Hi my name is Marc and today we're going to talk about bike lights, especially the relight. 60% of the movements in Groningen are made by bike, primary movements. So everybody has these small thingies lights on their bikes because these usually break pretty fast in a city full of bikes and these run out of batteries. And the business model is very simple you don't make them water resistant so and it rains a lot in the Netherlands so you have to buy them often. But then Axe came with a very nice improvement. They made these rechargeable lights which has various settings and can be charged via USB. Very nice solution but since they are very nice and a little bit more expensive and very easy to mount and this mount they get stolen. The relight is a fixed light and it's charged via the movement of the wheel itself via magnetic induction. They look very nice they're easy to mount so let's do a small review of these new lights.  The only thing is that this is very soft metal as is the screw itself. So you do have a good chance when you try to turn it too tight of screwing up the screw which is a big shame they should have used better metals for it and then when you turn the light the lights start flashing and that's basically it that's how the light works. A few things I noticed well the first thing is it's a very nice system which you do hear it when it's turning you do hear little bumps and there's a little bit of friction so it does have an impact on the on the friction of the tire itself it's not very big but it does have an impact. The second thing is it's now daylight and it's still flashing. I would have put a center in there to detect that it's that there's enough light during the day so that it stops flashing. At night you won't get a beam also that's not a big issue but if you want to use this lighting to see where you're going that's absolutely impossible. In totally dark areas I would go for a beam and with a little bit of a battery on the inside we charge during the day and then you can use it at night when it's when it's very dark as a beam and when there's some street light you can use it as a blinking light. The blinking light is very bright so people do see you're coming so for a security measure and that's what I choose for it's very good. The construction itself is a little it is strong but I don't know if it's strong enough to survive the city life here in Groningen which is hard on bicycles but overall so it's a nice set of lights but it's not perfect yet. So to sum it all up is it a goodbye? I don't know these are rechargeable they're 35 euros roughly and if you take them off your bike they're very nice good lights which do work in the dark and you can even get a beam out of them so you see someone see where you're going. You will never have to charge these they will never run out of batteries they will always work they're fairly easy to mount but they are 60 roughly 60 euros so are they are they worth the investment? I don't know but it's a very nice lighting system and and it's it wasn't a very nice Kickstarter project. Thanks cheers!


Are you puzzled by the latest Bitcoin price movements? One of the biggest questions I always get from traders is, Charlie, why did the S&P do this or why did Bitcoin do that? I usually just say to them, yeah, there was more buyers than sellers, you know. This technical analysis, the only tool to assess the market with. If technical analysis is so great, how come people aren't rich and super rich and everyone is so successful? And what are the risks involved in crypto trading? Leverage. Leverage kills. It just does. Learn the basics of crypto trading and technical analysis with John Bollinger, Charlie Burton, Tom Vase and Big Chunks. These are the highlights of Cointelegraph Crypto Traders Live. I always prefer TA on the most liquid market and while I really like doing TA on the Bitcoin market, I hate looking at TA and anything other than Bitcoin because it's just too liquid and it feels like penny stock trading, which I hated doing TA on as well. Oh yeah, I agree that TA for me works definitely best just using Bitcoin kind of as my standard there. I agree that a lot of the altcoins, especially the ones that have a lot of low liquidity, do trade and do look a lot like the penny stocks, which you really can't get the best TA on because you get wicks and crazy directions and you don't have really the volume that shows you the true price discovery you're looking for. But in terms of Bitcoin, when we just start with basic TA moving averages, exponential moving averages, all the oscillators we use, they're very clear, I feel, in terms of what they're showing in terms of patterns. Most recently here, when we just had this breakout, everything was kind of lining up that we were kind of have a very volatile move. The Bollinger Bands, of course, on the daily chart were extremely tight pinching and showing that we were about to get something. And then when you see where we are in terms of where we are in terms of the moving averages, how the price action has been above the meaningful ones, 50 day 100 and 200, it seemed like the bulls had the upper hand on this. And that's what we saw in the price action. Charlie, do you have anything to add on this? As far as I'm concerned, I'm a technical analysis trader myself. But really, the one thing that I find out there doesn't matter what market and what type of trader you're talking to, they all want to be right as much as possible. But I don't care about being right as much as possible. And we all know that you don't have to be right that frequently. And I think that's the main thing for me with technical analysis. It's not necessarily about trying to be right 80% of the time. In your analysis, I'm quite prepared to be wrong as long as my risk reward is there for me. So if I can get a half decent risk reward on some of these moves that are there, then does it matter if I'm wrong 50% of the time or even 60% of the time? It doesn't. One of my most one of my best technical analysis strategies I have is actually about 40%, 40, 45% success rate. And yet it's the most profitable one that I have. So if you think about it, there are two major avenues to profitability and technical trading, in all trading, for that matter. One is your frequency. What percentage of wins do you have? Can be 40%, can be 60%, it's just a number. And the other is the size of your winners versus the size of your losers. So I'm guessing that Charlie has a system. If it's only 40% effective, but yet it's making money, so probably has a win-loss ratio of two or three to one in terms of the size of the winners versus the size of the losers. And if starting traders would think about the relationship between those two sets of numbers and would really look at them in their own trading process, they would improve very quickly, I think. Risk management was just mentioned earlier because technical analysis may not be the most important thing in a trader's arsenal. So before we get on to the actual technical analysis tools, I decided to really quickly grab a slide from a recent risk management workshop that I did. And in this slide, I'm literally, I grabbed a page from Wells Wilder Jr.'s book from 1978, New Concepts and Technical Trading Systems, and it was like a 70-page basically manifest on technical analysis with one page being devoted to risk management. And here's what he writes. The message of this book is that there are three parts to a good technical trading plan. Using a good technical system, using the system on the right markets at the right time, and using a good money management technique. Of the three, the third is the most important being money management, the easiest to learn, and the hardest to do. And then, and what I did with the slide, I basically said, hey, there are infinite amount of places where you can learn technical analysis. I teach technical analysis, and I do my best to teach you proper risk management and how not to lose your entire account on one bad trade, but it's going to be the hardest thing for you to do. But number two, I can't teach you using the right technical system on the right asset, on the right timeframe. And I think that is also a challenge that a lot of traders need to solve, and those that can't solve it end up being followers of other traders. So what do you guys think about this dynamic of learning technical analysis, knowing how to apply technical analysis, and making sure that you have good money management and risk management? So let's head over to Charlie, and we'll start with you, because you do have groups and newsletters. And what do you think about this dynamic, and how should a new trader manage this dynamic? Well, yeah, I mean, I don't have newsletters anymore. That was years ago, but I do have groups. Yeah, I think there's a couple of things here. We've talked about groups and followers and stuff, and we all have them. Is that a lot of people are looking for help, and they're looking for people who have got experience in the markets for help. And so I'm quite happy to provide my experience in that regard. Wherever I can help people, then that's a good thing. But as always, it is the most important thing, as what we emphasize is good risk management. The problem that a lot of people have is they'll look at a chart if they're a technician, or maybe if it's the fundamentals that are going on. And if they really believe that everything's lined up, and as you guys know, sometimes you can look at a chart, and you can think, wow, that has got everything lined up. And what happens to those average traders? They bet the farm on it, because they think, well, all of my indicators are aligned. The heavens have aligned for me. And that's the natural tendency for most traders is to then think, right, I'm going to bet the farm on that. But so often, the ones that we think are all lined up are the ones that actually fail, and the ones that we actually in our gut feel most uncomfortable about are the ones that actually work. So, yeah, coming back to your first point about risk management, I mean, we just say to our traders, risk up to 1% per trade. And if you stay below 1% for every trade, then you're pretty much going to keep yourself safe. You can sustain a drawdown when drawdowns come along, but you can still make some decent gains and have some good results with that type of risk per trade. You can build your trades and build into them and all of that sort of stuff, but if you start out at a maximum of up to 1% risk per trade, then I think that's always a good advice. There are two aspects to this risk management piece. Number one, Charlie touched a little bit on it. I have to disagree with him a little bit. It's the amount committed to each trade, and there are very good formulas for determining how much you should commit to a given trade. I really commend everybody the work of Ralph Vince. He's done more on position sizing than I think anybody else. It's very mathematical, and if that's a little bit too mathematical for you, perhaps another practitioner, Van Tharp, who has written extensively on position sizing, might contribute to that. The second portion of money management for me, other than position sizing, is some sort of risk control. I personally like trailing stops. I've written a couple of my own trailing stops, but Wells-Weiler suggested one. It's called parabolic. It's sort of a relentless approach to a trading stop in that it increments each and every period no matter what. I prefer the work of Chuck LeBeau. These are called chandelier stops, and they progress as the trade progresses. So if the trade stalls, the stop will stall. That's the big difference between those two approaches. But they're both progressive levels. That will keep you out of trouble. So position sizing is absolutely key. I think you should try to determine what it is in a formulaic manner. But a fixed number can work as well. And then the second piece is some sort of risk control. And for that, trailing stops for me. All right. And Vic Jonas, tell us about your any lessons that you said you've been trading for about seven years. Any horrifying experience of not following good risk management rules you want to share? Sure. All the time, actually. Being able to control FOMO in this market is incredibly important. Bitcoin, for the most part, tends to range. And then every once in a while, like we've seen the past week or so, has a big move. So it's great that you're able to capitalize on those big moves. But during the times of consolidation and ranging, the wicks we see because of the leverage market that Bitcoin is in in both directions can wreck an account, especially an account you use on leverage trading. So in terms of me and how I approach risk management, A, obviously, never want to put all your eggs in one basket or one tray. There's always another trade. If you have a chart that you're watching and you miss your ideal entry or it does something and you just aren't there to make the trade, preventing yourself from chasing into the trade after you've missed your ideal entry is so important. As and the more I trade, the more I become more conservative, I've found in my trading. I when you're new to trading the temptation to up your leverage and to turn a thousand, make a thousand look like 50,000 with like a 10x move or a 50x trade and thinking about, oh my God, I could make a ton of money if Bitcoin has a huge pop there. But what the crypto markets tend to do is to kind of screw people on both ends of the trade.  