parties who had been allies of the NLD in 1990, who are the ones who did better in this current election. So I think that that's going to be a very complex process and it's also going to depend on the degree of unity between ethnic politicians and the ethnic armed groups. Bill, I want to come back to the electoral process itself, if you don't mind, because there was one dimension which you didn't touch on, which I'd like you to talk about, and that was this whole issue about the disenfranchisement of a very substantial number of Muslim voters. And the fact that there were many Muslim candidates for parliament who were disbarred from standing for the election. And this is the first parliament that we've had where there is not a single Muslim member of parliament. How did you deal with this? Can you give us some insight as to your discussions on this issue with the UEC? Was this an area that was off limits or was this something that they were prepared to discuss and how did that discussion go? I would say in retrospect, we raised a variety of points about global best practices, about enfranchisement, particularly for people who had white cards, whose white cards were then canceled. As to whether or not that would stand, we raised a number of practices, a number of concerns about decisions that the UEC was making or that the parliament was making. And in just about every case, we were told that this was a decision that had been made and it was not going to be revisited and have a nice day. And that's the easiest way to put it. And I think that all political parties and particularly the new government have a substantial obligation, particularly as a leader in human rights, to start to address the issue in their society of inclusion of a substantial number of citizens who've been living there for generations and who are being excluded on the basis of religion or ethnicity that has sometimes to do with the armed conflict situation, but sometimes not. And these are serious historical problems, if not fault lines in the society that they have got to figure out how they are going to address. Now, that's easy to say from here and as we are witnessing what's going on in our country in a very sad set of dialogues that seem or they're not dialogues, they're sort of news releases read by candidates, which I've rarely seen, and then walked back. Their society is going to have to deal with this problem and it's not. And you're right to highlight that this is the first parliament without any representation, which means that all parties who are going to be in the next parliament share the same problem. And it's a national problem and it's not being dealt with. And I want to also come back to a point that you made in your initial remarks about the fact that you said there were very few complaints that had been registered. So far, yes. Right. Now, I have different information. I mean, I'm told that at least the reports that I've heard from the Myanmar Times or that over 422 complaints so far have been registered. I guess that is few considering the size of the election and the number of candidates and so forth. But it's also 45, the 45 days are not up, which is the deadline for the registration of complaints. So we really have another 15 days to go before that happens and people are anticipating a large number of fresh complaints to be launched. How will these complaints be dealt with? How long do we expect this to continue? And will this have any material effect on the result? Okay, let's slice that question into two or three pieces. First of all, in the case of election complaints, you usually have them relatively quickly, right after the election. Secondly, the good part, if you will, is that the Union Election Commission and the Parliament have laid forth a process for complaining. All of that information is then transparent and open to everyone. There is some accountability, okay, to how they make decisions and when they will make decisions. So all of that is good because in many societies where we work, the electoral dispute resolution process is a mystery. And so this process is quite transparent. There are, from a global best practices perspective, some issues with the complaint process. One is the threshold for complaints. It involves a filing of a fee, but it also involves more than just a press release that somehow or other something happened. You have to collect evidence. You have to bring that evidence forward. That evidence then has to be public. That is a healthy part. There is a flaw which we have had multiple discussions with, but was a political decision by the Parliament, that the UEC is both judge and jury. There is no appeal process outside of them. They've known that from the development of the first draft of the strategic plan. But that is a political decision that that government has made. And now we have the standard of public accountability to see how they perform and what the results will be, which goes to your last point. I don't think there's enough complaints there for a significant or even marginal impact in terms of representation. Her majority is not threatened, okay? We're not dealing with if it's one or two seats, suddenly she goes below a threshold. It doesn't have, no, no, no, that's not the issue. So the issue will be the size of the majority, not whether or not the majority is threatened, which is the critical issue for governance. Thanks. So Ongdian, I want to now sort of come to you about this transition process. One of the big questions which everybody's asking is, who is likely to be nominated as the president? Or the two vice president candidates which the NLD is going to put forward. I'd like your views on that. And I'd also like you to comment on, I think today's news article, that Shreman seems to be once again coming into the mix. I don't know whether you remember, Shreman was actually interviewed here in this room some time ago, and he lost very badly actually in the elections. But he's coming back into the mix. So he's being considered perhaps as the next chair of the UEC, or maybe even the head of the Constitutional Tribunal. So perhaps you could comment a little bit on that. What's exactly happening behind the scenes as people are now vying for positions in the new administration? Well, first, who will be the next president? It is a kind of a million-dollar question. I think nobody knows yet. A few years ago, Unya Ume, who is a great company, a member of the NLD, spoke in Japan that said that the party has already chosen, had a short list of 10 candidates to be elected for the presidency. So their condition is that they are purely NLD members, loyal to the party, also they are no military background. So these are the conditions he set when they have the short list of the candidates. But you can also add that anyone, he or she, should be extremely loyal to the Don San Suu Kee because she could not be the president and she said she would be the above the president. So anyone he or she should accept the rule of the above the president. So that means there are so many names running around the town in Yangon, but I don't want to imagine any names because these are not very sure yet. But they will see some. For the first year of January, the new parliament will begin and their first choice is to elect the chairman of the both parliaments. And then they will go for the presidential election, then you will see maybe the first year of February or the second year of February, who will be the president of the Unya Umea. And we are not sure about what role she will take in the upcoming administration. Because maybe we thought that she would be the chairman of the lower house because she's a representative of the lower house. So she would choose to take over the chairman of the lower house. But at the same as she said, she will be very close to the president. So how she will do, maybe she will serve within the president, the cabinet, maybe as a minister, mentor, or like in Singapore. If she does, yeah, she will be very close to the president that she can manage the government by herself very effectively. But if she choose the way, she could not be a member of the National Department of Security Council. She could not sit in the top of her body as well. So we don't know yet even which role she will take over. And so I thought I could not answer the question you asked. But Shuman, Shuman. Okay, Shuman. It's interesting. I believe that she will have some kind of high level position within the NLD administration. Yeah, because the Osasuchi and the Ushaman have a very close relationship. We even learned that he played a lot of roles in facilitating between the Osasuchi and the senior general, Dhan Sri. And also he just finished the law degree from the corresponding course. So that means he's available.  