Hello, and welcome to The Launchpad. This is an offshoot of the Startup to Storefront podcast where we talk to the founders of companies that are just getting started and whose stories we find compelling. Today we talk with Ralph and Caroline Wald, co-founders and the husband and wife Chef Duo behind a Marac Peruvian kitchen. The restaurant industry is constantly evolving and trends can seemingly pop up and disappear overnight. But one industry trend that is looking like it has some staying power is the ghost kitchen. Brick and mortar restaurants begat more cost-efficient food trucks, which have in turn led to even more cost-efficient ghost kitchens. Today we cover how the coronavirus pandemic steered Ralph and Caroline into opening Aymada, the economics of taking orders through delivery apps, and how to progress from a cook to a chef. Hang on, hang on. If you're not subscribed, can you go ahead and do that right now before we get on with the video? It helps us out tremendously. That's all we ask and we're back. Now on to the episode. All right, bienvenidos al podcast. On today's show we're talking to Aymada Peruvian kitchen with Caroline and Ralph. Thank you guys for joining. Tell us a little bit about what you guys are working on here in Lincoln Heights. Hi, thank you so much for having us. Yeah, so I'm Caroline and this is my husband Ralph. We are Aymara Peruvian kitchen and we're a family business. This is us. This is my husband and I and we opened back in October 2020. So right in the middle of that crazy year and we do Peruvian food with authentic Peruvian ingredient that we source here in LA and then we import from Peru. We are a ghost kitchen operation. So we offer fast and fresh food with delivery, curbside pickup. We also do catering and our goal is really to deliver authentic Peruvian food in this crazy world of 2020 and 2021.  When you guys were going down the path of this and we'll get into all the delicious food after. But when you guys are going down the path, I know this is kind of a new thing for a lot of people in the restaurant industry where you have so many options. You can go with a food truck, which is kind of a lightweight, less expensive version. You can go full blown restaurant, which is super expensive and you have to hit. You have to like do really well for five, six years in order to get any sort of money back, especially if you're building out this brand new kitchen. And so as you guys were thinking about your options and it's COVID. So we throw another issue where no one can come in anyway, for the most part, right? And so what landed you on the decision to pursue a ghost kitchen or how did you even learn about the cloud kitchen ghost kitchen concept? Yeah, no, that's that's a great question. We had been looking to open a restaurant for years. We were back in March 2020, we were actively looking for a location. In fact, two days before the shutdown, we were having a meeting with a landlord about a space that we loved and we were having lunch and we didn't, we didn't happen, obviously, because two days later, you know, the whole world was shutting, we're shutting down. So it always been our dream to open a Peruvian restaurant. Now, after, you know, COVID-19, obviously we had to rethink about everything. What's going to happen? We've seen all the restaurant closures, you know, around the country, around the world. So we were like, okay, what's next? You know, and, you know, Ralph lost both of his job. I personally did not have any clients with my consulting business. So we were like, okay, what are we going to do? And back in May, you know, I literally called the health department, you know, of Los Angeles. I started to ask questions and they actually the one that told me about Ghost Kitchen. And then I started investigating and I was like, oh, that's, you know, sounds really good. It's going to be the right fit for us. And they actually, Ghost Kitchen, you know, were already successful before the pandemic, right? But then obviously it was, you know, what happened last year. It took that business model to a whole new level. Yeah. Well, first of all, congratulations on losing your jobs.  And, you know, while it feels very depressing, I think at the end of the day, it's a net positive.  And so things are moving in the right direction, which is exciting. As you guys got the Ghost Kitchen, right, like, there's so many unknowns. So if I'm, if people are watching, listening and they're thinking of starting their own Ghost Kitchen, just because of COVID or because it makes way more sense financially, what's the hard part? Like at the end of the day, you have to do all this marketing, right? Because no one can come to you. And so how does that work for you guys? Is there any training? Is there like groups out there that can help? Or is it just you guys doing social media and just plugging away little by little by little? Yeah, I think this is the most difficult part for everything because even we open almost over three months already. Four months? Yeah. It's going to be four months already and people are still calling. Hey, do you have a patio? Can I get a reservation for you? So it's difficult because we're inside of a building. So we have to explain to people, where I go to the kitchen, you know, you can order online or you can call us and we can bring the food to the side. No, but I want to talk with somebody. Yeah. I want to see the menu. I want to see what you have. Yeah, that we have pictures online.  So I would expect that people are looking, you know, so I want to make sure that your pictures are real from when I get it.  I can see you. The most difficult part is, you know, explaining to potential customer how they can, you know, order from us and reach out, right?  So it kind of helped our model.  Yeah, I mean, it's really is about social media.  We're doing, you know, a podcast with you for the first time.  