And in the end, the closing body kind of stays more or less where it was. And that's what we continue to see in this Bitcoin market. So preserving capital risk management is the most important thing, because I think the term wrecked is thrown around a lot these days, because people get wrecked very easily. And the volatility in these markets, especially in all coins, can come so quick. And if you don't have a stop loss in, if you're not protecting your capital and if you're not protecting your winners, it's okay to take a win. I think people when they're up in a trade and they're not used to being up in a trade, don't know what to do. They're thinking they hit the generational entry, if you will. And they're kind of just let it ride. And those are never, they just never work out that way. You know, that's why I look at trading in terms of scalping and swing trading and each trade individually. I'll take a lot of trades and try and make a few bucks on each trade. We're going to kick this one off with Mr. Bollinger. And I'm going to get very specific. We're going to get right to the meat. What are your favorite technical analysis tools? But I'm going to remove the obvious stuff. So no candlestick patterns, no chart patterns, like triangles or cups and handles, no moving averages. So we're talking straight up TA tools. Name three, one of them can be an overlay like Bollinger bands or Ishimoku clouds or parabolic stars, something overlays on the price. And two of them, oscillators. Your MACD, your RSI, your ADX have at it. So what are your favorite TA tools that aren't obvious that everyone else uses?  It's obvious. For me, it's Bollinger bands as the overlay. And then the two indicators that I would use as oscillators are percent B, which tells us where we are in relation to the Bollinger bands and bandwidth, which tells us how wide the Bollinger bands are. But having said that, especially in the crypto space, there are a ton of other TA tools that work really well. We talked here a bit about moving averages and such. They can provide some useful information. The classic oversold oscillators such as RSI and stochastics are quite useful. And I really like intermarket analysis in the crypto space. So I don't look at the tiny illiquid coins. I do watch an index of them, that shit-perp index. I find that pretty useful. But I look at the other major coins where there's a lot of activity, ether and litecoin, stuff like that. And I think that work goes back all the way to Bilohama writing Solongo. He called it his 3D method of trading. He's just look at related things and see if they're confirming your analysis. And I find that very, very useful in the crypto space. All right. Thank you, John. Charlie, let's go over to you. Okay. So very briefly, I do use moving averages. So I've quickly taken those off, as you said, they're not allowed. As you can see on the chart here, I've taken some moving averages off, but I use a MACD. I like using an NMA CD indicator for divergences. I find that works really well against support or resistance. So that's a favorite of mine. And just price action and trend lines and horizontal support and resistance. Literally just putting on those horizontal support and resistance. This is a chart of only enough euro-dollar. I know we're talking Bitcoin, but I've just bought this one up because I think this has been a beautiful pattern for such a long time. This building long-term trend line going all the way back to 2001. If I actually put this onto a maybe a quarterly chart, you'll be able to see it a little bit easier here. There we go. All the way back to 2000, this beautiful long-term trend line that we keep on coming back down and bouncing around. That's what we're bouncing off at the moment. Then we've got this declining trend line from the the highs of 2008-9. And so that's a, to me, is a beautiful chart there. And that's why I've been observing that. We've got a couple of horizontal areas of actually the first red line here. That first red line going back to 2015, that around 114 on euro-dollar has been kept on coming back up to test it. And I love it when price comes up to a resistance level or a support level and keeps on bouncing against it because at some point, it's probably going to break through under technical analysis rules. So basics really, price action, horizontal support and resistance, and trend lines, and a MACD. There you go. That's what I use. Jonas, what about you? What are your favorite technical analysis tools other than so one overlay and two oscillators? So I try and find what are the best RR setups for me, best risk reward.  I do like to use them. I have rules for how the price action responds on, let's say, the one-hour chart, the six-hour chart and the daily chart. I'm very curious in terms about the higher time frames as well. In terms of my oscillators, I really like to use the RSI and the stochastic RSI. I adjust my RSI and stokes settings slightly higher. The default for the RSI is 70-30. I go 80-20. And then the solve for the stochastic is 80-20. I go 90-10. And basically what that means for me is when the stochastic RSI, when both of our indicators are swimming above 90 or below 10, those are times when I'm saying, okay, is this an opportunity to long or to short? I do not long when the 15-minute RSI and stochastic RSI are above these lines. And I would consider a short or I consider a long and would never short if they're on the lower end of the oscillator spectrum. And that just gives me a sense of where we are on the overall wave pattern and where I can have my best chance to trade. When these oscillators are kind of in the middle, for me that's kind of no man's land and I don't see the clear signal to potentially take a trade. So I'm looking for extremes in those oscillators, mostly on lower time frames because I'm more of a scalper, and then try and take advantage of those. And those kind of offer me my best RR. I was just going to add actually I was just interested in the overbought stochastics RSI. I mean the one just interesting just because for me I'll look at a chart like that. If I put those types of indicators on, if I see them overbought we all know that markets can remain overbought for longer than you think. So is there another trigger that you'll use? Because sometimes you'll get your RSI or your stochastic or get up there and it will sort of just wiggle along the top as the market just trends. So do you use anything else to actually help you to decide that actually this is coming off and it's not actually just a strong trend? So these rules work best for me in a five and a 15 minute time frame. I absolutely agree with you especially in Bitcoin that on the higher time frames daily, weekly especially, you can have oscillators pegged way high. And that doesn't necessarily mean it's overbought therefore I must sell. We saw clearly with the weekly stochastic RSI that it was pegged at almost 100 for weeks basically during the big run of 2019 and a very frothy RSI as well. So you're absolutely right that a market can range and still rise while these oscillators are at their peaks. But that's why I only use these specifically for the very lower time frames because I'm not looking for a trend change. I'm looking for an opportunity of a scalp trade. Hey guys, let's move on to this dynamic between fundamental trading and technical analysis. So technical analysis is basically a new tool and the millennials and the new generation is falling more and more in love with it. But how much are the big institutional markets are taking TA seriously? And do you think that the amount of people that are investing in general is rising more towards the TA side because institutionals are still all about fundamental analysis. And what do you think that dynamic is? And do you think an at-home retail trader even has a chance to compete in the fundamental analysis game because I honestly don't think he does. But I'm curious about your thoughts. Yeah, the FA part of Bitcoin is really fascinating. There's so much more than TA that is available to analyze with Bitcoin, on-chain volume and other indicators, minor profitability, all these things that you don't necessarily see on your Bitcoin chart but can have a tremendous impact in the price action or determining what the future price action can be. I think a lot of altcoins tend to drive on news events, potential partnerships with bigger companies or something that tend to kind of move the price action sometimes more than the actual chart is suggesting. So FA does play a big role in this. And I think what I'm trying to do is enhance my FA side. I feel like I'm pretty strong on the TA side, but in terms of the FA side, when it comes to Bitcoin, there's a tremendous amount that you can study that can give you a lot more insight and data, I think, than the TA side can necessarily show you. And Charlie, what do you think about the fundamental analysis versus TA analysis? And what do you think about people tend to confuse news events that they hear with fundamental analysis? Because I always love to separate the two. Well, yeah, I think it comes down to innate human nature. We need to understand why something happened. And fundamental analysis sort of helps out that inner desire for people to be able to justify why something's happened. One of the biggest questions I always get from traders is, Charlie, why did the S&P do this? Or why did Bitcoin do that? And there has to be a reasoning and a sort of a fundamental reasoning as to why Bitcoin broke out last week or beginning of this week. And I usually just say to them, yeah, there was more buyers and sellers, but coming back to your point as well about fund managers and this snobbery sort of element to where we don't use technical analysis. And yet you look at some of the greatest traders of all time. And I always go back to the likes of Market Wizards. And you look at Paul Tudor Jones and Ed Secota and Richard Dennis. And some of these famous traders, they used a lot of technical analysis in their approach. So and I think for certainly for the average retail trader who is probably trading over a shorter time frame, then market sentiment is more important in the shorter term than fundamentals in my view. So and you can derive market sentiment from the charts a lot of the time and from obviously sentiment measures themselves. So I think for the big players, the big funds, then fundamentals are important because they're trying to understand those macro trends, which are important to the time horizon that they're looking at. But a trader who's looking to be in today and be out next week, I don't think it's as much personally, I don't think it's as important. There's the point to make in Charlie's idea there is that there are no people that do not use technical analysis. It doesn't exist. There are no pure fundamentalists. They just simply don't exist. You show me a fundamentalist that has never looked at a chart and I will show you a pure fundamentalist. But they all look at charts, right? So it's really important point. They're all practicing rational analysis. They're all using technical analysis. They're just not admitting it.  