They have learned they have taken the course of law degree for many years. So now they call it such degree. So they are really fit to be fit in the some high level position in the NLD administration. Also don't forget in the year 2020, 2012, when NLD wins the victory of 42 members of parliament. And even though NLD position is very minor role, but also Shuman has appointed Osasuchi to be the chairman of the law and rule of the law and tranquility committee. So they have the kind of the different age. So he gave father very high level job in the parliament. So maybe Osasuchi will give father high level position in our new government. Well, that'll be very interesting. All right, so I'm gonna ask my last question to the audience, to the panel. And then I'm gonna open it up for Q&A for the audience. So if you have any questions, be ready to ask them. But this is a question to you, Christina. You heard of this new upsurge in fighting in Shan State that's taking place. There's continuing problems in Kokang and so forth. How big a problem is this? Is this going to scuttle the peace process? Why did this happen in the first place? Does it complicate the whole environment for the dialogue that you were mentioning? Yeah, well, I think that for commander and chief Min Hong-Liang, he wants to pursue the strategy that the military has pursued all along, which is to enable the military to actually control all of these areas that have been under the control of ethnic armed groups or have been areas where you have a number of troops operating at the same time, but no one group in complete control. And so he has been continuing to press forward. Also another strategy that the military has used for many years is to try to divide and rule between the ethnic armed groups. So it serves the military commander and chief's interest well to see that now you have some groups who have signed this nationwide ceasefire accord and some groups who have not signed it. And these two groups are starting to move farther and farther apart. So that drives a wedge into the peace process and allows the military to argue that the peace process isn't gonna be successful and we need to continue with our strategy, which is ultimately going to result in our control over the entire land within the borders of the country. So Aung San Suu Kyi and the ethnic armed groups, the ethnic political parties really need to think about how can they address this? And I think for the ethnic armed groups, they're well aware that their actions of splitting do play into the hands of the military. But on the other hand, they find it very difficult to actually come back together. So it will be interesting to see if the NLD can come up with a strategy that can really bring everybody together and also get the military to pause in its strategy and take on the peace process more seriously. All right, thank you very much. So now let's open it up for Q and A with the audience. Raise your hands and please, when I recognize you, identify yourself, give us your institutional affiliation and then ask a question into the microphone. So yes, the gentleman at the back. Good morning and thank you guys. Paul Harrison from Blue Moon Fund. Sort of broad question, since many of the ethnic challenges are near the borders and obviously also one of the challenges of the country is to expand the pie, which means more development, et cetera. What's the role that regional economic, regional international neighbors are gonna play in all of this, China, Thailand, et cetera? In both the security and the economic growth that Aung San Suu Kyi will need to show to succeed. The role of the international community in the neighbors. Christina, perhaps you might want to take that. So all of the neighbors would like to see peace and stability in Myanmar because they would like to develop cross country transportation links. So linking India to Thailand, for instance, linking China to India. So these routes that would cross the country both horizontally and vertically, which would expand trade throughout the region and would benefit not only Myanmar, but also of course all of the neighboring countries. And that really can't happen until there's peace. But there are other interests as well. So in China's case, they have an interest in managing their relationship with both the central government and the ethnic armed groups that are along its borders. And the Chinese government sometimes plays one off against the other depending on the particular issues that are of concern at that particular moment. So we see kind of complex relationship between the powers that surround Myanmar and their relationships with the ethnic armed groups and the government itself. You want to jump in, Aung San Suu Kyi? Yeah, let me add a few things. In my opinion, this peace process now on the ring of callers. Because I know the leaders just said that they will not continue to use the NPC Myanmar Peace Center. And they don't like some contest within the nationwide ceasefire agreement. So when they take over the office, I think they will modify the whole process, beginning from the NPC to the nationwide ceasefire agreement. So this is kind of the uncertain future for the time being. At the same time, the unity of the ethnic troops are now collapsed. This morning, the UNFC decided to dismiss two organizations from its alliance, the Chinese National Front and the old national organizations, because they signed the agreement without the quality agreement by the whole group. And then now they are trying to follow another alliance with the war and the Khokyan troops. These are quite dangerous because the Burmese government actually already allowed them to follow the coalition and then the Burmese government already allowed to discuss with them as the whole group. But the whole group is not united. Now they are going to follow another group of coalitions with cooperation with the Myanmar and United States Army and Khokyan. This is kind of a danger. It will be quite difficult for the NRA to continue the peace process if there is no assistance from the international community. Right now the Japanese government has appointed the ambassador, the special envoy to assist the national reconciliation process in Myanmar. So the Japanese have been working together with the ethnic forces to facilitate their dialogues and meetings with the Burmese government. I think such assistance from the international community is quite needed at this moment. That's very interesting. Thank you. Priscilla, we'll come to you on this side later. Yeah. Wait, just wait. Thank you. I'm Priscilla Klap, senior advisor to USIP. I have a question for both Christina and Ongdian. The NLD ran in its campaigns in the ethnic minority states. They ran largely local candidates, which means that the NLD now has a large cohort of ethnic minorities within it. Secondly, if you look at the sheer numbers of people who were elected to the parliament, even though there were not many ethnic parties that won, some of those that won fairly large amounts like the SNLD and the Arkan party, and if I'm not mistaken, I think the combined numbers that they have exceeds the USDP in the parliament. So you can't really make a flat statement that the minorities lost out in this election. They may have more representation in terms of numbers of minority people in the parliament, in this parliament, in the next parliament than they have in the current one. So I think that it may not be fair to say that they took a bath in this election. There were many too many parties running. Would you agree? They really split the vote. That's number one question. Number two is on the Muslim issue. It's my impression that it was greatly exaggerated by election politics. That a lot of the anti-Muslim feeling that has or sentiment and activity that's gone on for the last year to year and a half has been connected directly or indirectly with the coming elections. Now that the elections are behind, maybe there'll be a better opportunity for beginning to tackle this issue. I mean, I think it's one of the things that the NLD is gonna have to do right up front, particularly with the Rakhine situation. It's going to come at them like a freight train from the international community. Okay, so there are really two questions. One is, are the ethnic groups really properly represented? And the second is, now that the elections are over, will this whole communal tension subside? Why don't we start with Aung Dain and then we'll come to you, Christiana. Well, first question about the NLD women's many seats in the ethnic states. I think this is a weaker call for the ethnic political parties. They are not united. And there's a lot of division within their own parties. And they are strong. They are influenced by a lot of personal interests. That's why they are now banished by their own people. So people are voting for the NLD instead of their own political parties. So this will be the weaker call for those political parties. Now they are starting to reform their organizations. They have reviewed why they lost in their own states. Now, I think they will be better positioned in the upcoming election. This is something I can say. About the even though NLD wins in these, ethnic state, ethnic candidates are also ethnic. And then maybe they will have the higher position within the union government and the state government. I don't know, but I believe that even if you found the state-level governments, I think NLD will choose their ethnic representative to run those state-level governments. But yet the organizational party and the traditional liberal democracy, they combine together around 42 seats in the union parliament. So they will have major seat in the upcoming union. And I think they might be included in the NLD government because those parties were traditional alliance of the NLD and they stood together with NLD for many, many years. So I believe that they will be included in the NLD new government. And then about the Muslim. Yeah, what I can say is that this is a blank mark for the NLD's victory. I don't care about the UEC or whatsoever because they have their own rules. They have their own friends of theirs. But NLD should include Muslim representatives in its candidates. But they intentionally excluded all those Muslim candidates. It