Maybe she's born with it. Maybe she is 11. That's the vibes I'm trying to have right now. Right now, the trends tend to be skewing hard towards the 90s, which is the only type of trend that I am here for. I feel like there's been a lot of videos that were like this. There was a trend going around that was like doing a full face of makeup using only Claire's makeup. And my girl Liza Koshy gave herself a dream childhood makeover, which was just going to Claire's and getting everything in there. A few videos ago I was wearing like those cute little clips that I used to wear when I was a kid. And I feel like so many people have been wearing so many like 90s inspired accessories and they look so cute and I love them. But as a 32 year old lady, I'm like how much can I get away with? So that's really the purpose of this video was yes, go to Claire's.  And yes, wear them to see where's the line? Cause I feel like I could wear those clips because they were brown and there wasn't so many of them. And I've been wearing this necklace for like a lot of years because I just, I don't take things off once they go on my body. I'm super into the 90s trends and I wanna see how much I as a grown woman that maybe has no business wearing some of these accessories can get away with. I say all of them, you let me know when it's borderline outrageously inappropriate. What I need you guys to do for me is make sure I'm not being that lady, you know? You're already being that lady. I'm not, I'm not. I'm a 32 year old lady. That lady. Here we go. Julian, here's your first purchase. Oh, this is also Julian's purchase. Thank you, extreme warhead. I like never got into those as a kid. I didn't like being in pain.  It's sour, but I weirdly remember being way more intense. Did they nerf these? All right, get outta here. Hi, editing Jenna here. So the next couple of clips were me really wanting a beautiful glitter eye look to go with my beautiful outfit that's yet to come. It's great, stick around. I know that Claire's in the past has had some of their cosmetics for children recalled because of asbestos. A lot of that was pulled off the shelves and there's a very small selection of products at Claire's right now. So I figured can't go wrong with just a nice little glitter, can we? Well, I'm here to tell you that many hours later and this is just my own experience and opinion. My face kind of burns. So I don't want anyone to purchase the product that I purchased and I don't want to say anything other than that's what my face feels like. So I don't wanna include the clips of me putting on the glitter.  Anyways, back to the video. Julian, obviously whenever we go somewhere where I'm getting things, he has to get his own thing. So Julian got himself two little rubber snap bracelets. I'll put on mine because mine are hella cute.  They were kind of low key, high key dangerous. What time is it? Stop. I actually like those. I like those a lot. They got a furry one.  Yeah, you can tell that they are shaped for a small child's wrist, but this is a dope bracelet. I would just wear these for a day that would get completely disgusting, you know, cleaning up dog pee, et cetera.  And mine if you like playing in the mud. That was me. I used to put bugs in my pocket and then pull them out later and show my mom and say this as my friend. What do you think? Yes or no? I think they look really cute. I say yes. Tell me if I'm wrong in the comments, but also you're wrong. I got a pack of these cute bracelets. I used to have a necklace that looked like this. It was a choker. It was just this material that I found and I used to wear it all the time. Julian, yes or no? Yes, they're bright and yes. One of my favorite things in the world is that scrunchies have just decided that they're fine again. Because there was a point in time when you would get really made fun of for wearing a scrunchie and I remember getting made fun of for having and wearing scrunchies, but I was also a gymnast in the 90s and my idol was Shannon Miller and she had scrunchies. She was the Jojo Siwa of hair accessories for little kids like gymnastics. Oh, that's dope. The look is coming together, I must say. Well, I mean, this is only one of many hair accessories that I got. We got so many chokers.  Did you ever use to make beaded necklaces and stuff because I did all the time? Blue. I don't think my neck is gonna fit. Yeah, huh? It's adjustable. My neck is thick. Quit bragging about your neck. Well, I'm proud of my thick neck. Finally, our friendship solidified in the necklace. Jenna, it doesn't fit around my neck. Stop bragging about your neck. Fits great. Show them your back. What did you do? I had to put a bracelet in there so that it would fit around your neck.  It really was. So how long do I have to keep this on? Until forever. I'm taking it off later. We're Best Friends Forever. Please don't take it off. The stretchy tattoo ones will probably fit you so we can give you one of those. If you're more comfortable with that but they represent the same thing and do not take them off. I had one like this with the daisies on it and I would make them out of scolpey and clay and beads all by myself. Why all by yourself? It was a weird carrot. Very happy. I love this necklace. I'm gonna get makeup all over it, which again, not necessarily a problem that a child has. I'm gonna ruin it. Why do they have like a closure? Oh, since when? I think you put the ball through the hole. I'm aware, thank you. I feel like, yeah, all of these together kind of screams like maybe stop it but like one at a time I think I could pull off. Maybe not this rainbow one with the star in the middle but the other ones I think I can pull off. When I was a kid, before my mom let me get my ears pierced she would let me have sticker earrings. These were my favorite and I would