And then we also do the traditional. We have flyers and we literally go to the neighborhoods, you know, the business neighbors in Lincoln Heights and we, you know, introduce yourself. We do some specials for the neighbors. So I also wanted to talk to you guys because we're building a brewery in Lincoln Heights. And so as we think about our grand opening, it's always good to partner with different people within the community. And so we can talk about that later, but that's something that's on the horizon. When you guys get your orders in, is it mostly like Uber Eats, DoorDash app orders? Or is it mostly people like me who order and then come up and then pick it up? What are you seeing the behavior and how has that changed maybe through COVID? I would say at the beginning it was only because nobody knows us, you know. So our brand was brand new. It was a baby. And we come from different backgrounds. I'm not a chef. I never, she never worked as a chef. So, you know, so we just pop out in Lincoln Heights and introduce ourselves, you know, to every single neighbor. Hey, you know, I'm from Amara. We cook for you. You know, we can cook. Yeah, nobody knew us. Nobody knew us. You know, and, but I think that the platforms, I call it the platform, like all the deliveries up, it's now it's about 20% of, you know, revenue. And the lower it is, the better. Yeah, the fees are too high. The fees are not favorable. Yes. And actually, you know, a lot of people seem that ordering for platforms, they seem that we're not paying commissions, you know. Yeah, there is customers don't know, you know, that's. Tell us, tell everyone, tell everyone the realities of this, because I've been saying this forever. I'm like, restaurants are not making money on this, on these, on some of these dishes and stuff. Yeah. I would say 95% of platforms, they charge us 25 to 33% of all the sales. From the net sales. Net sales. So let's say you buy something for $10, you're paying the platform $3.30, right? Yeah. And that's it. And the customer is already paying a delivery fee. And sometimes I think it's another fee, something another fee. So for sure, you have to have them, I believe. I mean, because we're still new, so we want to, you know, I don't think it's completely bad to have them. But for sure, the more the customer reach out directly to us, the better. And, you know, we have their name, we write, we do personal thank you cards that we write every night. And so when the customer reach out to us, it's very personal. We have a lot of repeated customer already. I know some cities, I know here in West Hollywood, basically the WeHo, the West Hollywood Chamber of Commerce is, is effectively having all of these delivery delivery apps and they're passing legislation like rules that restrict the amount of fees that each of these delivery apps or pickup apps or just order apps can, can charge the restaurant. And what's nice that I've seen here in West Hollywood is some of the restaurants are getting together and not allowing any delivery apps on like an like basically imagine 30 restaurants saying we're not going to be on any apps. And so what happens is people like me, we're looking for it, we don't see it. Then we go to their Instagram and they're all like, yeah, we're not on the apps, please come support us and here's why. And they're telling everybody like the dollar amounts. And I just think that education is super important because it's hard to survive as a business already. In your space, are there other restaurants too? Or are you guys the only one? Yeah, there is a few other retailers in our building. It's mostly wholesale and yeah, more wholesale. But there is another few. Yeah, but it's not the major revenue. Just from a cost perspective. So I think about it like this, like to build out a kitchen could cost somewhere between 500,000, 600,000, especially if you're buying all new equipment, leasing kitchen space, still kind of expensive. And so was the cloud kitchen model significantly more or less expensive for you guys? No, for sure. Building a restaurant from scratch can cost anywhere from a quarter million to millions of dollars. And with permitting, with the city and health department, plan check, it can take months, up to years sometimes. I've seen this before in LA. So ghost kitchen really is not only it's less investment, significantly less investment, but it's also a faster process. If you get all your paperwork together, you can open within two weeks.  Everything else is permitted already. So it really makes sense, especially for new concepts like us when you want to test the market. For me, ghost kitchens are what food truck used to be like 10, 15 years ago. You know, I think it's going to is going to keep on growing because COVID obviously, but also because it's so much easier for young chef or startup, you know, concept. And you can see ghost kitchen opening all across the country, you know, in Houston and Chicago. Yeah. So do you see this as a stepping stone for something bigger in the future? Do you plan on opening up an actual restaurant a couple of years down the line or whenever, whenever you guys feel like you're ready to make the jump? Yes. We were thinking to have a restaurant, but now because all the pandemics, we need a big patio. Just to make sure, you know, just to make sure we can run. This is our goal. You know, we were actually about to, you know, open a full restaurant with bar, with patio and everything, you know, and put all authentic Peruvian experience, you know, that I see that I didn't see so many Peruvians that are really authentic in Los Angeles, in my perspective. But we do something young, you know. Yeah, we were definitely looking when I don't know because I mean, with everything that is still going on, I don't know how the restaurant industry is going to be even in six months. But at some point, yes, we would love to, you know, open a break in more location and like you say, like give the full Peruvian experience with music and cocktails. You know, you talk about this full Peruvian experience and one of the things that I know about the restaurant world is that certain cuisines are looked upon more favorably than others. So for example, you look at which restaurants have Michelin stars handed out to them. A lot of them are either French or Italian, some Spanish, and not a lot else in terms of other countries, cultures and cuisines. So Caroline, I know you are from France. What was that decision like? Did you even consider opening up a French restaurant versus a Peruvian?  