is kind of shameful. So I agree with you that they have to do something to amend such a situation. We have the millions of Muslim population in the country. They must have proper representation in the parliament and all the administrative bodies. I hope that NLD will pay attention on this issue and try to amend such a negative mark on their victory. Sheila, you want to add something? Yeah, I do. So I think that for the ethnic minorities, their voting was certainly affected by the fact that the ethnic political parties were divided that in most states you had the 1990 party that had been affiliated with the NLD and you had the 2010 party that ran under the auspices of the USDP. And so votes were split and people were frustrated that their political parties had not come together. But another important factor is that a lot of ethnic minority people felt that only a big NLD win could bring about change in the country. So even if their political parties had been united, I think you would have had a number of people who still would have voted for the NLD. And so that's something that the ethnic political parties need to take into account. The other thing is that in regard to the Muslim question, for many people in the country, you know there is a sense of insecurity, a sense that with this transition that started with the Thane-Sane government, there are going to be people who are going to benefit economically and there are going to be other people who are going to be left behind. And within that kind of environment of economic transition, poverty, opportunities opening up that some people seem to have access to and others don't, it's easy to really propel a kind of thinking about nationalism that it can be very negative. And I think that that's something that the NLD is going to have to address, that there is uncertainty and insecurity and there are still going to be people who are going to try to inflame tensions around that issue. I'll end there. Bill, can I ask you a specific question with respect to the whole Muslim and Rohingya issue? We always, whenever you hear commentary on the Rohingya issue in Myanmar, we always talk about a path to citizenship for the Rohingya who live there, some of them live there for generations and so forth. But nobody links that issue to the whole question of immigration from Bangladesh and other borders into Myanmar. When you talk to the Burmese, they say, listen, one can't really be dealt with without the other unless we have some agreement on immigration. So if you do give citizenship to those who are already in the country, we don't then, we are not faced with another fresh wave of immigrants and then we have the same problems before. And this sounds like it's very similar to the issue of the United States. It's an issue which is being confronted in Europe and it's an issue now in Myanmar too. Did you have any discussions of this? Did this sort of issue come up in your discussions? This issue is now a constant because it goes to the heart of citizenship as well as identification for verification that you have the right to vote in that society. The European Union Observation Report highlighted the fact that many of the people who were turned away did not have their name on the list because they were in fact illegal immigrants to Myanmar but had lived there for more than 20 years. An issue that we have in this country and many other countries. There has got to be a larger discussion around both identification of citizens as well as immigration. And it's not just a discussion along the US-Mexican border or all of the borders of Europe or the borders of Bangladesh. If you visit with members of the Indian Election Commission, they will detail their concerns about illegal immigrants from the state of Bengal on the Bangladesh side coming into India and then qualifying as voters there so as to get into social benefits. So this whole conversation is going to be a dominant one in election administration and it's much larger than this particular country. It's a global issue. Thanks a lot, Bill. All right, from this side, the lady at the back. Come here, lady. Yes. Please identify yourself. Good morning. Andrea Montano from Crumpton Group. The NLD has been highly criticized over the years for being a very centralized group and the constituents often have to clear themselves through Aung San Suu Kyi to pursue any sort of initiatives. To what degree will the NLD MPs have independence within parliament to pursue the needs and issues of their constituencies? And the second part of that question is, is what are the red lines that Aung San Suu Kyi is currently facing with the military given that she has stated that she will be Myanmar's true leader and within the constitution, it specifically states that nobody will be above the president and the military has come out on several Facebook postings actually saying that they will make sure that they enforce the constitution. Thank you. Great question. So the whole sort of speaking to the authoritarian instincts, if you wish, of Aung San Suu Kyi. And then what do you say? Well, it's an NLD, it always helps the elastic crisis. The bodies solely depend on the elastic of Aung San Suu Kyi and over the 27 years, they haven't selected the succession of leadership. In 2012, we were very happy. When I recall for the first ever conference, we thought that it would be a good chance to set up the proper leadership at the various levels. But in the end, after the conference, NLD didn't set up the proper rules of the leadership. They only elected Aung San Suu Kyi as the chairman of the body, but the central executive committee was appointed by Aung San Suu Kyi, not elected. So even though central executive committees are now the decision-making body, but they are not elected by the members of the NLD. It is a kind of the leadership crisis. It will continue, it was for many years. So I hope that NLD will provide, refine itself and create the proper leadership through the election from the grassroots members. And if they would like to face it, they would like to win the election another five years, make another five years. So they have to do something to make it their party. And then the red lines. For me, I think that the military and the NLD, they were worked within the current system of power sharing. But so now they will be influenced by the many other ideas. And then on December 4th, before two hours before Don San Suu Kyi went to see Senior General Daishui Nijirou, Senior General Mayon Lai delivered a speech at the passing of the great ceremony of the Defense Service Academy, 57 intake in the U.N. He spoke about, in his landing speech, he spoke about the military's participation in the country's politics and he said, quote, since democracy system enhances one's value in due respect, we will have to proceed for the betterment of the country with a reciprocate arrangement, unquote. So by emphasizing the reciprocate arrangement, he made it clear that on San Suu Kyi and as long as on San Suu Kyi and NLD acknowledged the role of the military and treated with respect, the military will respond then with the same attitude. So I think this is a real lie. The real lie mean maybe on San Suu Kyi will be forced to consider some option. For example, the force of military to leave away from the power right away and also make herself to be the president by using the popular mandate and trying to amend that constitution, then there will be the real lie for the army's military, I think. All right, we've got about four minutes left, so I'm gonna take two questions this time and then we'll have to wrap it up. So there's a gentleman right here and Michael Martin, yes, come, if you could keep the question short, I'd appreciate it, yes. My name is Nyain Min, I'm just a regular citizen here. As a regular citizen, we are always interesting who will be the president of Burma and then nobody knows right now. But right now in Burma, there is one kind of news floating around. On San Suu Kyi, a serve will become the president. There is a way. So once on San Suu Kyi become the president, what will happen to NMD? Thank you and Michael. My question has Michael Martin from Congressional Research Service. Inside the new union parliament, assuming that they're allowed to take office, the actual largest opposition party is going to be the military. So want some comments about what the military's function will be or how they will operate within the new union parliament. Second, the current commander in chief is approaching supposedly the age limit for retirement. Is there any speculation on he may step aside, what role he might have post-retirement? And in that context also, under the constitution, the commander in chief appoints three of the key ministry positions, defense minister, border affairs. Ministry of home affairs, border affairs and defense. Any sense on who might be those three ministers and what implications that has for the post-April government? Thank you. Well, I'm not quite sure what you meant by saying that there's a view now floating around that Ong San Suu Kyi will become the president of, because I thought that she was not going to be allowed to become president because of the constitution. But can anybody speak to that issue? Would you, Christina, would you like to start?  