always save like my favorite one for like last and like never use them because I was too scared because like there's no occasion on which I could ever use that one that I really like. Because I now have my ears pierced, like how about a little like that? I love them so much, Julian. I kept them in a jewelry box. But you put stickers in a jewelry box? Yeah, because they wanted to get my ears pierced so bad. Because you were trying to pretend like they were real earrings? Yeah. That's actually really cute. Here, look. And I would always put them on all crooked, you know, because I'm a child. Yeah, I feel like as an adult maybe I'd throw on some lash glue to make sure that it's stuck on there but that's not outrageous. So another trend that has been going on lately along with these clips, which we have seen come back, thank you Ariana Grande, is little hair ties like this or like the hard ball kind, which I couldn't find any in Claire's. But what I think I'm gonna do is I'm gonna section off some of my hair, done.  Where's the line? As someone with the too much gene, where is the line? Yeah, I mean, I think you passed it. A few minutes ago, but it still looks really cute. I think you should use the powder pink bow. Good call, love it. Nice choice, Julen. Tell me when, when is too many? I would say when, when, no more. It's too many already. I like, I really like this ring. I feel like big, beautiful, plasticky looking jewelry is just like back with the vengeance. So I got these cute little cherry earrings. They're cute, but I'm kind of hungry now. The other thing that I feel like we're a little bit of the trend in the 90s, but are especially a trend right now, are these like tiny little bitchy teenage girl sunglasses. They definitely changed the vibe. Right, it was like, oh my God, fun, cute, amazing.  No look would be complete unless I had the perfect bag. So the first thing that I got is the cute glasses case for my bitchy sunglasses. Oh, they barely fit, they're too bitchy. I got an adorable fanny pack pre-stuffed with paper. Um, I like it, it's got good color. Wait, I don't know if this is gonna fit. I think it's dope, honestly. I'm gonna put my bitchy sunglass holder into my clear backpack. What, okay, I need my cell phone, please. Thank you, Julien. Are you ready for my look? Look at you. Now, but tell me, do I look like Jojo Siwa or do I look like a trendy Instagram girl? Yes. Both? Just yes to everything. I'm gonna go outside. I don't know which product it is, but I smell like fruit.  A little too much on the clips, but they still work.  Do I just look like I'm bullying you without saying anything? Yeah. I mean, overall you look pretty sick, 10 out of 10. Really?  What? Permit. They're just eating your bracelet. Maybe these bracelets were a bad idea. You like my accessories? Do you like this one? Yeah? Curvy. This is like the most fun, though. Bitch. You got a new toad. It's just the glasses. I genuinely like everything that I got, but I feel like if you were to wear them one at a time in small increments, it's cute. But I feel like we didn't need a video to know this. I just wanted to wear all of it at once because I have something called Too Much Jean and I'm gonna write about it in my burn book. You can see through your backpack.  I can't be the only one that has all the fun, so here you go. What? All right, this might cut off your circulation, but it's cute and worth it. This is as large as it goes, so you're probably gonna need to just sling this over one arm. How are you feeling? Sick. Oh my God.  Oh my God. Oh my God. Wait, why does it like genuinely looks good, though. Kind of such a look. Oh, damn. I gotta take this. There's my mom. She said I can't hang out there anymore. Why not? That's why. Who texting? Your man. Does it feel good though? Yeah, I kind of feel dope right now. You look dope. What was that? Breathing.  He's a grown man. He deserves respect. Good boy. Wow. I'm hungry. You have a phone call, sweetheart. Bunny! Hi! I wore a hat last night with little pom-poms on it, and she wanted that hat so bad. I'm a little concerned about these furry bracelets and pom-poms in my hair because she will try and eat them. Julian, do you like my makeover? I love your makeover. Don't cry, I'm on the phone. You have a phone call. I feel like anything that makes you this excited to wear and like feel fun, if you're gonna make fun of me, how dare you? It makes me happy and look how happy it is. I'm just gonna like sassily shut my phone at the end of every sentence. It's pretty intimidating. Yeah. No, no, no, no, no. She's so cute. I mean, that's what I said to your face, but behind your back. You're talking about your own dog. You look so pretty to me. Just kidding. Even as a grown woman, I don't care what people think. I think it's so fun, it's so harmless, just like any type of fashion or anything. I just think it's for fun and whatever makes you feel good and happy and don't let anybody tell you otherwise. You hear me? This is a good time.  That's mommy's. Please don't take that. Anyways, I hope you enjoyed my Claire's makeover. I hope it also gives you confidence that even if you feel like you might be too old to pull off any of these trends, yes, you can and you should wear whatever you want. I'm in the middle of something.  Anyways, let me know in the comments how much is too much and or also you're wrong. Make sure you subscribe to my channel. I put on a visa every Wednesday slash Thursday. I'm gonna write about all of y'all in my burn book. It's not for you. It's not for you. It's funny, it's a snap bracelet. No, it's not a toy. You can smell it, but it's mommy's. Thank you, that was so respectful. 10 out of 10, respect. All right, we have to end the video because everything in here is something Bunny wants in her mouth, so we have to go. Goodbye.