I think that there are not enough authentic Peruvian restaurants out there in the world, let alone LA. So I applaud you guys for going the Peruvian route. But what do you guys think about that whole culture of exclusivity in terms of cuisine in higher-end restaurants? Yeah, no, for sure. I feel like French and Japanese are like, you know, on the top of like the Michelin criteria. I don't know. It's funny you say that because I always say it's always these are French or Japanese. And then sometimes there is a little bit of Spain or I don't know, Italian, but Peruvian food in general is actually very, for the past, I believe, what, five, seven years? Peruvian food is really booming. There is a lot of great chefs in San Francisco. In Peru, actually, there is three Peruvian restaurants on the top 10. And they have Michelin star. And they have Michelin star. So it's actually Peruvian. It's becoming fancy actually. But no, I think for us, it makes sense to open Peruvian a Peruvian restaurant rather than a French restaurant because we love family, comfort food. And Peruvian food is more about that, like amazing flavor, sharing the meal with your family. And obviously, you know, French food is amazing. I mean, that's my roots, right? But I don't know. I feel like in LA, specifically for LA, Peruvian is more approachable. And also it's a little more mixed.  You're welcome to come, please. So you can get ceviche is Peruvian Japanese. You get fried rice, Peruvian Chinese. You get pesto pasta, Italian Peruvian. You know, there is a mix of every single country. So you have a lot of variety that you can get Italian, Chinese, Japanese. Yeah, you can never get bored with Peruvian food. There's so many different dishes. I agree. Hey, show us the can you're drinking. I just want everyone to see this beautiful icon of culture right here, that little Inca cola. La bebida del Perú. Lo mejor, lo mejor del Perú. I grew up with this. So Nick, I would play soccer in Peru and then I would drink Inca. I'd run home and drink Inca cola. I don't know. It's not very healthy, but that's what I did. Probably not recommended by dietitians, but yeah. Not anymore. At one time it was. And so from you guys as you, I'm just thinking about this as like a growth model, right? So it seems like, and in talking to you, I'm kind of learning this. It seems like if you start a ghost kitchen, it's kind of a lightweight way, lightweight in the sense of not building your own restaurant. It's, you know, like cost way of building a brand while testing the market, let's say, right? And so then it kind of allows you to build a momentum before you start probably opening up a location. What's interesting is you guys are still considering that as a as an option. And so the ghost kitchen just kind of kind of gives you like a way to test, right? Do you kind of look at it like that? Like you can test new recipes, test new products and see what works or I'm sure you guys are already collecting data on people love the lomo. Let's say you're like, don't like this so much, right? It's 80. I would say what 80% of the sales is the lomo saltado. Is that the dish? Is that your, is that like every, every Peruvian place that I've ever been to kills one dish? It's like they make one thing better than anything else ever. And would you say that's the lomo for you guys?  Because that's every order that we get, there is always a lomo. Yeah, sometimes it's only, we were thinking, we're joking, you know, sometimes we were thinking we should change the name. Call it House of Lomo. House of Lomo because every day it's lomo, lomo, lomo, lomo, lomo, lomo, lomo, lomo, lomo, you know? That's not a bad idea.  Do you ever really push other dishes out to your customers to be like, hey, we're not just the House of Lomo. We're also the, whatever it else might be. Yeah. But, you know, I think it's in a good way, it's really interesting because they got the lomo, they like the lomo. And then they feel confident to try the different stuff. So sometimes, you know, people ask, why do you recommend Ohababa or Rochalfa? Would you like pasta? Would you like something light? So you can recommend, but the lomo is that. The go-to dish. That everybody knows. Yeah, you fall in love with the lomo. That's the one that you fall in love with. But we do have, we created some dishes that are not like traditional Peruvian because we wanted to give it like a, like a new touch, like the Peruvian street corn. We have a rotisserie sandwich. So it's, we use the pollo, the chicken, the rotisserie chicken. And then we put it in a sandwich, right? So this is also a dish that we created to make it. I don't know. A new touch. A new touch. We use authentic, you know, we bring the chocolate or the Peruvian corn from Peru. We use spices from Peru. We use the pasta from Peru. Sometimes, you know, the way that we try to present is like, this is the inspiration from our grandmothers. My grandma is from the Andes, from Peru.  From Normandy. From Normandy. But we try to put, it's like, okay, let's see if you are, you're eating, but it's like my grandma and her grandma is cooking for you. Yeah. Doesn't have the fanciness of like a Michelin star, but have the freshness, has the authentic. The quality and the taste. And we try to do the most authentic that we can. So people, they will sing, people who went to Peru, it's like, oh my God, it tastes like Peru. You know, I remember I was in the cost of Peru and, you know, this is how the ceviche tastes. Even sometimes the fish we bring from Peru, we try to put all the experience. And if you never went to Peru, it's like you're traveling. You're traveling, you know, from Los Angeles to Peru without paying ticket, without anything. You know, yes, getting the all experience in one place. And it's a family recipe. I love that. I love that a lot. Oh, Aymada. Aymada is a Peruvian word. It used to be a language kind of like, get you on Peru. Does the word mean anything specific to you? Is that