Yeah. There's speculation about her presidencies, because after she met with senior general Dan Shui. So people have shown that this is a great life for senior general Dan Shui to amend the constitution, especially the section 15 and a half, to make her eligible for the president. So it was a rumor circulating around, around Rihangou and many other cities. But for me, I don't think it's possible. The first, even Dan Shui allowed, Dan Shui made the generalize and the military allowed to make such an amendment to the constitution. They would not have been right away. So when the new parliament, sorry, in February, when the new parliament started to take office, their first duty is to elect the chairman of the board parliament as well as to elect the president. And during the month of February to March, the president-elect will nominate to fill the positions at the union-level ministry. So he or she would spend maybe about two months to fill all the positions and he or she would submit those names to the parliament for the approval. And only in April, it was that the new president would take office. So to amend the constitution, by the new parliament, I think it would take longer time. Longer time, maybe two months, three months, I don't know yet, but at least 20% of the MPs had to submit a single resolution, single drug bill to amend the constitution. And then one of the parliaments would take over, first, discuss, and if drug bill was passed by one of the parliaments, they would move to the second voting of the parliament. So even the parliament had a strong agreement, more than 75% of the people to support such an amendment, it would have to go to the national referendum. So it would be long time. So I don't think it is possible for Donaldson to become the president at least within a year. And another second point is that even though she met with Aung San Suu Kyi, now we've got a lot of negative responses from the president office and the commander in chief's office. Both said they don't know. They were not informed in advance. They didn't know about such meeting. And some of the elements, even playing, they should be on hold of federally meeting such a meeting without informing those are president and the commander in chief. So I don't think it will happen. Yeah, Christina, what about the part of the military being the largest opposition party in parliament? How is that going to affect things going forward? Right, I think the military is going to play the same role that it's actually played under Thane Sainte's government, which is under Thane's government, they assumed that they and the USDP would be united. But in reality, it didn't work out that way. In many ways, the USDP led parliament was challenging interests of the military. And so the military's role was to ensure that its interests were protected. And certainly they're going to feel under an NLD dominated parliament that that's an even more important role that they need to play. I don't see the commander in chief retiring quickly. I think that it will be important for him to see that the military's prerogatives, the military's powers are maintained or that any compromises or reductions in power that are made are made under his watch and would not overly reduce the influence of the military in politics. Bill, you have the last word. Okay, what I would say is both questions highlight the fact that the society is in transition. The political process is in transition. This transition is going to have great implications in the next year, two years. It is why we as an international community, not just as representatives of the United States or wherever, can afford to take our eye off of the political developments that are going on in this very complex society. In my business, elections are one day affairs and then suddenly goes to governance and everyone walks away and says, well, democracy worked or democracy didn't work. No, the reality is the challenge is ahead of us. Evolution of ethnic representation, evolution of the political party system, how the parliament is going to work, how the military is going to engage with it now in elected civilian government with a mandate. All of these are issues that in democracy and governance are central to whether or not the people's voices and votes ultimately rule. And just as I ended my presentation saying, something that's going to happen next spring is she gets to appoint a whole new union election commission and there is a constitutional reform process underway, it's going to issue a report. Does that come back out to another referendum and we have another major national election in 2016, 2017, that's not inconceivable. And just in the case of the military relationship, if we decide that we've got to give the military a year rather than have a substantive military to military exchange, it'll be a year lost. And it won't be a year moving forward as we as the United States have been able to develop substantive military relationships with other countries and their transition to democracy and then made the military in effect, agents of protecting that democracy going forward. And that's the challenge for all of us the next 18 months to two years. Well, that was a superb concluding statement, I thought it was absolutely superb. And I just want to emphasize that reflecting what Bill said, we continue, we hope to continue to have events like this as part of our Myanmar votes series. And I just want to add that this has been done in collaboration with the Southeast Asia Studies Program at Johns Hopkins University, School Advanced International Studies and with the Asia Society Policy Institute. And of course, we're always grateful for the support of the Japan External Trade Organization which supports the series as well. So with that, thank you very much to all of you for coming and please join me in thanking this outstanding panel. Thank you. Thank you. Thank you. Thank you.


Thank you very much for the invitation to participate in this very interesting conference and to speak. It's a great pleasure. So I'd like to talk about WKB, and this is, I think, what Professor Iqal calls, Varroes Resurgence. So the plan of the talk is one to talk about how to do the endless continuation in some particular case. And then the second part, I'd like to talk about some more recent considerations to try to compute the exponent. And the second part is joint with Ludmil and Khabzarkov, Pranav Pandit. And then for the first part of this work was also with Alex Nohl. Then for kind of a subsequent part, which is not really related exactly to this question, subsequent work in the symbolic geometry with Fabian Haydn. OK, so first the basic setup. So the basic setup is we have an equation. Let's start with an equation of the form, so I'll try to write this in a kind of standard form with an h bar. So h bar d plus or minus, let's say, plus a of z times a vector equals 0. So this is our basic ODE. And so it's singular in the variable h bar. So h bar going to 0. And we'll really think of this as a variable 1 over h bar going to infinity. So then let's diagonalize the matrix. So this is going to be the spectral curve. If we try to diagonalize the matrix, of course we want to know whether the eigenvalues of the matrix, the eigenvalues of the matrix, are multivalued functions and that forms the spectral covering of z. So what assumptions would that be? A of z, yeah. Well, some assumptions. Let's not be too specific. Let me make some assumptions. Let me first diagonalize, and then we'll make the assumptions later, OK? If particular is diagonalizable, yes, one assumption. For example, yeah. We'll have a more specific problem in a minute. But kind of the problem is that part of the discussion isn't going to not really exactly applied to this case, as you'll see. But anyway. OK. So that means, well, let's choose a matrix, s of z. Also, I'm being a little bit nonspecific about what z is. So z is a one-dimensional complex, z is a Riemann surface. Come back up? No, no, I mean, if it was come back, we would really want to look at the universal cover anyway. So roughly speaking, it's the disk, OK? But there's this question, but I think which has already been evoked in previous talks, the question about the completeness of some kind of metric, you know, whether you sort of, and we're going to somehow or other assume that you're not going to sort of fall off the edge of z when you do your flows, OK? So let's choose s of z so that s inverse a, s is a diagonal matrix, which I'll for now write a1, an. So let's just sort of, I mean, a is really the matrix of one form. So maybe when I write, if I write the variable, then I'll have a dz, and if I don't write the variable, that includes the dz, OK? So let's just choose, let's just look at an example. So I think it's important, I never really did this example previously, but this is important to do this example, which is a is the matrix 0, 1, v of z, 0 times dz, and then s, so s, the best thing to choose for s actually is v to the minus one quarter. Sorry, v to the one quarter, I think it's minus one quarter. There's a plus or minus, maybe, and then s inverse, if I'm not mistaken, should be, but this might be mistaken. Something like, you can do the thing and tell me if I'm, but anyway. And now, what is s inverse times ds? So s inverse a, s, so the diagonal matrix is just what you think. So the v of z, it's really the coefficient of a quadratic differential. And it's v to the one half. The diagonal values are v to the one half and minus v to the one half. You guys all know this better than I do. Then s inverse, but maybe an interesting point here is s inverse dz, ds. So when we make the gauge transformation, we get a term which is s inverse ds, which is kind of important. That, if I'm not mistaken, is like, so the