Hello, my name is Brad Langdill and I want to talk to you about algebra, which is so important if you're doing physics, you're going to have to have some basic algebra skills to even get started. So let's review some of those things you should have picked up back in your introductory class of physics, maybe Science 10 if you're in Alberta. A couple of things we're going to look at, basic rules of algebra, opposite operations undo. What you do to one side you've got to do to the other side as well. So I want to go through some questions from a document I give my kids, it's that algebra review, it's on the website www.ldindustries.ca. Let's try a couple of problems. We've got v equals d over t is our formula. I'm telling you that v here is 20 meters per second. I'm not going to put in the 20.00, but I am going to put in the units. You're going to see why here a little bit later on. I'm told that my displacement is 45 meters and we're asked to solve for the time, this variable in the denominator. So how are we going to get that time by itself? We're going to use an opposite operation. This is 45 divided by t, so I'm going to do the opposite. I'm going to multiply by t. And what I do to one side I'm going to do to the other. The reason I'm multiplying by t is because that t on the top and the bottom will now cancel out on the right hand side. All I've got left is 45 meters. And on the other side I'll have t multiplied by 20 meters. Now that might not seem like it did anything. You didn't get t by itself. Well, it's okay. You can get rid of the 20 meters per second by dividing both sides by 20. The reason we're choosing division here is because this is t multiplied by 20. So I have to divide by 20 to move it to the other side and cancel it out. And what's left over here is a t on the left and on the right 45 meters divided by 20 meters per second. Now why did I leave those units in there? Well, look, you can use this as a check. A meter divided by a meter per second is equivalent to a second. That's what's left over when you cancel those out. And because time is measured in seconds, you can be sure that you did this properly. So I type in my calculator 45 over 20 and I'm getting 2.25 meters, 2.25 seconds. That'll be 2.3 seconds to significant digits. So here's our first one solved. Now you know what, check out what we actually just did here. The only thing we really did, if you want to see the shortcut, is we just took the velocity, that variable that was on the left-hand side in the numerator, and it just switched places with the variable and the denominator on the right-hand side. That's all that happened. So you can use that as a shortcut if you like. I guess if you use the shortcut, hopefully you understand the algebra behind where it came from, so that you're not just cheating your way through. But this is certainly a little faster than going and showing all those steps. All right, let's take a look at the next one. We've got the accelerated motion formula. Acceleration is final velocity minus initial velocity divided by time. By the way, you don't have to know what any of these variables mean to do the math. It can be anything you want. We're just worry about the math here, really, not the physics. 23 meters per second is my acceleration. My final velocity was given as 5.2 meters per second. I'm trying to find the initial velocity and the time is 1.5 seconds. So it's a lot like the last one. I'm going to start off by getting rid of this 1.5 seconds. And to do that, I'll multiply both sides by 1.5. That'll cancel out the 1.5 seconds on the right. And on the left, that'll give me a value of, check on the calculator here, 34.5. Now let's think about our units. We have a meter per second squared multiplied by a second. One of the seconds will cancel out with one of the seconds. So we're left with a meter per second as our unit here. If you're not sure about the unit conversions at this point or the canceling out, not a big deal if you're still getting the steps, that's fine. All right, now we got to get this VI by itself. There's a few ways you can do it, but here's the way I think this is easiest. Again, just opposite operations, I'm going to subtract 5.2 meters per second from both sides. So that's going to give me, on the left, 34.5 minus 5.2 is 29.3, and the units again are meters per second. Now here's the thing, don't forget about what you have left over on the right-hand side. You don't just have a VI, you have a negative VI. And that's actually important because you want to solve for what positive VI is. You've got a negative one more time with the opposite operations. What I'm going to do here is you can do it two ways. You can think of this as either multiplying by negative one, or if you're thinking opposite operations, divide by negative one. Either way you do it, whether you divide by negative one or multiply by negative one, you're essentially just going to switch the sign on whatever you had on both sides. I'm going to get 29 meters per second to two significant digits. So all I did was basically take the negative sign off this side, move it over there in that last step. You don't only do that in the last step, don't do that earlier. Okay, so there's number one and number four. I want to show you two more here. Here's a little bit more complicated of a formula, but again I'm going to substitute in, including my units. I've got the displacement. I'm looking for the initial velocity. I'm told the time, which is 12.5 seconds, plus one half of the acceleration, which is 13.55 meters per second. Meters per second squared. Multiply by the time again. Okay, so I'll put that time in again, and it's squared. All right, now this looks pretty intimidating, but it's not too bad. The first thing I'm going to do is I'm just going to evaluate what this term is. This is all one term, all one number, that I can simplify down and make it look a lot prettier. So one half, 4.5 times 13.55 times 12.5 squared. That whole term is about 1058.6. Now I'm