If technical analysis is so great, how come people aren't rich and super rich and everyone is so successful trading? And why is it difficult? I have my answer, but you guys are a panelist. Why is it so difficult to wrap your best technical analysis thinking into a script that automatically trades your market profitably, professionally? What is holding that up? So I guess, you know, let's start with showing us on this one. Yeah, it's understanding how to trade a specific time frame. You know, if you're using TA based on a one hour or a four hour, it feels like it's very important to have a sense of that particular trade. That's for me, would be more of a swing trade. I would expect to be in this trade for hours a day, maybe several days because I'm on that higher time frame. If I'm on a lower time frame of five or 15, I'm looking for a scalp trade. I don't expect to be in this trade more than 10 minutes to a half hour, probably max, or else I probably didn't have the best entry in it. It's a great question because we have these tools that are supposed to show us the way. Either here's a buy signal or a sell signal, but the markets don't necessarily then trend in one direction, like straight up or straight down. Along the way, you get your troughs, wicks, stopouts throughout it. Even though you can have the best TA and really trust your tools, then you have the forces of other traders, bought trading, the exchanges themselves, and it behooves the exchanges to get you out of your position. You're fighting against all these things uphill. I trust my TA, but you have to understand how to use it in the context of the time frame you're actually applying it to. Charlie, let's go over to you and we'll save John for last on this one. I'm going to pick up on the first element of your question, which is why the technical analyst is not rich or whatever it was you said something about the richest people. Some of them are, but there's this expectation that if I learn technical analysis, I will be a gazillionaire and there's reality somewhere in the middle between those two. Yeah. Well, certainly the average retail trader, the problem they have is they have a very short time horizon. They think that they can read a book and then become a gazillionaire and they forget about this whole thing called volume in the market. If I just carry on compounding at 10% a month and I've started off with my £10,000 or $10,000 account, then yeah, I'll be worth trillions in a few years' time. It doesn't quite work that way. The other thing with most technicians, as you said there, the good guys either just carry on just trading their own money or actually become money managers. The very wealthiest people, traders out there, are money managers. Just mention any name and John, I'm sure you've been a money manager and maybe you still are. Sorry. The wealthiest guys tend to manage other people's money because it's the easiest way to trade very large sums and to derive performance fees on the back of that. I would say that the reason for lack of success, whether it's huge success or just success period, there are two reasons. First of all, discipline, specifically a lack thereof and emotions which cause a lack of discipline. That's the big problem for traders. If you want to have one more piece in that puzzle, leverage kills. It just does every time. You look at every major financial problem the bottom line was leverage every single time. The overuse of leverage, allowing emotions to rule your process and lack of discipline, those are the reasons that people don't get wealthy or even rich or do well or lose all their money. I have a follow-up question to money management, but we have a good question from the audience that fits into exactly what we were talking about. Are bots better than humans at trading? Are emotional trades a good thing for market volatility? What are your thoughts on putting your ideas into a bot versus doing it yourself? Or does it depend on the person? Bots are fine. They work perfectly well as long as the market remains kind. When the market turns wicked, the bot dies. That's just it. If you're fast enough to turn it off and pick another approach or another bot, then you can be successful at that. Bots only are able to trade the markets that they're matched to and markets evolve and change all the time. There you go. How do bots affect technical analysis? Charlie, go ahead. Feel free to answer both questions. I've never been a fan of bots. You look at the institutions. They have very, very deep pockets for developing all sorts of elaborate, quantitative systems. Yet you get your average retail trader who wants to develop a bot and have it scalping all day long. The problem is with very short timeframes is that there's always going to end up being execution errors at some point even with a system. My view is that, yes, they are useful, but as a supporting tool to the trader. They can be a great support tool from a testing perspective and from an alert perspective. The trader still uses their skills to then take the signal and decide whether that signal is a good signal or not. Much like any discretionary trader, anyone here who we are all looking at the charts, I'm a top-down trader. I use the higher timeframes and go down to the smaller timeframes. You can make that decision based on your experience as a trader, but if you're just letting a robot just trade, it's not really going to be able to do all of that. As you've said, they can come and go very easily with the market environment when that changes, just like what we saw back in February, March of this year. I'm more pro-automated bots if they are trading off of higher timeframes than if they're getting caught up trying to scalp all day long, which I think are much more dangerous in my view. This is my last question to you guys. Let's kick it off with you, John. If you can go back in time and give a young you some advice about technical analysis, what would it be and at what point in your life? It would be to get much more serious about technical analysis much sooner and to pay a lot of attention to the classics. Those books that were written 50, 60, 80 years ago by the likes of Wycoff and Drew and Edward de McGee. That would be me. Charlie, how about you? To my young self, I would say focus. One thing that I did most traders do in the early years is I was a searcher, like so many people are. I went from system to system from indicator to indicator and never really got anywhere. The late Mark Douglas, I met him maybe 20 years ago and I remember him saying to me, if you locked yourself in a prison cell for six months and I just gave you a 10-period moving average, I bet you after six months, you'd be able to make money because that's all you had. The problem we all have nowadays is so much choice that we just jump around too much. If I could go back to my former self, then I'd say focus on a few things and get really good at those. Charlie, how about you? Knowing when to take a win has been one of my things I've been battling with as a trader for a while. When you're in a winning trade, protecting that is so important. I can't tell you how many times when as a young trader, I was in a winning trade that became a losing trade very quickly because I just didn't want to take the win. I wanted higher, I wanted more and in waiting and not selling, it just cost a lot of money. Real quick, scaling into trades. You never will hit the bottom or the top, but if you don't scale in, if you put all your eggs in one initial entry, you don't have the leeway to dollar cost into that trade more effectively. Nibble into a trade, nibble into a position and you'll have more options on how you can trade it. Once again, we had Big Jonas, Charlie Burton, and the one and only John Bollinger. Thank you so much guys for joining this Coin Telegraph trading experience. It's been awesome. Thank you guys. Thank you. Thank you.


Boards are visible, it's okay? Okay, not immediately, okay? So first of all, I'd like to thank the organizers for inviting me here. It's great to be back in ICTP after several years. So my lectures will be on de-instanton effects in string theory. So let me write this. Is this writing visible from back? And I should also say that please ask questions whenever you have any instead of waiting till the end. So let me begin by just saying a few words about string theory, okay? And then I'll come to the instantons. So the original formulation of string theory was perturbative. So original formulation is perturbative, okay? Which means that we have an algorithm to generate a perturbation expansion of various quantities. So in particular, if you are given some background and this background is given in the form of a 2D CFT or you can think of this also as a compactification. So what we can compute is the following. That first, the spectrum of states which typically contain a few massless fields and infinite tower of massive fields, massive states, few massless and infinite tower of massive states. And the other thing we can compute is scattering amplitudes involving these states. But when I say that we can compute this, we can compute this only in a, as a perturbation series, okay? So let's take the example of case of scattering amplitudes, okay? So this typically has the form. So the scattering amplitudes in string theory are expressed as a sum. So this Gs is what is called the string coupling and the expansion is in parts of Gs. This is some constant, okay? Some integer typically or sometimes mostly it's integer in perturbation theory, okay? And these are the non-trivial object. These contain information about the scattering amplitudes. These are functions of the quantum number of the state, of the external states which includes momentum, for example. And string theory tells you how to calculate this, okay? At least it gives you an algorithm for how to calculate this, okay? And the algorithm involves integrals over modularized spaces of Riemann surfaces. Now if you haven't seen this before, you don't worry too much about it, right? Because you will not use this explicitly, okay? We'll encounter some integrals of this kind, but those will be reasonably simple kind, okay? And I'll explain when they come along, okay? But this is a general framework of string theory that we have a way to calculate scattering amplitudes as a perturbation expansion in the coupling, okay? And the coefficients of expansion are computable according to fixed algorithm. And that algorithm involves, you have to do integrals, certain integrals over modularized spaces of Riemann surfaces. Now from quantum field theory, we know that there is more to it than perturbation expansion, okay? So in QFT, we have additional contributions, non-parturbative contributions, okay? So these are the terms which cannot be, which basically