point here is that this has a logarithmic pole on the off diagonal pieces. And we chose the one quarter here so that it has zero on the diagonal pieces. Okay, so now we get a new equation, which is so let's call the new a is just the diagonal matrix. This should, sorry, this should be r. This is the rank, this is the rank. And then b is this extra gauge term. And the new equation is d plus one of h bar times the a, the new a plus b. So this is the equation I actually want to look at. And then in the example, b actually has logarithmic poles at the turning points. The turning points, well, in general, that's for the example. But the turning points in general are the points where a i minus a j vanishes. Now what's the question? So the question is we fix two points in our Riemann surface. We fix a path from one point to the other, and let's let m, so m depends on h bar, is the transport matrix from p to q, okay? So this is gonna have logarithmic growth. So this had logarithmic growth which is bounded by some constant in the size of one over h bar. The constant is basically the size of the matrix a along the path gamma, okay? So this is an entire function of h bar, let's see. It's a function of one over h bar. I mean, I'm calling this h bar for obvious reasons here, but maybe the better parameter to think of is one over h bar, which I think some people are calling eta, okay? So that's the question. So that's supposed to be a function. So that's the function in the non-Barrell plane. That's the function that works we're gonna transform into the Barrell plane, okay? But before we do that, let me just write the expression for this function. So this is kind of important. Let me not derive this expression, but I'll let you guys imagine. So m is gonna be a sum of mi of h bar. So the sum is over, the i are multi-endices i0, i1, in. This is n not, this is different from r. So these are the matrix, these are the indices for matrix coefficients. And mi equals, let's see. Let me write the formula and then I'll write you the definition of the terms of the formula. Mi is the integral over delta n of e to the gi of z over h bar times B. Now what are the terms in this formula? So here, z means z1 up through zn. It's a point in capital Z to the n, okay? So the terms in the formula, so gi is a function from capital Z to the n into C. So gi of z1, zn is the integral from the point P to z1 of ai0 plus the integral from z1 to z2 of ai1 and so on. On the spectral curve, you should make a nursing curve or purchase a pass. Yeah. How do you follow your pass? Yeah, okay, so sorry, thank you. So we've kind of replaced z by the, the cameral cover, actually, where the, where the, the different diagonal terms are distinct. Yeah, z new. So I should, well, right, well, I guess what I wanted to say here is really, sorry, this first part was to reduce to this case. So what I really want to look at is this equation where a, I really want to look at this equation where a is already diagonal, okay? This example is to explain how, for example, in this typical quantum mechanic case, you can reduce to that case. But of course, you have to make the covering where you take the square root of v.  In a sense, I'm just fixing two specific points of z and a path from one to the other. So that's going to be a little bit different from, for example, what happens if you try to use Fokken, draw of coordinates, where you need to choose, choose flat sections that have a certain asymptotic property at singular points and that kind of thing. Something like that, yeah, yeah, yeah. And, excuse me, do you assume that the AIs are these things? Well, let's assume that they, yeah, let's assume that the AIs are distinct, yeah. Assuming that, yeah, yeah. And in fact, maybe I mean, kind of have, well, okay. Let me not be too specific about the precise hypothesis here. Anyway, okay, yeah, but the AIs should be distinct, yeah. Sorry, and maybe the other hypothesis which I didn't say is that the BII are zero. We can assume that also by making a gauge transformation, that's kind of important. But again, you can see that in the example. In the example, we had to choose the one-quarter there in order to get that property, okay, anyway, so this is the function. So this is the main function which controls the asymptotic, the exponential growth of our problem, okay. And it's probably useful to notice that this is also equal to gi0 of p, maybe q, I'll say, gin of q minus gi0 of p. So if we choose primitives gi of the ai, then we have something like that, plus the sum of gi k minus 1 ik of z, okay. So if you vary one of these points, z1, for example, the variation of the function g there is given by the difference of the ai1 and the ai0. Do you want to apply it on the same path? So for now, the points line, that's the next statement, which is the delta n is the set of points of the form gamma of t1, gamma of tn, where 0 less than or equal to t1, less than or equal to t2 and so on, less than or equal to tn. So for the moment, the points, the z's are the points on the path, okay. And then what's b? So bi, so bi of z is really a form. So it's just a, it's the form that you got by taking the matrix coefficients in an obvious way with these coefficients. So it's bi, 0i1 of z1, bz1. So b should be an n form, right, because we're integrating over an n-dimensional real cycle. So this is n. So we're integrating over an n-dimensional real cycle in an n-dimensional complex space and we're integrating a complex n form. Let's see who does this most often. Okay, that's all for the formula. Now, okay, let me, before going to the Burrell plane, I think this is maybe important to say before we get to the Burrell plane because then we'll do the same thing in the Burrell plane, but before we get to the Burrell plane, the main point here is we would like to apply some kind of saddle point or steepest descent method for this integral. What does that basically mean? That basically means we want to move the cycle, because this integral is basically independent of the choice of cycle and integration because it's the integral of a holomorphic form which is closed. This is a holomorphic form, but we multiply by a holomorphic function so it's still a holomorphic form, so it's still closed. So we can still move the cycle of integration and we try to move the cycle of integration so as to minimize the real part of this function g. Okay, that's if we're trying to analytically continue in the plane, I mean in the, maybe I should draw that picture about something. H bar is real? Yeah, that's, sorry, I realized I should draw that picture now. So for the moment one over H, let's see, H bar is a, one over H bar is a complex parameter. So one over H bar is really any point of c. And the point is that this function, well I guess we're not quite there, but yeah, but yeah. So if we think of H bar as being real and then we want to make the function as small as possible then we're interested in the real part of that. Thank you. So H bar is real or complex? No, let's keep H bar complex, but in the example I was talking about diminishing the real part of g, that's for the case of H bar real. If H bar has some other direction then you would turn by that amount and instead of the real part of g you would diminish the real part of e to the i theta times g. So let's do, okay, let's do the Braille transform. So now let's go to the Braille plane. So the variable c is going to be dual to the one over H bar parameter, okay? So let's define m hat of c defined to be equal to the zero integral from, what I wanted to stress but I said it already is that this function has exponential growth of exponential order one of one over H bar. So we can make the following integral, integral from zero to infinity of e to the minus, I guess it's a minus, e over H bar times m of H bar times d of, so I'm sorry about this but this is d of one over H bar. So I guess if we wanted to do dH bar it'll be there's a factor of H bar in there somewhere. As I said I would really think he in terms of the parameter one over H bar and this is going to be a sum of terms, so we can also do the Braille transform of each of the terms in the sum and if I'm not mistaken the formula is the following that the mi of c are the integral over the same cycle delta n of, there might be a sign problem, of bi divided by gi of z minus c, up to a plus or minus. I'm not sure, I don't remember if that was a, if there was a c minus gi or gi minus c. Basically when you Braille transform this expression you get that thing. When you plug that into here in Braille transform you get that thing. Okay. So I guess this is probably a good place to point out but so my whole investigation of this question was actually, I think in actual fact has to be said was strongly influenced by Professor A. Call's work. Although I didn't necessarily really quite realize this at the time, but I was following J. Arnaud Moll's class as a graduate student, I was following his class on Fourier transform for eletic sheaves. And, no, but yeah, okay, so I'm not sure he's laughing, but you know, at the time, especially as graduate students we became extremely adept at passing between the eletic number theory kind of picture and the demodule complex geometry type of picture back and forth basically. So, and also Le Monde said and somewhere in his course material he's had, you know, one of the references for this course is a called theory. So of course this was a whole course about eletic, Fourier transform of eletic sheaves but then when it came to have a problem in complex