going to leave it as just 1058.6 on my page, but I'll keep that number in the calculator. And if you keep in track, actually what we have here now is a meters, is the unit. The second squared canceled with the second squared. Okay, that's equal to 30 meters equals Vi times 12.5 seconds. All right, now I need to keep getting that Vi by itself. So I'm going to subtract 1058.6 meters from both sides. So 30 minus that number that I had there. So I can either just type it in again or if you push second answer in the TIED model calculators, the answer will be whatever was in the last line. So this is 30 minus that number, which is negative 1029 about. So I'm going to write negative 1029. Still meters is initial velocity times 12.5 seconds. And again, opposite operations. Now I'll divide by 12.5 seconds. So the initial velocity is whatever that number there was divided by 12.5. So I'm getting negative 83. Well, I guess it doesn't round 82 meters per second. Well, of course, we want three sig digs. So I guess I'd say 82.3 meters per second. So there's one that's a few more steps, but the basic idea is the same. We're just using those opposite operations. I hope that was helpful for you. If you have more questions on algebra, definitely check out the website. There's more resources there at www.ledindustries.ca.


So, we have our next session by Tyler Urbeck and Kanza Kavili, and they will be talking about it wasn't DNS in CICD with Kubei Redd and Tecton. I'm just waiting for them to join in. Hello. Hello. How are you doing? Thank you. I'm fine. How are you? Good. Just waiting on Tyler. I think he's trying to connect, but let me see if it's here. There we go. All right. I figured it out. Perfect. You guys have the floor. All right. Let me share my screen to start. Present. Yes. Screen two. Is it all good? Cool. All right. Let's kick it off. Welcome, everyone, for our talk called It Wasn't DNS. We checked. It's CICD for infrastructure with Kubei Redd and Tecton. Hello, everybody. I'm Tyler Arbeck, I'm an architect at Red Hat Open Innovation Labs, focusing mostly around site reliability engineering. Kind of have a passion for this space of automation and pipelines and things of that nature. And as you'll see soon, making things do things that they were probably not planned to be, how they were planned to be used in the first place. So, if you want to feel free to reach out, if you have any questions after this, here's all the places you can find me. I'm here with Chansu today. Thank you. My name is Chansu. I'm a site reliability engineer at Red Hat. I work with companies to help them adopt DevOps cultural practices, help them to grow a SRE mindset within their organization. And well, it is at the beginning of September. And as Tyler said, you can reach out to release our links. Feel free to send a DM or reach out to us if you have any questions. So, let's get off. Okay. What are we going to talk today? So, we're going to talk about problems that we have today and how can we move us closer with the stuff we have already.  So, I'm sure that we are all enjoying our CI CD pipelines, you know, the benefit of having an automated pipeline is places already known and experienced many of us, I'm sure. So, it checks my, well, my automated pipeline checks my code quality. It runs tests for me. Then it checks some more security stuff. Then it deployed.  And it's all good. It promotes my code to the next stage. So, it helps us basically live in the good life because it just saves me from myself. But yet, I know that some of you can think some examples, even though when your pipeline is green, everything was fine, but still something was wrong. And why is that? Because having a reliable application pipeline is only half of the battle. You need some reliable infrastructure too. And I know that we all do our best for our infrastructure and we all practice an infrastructure as code as much as possible, which gives us the option to share the understanding over our infrastructure. They happen to us test our infrastructure in a repeatable way. But do we really have the chance to test everything? What do you think, Tyler? Yeah, absolutely not. I mean, there's a phrase saying that it's always DNS for a reason, right? There are just holes in the testing strategy that we see in a lot of places today where an application may be fully tested from front to end. But any time you start touching on infrastructure, oh, that's too complicated. That'll cost us too much money. We don't have the resources. We don't have the hardware to be able to test this out. So from what we've seen out in the field, there's just this gaping hole around infrastructure style testing that we decided, hey, it's time. We need to have a better way to do this so that we don't need to scream at the sky and say it was DNS again. That's why we wanted to introduce you with some, I can't say enough analogy, but it's a nice way to put this in, which is ghost ships. Tyler, would you like to say a few words about ghost ships? Absolutely. Let me weave you all a tale here, right? So for those that aren't familiar with the term ghost ships, ghost ships are just these, for one reason or another, whether fiction or fable, are these ships that just roam the sea with no crew, whether something tragic has happened to this crew, or if it's something like the Flying Dutchman where it's a haunted ship, right? But ultimately, there are no live passengers that can be hurt. I kind of came across, you know, I was probably watching a movie with my daughter and there was a ghost ship on it, but kind of came up with this similar idea of, hey, why can't we do the same thing with our technology environments, with our hardware, with our infrastructure environments? We have these ghost environments that ghost ships look like a ship, float like a ship, kind of go along the water like a ship, must be a ship. Same thing with these ghost environments. Looks like prod, feels like prod. Just no real people operating in that environment, right? So we really like, we like talking about these environment, these ghost environments.  