where your family is from? Or what's kind of the background just behind the name? So Aymada is different meanings. Aymada is a language. It's a culture. But we like Aymara because Aymara has a meaning of the name. The meaning of the name of Aymara means beautiful young woman, really creative. But it's shy. It's a female inspiration because the Aymara is really, Aymara Peruvian Kitchen is for us a tribute to both her grandmother, maternal grandmother. Because it's really, it's all the recipe that we have and all the Peruvian food that we have comes from Ralph's family. So it's, you know, his grandma that shared all the recipe with us and we practice with her. And then it's also my love, my love of cooking. I've always wanted to have my restaurant and cook my own food. It comes also from my grandmother, from Normandy. And so it really is a tribute to them. And so that's why we chose Aymara. That's beautiful. I love it. Obviously being in LA helps, right? There's a lot of Latinos here. There's a lot of Latin culture here. But at the end of the day, you guys chose Lincoln Heights. And I know there's cloud kitchens everywhere. And so how did you guys go about that? Obviously Lincoln Heights is also very Latino. But how did you guys choose Lincoln Heights and were you looking at other options? And it just made the most sense. I think we really love, we love Lincoln Heights. We've been living in this, in downtown for many, many, many years. We're downtowners. So Lincoln Heights is really close. So we were familiar with this area and we love it. Also, one of the reasons which is Lincoln Heights is when you do delivery, you kind of want to be in the center and then go five miles radius, right? So choosing Lincoln Heights allow us to be able to deliver downtown, Echo Park, Glendale, Eagle Rock. So we can really touch a good part of the city. And the team here is also everybody is so kind, so nice. Sometimes that's the feel of Los Angeles.  So it's very inspiring. It feels like in some way you guys are kind of at the ground floor of this new world, right? It's like cloud kitchens are a new thing. Everyone's moving the marketing online. COVID hits. It makes perfect sense for you to be in that industry. And it's interesting to see how what's going to happen later. But I do love the fact that you guys still want to bring the culture aspect of Peruvian cuisine, which you kind of need a restaurant for. And so there's still that gap, but nonetheless for now you guys have found some success. And it sounds like things are going really well. So your recommendations for all entrepreneurs out there are 100%. Cloud kitchens make a lot of sense. Did you sign a long term lease? Is it like a two year lease, five year lease? How does that work? It's a one year, one year lease. Yeah, but I think you can do months to months. It's very flexible. It really is. And that's also a good point you mentioned that. Because usually when you do a commercial lease, a real restaurant, it's your tie for three years usually. Minimum, sometimes even more. Yeah, it's super high investment. One of the things we're doing, you mentioned this before where you were saying like food trucks, like cloud kitchen is the new food truck. We're doing this project here in West Hollywood where we're putting a coffee truck inside of a building. And so it used to be running around all LA and then COVID hit. So that got shut down. And who knows when crowds are going to be a thing again. And so we just said, well, this coffee truck is actually really, it's a really beautiful 1950s vehicle. And so we said, it's a Citroen. It's a French Citroen Citroen. It's a French old vehicle. And so we're putting it inside the building. And I think as we're doing it, I'm like, you know, this will be great because there's so many entrepreneurs. That have spent a lot of money building these food trucks out. And it would be cool if you just put them in a building because it's still cool, right? It's still branded. And that way, no one has to like lose their investment in the concept that they already have. And so whether they're making pizza or whatever it is. And since the, since it's a big box, it's already approved by the health department. And so it's kind of cool in that way where everything makes sense and the costs are already spent. Now I'm all about finding innovative way of serving food. I mean, 2020, you know, forces to sing that way. But now actually it's fun. It's actually a good thing, you know, to, to find new ways of serving food. But in reverse economy, you can actually set up a food operation in your home, in your house and serve people there. So things like that, I think we're going to see it more and more happening. Obviously the whole patio and outdoor dining is, is going to only get bigger. And our background, Ralph and I is really like the fine dining restaurant. And I, I don't know, hopefully we'll go back to that one day, but who knows. One of the final questions I have is if I haven't eaten in four days, what am I ordering from you guys? Right? So I'm super hungry. What are you going to bring out to me? What are the four, five, one, two things that I must have on the Aibara menu? Lomo saltado. Lomo saltado with beef, ceviche, for sure, the ceviche classico. The arroz chaufa, which is the fried rice with shrimp. That's like the, that's amazing. The rotisserie chicken sandwich, it's one of my favorite. And of course I have to pair it with Inca cola. Inca cola. Or cola inglesa. One of the things I wanted to circle back around to is something you said, Ralph, where neither you nor Caroline were professional chefs prior to opening up this ghost kitchen. And I used to work on Hell's Kitchen.   