whose Taylor series expansion vanishes to all orders, okay? So this is why they are not captured in perturbation expansion. And we expect that similar effects also exist in string theory, similar terms to be present in string theory. In quantum field theory, we know that such terms are present, okay? Because you have a path integral expression, okay? And manipulating that path integral, of course, you can generate the perturbation expansion through Feynman rules. But you also know that the path integral gets additional contribution from other saddle points, okay? And those are the instant terms, okay? So while we expect that similar contribution should be present in string theory, okay? We don't, a priori, have a systematic way to compute this, okay? Because we don't have a path integral formulation, okay? So we need a non-partramatic formulation like path integral systematically compute this. Now, unfortunately, at present, we don't have a full non-partramatic formulation. So at present, we don't have any one. There are some exceptions, okay? But those are very special, okay? In the sense that those are for a very specific background. And let me just list them anywhere. Exception, specific background, okay? For example, for some string background, we have a dual matrix model description, okay? Which is a full non-partramatic, well, you can try to make the matrix model into a non-partramatic description of string theory, okay? Although given a matrix model, it doesn't necessarily imply that you have a full non-partramatic formulation. ADHCFT certainly is an example where you can try to use dual conformal field theories to give non-partramatic formulation, okay? And most famous example is typed to be string theory on ADS5 times S5, which is given by a dual Young Mills theory. Or in some cases, even though you don't have the full non-partramatic control, we can use S duality to get some insight into the non-partramatic effects. But these apply for very specific backgrounds, okay? For a generic background, we don't know how to define string theory non-partramatically. No question? Yes. Is it known this AN, how do they behave for large N? Typically, we expect them to be an asymptotic series. Right? So they are not borderline summable. We don't expect them to be borderline summable. They are poles on the real axis. So that's the general expectation. Is it an expectation or is it a calculator ball in some instances? Well, see what people do calculate is the growth of the volume of the motorized space, right? Now that's just one aspect, right? I mean, we are not, and the full amplitude involves also correlation functions. And those are harder to calculate, right? So they estimate that one makes is just how, how fast the volume of the motorized space grows. Right? And it's based on that, we expect this to be not borderline summable. Okay, so these are some of the shortcomings of the current formulation of string theory. Nevertheless, it turns out that there is one class of effects, one class of nonpartisanal effects that we can compute in a wide class of backgrounds. So despite the shortcomings, there is one class of nonpartisanal effects that can be studied systematically. Yeah, and these are the re-instantal effects. Okay, and I'll describe what these are. Okay? So these give additional contribution to the amplitudes besides the perturbative contribution. So these gives additional contributions. And the general form of these additional contribution is, let me write down the general form first. So first, okay, let me first label this. So this is a constant. This beta is also a constant. And these BNs are, these are functions of the quantum numbers of external states, just like the ANs. And these are also given, just like the ANs, these are also given by integrals over modular space of Riemann surfaces. But this time, the Riemann surfaces also have bias boundaries. So first, you see that because of the C to the minus C over GS, if we try to do a Taylor series expansion of this around GS equal to zero, every term in the Taylor series expansion will vanish. Because if you take derivatives of C to the minus C over GS, however, many derivatives you take and evaluate it at GS equal to zero, the result is just zero, okay? If you go from the positive side. So this is the reason why you don't see this. This is distinct from the perturbation expansion. The second difference is that the power of GS, if beta is a fixed constant for a given amplitude, the power of GS, you see, there it is coming as parts of GS square, here it's the power of GS. This is some of the, these are some of the references that happen between the perturbative contribution and the non-parturbative contribution. But the main, yes? GS square. For D in sentence, it is this, right? With only one unique coefficient. With one? With just one coefficient, I mean, there cannot be any other coefficients like two C, three C. Yeah, because there may be different kinds of D in sentence or multi D in sentence, right? But it's always some constant, right? It's not that there is only single contribution of this kind, right? There are other contributions of C prime, right? Or two C, as you said. So those are certainly there. For a given D in sentence, this is the kind of contribution one gets. So the main problem, and this is what distinguishes the instant and contribution from parturbative contribution. They simply look like infinite integrals. And I'll just write down some examples. So some examples we encountered. So we'll see in our discussion later that you have an integral like this. This integral is finite at T, at T equal to zero because as T goes to zero, this vanishes. But clearly it's divergent from T equals to infinity, right? This diverges exponentially, this diverges logarithmically. Another example is, okay? This integral, you can see diverges from the y equal to zero n, right? This is one over a T y over y square, or this gives you T y over y, right? Both are divergent. Here is a more complicated example. A double integral. The omega are just constants, okay? The omega one, omega two, omega these are just constants. But what I want to draw your attention to is that these integrals are also divergent, both from the v equal to zero n, you can see that they are divergent integrals and from the x equal to zero n, okay? So when I said that we have algorithm to compute bn's, we have algorithm to write bn's as integrals, okay? And these integrals come from integrals of what the modular space of Riemann surfaces. But these integrals are divergent and the main issue is how to deal with these divergences, okay? So this will be the main goal of these lectures, is to extract unambiguous finite answers from them, okay? So let me write down the answers that we'll get eventually, right? But this is just, I'm writing down the answers right now and I mean, during the course of the lectures, I'll explain how these answers come. This integral, for example, we'll see we'll give you i over four pi square. This will be minus half and this will be minus half omega square log four, okay? So these will be seen in the lectures, okay? I'm just writing down these answers because we, so that we know what we are aiming for, right? We really want to get finite answers out of these integrals because these are the integrals that enter the expressions for these bn's, okay? And unless we can get finite answers out of this, we cannot claim that we have understood the n-sentence. Are there questions? The n-dependence? Yes, so these are for low values of n, right? As you go to higher and higher values of n, you get more and more complicated integrals. So n-dependence, I mean, this is for specific n that I have written down, okay? Because higher n will mean, there will be multi-dimensional integrals. The number of integrals and variables themselves will become larger, okay? And the integral and the divergences will also become more complicated. Any other questions? Now we'll also be able to test this procedure, although I may not discuss it in these lectures, okay? But we can't test this. So test, okay? We'll use it whenever a dual description exists, okay? Namely that I, we use the procedure to get a result like this. But then I say that in some cases, you also have dual description, okay? Which is a nonpart of the description that allows you to calculate these coefficients, okay? So if you do have a dual description, then it better be that whatever result you get by using this algorithm to extract finite answer sort of these, agree with what you get from the dual description, okay? So this is the test that we can perform, yes? So are these dual descriptions always unambiguous or do you also sometimes sort out an ambiguity in a dual description? Yeah, sometimes you sort out an ambiguity in the dual description, but sometimes it's also unambiguous, right? For example, the ace duality in type to be, right? Gives quite unambiguous prediction of what the instanton correction should be and we can check against that, right? Matrix model sometimes have ambiguities, right? And you can sort out those ambiguities using both sides.  That's right, yeah. This has no ambiguity whatsoever. Okay, thanks. Well, the only ambiguity in this formalism is what you have in a quantum field theory that we have to, this ambiguity exists even in path integral. That when you write a path integral, you give the action and you have to specify an integration contour, right? That integration contour you choose based on various physical inputs, right? But if you change the integration contour, you may get a different result for the path integral, right? So that ambiguity is always there and that will also be present in this case. But that will be the only ambiguity that we'll have. You said that this is one class of non-perturbary effects and it's associated to some specific backgrounds. So which kind of backgrounds we are talking about and why this class is special with respect to other non-perturbary effects? Okay, so the backgrounds that we are talking about are type two string compactivations, type two are bosonic. I mean, where the world sheet is left-right symmetric, right? For example, the heterotic string theory doesn't have the incentives, okay? Or any d-brains, for example. But when you do have non-perturbary effects, these are the leading non-perturbary effects. Because the other non-perturbary effects, the usual instantons have to be minus c over gs squared, which are subdominant compared to this. So when the instantons are present, they are the dominant non-perturbary corrections. So it's very important that the n appears with the coefficient one. What appears with? The n in the particularly expansion, right? This one, no, not this, okay. This is related to this, but the important point is that the power of gs here is e to the minus c over gs and not c over gs squared. The usual instantons have e to the minus c over gs squared. So that's why they are more suppressed when the gs goes to zero limit. Okay, now before I go on, let me ask one question that is often asked in this context, okay? And I suspect that this question has also been asked already and that is the following. That does it make sense compute instanton corrections? Because as you saw, the perturbative series has this structure, sum over n gs to the power 2n plus alpha. And clearly every term here in this expansion is in the small gs limit is larger than this one. Okay, so I may ask is it, does it make sense to talk about instanton corrections before we even sum the perturbation series? So here I'll try to give two answers which one is practical but one is more conceptual. So the practical answer is that for many quantities, practical answer that for many quantities. So in such cases clearly it makes sense to talk about d instanton corrections because the