But, you know, spin them up, make them look just like prod, but no people there to be impacted with it. So that's pressure one. Point one is like, hey, there's no people that can be impacted by this. So even if something does go wrong as part of our tests, we are not hurting anybody, which is the key part there. The second part is, you know, on top of that, this type of testing allows us to get to the point of, we don't need to actually have this hardware that's solely dedicated to this.  Why can't we just spin this up in, you know, in a virtual environment or on a cluster with, you know, various amount of tools that we have, so that we can, you know, one, take advantage of common platforms, but also we don't need to, you know, have all these expenses to take care of, you know, these dedicated resources. So we decided, hey, what tools do we have that will allow us to do this? So that brings us to bring our first members on board this, on board these Go ships. And Chanse, I'll let you take it from there.  One is Cubebird, which is absolutely our favorite, is basically here to help us bring our virtual machines into container workflows by running a virtual machine within a container. It's super exciting, it sounds super exciting. Whenever I try, I work with Cubebird, it just makes me super, you know, hype and because we can develop, manage and deploy virtual machines side by side with our containers and we can take advantage of all the simplicity, all the speed of containers and Kubernetes and this really, really empowering. This really empowers us with all the flexibility, all the agility we gain with containers and, you know, it's easy to deploy on top of Kubernetes in no point shift. It brings some custom, custom resource definitions. It's easy to spin up a virtual machines and it's really helped you to standardize things and it's helped you to use all these best practices from Kubernetes like scaling, overcommitment, high availability, all these things. And another thing that we onboarded is, I'm just a bit teared down, sorry for that, but we love it, it's our peaceful cat tecton and we use tecton for CI CD part because we again wanted to go with another Kubernetes native framework. So tecton is here to help us build our pipelines for testing and tecton pipeline is quite, to be honest it's quite different what we used in terms of CI CD tools because there is no engine to manage to start with. There's a core component of tecton, there's pipelines, runs as controller in Kubernetes. There is no engine or plugins that you need to manage. There are bunch of custom resources that you need to deal with which is, it seems intimidating at the beginning but we're gonna go through it in a minute. So once you get used to it, it seems super handy and alongside with Kubernetes, alongside with Kubernetes, we can make this ship work as our needs for our needs. And one thing, we get this anytime we kind of start talking about this. Oh, does it need to be tecton? I've got all these other CI CD tools. What about Jenkins? What about system XYZ? And really it could be any tool that you would like. This doesn't just work. This isn't a tecton specific thing. This is a whatever CI process that you want to use. We really like tecton because I'm sorry, I'll use some buzzwords here. We like the cloud native approach. We like being able to declare, to literally define all the stuff. We love our YAML, so give us all the YAML you got here. But tecton is just one approach here. You could substitute in your CI system of choice but what we'll show here today is going to be tecton. All right. It's a good thing that this is live but let's see if we're gonna sync or... So I'm taking my ship away and we're gonna do a little live demo of how this is in. So which one would you like to start with Talon? Would you like me to go through the code first or try to see... Yeah, let's look at the visual first to give folks an idea of what we're looking at and then we can make them break out the spyglass for looking at some YAML here. All right, so we have our pipeline here which is, well, we tested right before we come so it's all green. So basically this pipeline, what does this pipeline do is it gets the... Let me start from over. So we're gonna test our Ansible Playbook which we use for installing the DNS and configuring the DNS on top of it which is a very, very core component and important thing that you need to test whenever you do some changes or you need to do some tests before you roll the changes on the production you don't have to necessarily have a test environment or just for a single line changes in your playbook you don't really necessarily have a test environment to test this. So in this pipeline, we get our inventories, get our playbook and check our playbook if it is healthy or not. In the meantime, we are creating the virtual machines inside the apprenticeship and well, it takes a bit of time so we wait for this virtual machine to be out and then since this is a new virtual machine it has a new IP we get this IP to create our inventory and then we test our playbook towards this and then verify our configuration with an additional tasks to see if that DNS is configured and work as we expect. Taylor would you like to add something more because you love this. No, that was all good. It's definitely this whole process is why are we doing this? DNS is a fun thing to poke at because everyone has scars from DNS. And the way that people operate DNS isn't always the... What's the nice way to say it? It's not the most practical or best maintained system. It's always let me go in and update this record and let me go in and just update this config and human hands make human mistakes. We forget the bracket. We typo the name that we want and we'll end up with errors. We start impacting our users which at the end of the day is the thing that drives this whole idea of why we want to do this. Creating