And that's not easy. I don't know from personal experience, but I know from close hand watching other people go through that, that transition from cook to chef. What was that like for you in learning how to become professional chefs after not having done this before? At the beginning, for me actually, I never cooked too much in my life to be honest. So how it works is my grandma taught Caroline, Caroline, talking to me. Well, I always love cooking. But that's like you said, I've always loved cooking at home for my friends, for my family. There's always been something of love. But then, yeah, once you start a real food business, then that's a whole different thing. You have regulation, you have to follow certain rules. Cooking at home is not the same like cooking in a real kitchen. And the consistency is key. And also the prep. That's for us was a whole thing that we underestimated the amount of prepping that you have to do in the morning. So you're ready for service. The mise en place. Yeah, the mise en place. So this was for us, I think, the most challenging. We had to rearrange your whole schedule because, oh, we're fine. Two hours before, we're going to be fine. No, no, no. You have to be here early in the morning to receive your deliveries, to inspect the product, and then store it, and then prep it, and then, you know, do all your sauces. And even for us that we have a ghost kitchen that it was, it's really small. You know, it's 125 square feet. So every single item has a specific space. If you move it, everything is wrong, you know, then you get lost. So we changed the way that, how do you call it? Yeah, we changed it three times. The layout, we changed it three times until we find the perfect one for, like, total efficiency. But now we're good. Yeah. Now it's all good. So you'd say that all the growing pains are over with, and you guys have kind of hit your stride? Yeah, in the first months, we had to scale back on the menu. So we sink after a week. We were like, okay, we have to take out of the menu maybe like four or five dishes. So we can really concentrate on making less dishes, but we make sure we make it good. And then slowly we reintegrated new dishes. So with that train of thought, are there any new dishes on the horizon that you are thinking of adding? Yes. Pescadolo macho. That one is a big one. And we've been working on the recipe for a long time now. It's actually overdue. We have to put it at the next one, Pescadolo macho. And then Tairin verde con milanesa. So that's the pesto, kind of, it's not completely pesto, but it's kind of like a pesto spaghetti dish with a chicken milanesa. So these two dishes are coming soon, really, really soon. You know, we don't have to hold you to this, but like give us an idea like how soon can we expect to be ordering? Okay, the pasta dish with the milanesa hopefully next week. This coming weekend or next week, the Pescadolo macho, I would say in two weeks. All right. By the time this is out, our listeners can try them. Listen, thanks guys for coming on the podcast and sharing a little bit about your story. Just tell everyone where they can find you guys, where they can support you guys, and where they can order. Yeah, thank you for having us guys. So we're I'm Mara Peruvian Kitchen. We are located on 242 North Avenue 25 in Lincoln Heights, Los Angeles. And you can find us on our website, I'm MaraPeruvianKitchen.com. You can order there. You can also order directly from Instagram. Yeah, just give us a call if you have any question. We're here every day. So if you order with us, you're going to see us giving you the food right to your car. I love it. Thank you guys for coming on the podcast. Appreciate it. Yeah, thank you. This was a pleasure. Thank you guys.


In this section, I will explain the concept of the implied cost of carry. So the implied cost of carry is defined as the various types of costs that are associated with carrying value of an investment. So there can be different types of financial costs which you have to pay in the form of the various interest rates. Suppose if you have borrowed some money in order to make an investment, then the interest rate that you are going to pay for that will be accounted for as the cost of carry. And then there could be, if a physical asset is being purchased or the investment is being made on a physical asset like wheat or gold or silver or any such thing, then we will have to account for the storage cost also and that will also be included in the implied cost of carry. So implied cost of carry can be calculated by using this very simple formula where we subtract the spot price from the forward price to find out the value of the implied cost of carry. And if we know that we are going to pay some interest rates and then at the top of it we are going to pay the storage cost also, then the forward price will be equivalent to the spot price multiplied by 1 plus R plus S where R is the risk-free interest rate, S is the storage cost, this little s and this capital S is the spot price. So by using this particular formula and solving it for little s, we can find out the implied cost of storage also and that would be simply the difference between the forward price minus the spot price divided by the spot price minus the risk-free interest rate. So we use this formula to find out the storage cost. So I am going to explain this concept using an example. Suppose we are going to invest in gold and the spot price of gold given in the market is $300 per ounce and we are intending to make an investment for one year. So the forward price is $334 for one ounce and again we also found out the risk-free interest rate which turned out to be, we are assuming it to be 8%. So by using this information we can find out firstly the implied cost of carry and that is simply the difference between the forward price and the spot price. So it would be the value of $330 minus $300 and this will give you a $30 per ounce a year implied cost of carry. And then if we want to find out the implied storage cost, for that matter we need to plug the values the given data into this formula for storage cost and that would be simply that has been turned out to be 0.02 or 0.02 and in percentage form we can say that the storage cost which we will have to invest in gold whose spot price is $300 per ounce and the forward price is $330 per ounce the storage cost in this case would be 2% a year.