geometry then it was natural to do a Braille transform and then try to look at the properties of the function in the Braille plane. Okay, so now let's see. What comments about this? So the first comment is that this path of integration depends on h-bar. Okay, so sorry, depends on c. So this is well-defined for absolute value of c bigger, let's say strictly bigger than this constant c2 that shows up here. And the path of integration the path of integration from 0 to infinity is going to depend on the argument of c. So depending on whichever, if you have c which is big enough then there's always going to exist a path of integration with the property that this is exponentially decreasing. Okay, as 1 over h-bar goes to infinity because of that estimate. So that's kind of the answer to this question about whether h-bar is real or not. We have this function which is defined on the complement. So in the Braille plane our function is defined on the complement of a disk. And then the inverse transform in this situation is that m of h-bar is going to be the integral, a circular integral of maybe e to the c over h-bar times m hat of c, dc, up to a constant. And the circular integral to define m is taken around this region. Now geometrically what is this region? Geometrically this region is obtained in the following way. It's just take the image, so let's say z dot is a sort of disjoint union of things of the form zn, zi equals z to the n, okay. And then we have just a function g from z dot into the complex plane into the c, and we should really think of this as the c plane. Then we have this delta dot is sort of a sum of delta i. So we can just write this whole integral as a formal sum, you know, it's just an integral over a single cycle. So we can write sort of m hat in a formal way. And m hat of c is just the integral over delta dot of v divided by g minus psi. Sir, I think that this m hat should be a multivariate function, yeah? That you cannot choose its variable. No, no, no, but that's, in this case, so this may be, this is probably a slightly different case than some of the other resurgence properties that we're looking at. I mean it's kind of the same, we don't have like this infinite collection of poles on the imaginary axis or something like that. In this case, this m hat of c is a well-defined function, perfectly well-defined function on the complement of the disk of radius c2. Just look at the definition. This m is an entire function of 1 over h bar. It's also defined at h bar at 1 over h bar equals 0, kind of trivially. Okay, m is an entire function of this growth hypothesis. So for any value of c, we can choose the path of integration. Can you define that in half-blades? But you can just, those just glue together. No. They don't. No. Why not? We just defined this in a number this way. It's not convergent. It's real patterns. Half-blades. It's only in half-blades. Yeah, but then if you choose a different half-plane, we choose a different path of integration. Yeah, it's only good cuts, yeah. But it's the same function. No, but the picture we should draw, I mean, it's not only half-blades.  No. Why not? Because it's counterintuitive. Yes. No, I don't agree. I mean, let's just write down this function. This function is perfectly well-defined for any c, which is what I wanted to say now. So this is well-defined. So m hat of c is defined if c is not in the support of g-lower star of delta dot. And this g-lower star of delta dot is supported on a compact subset. All of these cycles have the property that g of the cycle is supported inside this disk. So if we take a value of c, which is not in this disk, then this integral is just well-defined. And this integral, sorry, this function m of h bar is just equal to the path integral around this thing. I think the reason, so we were discussing in the train with Jean-Pierre, the reason why this is maybe a little bit confusing is because here we're taking, we're not talking about irregular singularities. So if you introduce irregular singularities into the question, then the direction of the stokes lines are going to depend on h bar. So you can't, so the irregular monotromy is not of this form just fixed two different points. The regular monotromy is going to be an irregular monotromy in some stokes directions, but which depend on the direction of h bar. That's maybe in a professor I call this talk was the combination of equational and co-equational resurgence. In this case, we're just talking about, for example, a compact Riemann surface. We don't have this essential, this irregular singularity question. So anyway, I mean, if you're convinced that there's a mistake, please let me know, but I don't think for the present purposes I don't think that's... Okay, so now what are we going to do here? So now what's the goal here? So the goal is to, let's write this over here. So supposedly what we're going to do here should work in that type of case also, I suppose, but that's not what I'm claiming. Okay, so now what's the goal is to do an endless analytic continuation of this function, m hat of c. So what's the idea is that the one we just noticed that each mi has an endless continuation. So this is just sort of some slightly infinite version of Gauss-Mannien for finite dimensional integral. So if this map g were a map of, a proper map of algebraic varieties, then this would automatically satisfy this property. And here we have a slightly infinite version because this integral is defined on this set z, which is typically going to be like the abelian cover of a compact Riemann surface that you get by mapping it into its Jacobian. So there's some periodicity. But the singularities themselves are sort of at least either containing, I mean either finite points or maybe in the worst case, if you have to blow up something or something, are just going to be compact subsets of z to the n. So whatever happens around a given singular point is just like the algebraic geometry situation. So this kind of adds, I mean that that's not really approved exactly, but sort of in terms of general principle. And then, so the main question too is how is that they converge? The sum, the sum of continuations converges. So let me just give the definition of endless continuation, or weekendals continuation. So let's say fix a disk. So let's fix a disk where our function is defined. And then it says that for any m, there exists a finite subset, s index m inside the c plane, such that for any path, we should start at a disk because our singular set might well have points inside that disk. So we can't just fix a singular starting, a single starting point. We need to just fix a sort of infinite set of possible starting points. But we assume that our function is continued inside the disk already. So for any path starting in D0 we need to pass m of length less than or equal to m. So this is the property which I'm claiming we can prove here. I think it's probably useful to consider a weaker property. That's why I put the word weak here. I think it's probably useful to consider a weaker property because this is kind of a rather strong property actually. So the weaker property would still require that the winding number of the path also be smaller than m. Then the statement is there exists a continuation along the path. If we don't put the winding number condition then that actually tells us that you can go any number of times you want around a given singularity without sort of introducing new singularity. That doesn't seem like it would necessarily be true in general. So this is the definition I'd like to use for endless continuation. I think there might be other possible definition. So that's the thing we'd like to prove here. Now what's the technique? So to illustrate the technique, the technique is that we need so we can make a general statement about one but the point is that if we want to get the convergence then in part one we actually need a very specific continuation procedure. Rho is a path. So any path in the c-plane of length less than or equal to m then... You can draw the picture. Yeah, so let me draw the picture. Let's draw a bigger version of that picture. So our function is a priori defined on the complement of this disk of radius c. We start out with our D0 here. This says that if I choose a length like the length of this backboard there's going to be a finite set of singularities which could be outside of here also such that if I continue along a path that goes like that then I can continue my function along any path that goes around these singularities of length less than or equal to m. Then as m increases the set of singularities gets bigger and bigger. That's this resurgence phenomenon. So now what you might say is the first thing to do of course is to start from this point sort of continue around the region and see which singularities you hit first. This property implies that there's a finite set of singularities that are hit before any other ones and then the real domain... the real sort of complement of a convex domain on which m of psi is defined is going to be the convex hull of that finite set. We're claiming any rank here. So the point here is to use a specific continuation procedure in order to get a control on the convergence so that we can treat the convergence question. And what's the procedure? The procedure is to use gradient flow. In the talk I would like to discuss the case where we're just... rather than trying to continue along some complicated path we're just trying to move this domain of integration over to the left here until