these ghost environments we're able to spin this up just like our production DNS server and then at the end we check to make sure that we get the responses we would like based off the changes that we're making and if it's all green then you can build out your pipeline from there. You can automatically progress it through your other environments until it hits production. So that's the whole thinking behind this and why we are using this example because we see this a lot so we want folks to kind of latch onto this idea. But I promised a live demo so it's better if I should kick this because it takes time and then talk about it a little bit more detail so let's see if I have my little code here. While you're kicking that off I'll explain why we keep saying it takes some time. So we are running on a fairly small cluster this is just one of our dev clusters and also we're running in an emulated environment so the performance gets drastically better when you're not emulating when you don't have emulation turned on with Kuber so if you're working on bare metal or systems that you don't need to turn on emulation for you're going to be in good shape performance much better but since we're just virtualizing and emulating everything a bit slower which is why here in a second when you see how long it took for some of these things to run you'll see like a 40 minute runtime what are you dealing with? Give me a sec I just wanted to check if everything is fine with my webbook it should have triggered this one I don't know why it didn't but because it's live demo it just worked it's not 45 minutes ago as it's in here but not working that now because it's demo God's it's just hating us okay now we are going to back in good shape sorry for that we've done this like three times some of the problems three of them were different and that's why we have CI to catch those problems it's because I didn't push it I committed but I'm too excited for it sorry I didn't push it anyway so what components we have of course we have pipeline I'm going to come in a minute but Tecton gives us the a component called event listener which basically gives you a webbook for you to set up in your g3 repository and you can set up for different events listeners for different actions like for one push and each of them have these definitions for trigger which one you're going to trigger and what sort of values that you're going to bind from your payload so and we have we have that's why we have all these trigger binding definitions and some trigger trigger template definitions yes it's hard to remember this and these are basically helps you to utilize from utilize getting the values from your payload and put them into the into the pipelines that you're going to trigger which is this pipeline and this pipeline consists of all these tasks that you just saw and it basically takes the values and pass them to the tasks and you can do this some sort of ordering or some parallelization or retries et cetera all these kind of things and you have these test definitions that's why I said that it's a little bit hard to get on board with Tecton at the beginning but once you get used to them it's it's fun because one it really helps put around base scripts I don't have to deal with Grimby and all the other stuff I love Bash I write base scripts to do some stuff in here but don't be intimidated with all these long stuff because we didn't write some of them you basically and thanks for this for the Cupid community we got some ready tasks from Cupid itself like creating the virtual machines waiting for if virtual machine is ready or not cleaning up for the virtual machines all they need to do is just provide some values or our virtual machine definitions or the name of the virtual machines things like this and thanks community again for this it takes care of it all and we just add additional tasks around like cloning the guitar, ensemble playbook creating the inventory based on the new virtual machines and taking off this ensemble for that and it should be still running should be still running yes but also I can tell about this Tyler yep no I just echoing what you said we prefer to be sticking with the ship theme here we prefer to be pirates we much prefer to plunder things that we can find in the community versus having to write our own I think throughout this whole pipeline there was maybe one task that we wrote ourselves everything else was just things that we were able to pull from the community provide our parameters to and off to the races so you know this may look like a lot of yaml and it is a lot of yaml but we didn't need to write all of it right we were able to just pull it in apply it to the cluster and it was available for us to use and while it is still running the ensemble part is also coming from our own infrastructure and simple playbooks because we use ensemble heavily to manage our own infrastructure and look at the number of these ensemble roles and playbooks it's it's a lot the idea was coming from basically this these are we have all these environments okay we have open stack environments we have our virtual machine environments but I just want to check something based on my little changes like trigger something and to see if it works fine to see if it is fine etc and you can't really have different testing environments for it or you have a bunch of people working on different stuff you can't have well you can't have some sort of consolidated test environment but still it might not be enough for you so with all these sensible playbooks we basically come from that idea saying that just want to test this little stuff I don't want to break anything else but it's on our other side and we all know that reliable infrastructure is really important so yeah so let's actually take a look at our pipeline while this is still likely going to be running and to take a look at what it's actually doing right and I think this is a really good example of how to bridge the gap of some of your infrastructures