So, yeah, so I'll talk about the accessibility for big panel labels, in a sense. So this is some drive work we've already done, which also, my study staff work in progress, so that we're still fitting the optimal way to really present results with the right spark for good, in a sense. I also mentioned that there is some quite related work by Dalash for example, that will be talked about in this conference. And also, I'll speak about this a bit later, but some similarities have also been brought up by Antonio Giuseppe, and he kindly, I'll be, I'll be back. So this is the first talk, I'll start with some history. So the starting point is that we have a compact flex, and we want to understand some conditions that ensure when our carotidometrics relates. So, a carotidometric is a carotidometric, which actually means that it's proportional to its curvature. So for a carotidometric to exist, we first need some of the logical conditions to be satisfied. So the expression plus of kx, so kx here is the mechanical bundle, which is minus the expression plus of the mechanical bundle. So this plus must be signed, because there cannot be, because the kx has to be equal to minus 1, 3, 1. And so, I mean solving some equations. And so, the information in this equation is that we want a carotidometric media, which is the curvature of the right side of the sun, which is the right side of the sun. And it's equal to some normalizing constant, which will exist. Next, this thing, which I call the exponential of the right side, which is really a volume form, so we're not going to need to really just take individual potentials of the matrix taking exponential of that, because this matches very nicely to a volume form. So, a carotid equation is solving this. So, strictly, the kx not like was 1, so we can paperize kx, which is that kx is not all. That was solved a long time ago, so that was solved by Yoban, so it's 6 and Yoban is 28. And so in this case, there are no obstructions. There always exist the carotidometrics. On x equal to 0, so the Calabria case, Calabria against those part, when he got his physics medal. And he also showed that there are no obstructions due to the existence of carotidometrics. So, Calabria case, such a matrix, it always exists as well. This question is much more related in the family case. So, on that, this makes one, which is that kx example. There are obstructions, they're not always carotidometrics. And furthermore, these obstructions are algebraic two-metrics in nature, which has been solved now, so the problem is that we understood in the case of xkx anyway. So, we have solved by many people, but the main contributors, as there are Tian, and then Chen Dawson soon, that's built the final structure. And so the final result is that so with my xkx example, then there is a carotidometric on x, if and only if x matches the x, is capable of stable. So, I'll actually never define this as a capability, but the thing that really is... The important part is that this capability will eventually be solved very quickly in nature, whereas the carotidometric the question is something that I like to use to complete the useful. So, the statement really means that we can check this quite difficult existence of PDE problem using some easier by nature algebraic condition. And so, with the method I talked about, I mentioned the disability. So, the disability is a thing that we find, right, when there is a resonance of yd in this case as well. So, I'll show you that. So, if there exists a current in x when x is things to be stable, and if there are more of these which are unique, then uniformly they're stable. So, I'll explain this if some people say it finishes. And, firstly, if x matches the x, if you currently think stable, then there exists a carotidometric on x. So, the problem, everything is unknown. So, there are multiple directions that we can look into next. So, one thing is to change the improvisation, so to not look at my SKX, but to look at any of them to see if there are cck-metric selects. And the right direction is to weaken the positivity condition of my SKX in a sense. So, that's the direction that my name is going to go. If L, so in this case, as my SKX, these are real facts. For example, then L is the eventually basement tree. So, I have powers of L, there are no points at which it points. That's the dimension of the space of the sections of the powers of L at maximum. So, this image, if you call the volume L, which is the dimension of the space of the sections of L, exists so it's in actual limits and it's also positive. Really means that's a function which is the sequence of dimensions of the space of the sections. It's a big goal of an enterprise and so it's a maximum of a single group. Maximum example is the train to space. It's identified by alpha-s, but there are less than a part of alpha-s. Okay, what we do is I define it as a function so we can say that L is the big if this volume exists and it's really big. Which means that the space of sections of L really have the maximum number. But that's all based on it. So, one of all the nice things we have actually is the space. It's important that we have base points. So, all the sections of the power of L are in Spanish and also we have the synthetic base of this which is really realized as part of L. So, we have this sort of scheme of the next image. All the sections of all the sections of all powers of L are present in this case. So, sorry, yeah, in the strictly big case. In the big one, that's something I hope we'll do. Yeah, yeah, so this can be an internal field. And we're going to want to look at their effects or positive effects in that sense. And we'll also see the other things about this synthetic base because it exists. So, we have to deal with taking as infinity some set of x to define the sort of weaker notion of the case. It actually gets in the way. But that's a strictly big case also, right? So, yeah, so I say it's strictly bigger than the big one. So, yeah, so, why is this definition in the correct way? Yeah, if... So, look at the current same problem in the case where plus minus k is big. So, we can make sense of the problems of this due to the heat papers which have also come up in my thesis talk this morning. We can make sense of the motion by equation. We see phi super of