it hits its first singularity. That's kind of an easier question. But what I would just like to point out is that it's the same procedure that works to continue along any sort of piecewise segmented path. We just apply this moving procedure along some neighborhood of that path and then move in this direction and so on. That requires some technical things that are not really very interesting. So let me just not discuss that here. But you can do that. Let's just assume that we're just trying to decrease the real part of G. If we're trying to decrease the real part of G then we use the gradient flow of... So what we really want to use is the gradient flow of Gij of the real part Gij. Excuse me. The path of the Riemann surface is of infinite type. Is not a problem. So as I said, I wasn't saying really what hypothesis there are. You need to make a hypothesis that says that if you actually sort of flowed to the edge of the Riemann surface then you would have decreased the real part of G by an infinite amount. I mean, to do this... To do this process we only have to decrease the real part of G by a finite amount and even along our path of a fixed length we only have to sort of decrease all the different real parts of the different rotations of G by a finite amount. So the kind of completeness properties that we'd like to make sure that we don't get to the boundary of the Riemann surface before sort of an infinite amount of decrease. That's obviously a big problem in the case where B has poles because in the case where B has poles you really need to not hit the poles of B. So you need to draw a little circle around the poles of B which causes exactly a problem of this sort. That's more complicated. I tried to discuss that in a preprint I wrote for Jean-Pierre's birthday celebration. It seems pretty incomprehensible to me so I don't necessarily claim that it has to be without error and so on. The claim is you can actually even do that too so that's why the claim says that even if B has maybe let's say loving any poles this should still work but that's a little bit more delicate. My original discussion of this was just in the case where B is holomorphic but which unfortunately doesn't apply to the example. Okay so the status of the proof and the other statement on that level is that in the case where B is holomorphic you can get a better control over the type of the singularities that are met. In the case where B has poles I don't have any idea how to control what type of singularities the function will have here. I think there's sorry. No just I mean the singularities at the singular points. No the values of the singular points no but the singularities of the function the singularities of m hat at these points could have an essential singularity so I think I mean it's going to be it's definitely going to be a trance series maybe not convergent you said probably not convergent in general I have to say I don't even know that there exists even one point where it's convergent so that may be a caveat here. In the case where B is regular you can at least show that the singularities have some kind of as in product expansion and so I'm hoping that in the case where B has logarithmic pole I'm hoping that you would be able to show that it has at least one over you know one over C minus A0 I'm hoping you can show that the function has at least growth less than that but that's that's conjectural for the moment it's a sense of curve actually finite dimension is not one dimension it's almost a problem yeah these are finite each term is a finite dimension integral so each term is pretty much controlled it's a sense of curve in product of corpus of curves yeah that's easy so I mean that's easy so one in principle is easy two I won't be able to explain really why it's true anyway but what I would like to just say is that in order to do two in a good way you need to treat one in a systematic way rather than just by making a general statement like that which is as follows but this leads to something interesting leads to an interesting geometrical thing so let's see how to do that but so for now what we would like to know is that rather than treating a general path let's just treat analytic continuation in the plane like that which corresponds to the case h-bar real let's just try to push our cycle as much to the left as possible and to push our cycle as much to the left as possible we're basically just going to flow by the gradient flow of this function so now let me just explain what the basic problem here is that this is kind of the main phenomenon that's happening I think I'm not going to get to the second part of the top unfortunately ok so the main phenomenon is that this integral is that delta n you know delta i which is delta n is a relative homology class it's a cycle of boundary so remember this is a real it's a real triangle in a real n-dimensional triangle in an n-dimensional complex space this is z to the n so what are the singular points of delta delta should be on the board here or I just erased it delta is here what are the boundary points of delta well it's when t1 equals 0 or t2 equals t1 and so on or tn equals 1 or you can just see in this integral the singular points are when z1 equals p z1 equals z2 and so on up to the zn equals q so the singular divisor is z1 equals p union z1 equals z2 so it's a union of I guess n plus 1 divisors inside z to the n so it's just a complex simplex and this integral is going to be independent of the choice of representative in here in this relative thing however the gradient does not preserve the boundary so what do we need to do we need to descend the cycle so we need to inductively we need to inductively descend the cycle the boundary first and then descend the whole cycle so let me just draw the pictures I think this should become relatively clear with the drawing but the point being that we need to we want to do this in a systematic way so we want to apply some actual flows to descend the cycle because that's the only way we'll have a control over the size of the cycle as a function of n so what happens if we do this for delta 2 so delta 2 is a cycle like that so if we draw this inside if I'm not mistaken one way direction here so this is z1 equals z2 this is z2 equals q this is z1 equals p so these are complex planes these are complex remount surfaces so this is z2 and this is z each of these things here each of these guys is zn-1 and they intersect in zn-2 and so on so what we need to do to descend so if we apply the gradient flow on this triangle only then it's no longer going to have the boundary on the boundary of course that gradient flow is a part of the picture but we should first apply the gradient flow to the path on the boundary like that then do that on each boundary piece so one thing to notice is that boundary pieces have their own indexation if this is a zi this is going to be like a zi prime the functions g are compatible so the function g on the z with its indexation on the boundary is compatible with the other one so we apply the gradient flow on the boundary then we take the triangle plus the homotopes on each of the boundary pieces I mean this is the flowed path that sort of might have hit a saddle point here for example so this is a flowed down path here but we have to take the full homotopy of this path and then add that to the triangle and now we can flow this entire piece down now the new cycle so this part here is on the boundary so we can use this as a new boundary okay so the new cycle is going to be everything obtained by applying the flow plus what was obtained by applying the flow to the boundary pieces okay so it's going to be sort of the bottom of this picture plus the side okay excuse me I don't understand why the vertices are separated by the gradient flows because the g function on this thing is different from the but here we're flowing by a gradient flow which might does something to the points p and q also but of course it means that the flowed path of this boundary is this plus this plus this I'm doing the two dimensional case this picture is the one dimensional case I want to try to say here in the two dimensional case there's the flowed down part from here we flow down this segment that gives us this segment that we need to add this piece and this piece which are given by the flows of the boundary so the same principle in two dimensions is going to tell us that the full cycle we want is the flowed down cycle of this stuff plus the boundary pieces okay now the point is that the resulting cycle is that my gradient flow of the given function is always I should take into account the period of boundary which I should start with now yeah that's basically the idea so the new boundary of the cycle is this so it still goes through the vertices okay but when you write the new ones on the boundary no the vertices of the new triangle are still the same as the vertices of the old triangle but we had to flow I mean so what happens if you think about this maybe it's hard in two minutes but if you think about this for a little while if you've got a bunch of different flows and I think Misha even wrote a paper about this if you have a bunch of different flows you actually get the following structure which is you have a sum over labeled trees let's call that delta for the tree T or something like that what's delta for the tree let me just draw this like this so this is our original path gamma and then so in this picture there's a piece which corresponds to the original triangle that's going to be the tree these two