perturbative contribution is completely understood, right? It either is not there at all, okay? So this happens for example in the computation of certain terms in the superpotential, right? So certain kind of terms, if you take in n equal to one super symmetric compactification in four dimensions, okay? Then certain class of terms are simply not generated in perturbation theory and they are the d instantons often are the leading contribution to such terms, right? So there it certainly makes sense to talk about d instanton contribution. In type 2b theory in 10 dimensions, okay? There are perturbative contribution to certain amplitudes but those series terminate, right? Other after one order up to second order, all hard terms vanish, okay? So then the perturbative contribution is completely understood and then the d instantons are the next leading corrections, okay? So in such cases clearly there is justification of why you want to study d instanton. There are also examples without super symmetry by the way, there are, we'll study this c equal to one Bosonic string theory in some detail, okay? And there we'll see that the certainness amplitudes have imaginary part and the imaginary part doesn't receive any contribution from the perturbative series, right? So they are d instantons are the leading contribution to the imaginary part of the amplitude. So they are examples of this kind. So this is a practical answer but there is also a conceptual answer and that is the following. So in QFT for example, instantons, QFT includes quantum mechanics. Instantons are subdominant saddles in the path integral, okay? They are subdominant in the sense that their contribution is exponential suppress compared to the leading contribution which is what the perturbative contribution is. And the instanton amplitudes, contribution to the amplitude from the steepest descent contour of the path, steepest descent contour of the saddle. So in the field space, if we think of the location of the various saddle points, okay? So in the field space, there may be various saddle points. This is the perturbative, this is the instanton one, this is the instanton two. And then for each of these saddles, there is a steepest descent contour, right? Then in higher dimension, the generalization of steepest descent contour is what are called left side symbols, okay? But there are some surfaces, some subspaces, okay? Along which in the, in this is the complex field space, okay? You always draw the steepest descent contour in the complex field space. So there are some subspaces that pass through these saddles. And when you talk about the instanton contribution to the amplitude, okay? What it is computing in perturbation theory is a result of the integral on those surfaces, those steepest descent contours. So it is true that if the steepest descent contour of the perturbative saddle gives much larger contribution compared to the steepest descent contour of the instanton contour, okay? Nevertheless, it certainly makes sense to ask, okay? What is the result of the steepest descent contour through the instanton, right? In the field space, if I specify a contour, I can ask what is the result of that integral, right? And that's what the instanton contribution computes. So it's an interesting quantity by itself, okay? Even though the actual integration contour may be involving both perturbative and some of the instanton saddles, and then this one may dominate, okay? But if you have chosen the integration contour to be the steepest descent contour of the instanton, then instanton amplitudes are all that you'll get. Now in string theory, of course you don't have a path integral description, a fundamental path integral description, but one expects that there should be a similar interpretation also in string theory. So when you say that you are trying to compute the instanton amplitudes in string theory, okay? Effectively, you are computing the integrated, result of path integral, okay? What about that maybe? The result of path integral over certain contour, right? Which passes through these non-perturbative saddles, okay? And the fact that they are dominated by the perturbative contour, okay? We do not need to take into account, right? This is a quantity that is of interest by itself. What is the result of the integral over the steepest descent contour of a given saddle? So that's a more conceptual reason why the instanton amp contribution to the amplitudes are useful quantities to study, okay? Even if in practice, they may give the subdomain and contribution. In quantum field theory, we also have some other non-perturbative contributions which has no such interpretation like a renormal ones. Okay? How do you know that these instanton says no, these are not of this kind? Well, I think we know it because of this fact that you have this e to the minus c over gs application, right? And this is typically the signal that there is a, there is a saddle whose action is c over gs, okay? And in fact, we can specifically identify the saddles as d brands, okay? So in that sense, I mean, you already know that there exist saddles, right? Even though we don't have a path integral description, we, in strength, we can identify solutions to equations of motion, okay? Just by saying that they are conformal field theories, right? So in that sense, you already know that there are saddles with action of this kind, okay? So it's more natural to interpret the instanton contribution as coming from the steepest descent contour of the saddles. Okay, so let me then say what the instantons are. And here I assume that you have some idea of what d brands are, okay? Because d instantons are special kind of d brands. So d instantons, okay? And I'll use what d instanton is a somewhat general essence. So we'll define d instantons as a follow, as a following. These are d brands with Dirichlet boundary condition, all non-compact directions, including time, okay? And we normally describe d instantons in the Euclidean spacetime. So in the Euclidean time, okay? So in order to describe a d brand, you have to specify for each spacetime direction, whether you impose Dirichlet or Neumann boundary condition, okay? Sometimes you may also consider mixed boundary condition, but let's just do Dirichlet and Neumann. So for each spacetime direction, you have to specify whether you're considering Dirichlet or Neumann boundary condition, okay? Here the idea is that along all the non-compact directions, you have to put Dirichlet boundary condition. Along the compact spacetime directions, you may put Neumann or Dirichlet, okay? All of those will be classified as d instantons, different kinds of d instantons. But because you are putting the Dirichlet boundary condition on the non-compact direction, this means that these are localized all non-compact directions, okay? In particular, it's localized at some particular value of time. And because these are localized along non-compact directions, what they describe as finite action solutions and strain theory, okay? And the action is, has a form, some constant over gs, okay? And this follows from the standard argument that all d-branes, okay? The tension of a d-brane, it goes as one over g string, some constant over g string. At the same argument, it goes as so, tension here goes over to action, because it's also localized in the time direction. And the standard calculation that you can find in Paul Chinsky's book can be used to calculate the disc coefficients, okay? So the action of the d-instanton, you can compute. Given, once you specify what boundary condition you're imposing, on which direction, you can explicitly compute the action of the d-instanton following the standard technique. So it is in this sense that d-instantons are generally saddles of strain theory, right? Even though we don't know what path integral describes in strain computation. So these are analogous to instantons in quantum field theory. And except that in normal instantons in quantum field theory we'll have a g-square, right? The action typically goes as one over g-square, here it goes as one over g, right? That's the main difference. And this give nonpartner very contribution to string amplitudes, okay? These amplitudes, as I have already written, takes the form to the minus c over gs and dn gs to the power n plus beta. And these are what are given by integrals over the modular spaces of human surfaces with boundaries. Why with boundaries? Because once you have d-blend, right? You have open strings which end on d-blends, right? And the open string wall sheets have boundaries, okay? That's the reason why the d-instanton amplitudes have boundaries, the wall sheets have boundaries. Now, in these lectures we'll consider single d-instantons, but that's just for simplicity, okay? The procedure that I'll be describing can also be generalized to multiple d-instantons, okay? It just requires a little more work. For multiple instantons, suppose there are n-instantons, the first difference will be that there'll be e to the minus n c over gs, okay? Because there are n-instantons total action is n c over gs. And then the calculation of bn's will be a little more complicated, right? Because the boundary can now have different boundary conditions because it can end on the first d-instanton or the second d-instanton or the third d-instanton and so on. So now, let me give some systematics of d-instanton amplitudes, okay? Because this will be important. So first, we now have, we have open and closed strings in the presence of d-instantons. So if you think of d-instanton as a point in space time, okay, at least among the non-compact directions, it may have extension in the compact directions, which I have not drawn. Then there can certainly be open strings whose ends are on the d-instanton, okay? So these are open strings. But we can also have closed strings in the vicinity of the d-instantons, right? Or far away from the d-instantons. So both of those kinds of strings are present. But there is a crucial difference between the open strings and the closed strings, okay? Namely the open strings, okay? These exist only for limited time. Because d-instantons are localized in time, right? They occur at some particular value of time. And because the ends of the open string are tied to the d-instanton, right? The open string cannot extend the wall volume of the open string or the wall sheet of the open string cannot extend too much in the time direction, right? It has to be confined in the vicinity of this where the d-instanton is located. So because of this, okay? These cannot be asymptotic states. These are not asymptotic states. So the interpretation of the open strings is that the d-instantons are localized. Yes, go ahead. Sorry, just a quick clarification conceptually. So of course the instanton is perfectly localized in time. So when you say limited time, you mean because they also will have a finite energy excitation. So you can allow a vicinity also in time. Or do you actually mean that it just exists for one instant in time? Well, d-instantons exist for one instant of time. But the open string, of course, the middle of the open string can extend in time, right? It cannot go very far away from the time, right? They will cause infinite energy, energy, or... Yeah, that was my question. So it is related to finite energy. That's right, yeah. Okay. That if you stretch it too much in time, right? That's like infinite tension. So open strings are not asymptotic states. So when we talk about d-instanton amplitudes, okay? The external states, whose scattering amplitudes we calculate, okay? Are always closed strings, okay? It's like a normal instanton in quantum field theory, right? If we take instantons in quantum field theory, what do they compute? They compute the usual scattering amplitude of the excitation of the quantum field theory, right? The