n equals e to the power of 5 as before. So, in this case, phi has similarities, but we can really just define this as a measure in the same way, away from the normal case to measure e to the power of 5. And by instituting it here, I can solve the current same problem in the journal 5 case. So, on the x to the power of 6 is the senior or weak current same problem. So, in this case, there are some things that make the problem a lot simple to examine. So, the kind of covering is quite iterated, and there is a kind of equal apple model which has some similarities with the apple model. For x, in that case, we can solve it here. We see it here. And this is a fact that we use when I'm asking you to prove the existence of the current in that case. But if we look at the big fellow case with minus x, it's just big. We don't have a connectable model in this way of iteration. So, we have to solve it here. And in that case, it's even false in general, right? So, the other example. Yeah. Yeah. So, first of all, for things that make sense, we have to assume a singularity condition in a sense. As I said, there is work with singularity tricks. There is a subset of nicerly tricks which have minimal similarities. And we have to assume that for any such metric, the measure e-minus 5 is associated as 5 volume, which is not guaranteed. So, tie for it to this actually guilty conditions. It really just means that nicer, positive metrics have minor similarities. This is more or less a condition that you can make all too brick, but they're going to initially belong to the asymptotic base locus, or different base locus, which is ultimately advised. This is an alternate condition. So, the result of that measure is one direction of the utenal subjector in the big case. So, the work of the Tanashian QA dimension knows the other direction of the user from the national disability. Let's go into the if x is big and if x minus px is kLt in that sense, then A inter-exists a weaker geometry on x than x is least stable and inter-exists a unique worker geometry on x than x minus px is uniformly stable, which I will try to explain in the spectrum of actually defining kLt. So, one thing that we've not come out from this data, but that we don't actually have would be to understand if uniqueness of asymptotic bricks is related to the automorphism group. So, we really want to look at automorphism that prescribes, that preserves the singularities of three abled inseminative matrix. But, because this is alternate, this means preserving the main focus of xkx asymptotically, this should be just the automorphisms of x. We have a version of both here on strict positivity as the thing functional in that case, so we don't actually know if uniqueness of weaker geometry comes from the fact that the automorphism group is just real. So, we can still formulate the state of the state of the state. Yeah, we haven't really tried to work that out. Really, is it important to us to know if there is something that's sort of wrong? If there is something in this question as well, because in this case, why is there a case in here? And so, these indices are in the sense of currents. The singularities of the singularities of the currents, or is the equation just a singular set? And then some kind of a singular set, it's a literal standard equation. They also mean something about the singularities. Yeah, it really means that the... So, ultimately when you solve the equation, you're going to have something with the most similarities, and so this means that you control the similarities of the metric, and the singularities of the metric are also determined by some algebraic things in the TQX. It really means that the asymptotic base of the case is not to... So, to redefine the usability, I need to redefine the notion of test operations. So, the idea is that caseability is kind of the three-dimensional version of JAT stability. And JAT stability to test the stability of a point. So, to sign up some invariance at infinity, touch to it. And so we need to define a sort of notion of one parameter separate, but more... in a sense, because you can see just the point, in the general space. And the correct notion for that is the notion of a test integration. So, in the classical scenario, it's just a scheme of our family which is the scheme of our Q1. We have a system action which is the usual system action of the line bundle, which is unirrised. And we want that over the fibrat one, where the every fiber starts the restriction of your disproportion is identified with the... But so, when we work with big things, it's usually more trouble to work rationally, in a sense. For example, so it's usually good at each and every work also with irrational models of X. And the classical way to really encode all of these data compactly is to use the Zaris scheme in those spaces. So our project is going to make sort of all the irrational models of X. So, these things come up already by the work of the remuneration of the system, which is terrible terminology. Sorry. So we're going to have a sort of path of version of this structure. So we find part of the remuneration of space, and the rest of the space which writes X more which is also representation. So it's the predeterminates of the system these sort of objects are contractions sort of from some Y to X. So, just the quantitative morphism with native fibers. You want the exceptional quite responsive and also make us that's the predeterminates of the time model which pushes forward to write X. And we also want the volume of the process. We want the volume of this. We want the volume of X to move up here very soon. Let's actually find the objects into the system. So we want some sort of order which we will take to the next minute. And it's really a natural order that I say that this one dominates this one if there is a piece like this which is greater or not. So that's the angle here which is more into the angle here. So this domination relation in the system that we take to the next part of this. Yes. Excuse me. In the category of so the things that we come up with building the big writer in our definition as well