trees that's going to be trees like that okay so with a one so this is the segment zero one okay the top thing of the picture is the segment zero one where these attach those are you might say the places in the original cycle delta which are at the origin of the point okay so if we take our original triangle and flow down we get the picture T1 T2 1 1 okay but we have some other pictures which are for example just T1 now I'm probably going to have a mistake here but there's several different possibilities we need a label here so there's going to be like S1 1 or there's going to be a S1 S for example there's several different parts of the picture which correspond to this to a point here right the point here we got flowed I guess so here we flowed down by the gradient flow of we flowed down all the way by this gradient flow I guess the point is that so kind of a detail here is we don't really want to do the gradient flow inside the Z2 we really want to do first the gradient flow in one direction then the gradient flow in the other direction so those are going to be either the 1S or the S1 cases so there's maybe two two segment maybe probably S0 there's going to be really two segments so this picture okay and the the picture on labeled trees is we have a tree labeled with 0, 1 or some variable S and we have the top edges are labeled T1 up through TK okay so there's going to be variables S1 up through S and minus K the variable is T1 up through TK okay and the image of this so this diagram is labeled by the now in the regions of the diagram we have the indices and so on and the image point corresponding to this diagram is obtained as follows which is you flow along the gradient flow for the function G you follow along the gradient flow for the function real part of G I K I L for the time designated by the variable okay now what are the critical points I should probably finish here what are the critical points the critical points are the case where you end on all the different critical points so the critical points of this whole picture are the case where the bottom of the tree these are all the different critical points okay so if you think about it this is exactly the picture of spectral networks so these gradient flows so to be more precise there's really spectral networks but not for an imaginary direction but for a real direction and the real direction you could actually choose because in here you could either flow this way or that way it doesn't really make a difference if you're trying to move to the left okay I'm trying to follow the structure that you say that each leaf corresponds to a critical point right so the what are the places where you can't flow any further the places where you can't flow any further when you've hit a critical point in all the different variables if you hit a critical point in some of the variables but not the other ones then you can keep flowing in the other variable so the places where you can't flow any further so these are gonna generate the fimbles the places where you have critical points on all the bottom vertices of the tree basically so it says that the locations of these critical points are things obtained by by doing the gradient flow down to a critical point along each of these edges of the tree basically that's essentially some kind of spectral network type of picture so let me just finish by a caveat which is that in the case where that we were discussing before the more advanced case where the B has maybe first-order poles at the turning points then what I don't know how to control with this procedure is the fact that any variable is supposed to stop at a turning point so this point here might be a turning point but for a different variable not necessarily the I0, I1 variable so that's different from Gaia Tomorowski so a priori from this procedure in any case the locations of the poles you have to add extra possible locations of the poles basically and that's why I wanted to say in part 2 which is that maybe there's some hope using our work with Ludmila and Pranov on harmonic maps to buildings maybe there's some hope at least in the case of SL3 of getting a more precise information on the location of at least the first pole basically namely I think the conjecture is that the location is going to be this type of picture but where this is the I0, I1 turning point and so on I guess I should stop here let me just comment just how would you want to prove that this converges well basically when we do this flow we're always decreasing the real part of the function okay and then we're going to cut off our we're going to cut off our cycles when we decrease that by a finite amount so the size of the cycles is going to have some kind of condition like the sum of Si less than or equal to some constant and this generates an exponentially small region in fact together with the fact of course obviously the original delta is exponentially small sorry and factorially small this generates a factorially small size and the original cycle has a factorially small size so rough and then the calculation is that sort of the number you have to calculate the number of cells you get here is some constant to the n so constant at the n divided by n factorial and that's kind of the very rough so I'll stop so comment in the spectrum nature this is still open it's an exponential bound it doesn't appear on the number of spectral networks yeah it's a little complicated because it has trees no but so okay and this gives a slightly more precise information which is that it's only the spectral networks that you get by this procedure so it means that they have to go up and then cut the path so I think there's only finitely many we don't have closed cycles yeah it's good well for a given path and we're fixing the p and the q and so on then the number of spectral networks that are going to cut through the path in that way is fine yeah it seems to me that this aspect of the theory which you have covered should go over to higher dimension and I especially think of the banyan block formalism which I briefly flapped on which is a system of integral recursion with integrals exactly like the one on the top there with the denominators and so this would be very nice if you can prove because banyan block is formal if you can use to prove resurgence in higher dimension yeah maybe that was certainly being fun to do let me just comment maybe that as far as I know I mean but maybe I mean you know better but I mean from just kind of a very a priori perspective we're really using the fact here that you have a closed form formula for the function we're trying to compute so we're not so this is kind of not going in the same direction as what you guys are proposing which would be fantastic which is to take the perturbative theory and sort of create the resurgence function here we sort of already know what the function is we want to maybe prove some additional properties like continuation is very similar to what banyan block wrote in terms of iterated integrations but of course there's a lot of rigorous work to do but are they finite dimensional integrals? yes okay okay special networks in higher dimensions well maybe I mean I mean the initial the initial idea is just to use some kind of gradient flow to find the critical point so in the rank 2 case the quantum resurgence the ridiculous case you recovered the location of the singularities as found by a car found on a bar and in the location of singularities okay but what about the nature of the singularities how come that in your formalism you don't reach the nature of the singularities because they have very precise predictions for that well so in the general case this is kind of related to the each term m i c I mean if you look at this integral what are the singularities if bi has logarithmic singularities then we have we're gonna have some kind of integral like maybe Marcin can do this on top of his head something like d z 1 up to d z n divided by something like z 1 up to z n but then times some kind of summation of z i minus c I think the integral maybe something like that so I think you can show that this integral has one over you know norm of c type of a behavior but I was just doing that this week actually I was trying to think about but that's gonna be the same that we're gonna have this type of behavior for any value of n so what that really means is that each m i is gonna have a series expansion perhaps at the singularity points but the series expansions all have the same order of initial term so the when you make the sum the series expansion if it existed the coefficients of the series expansion in the sum will themselves be series in the coefficients of each of the coefficients here which is different from and that's like one of the main simplifications in the original case where b is regular in the case where b is regular the powers of c that happen in the series expansion go up so any given coefficient is just a finite sum as far as I can tell you also have powers of logs in those series that also go up so the sum is not gonna be a regular thing it's gonna be a trans series with higher powers it's gonna be like sum of c to the n times log c to the n something like that but where m the value m goes up as a function of n at least that's in the regular case in the irregular sorry that's in the case I mean don't mean regular I mean the case where b is holomorphic in the case where b has poles I don't even see why the powers of log could all happen at the first term as far as I can tell maybe I'm missing something but