instantons have their own modes, right? The instanton can get translated, it can vibrate, it can do various things, okay? But those are not the modes whose scattering amplitudes we calculate, okay? Those modes are useful in computing scattering amplitudes of the external states, which are the usual states of quantum field theory, okay? So here, they are in the same spirit. Open strings are describing the dynamics of the d-instanton, okay? But they are not asymptotic states. So when we talk about scattering amplitudes, the external states will always be closed strings. This is something we should keep in mind. Is it okay? Are there questions on this? The second important point, okay? Which is again different from the usual perturbation theory, is that because we are imposing this boundary condition, okay? We have d-instanton located at a particular time, for example, right? So time transition invariance is broken. It's located at some particular value of the space coordinate. So space transition invariance is broken. And because this transition invariance is broken, that means that there is a energy momentum conservation by the usual wall sheets, okay? Is there wall sheets with boundaries? Because if the boundary is which break the transition invariance, okay? Eventually, of course, we'll see how the transition invariance is restored, how the energy momentum conservation is restored, okay? But at the level of computation, okay? When we use the standard string calculation, okay? Transition invariance is broken, and hence we don't have energy momentum conservation. And this has a non-trivial consequence, okay? Namely that now disconnected wall sheets, okay? Are on the same footing as connected wall sheets. You think in terms of quantum field theory Feynman diagrams, right? When you draw Feynman diagrams in quantum field theory, we are both disconnected and connected diagrams, right? In QFT, if you are doing four-point scattering, you can draw four-point scattering diagrams like this, okay? You can have four-point scattering diagrams like this. This is disconnected, this is connected. Normally, the reason that you don't worry about these is because these diagrams require additional energy momentum conservation than the overall energy momentum conservation, okay? This one, for example, will tell us that the energy momentum of this should be equal to the energy momentum of this, and energy momentum of this should be equal to energy momentum, okay? Which means there are two separate energy momentum conservation, okay? That have to be satisfied for this diagram. Whereas for this diagram, there is only one overall energy momentum conservation. So if we take a generic external momentum, right? Which satisfies just that overall energy momentum conservation. Then typically for generic external momentum, this diagram will not contribute because the delta function constant will not be satisfied. Otherwise, in quantum field theory, these diagrams are there, and similarly in string theory also, disconnected wall sheets are very much present. But because deans and tons don't have this feature that individual wall sheets satisfy energy momentum conservation, okay? They are in no way different from the standard wall sheets which are connected, right? So you have to include all of them. In, for the instanton amplitudes, we need to include disconnected wall sheets, yes. When you say that translation invariance is broken, you mean spontaneously broken, right? The time transition and also the space that transition are going on compact directions. Yes, okay. I mean from the point of view of wall sheet, it is, you are choosing a different volume in which the translation invariance is spontaneously broken, is it correct? Well, I would not say the spontaneously broken, it's just, there's a boundary, right? And at the boundary, the energy is not conserved, right? It can just flow out of the boundary, or the momentum is not conserved. That's what is happening, right? Because at the boundary, you don't, if the boundary is the one you're just breaking translation invariance. That's, I would say it's more explicitly broken because you have just broken it by putting this boundary condition on the wall sheet. But keeping into account that the instantons are dynamical object in the full theory, translation invariance will be restored. Yes, yes, it will be restored eventually, right? But at the level of individual wall sheets, they will not be restored. We'll see later how the full translation invariance is restored, but individual wall sheets don't have that property. So now, let me describe how to organize the instanton amplitudes, okay? Because you want to do this power series, right? Which are the ones which give dominant contribution in this power series, okay? And here we are going to use the usual rules of string perturbation theory, okay? And that is the following that wall sheet with Euler number chi gives contribution of order gs to the minus chi, okay? That's the standard rule in string perturbation theory and that holds even for, in the presence of the instantons. So this means that in order to get the highest negative power of gs, that means lowest 10 in this expansion, we have to maximize the Euler number. And this is, okay? So how do you maximize the Euler number? Okay? Discs have Euler number one. These sphere, of course, have more, but sphere has no boundaries. So we are looking for surface with boundaries, right? Because those are there, we can also explore the fact that the energy momentum is not concept. Anulus, okay? Anulus is this topologically, right? A disc with a hole. This has Euler number zero, okay? And then you can list various other things, but these are the ones which are low Euler number. High Euler number, okay? Others, there are also many surface with negative Euler number. So because of this fact that the discs of Euler number one, we see that the way to get the maximum inverse power of gs is to maximize the number of discs. So to get the leading contribution, we need to maximize the number of discs. So this is the first observation. Second observation is that because Anulus has Euler number zero, in respect to how many Anulus you use, the power of gs remains the same, right? Because it has gs to the zero. So we can use, can use as many Anulus as gone, without a cost in gs. There's a question? Yes. Should I think of the Anulus as one instant or as two instantons? No, one instanton only because when I say Anulus, on both boundaries, we'll put the same boundary condition. So the instanton is just one point in space tab, right? The number of strings that can end on it can be anything. So Anulus at both ends of the open string are ending on the instanton, right? So it's like, you can think of this as a loop, take this one open string, and it's a loop of that open string. So the instanton action is still one over gs. It's not two over gs. No, it's not two over gs, it's still one over gs. Right? So given a single instanton, you can have as many wordsheet as you want ending on that. There are just different excitations of the same instanton. So the leading contribution, okay? With this we can write down the leading contribution, okay? So the leading contribution has the following structure. We have this exponential of minus c over gs, which is the suppressant due to the action, okay? Then we have the exponential of the Anulus, okay? Because you can use as many as you want. So you can use zero or one or two, et cetera. And the combinatoric factor is such that it just exponentiates. And then we have a product of disk one-point functions. So these are the closed string vertex operators. So you have n closed strings, right? The idea is that you take n disks, insert one closed string on each of these disks. So you cannot have disk without a vertex operator because that vanishes, right? Because of this, there is a sl2 or volume you have to divide by. And that makes a disk without vertex operator vanish. So you have to insert at least one vertex operator. So you maximize the number of disks by inserting each external vertex operator on one disk. Maybe you could say a couple more words why this exponentiates exactly. If you have an arbitrary number of boundaries but you tie them up to annular. I mean, you said the combinatorics works out but it's maybe not obvious that it does. Yeah, okay. Basically, okay. So first of all, one corresponds to no annulus, in this expansion. Then you can have one annulus. For the two annulus, I don't know how that I can do it often. Basically, there is a one over two factorial because the exchange of these two annulus gives the same diagram, right? That's the argument, right? And you can repeat this for any annulus, right? But I think if you want more details of this I have to work it out. Don't want to do it right now on this spot. Okay, but roughly that's the idea that you have multiple annulus that is the exchange symmetry, right? That gives you one over n factorial and that's why it actually exponents. So this exponential basically comes from these all of these. Yeah, it's roughly that exactly, yeah. It's like a zero point function in quantum field theory. Hi, I should. So are there a fermionic zero modes that you have to soak up? I mean, do you have to? Yeah, yeah. So if there are fermionic zero modes you have to do a little more work, right? So this is a leading contribution provided the answer is non-zero, right? I mean, it may happen that in some cases this answer is zero, right? Then you have to look for what is the first non-zero contribution. So we'll discuss the fermion zero modes but certainly if there are fermionic zero modes you have to insert them appropriately here. So next order, for the leading order there's nothing else, right? This is all you have. At the next order what you can do, okay? There are many ways you can increase power of gs, right? You want to increase the power of gs by one. So what we can do is we can give up one disk. So instead of having each, that each disk having one closed string vortex of water maybe one disk has two and the rest have one. So here is a possible contribution at next order. Okay, so this basically means that we have one less disk. So we lose the factor of gs, right? Because on one of the disks we insert two more closed string vortex of water so we are using a disk. So this is one contribution but there are others at the same order, okay? You can have this. You can replace a disk by annulus. So all of them are disks except that one disk is replaced by annulus compared to this. This is over here, right? So again you lose one over gs because this instead of being one over gs is a water one. Or you can do, you have these as before but then you add to this a disk with two holes, okay? Disk with two holes have Euler character minus one. This has chi equal to minus one, okay? So because of this we lose the factor of gs, right? It's gs to the minus k chi so you just get a factor of gs. So these are the various ways you can build the other question. Now the problem comes because most of these diagrams are divergent, okay? Disk with one disk one point function is okay. Okay, that's in fact the only one which is finite. But this one for example is infinite. We'll write down there as a result for this next time for some theories, right? This is infinite, okay? And the question is what do you do about this? These are both infinite. These two point function annulus one point function are all infinite, okay? They and some of the integrals I showed you essentially come from this. So we have to understand what the origin of these infinities are and then understand how to extract finite result of these infinities, right? So that will be the goal of this next two lectures, okay? I think my time is up so I'll stop here. We can have some questions or comments or.