is kept in the category of schemes with and on all these ones. Is it the same as the model of the pullback or is it the same? Is it equivalent to the model of the pullback of minus k in the end? That's not the same. So before I say that in general, I know that we ask the egos that I will know a bit soon. Yeah. So if we push forward as a cycle we can think of it as a cycle. I see, so yeah. Are you not pushing forward the shift of sections? Yeah. You can formalize it in different ways. Yeah, so if you push forward the shift of sections but then you also ask that 280 is associated by model, so you have days invertible and this makes actually the weak minus kx. Days actually? Ah, sorry. If you want to see how wide as the shift and then you push it forward you ask that the forward is invertible and it actually makes the shift of sections to make the x sign. Okay. The function is subjective fractal dwarfism which has connected fibers but really you want to make a base of it. So if we have something like this then there is an observation which we did as a verification of positive matrix on the right angle of stairs and on the minus kx so we can work in the same way under a line under the minus kx and devise the matrix for mean multiplicities but that's kind of why we have to add this condition. So that's the variance of space and then we can define a test comparison for the variance of space. Okay, so if for each such Y we ask that there is a test comparison for Y which is super effective which really means limits of big things which is a minimal visibility condition such that there exists positive matrix there. It's compatible with the order and that's the line model currently LY pushes down to the line model currently LZ and the last thing that needs to be approval for this integration for X times kx which is just nice to work with because then we can pull back this integration and work with the variance of Y and there is an actual condition so we work really over some days and then we have asymptotic base so we want to say asymptotic base so we for some technical reasons we need to compare between these weights of size so we just assume that they are the same which is a function that's chili issues for example like yours would be these configurations as well. So here I mentioned the work with Christiane he was in the front of the case but with first comparison parity this is a senior optimistic metric on YSKX and he asks for characteristics in the weak sense that have the same similarities and in doing that he also basically comes up with the same efficient as this progression I just want to say that this is something that he also proves in the pantheon this paper is also as well as I said but it's basically so there is one part which is really the volume part for the asymptotic voting parts which is defined using the theory of intersection of mid divisors which is some of our Janssen and then it's been treated by also Amalfa so it's a sum of that and some local critical term with respect to the base of this and so we state that X is the probability stable if this mean of variance is not written as a uniform as you've done but X is greater than that so normal 5.0 should be followed as a normal project so that this is your oldest appearance this is what we call uniform possibility and we can actually define it yes it is algebraic and it is a positive quantity so it's actually it can be like a norm I guess same is the ability to be easily defined it's only just 0 yeah yeah that's the last interesting part yeah it's easier to understand but I think there was a complexity but also as a conjecture part about the torrid case so classically if X is a torrid file so there is the torrid section of X Y is uncle and linearized so then the Y is the conjecture was solved way earlier usually I've done some general case and so the issue that's a case to deal with if you want to really explicit non-extraetric condition so X Y is a torrid it defines a pointer and then it is case table if you don't have the associated pointer that's very center of the origin that's the complete conjecture entry description so we can ask the question the big case so in the big case there is a disruption of the pointer based on its release of this factory we can't, for example, reconstruct X from the pointer so X and the pointer so what I think might happen is that we go to the base loci of the of the MSKX and its powers and because the base loci has this subactivity property in a sense we have a direct system of polytips which should really be an inclusion of polytips non-indistability that's and so some work on that material the focus is sort of systems of polytips in a sense and so I think that the limit of the system of polytips to obtain it without should be convex poly so it should be limit of polytips just convex so is this part of the conjecture it's a fact is this part of the conjecture everything in green is conjectural everything in green is conjectural except so the other part is not it's a larger part it's a smaller part everything from here on sorry I didn't see it it's even written conjecture should have taken from here should have written so we have a limit of polytips so you just need convex poly to compact the excess which should be a underbody so underbody's appear when you try to do the other reconstruction you can't do it in action so you just evaluate sections against the motivation and then rescale but it should have the same volume as now because that's really pretty type of estimation and I was also thinking about this post-correctional urethase case and in this case this goes to the work of Wing Chun who defines the good bodies that work with post-correctional urethase this limit of system of polytips in that case you can recover some of this work or say that's in this story case we have the input visibility you can only if the body center of this limit of convex poly is actually the origin and if it's if this is not cured from the work of the terra corpus there is still a notion that there is center for limits of polytips and that's that we should still be able to relate some projections