code your config management tools like Ansible can be bridged with a Kubernetes native way of testing some of these things because we're not just testing the deployments the things that pop into our cluster but we're also in this pipeline we're testing the things that help us build out our entire environment so we're not just testing that our manifests look good we're not just testing that we can spin up a VM inside of Kubernetes if we dig over to the pipeline one thing we're actually doing is we're linting the Ansible because if something goes wrong and there's something wrong with our Ansible we don't want to waste all the time to see a failed VM build right so we're testing everything the whole way through our process from the things that we're going to use to build our VM to the building of the VM to what pops out after the Ansible has run so you can see we've got Ansible linting happening there and a lot of times there are things we like to ignore so you can see that you can even throw in a skip list of Ansible linting roles that you don't like and this is just a warning but it's still a good warning it says hey you're referencing a file that doesn't even exist in there so it probably should be more than a warning but it still works nonetheless we obviously are not referencing that part of the play book so it's cool to show even running inside of Kubernetes running inside of OpenShift you're able to test out this full platform and again this takes a while because we're testing it from front to back but then one thing you could do even in the future is okay I don't need to test out the building of my DNS server but I just want to test out the configurations on top of it well Kuberit has a bunch of Ansible linting tools that allow you to just bring a custom image so you could have that fully baked DNS image your kind of gold DNS image and then just spin that up so now rather than waiting the 20 minutes for your DNS server to build now it's okay this thing just spins up in 3-4 minutes and then you can apply it you can test out just the configuration end of it so they're really cool tools you can speed only test the pieces that you actually want to test that's a good point basically you can take the image of your virtual machine and load it in here and then you can test on top of that so yeah good shout out and here I think we're seeing the Ansible run of where things are actually happening so we're going through our install we're installing the Python packages we needed all the supports all the Ansible goodness that we're looking at here until we get to the end that's where we just configure we add our zone in there that we'd expect we just have our dummy zone in there but that's just one part it's cool to see that you've installed a DNS server but we actually want to check things we want to make sure that things actually happen so I don't think there's a lot of good I don't know but I can't show let's take a look at what's actually happening in that execute in VM again yet another great task that we were able to pull from the Kuber community and it just it literally connects to your VM from your pipeline based off the secret and stuff that was generated as part of the pipeline we generate random SSH keys because you should not submit your keys to your repo speaking from experience but if you if we look at the last task as part of the pipeline Shansu we'll take a look at what we're actually testing for and I'm if we just go into the pipeline itself not the tasks sorry yep no you're good yeah so it's not a very complicated test I'm just digging to see that I get a response from the zone that I configured in our case it's just our labs kind of zone that we configured and I said hey if it's empty it's not there and it's broken obviously we see it's green so it's there but the cool thing there is they're they're also tasks you can you can start you know probing at records you know it's making sure you get the right C name or the A records or any type of records you want to kind of poke around that and really you know that that's that this is a very plain example because we wanted to kind of give like an approachable example to this really the sky is the limit as much as you want to test and poke around at inside your VM the tasks are there you just need to inject what inject your logic right since this is running and we have only a couple of minutes I can just jump into the next slide and quickly saying that the echoing like the other side the possibilities are endless well sort of endless as long as you have any sources to run firstly in your virtual machines or if you want to wait like 20 minutes like us during a talk so that's fine too but now that you know that you can run virtual machines in Kubernetes you can pretty much emulate you know we can pretty much try to run everything in here your imagination is really just constrained by CPU and memory at this point okay I'm just going to fast forward and we also have this slide for talking about what sort of things that we do we were doing while we were preparing this demo and well basically minus resource if you are running in virtual environments and using the emulation so I would just repeat the second thing is about the tecton and having to retry many process and volumes if you would like to use the same volumes for the parallel test or if you would like to run a couple of same pipelines that's using the same virtual same persistent volume to clone the playbook or something like this not everyone has retried many volumes so this might be a constraint for you what else Tyler we can say quickly yeah the two things on the Qvert side is these are virtual machines but they're virtual machines built on top of your container platform so take advantage of that a lot of the times your pipeline will try to connect to a VM not ready yet well kubernetes open shift we have things like readiness probes so we can sit there and wait until this thing shows it's ready we can just run a kubectl wait for