About a week ago, I received another malicious document and when I took a look at it So it was actually a doc file The extension was doc, but when I took a look at it, I saw that It was actually an XML file XML with utf 8 encoding if you look at the HexDump here You can see the sequence EFBBBF Now if you see that sequence at the beginning of a file Then it is an indication that the file is a text file with utf 8 encoding So you can recognize the XML now this time The XML file here Did not contain macros So if you look here at this property W colon macros present the value is no so it doesn't contain macros But it contains something else this time. It's yet another trick W embedded object present This one is yes So the value of this attribute is yes, which indicates that this XML file Contains an embedded object. So an only object So let's scroll down and we will find The embedded file Okay, here you can see it bin data and The name of the file or a data dot MSO So this is the base 64 encoding of that file. Let's select it and decode it Like this okay, I copy it I Start a new file and I do a paste from base 64 Like this and now you might already recognize this. This is actually the header of an OLE file Let's look at the hex. You can see D0 CF 11 E0 With kind of reads like a doc file So this is the indication of an OLE file So let me save this OLE file like this and Now I can have a look at it with OLE dump I'm going to use my send to CLI tool Sorry Like this send to CLI This is just Go interface for command line So this is the file I'm running OLE dump like this Okay, and it contains one stream So let's select this stream stream one Okay, and you can see zero zero sixteen zero zero zero and then seven eight nine C and so on Now seven eight is often an indication of a compressed ZLIP compressed Stream, so let's try this out Let's try if it is indeed a compressed stream So I do a hex dump like this I copy it and I take again My clipboard transformer So this is the hex dump and I'm guessing that this is compressed data, so let me delete this one here and Now I can use my Option here inflate Okay, and it worked. I got no error. So this is indeed a compressed file and as you can see here It starts again with doc file. So this doc file Contains another doc file. So this only file contains another only file So let's analyze this again So in my ex editor, I create a new file and I paste from hex text like this and Here I have again my only file and here you can already see some VBS code So let's save this file and let's have a look with the only dump Okay, and here we have a stream with name welly 1 0 native if you see that You know that this stream contains an embedded object So you can select this stream. That's stream 3 And here you have the exile asky dump now We Know that this is an embedded object. So you can use option I To get the information of the embedded object the metadata So this is the name of the object File that was embedded. So it's a VBS file This is the folder where it was Located and this is the temporary folder where it was saved to execute and this is the size We can also view the embedded object itself by extracting it. That's with option E like this Okay, and as you can see here it is VBS code this here looks like base 64 So let's try this Let me copy it a New file in my hex editor and then paste From base 64. Yep, and indeed it decodes as base 64 and you can see that it launches a PowerShell command So after launching a PowerShell shell This script here downloads a file from this URL Saves it in a temporary folder with a dot cap extension Then it expands the downloaded cap file to an exe file and then it runs the exe file


Everybody forced here ripping Sunday fund a NFL week nine regular season 30 box 2017 immaculate and more football mixer random teams I'll show the results right here. I have all the card boxes on the table I got all the helmets back here that we'll get to later the helmets last five authentic fanatics mystery helmets Let's go hang it started everybody a lot of rare boxes in this break. So let's start with some elite football Get the list here Yeah, 2022 elite Remember guys after this we're done tonight got personals tomorrow 5 p.m. Eastern with Sam That's doing daytime baseball breaks at 10 a.m. Eastern He may have time for baseball personals as well during the day You wear that we'll do a recap at the end of this break in the same recording Kyle Phillips rookie going to the Titans to 999 She's going for two to tie it up right here with about three minutes left They have all their timeouts though Playmakers Kyler Murray, but they got to stop them, you know, and they got him a homestuck it in himself Dürbinator 399 full throttle Ravens But a 349 excuse me my home is magic rookie on deck Kenneth Walker the third Seattle Yeah, my homes is silly good. The more I what the more I watch him like Just so much point like just so much command of everything that's going on Bucks Chris Godwin 133 of 399. He really is impressive to watch Jersey card Packers Charles Woodson first hit of the break goes to the Packers Him and Josh Allen are wild David O'Jabba rookie numbered one of 25 Ravens The Josh Allen thing is crazy because he just was not good his first two seasons and then the third year was just that like honestly the biggest jump from like a Quarterback I think from year to year that I think that's ever happened statistically quay Walker rookie 324 to 399 Packers Like Josh Allen first a second here, I just think of like this dude that just Takes way too many risks and overthrows dudes all the time. This accuracy is super inconsistent And he became this just you know Probably second best behind my homes, that's it Turn of the century Browns rookie Otto David Bell to 99 Mantra Washington rookie Broncos to 99 This is a great That's right. Gino Smith for nine seasons Got a Britain Brown to 999 Raiders rookie rookie on Deco Lave Saints Darren Waller to 83 Raiders Sauce Gardner jets pen pals rookie Otto nice hit jets dude is legit Reese Hall elitist to 999 Skymore Chiefs rookie Seriously James. There's nobody else Only nine years ago. It wasn't that long ago. Got legacy next Famous James 399 Saints. Come on Malik get it done Many chase young commanders to 125 All right, so the Titans Could only hold off for so long Matt Corral to 199 Panthers rookie Hamilton James Cook Malik is Malik Willis likely Ritter Sauce Gardner Trent Mcduffy to 35 for the Chiefs rookie Otto here week Willis um To really to save he's good yet. He's exciting He's got physical talent like crazy Trevon Walker John met she Darren Waller Raiders number 2299 But he's similar to Josh Allen that he's gonna be time to develop and you know own his accuracy and all that good stuff But cannon for an arm Runs very well rookie silver Danny Gray Niners It's a third rounder for the Titans Very high upside just tricky part is hitting that upside right Trey McBride Cardinals rookie Otto pickings you got many rookie Kobe Bryant Seahawks Pull the Kobe Bryant rookie about that Jalen Hurts is walking on water. I don't know about that. He's having a very good year He's not the best quarterback in the league, but I mean, hey, he's definitely good enough to win a Super Bowl Aaron Jones 152-199 Packers after the Bills. They're probably what the most complete team I would think Yeah, you're strong son Haskins definitely the best and then again the Bills have lost twice Eagles have not lost That's true. I'd consider it weaker, but are the jets a good football team I'm not that the jets are bad you can't be bad and be this part of the season it'd be you know six and three but The good news is that like what if the bills has to play the Jets in the playoffs There's seven seeds now seven spots Jackson Hill Garrett Wilson Rucker Walker James and Williams rookie for the Lions to 35 31 to 35. All right, let's do score now. I'm not gonna show all this vet base. There's so much We'll get to the rookies though. I'll go through those like this my favorite practice how much of the giant the giant helmets a Toe the line to 35 CD lamb cowboys a lot of score That's a lot of cards y'all Y'all thought tops flagship was that hot rookies Kenny pick it Points coming up. I think I'll roll a die here for these Fantasy stars cards, so we'll go one two left three four middle five six right One left on these wild card points random at the ends to everybody Malik will it's right there Starting quarterback Malik Willis Garrett Wilson Mack Jones Maybe the Titans get to stop here and the Titans get the ball back, huh? Let Malik lead him to the Lins of the promised land Let your Malik flag fly Trailer first you got John Mets you the third Texans rookie auto three trees for one box of score. Oh They stopped them Chiefs go for it. Hey, there's K. Dotten Let buccaneers let he actually is looking pretty good for like a receiving diamonds. Yeah, can you pick it? Bailey's happy. I don't like that tall and dirty one of the chiefs Let my home is run around the edge for it You be doing that Desmond Ritter After this we'll do some we'll go for 2021 just letting those eggs and Chronicles Try to space out the years as much as I can Obviously would do all the very high end at the end James Williams Reese Hall Damian Pierce Hey Michael Thomas on the four of ten first down nice one Saints Five one oh two that is how it's that's insane Mike. That's insane.  Yeah, I Thought the Red Sox might take her on Adam for like the right price 20 million year for a closer That's crazy. Oh My god Hey, I mean the Mets are serious There's one thing about Steve Cohen that you cannot deny and that he is serious about winning with that team hot rookies a lava You know Mr.. Red Sox owners are like that. I don't have him to talk though. You're raised fan You're probably like yeah, I wish we would give out a contract Sign a bat for once It's not trade for what's the name last year Got a Chargers Jared Cook auto 17 out of 50 chargers and blue rookies Amir white to 35 for the Raiders. Yeah, I know some cruise Kind of crazy. What's up trash? How's it going man? Yeah, du Grom is the big question, right?  Oh, man Channing Tyndall Dolphins rookie auto to 50 Dolphins on the Tyndall that sweepstake is gonna be insane Let's do 2021 was a now as an angel sign Sign who to ground.  You need to like Top of the line Every five day go out there only allow like two runs or less.   Just thinks that like He would have just helped so much this past year. I'll feel was the weakness I'll feel the first base purple mosaic Matthew Stafford Rams Numbered 44 49 Silver Kyler Murray Mac Jones rookie base The reds aren't missing a lot of stuff. It wasn't like rent for only would help so much They wouldn't make the playoffs if he was there if it was just him there, you know TJ Watt Aaron Jones Silver blue chips Justin Fields for the Bears Payton Turner rookie autograph Saints not numbered Josek Derwin James Charger silver rookie debut Zach Wilson jets Fields debut Bears Yeah, it's good game at least Tynes defense really showed up Story of the game mosaic Tom Brady bucks silver Montana Niners Introductions mosaic Mac Jones Patriots mosaic Dante Culpepper red mosaic rookie Kenneth Gainwell Eagles Tom Brady mosaic in it to win a Buccaneers Davis Mills Isn't Matt Barnes done with the Red Sox now? How much longer is his contract? They didn't give him a ton of money Mosaic Washington Terry McLauren rookie mosaic Jets Elijah Moore. He really fooled us though. He did fool us Blue mosaic center stage Jalen Hertz Eagles Numbered 42 out of 99 That's what happens.  Oh good. We finally got someone Michael P right a red mosaic Aaron Rodgers Packers Blue mosaic rookie is he's ojolari Giants numbered 17 of 99 silver Lamar Jackson Ravens Chase introduction silver swagger D hop right not the best box in mosaic Let's do this to 2021 chronicles now Chronicles hobby Overtime he was like nice turn of the century Mac Jones rookie auto Patriots 45 out of 99 Congrats Pat Awesome starting chronicles get that bag for you Engel Jones to 399 Giants Silver Javante Williams Broncos from score Fry Booth rookie clear vision Steelers to 199 Davis Mills prison black Texans Falcons on the signature Gerald Riggs Wilson Ron Dale Moore to 199 Cardinals Carter Caleb is yelling about something Chiefs Hail Mary Silver Falcons rookie from Flux Kyle Pitts Purple Najee Harris from Flux Nice card Steelers numbered one 19 of 199 Jersey card Packers Aaron Jones Let's do 2021 prism team all two boxes Who is it Steve? Who is it? Kevin Jordan ETN rookie. We've got a silver rookie dolphins Jared Dokes Red and yellow Packers Aaron Jones 32 out of 39 Steve isn't no Slee there's a JC Horn rookie Penny Sewell rookie silver Vikings Kellen Montt and Yellow Red Adam Thielen 14 of 39 Vikings 22 elements Dolphins Jalen Waddell numbered 161 of 199 Bears tungsten David Montgomery 15 of 74 Steelers George Pickens 51 of 75 rookie Jersey the auto is going to the Cowboys It's Tony Pollard 33 of 50 neon auto and Cowboys RPS Jalen Tolbert rookie steel signatures 86 of 199 good Cowboys box two autos for you gold standard 22 Got Packers Christian Watson 10 of 30 rookie Cardinals DeAndre Hopkins 99 of 99 Seahawks DK Metcalf Goldgear Jersey 177 of 299 Falcons Kyle Pitts White Gold Jersey 99 of 299 Hackers five-way Jersey Aaron Rogers 166 of 299 Nice RPA Steelers Calvin Austin a third to 11 of 49 Yes, Steve. What are you doing, man? And commanders Sam Howell rookie Jersey Otto 123 of 199 you go commanders Two Jersey autos in the box. That's a good one On to let's do that 2018 limited 2018 limited Show me a Lamar or an Allen. Come on You know what or sake one. He's having heck of a year 18 limit with Donald box I get the RPA in the first one. I think I did I think I did Richard Sherman 8 of 49 Niners Crime time patch card Leonard for net 5 out of 10 Jaguars Oh, man, that happens. There's those days for sure Your four color patch Leonard for net Jags Player worn. I don't know which one has the rpa. I can't tell Ravens rpa Jaleel Scott 162 of 299 Not one of the players you're looking for unfortunately Here's the sticker though. Z Royce Freeman horizontal rpa also 40 of 125 Two RPAs is good. Just not not the players we're looking for I thought Freeman was going to be better for sure And he was let's see. Let's do 2022 certified All right, she's got the ball first in OT Brady five of 50 bucks Got that Brady dub today Typical Brady fashion That's when I was saying watch them pull a win out of nowhere Lamar Jackson certified stars 47 199 Ravens Brady magic Sam Howell commanders on these uh freshman fabric rpa 156 of 199 Hopefully we'll see how we'll play this year Kenneth Walker the third rookie 127 to 275 Seahawks nice pack Mike Evans 82 of 149 Buccaneers Bucks Chris Godwin on the on the ball relic 35 out of 50 I think my fantasy would be happy if they threw the Chris Godwin more Packers rookie out of quay walker numbered 113 of 149 AJ Brown's trolling the Titans The Titans receivers have zero receptions tonight That's so crazy Is that is that true? Pulling like a Patriots the last year when they beat the bills 185 105 at 390 349 Jalen waddle dolphins James Williams rookie Lions 155 at 325 Seahawks rookie patch card Kenneth Walker the third 90 out of 99 Drake London graffiti for the Falcons And are moving on let's do the 2019 contenders boxes Two of them well, let's see a kyler or a jones Like a jacob's or like a renfro or Pollard. I think is 19 Obviously a few other receivers too. Yeah, I think the issue with DK's is redemption. Yeah, that's the issue with Deboe McLauren Adia Brown Such a good receiver class And not even like any really high drafted receivers Dwayne haskins rest in peace There he is dude Dwayne haskins rookie on-card auto rookie ticket That's a cool hit there you go Washington. Yeah, that's a cool one, man You go Washington. Nice card there To Marco Murray cowboys nfl ink Number to 10 to Marco Murray auto cowboys It's a good box Rock is signed Colts on the rookie ticket auto He still plays for them, right? I think he's like a nickel for them. It's pretty good. This is definitely a good box Not huge, you know, but Rodney Anderson rookie auto for the bangles rookie ticket there I don't know why in 2019, but the autos are back to back to back like every time Ben Burr Curvin rookie ticket auto seahawks Burr Curvin Kylie Murray rookie of the year contenders He signed us on the Raiders now Drew Brees 40 of 49 winning ticket Saints She's the one there by the score Rather than mintues rookie here gonna roll a die one two three top four five six bottom A three gonna go top unless there's an auto Or a one of one of which case will random on those round numbers next two boxes It's gonna go that way Or this box in the next one It's weird a lot of them this year in the 2019 class are like the same team Daniel Jones rookie of the year contenders one more 19 contenders Then we'll finish up the 2022 products and get into some select prism nti mac flawless That's where we're headed our marvel tell the third championship ticket auto 41 to 49 Colts Tracing sorely don't so don't show sam these trace makes worldly cards, please 250 points and to all the end Joe mixing on the championship ticket two out of 99 bangles It's on that championship juice today, man I'll tell you that Baseball breaks start at 10 a.m tomorrow guys That is not far. That's not long from now actually They want a far more than one and got it. Oh, they're trying to Touchdown here. Deandre Baker at ticket stub giants rookie auto 22 of 27 autos were yet one of the rest of you What are you going my homes? Debo rookie the year contenders There's a redemption we did have points in this one Redemption tj. Hawkinson rookie the year contenders auto rps that is going to be a lions redemption and it is expired So lions and that redemption is expired. They might still have that. That'd be a pretty cool one to get And a david, how do you say that name david blau david blue? Lions ricky ticket auto started on Thanksgiving last year Did he or was it christmas?  All right. We got a stafan dig 72 of 75 bills force field seahawks dk metcalf Nice short printed force field not the perfect corner on the bottom right there some white on it Niners janny gray rookie patch numbered one out of 10 rookie auto browns gerome forward 193 of 199 and a lions sizable signatures aiden hutchinson six of 39 rookie jumbo jersey auto Two good boxes of black football. Let's do the origins now the last of the 2022 product four origins by mac jones rookie sam howell commanders marquise brown the 99 cardinals and dollfinch dealing wattle to 299 panthers matt corral rookie patch 113 of 199 giants rookie auto wandale robinson On card not numbered And a cardinals rookie patch auto 7 of 49 is tray mcbryde devonte price rookie colts A blank slate a rookie lions aiden hutchinson case hit Awesome card lions love the blank slates lions almond rossane brown to 199 and a patriots remandry stevens into 299 Patriots rookie jumbo patch tyquan thorton numbered 66 or 82 of 99 actually Not 66 of Backwards 28 Steelers rookie auto to 25 calvin austin the third on card And desmond ridder rookie jumbo jersey auto falcons nice box there All right, two more origins. We'll do some select starving jake.  Not my thumb prints, dude This one has it too like right on the bottom. What is that? It looks like a thumb. Yeah, that's like a it's definitely a fingerprint Let's see if those will come off Cowboys is equal elliot jersey card six out of 99 Saxons demian pierce rickie on card auto not numbered You did no, all right. I'm grabbing a box of both of those and patriots rookie jumbo jersey auto pier strong jr Yeah, those are not coming off. So all right last origins, bro. We got rookie james of williams lions saints michael thomas to 199 commanders terry mclauren to 299 chiefs travis kelsey jersey card 88 of 99 titans on card rookie auto hassan haskins And that'll do it and raiders a mere white rookie jumbo jersey auto chiefs survive and over time They did not cover that 13 and a half point spread though. That's for damn sure All right, 21 select now and 21 prism hobby Stevenson try color concourse rookie jacob harris rams 98 of 249 That's Fitzpatrick 67 of 75 titans rookie auto blue sublake Yeah, man Half the time you're supposed to you should be in chat even we will work in here. Anyway club level silver rookie texans brevin jordan What do you mean shorts premier level rookie tray lance niners? I don't see any other comment That's the only one I see Silver sensations zack wilson jets silver premier level rookie niners is tray serman Purple premier level rookie chuba hubbard panthers with a big That's an issue with the card that's not on the surface is underneath the surface starting on his 75 panthers, but that is like a Before it was like finished with the chrome or something. I don't know Look at the empty box wrapper out to the panther spot chuba hubbird Yeah, but I thought that was that was that was just an absolute insanity club level silver randy ma's vikings more chase Premier level light blue packers erin rogers 33 out of 99 premier level silver rookie semi fahoko cowboys Premier level rookie blue chuba hubbard panthers Number six out of 1 to 49 concourse silver rucky zack davidson vikings michael carter jets 47 to 75 rookie jumbo jersey auto had a good game today fill in for brice Concourse blue joe montana 49ers 54 of 199 field level silver rookie semi fahoko cowboys Concourse rookie silver nazi harris steelers LaHosier's 68 passes. Oh my god Kyle pits concourse concourse silver 20 genzales for the chiefs Mekstron Stokes you got kellen mawn 26 of 49 vikings rookie jersey sake one barkley premier level silver giants And silver concourse zeeke St. Brown, right 2021 prison prison hobby rookies nuesome and collins hyper brock lesnar vikings nine of 175 silver texans david johnson burrow second year from andre stevens and rookie those rike purplish rookie vikings kellen mawn with that color match 108 of 225 twy freany I'll see something massive again rookies trace serman jail in camp purple daniel sorenson chiefs 92 of 125 rookies javon holland dea me brown orange rookie jaguars jail in camp 14 of 249 silver panthers lute keekley snakeskin coming up Let's see something big Yeah, kylan hill jamar chase base and snakeskin of josh palmer nice one chargers Good second year receiver right there rookie snakeskin case hit chargers josh palmer The Magnus one there we go. That's a really good-looking one too the bonte smith emergent rookies monti rice ron dale more blue wave bills jordan poyer 44 of 199 and silver eagles dallas goddard my homes is everything that makes the chiefs go They do not have a very good group of receivers green scummy colhardman chiefs 47 to 75 or they're like average, you know They don't really have a number one receiver Yeah, kelsey though. He's a beast Molden farley orange wave colts rocky sign Number 48 of 60 silver rookie rams urnish jones rookies raci mcmath desvits patrick orange rustle gauge Falcons number 97 of 249 rookie jail and waddle Trayvon morrig orange wave divante parker dolphins And a green scope jets rookie otto zack wilson 62 out of 75 What a color match what a hit for the jets The biggest win of his career today Awesome car there. There is like a print line on the bottom See where it kind of cuts off the centering is like, okay, but there's like a print line there. I'm gonna send the box around