condition equals ready it'll sit there and wait for your VM to be up at the same time you might have seen I think we've got the link in here so you can take a look at the repo we define a virtual machine custom resource it's part of our pipeline that spins up a virtual machine but the actual running VM itself is a virtual machine instance so if you don't say spec or running inside of your spec to say running the true it'll create your VM but it doesn't spin it up because you'll have to have another task that sets that to true or kicks your you know it's like vert CTL start or something like that so the thing that you want to test won't get created if it's not set to true so keep an eye on that we only have two minutes so we just had to run this really quick so if you have any questions please feel free to reach out to us the repo is out there also just for the example tasks or not for the example playbooks but it was fun to prepare the demo yeah I guess kind of our call to action right get out there write these tests write these pipelines for your infrastructure it is worth it it will save you all the sharp edges in the bleeding that you will experience testing and prod so hope to see everyone kind of taking this approach thank you again to all the community folks for letting us take all the tasks and having you know kind of being able to assemble it from that and also take for the live events opportunity it's the closest things that we can get for face to face so that was fun thank you and thank you so much both of you for such a fun and knowledgeable presentation it was definitely fun watching all the visuals so thank you for that and I don't think we have any questions yet so I think that means that it was a flawless presentation love you guys thank you thank you so much for coming in and presenting have a good day bye bye


Hi, I'm Eric Barsnes, conservation agronomist with the Natural Resources Conservation Service, and I have a few quick modifications I can show you to a handheld soil sampling probe. So here I have my standard soil sampling probe. I've made a few little adjustments to it. I've added a simple piece of PVC pipe to hold my cleaning brush. And as you can see on this brush here, I've actually added a little dowel. I just drilled a hole in the end of that. I added a wood glue to dowel in there to make cleaning the end of the probe a lot easier. That just gets stored right on there. And I've also added a couple small things. It might be hard to see, but I've got a couple marks there, and that's strategically placed right at six inches. And that's exactly the depth I need to take for my immobile nutrients, the phosphorus, potassium, things like that, right at six inches. I also made a small mark up here, so when I do a deep sample, I can take the top six inches and put that in a bucket. So depending on my sampling needs, if I'm just sampling for P&K immobile nutrients, I can only go that deep. If I do the full depth of the sample, then I'll take the top six inches. So I've got two marks on my soil probe to make my sampling more precise. I added a brush holder on here. I just took a piece of PVC pipe, one exactly the size of the brush, I just used some zip ties and zip tied it onto the handle there to hold my brush. When I'm sampling, I'll have my probe upside down, pull the brush very simply, clean out the end of that, and move on to take the next sample. Some people will just put the brush in the handle, but for the most part, when you're sampling and you go to cleaning this out, the brush is down there and the handle is not very handy. So I put the brush holder right on the main part of the soil probe. So when I go to clean the tube out, I have it right there and handy. I also left this thing so it slides a little bit. So when I'm taking a zero to six inch sample, I can leave it down here at the end. If I need to go deeper into the soil profile, I can slide that whole brush holder up there, allow myself to get a lot more of the probe deeper into the soil.


Okay, well thank you very much. It's really a great pleasure to be here today and to be able to see again so many old and good friends. As you can imagine this is not an easy lecture to give, so I think I decided to sort of approach it the only way I can actually approach it, which is to sort of tell you a little bit of my own sort of interactions with Ricardo. And while I do that I try to sort of convey a little bit about him as a person and as a mathematician. That's really the only thing that I can actually do. So let me begin first by telling you a little bit about him. Maybe most of you know all of this, but we might as well run through some of this very, very briefly. So he was born in 48 here in Montevideo. He began studies in engineering at this very same institution. This was the case of many Uruguayan mathematicians. I guess at the time there was no formal studies just in mathematics and the natural path if you wanted to do math is you will come to the School of Engineering with an eye of doing sort of engineering and then maybe switch it off. And I guess many of us did that, I did that myself and then I switched into math. I guess that was the case of Ricardo too and many here in this audience I think. So he completed his PhD under the guidance of Jacob Palace in 1973. He made spectacular contributions to dynamical systems. I think what Enrique said in his lecture is very much true. A lot of his ideas are very much alive and sort of going all over the place. So I think Enrique has told you about only a sort of fraction of the volume of his work. I'm going to tell you in due time about an even smaller fraction somehow the one that I had more contact with. He was invited twice to the ICM which is a sort of remarkable honor. Okay, and he passed away in Montevideo as well in 1995. Just a little bit before that meeting that has been mentioned on serial locations during this conference. That was also a memorable meeting for me. Not just because it took place at the bank, as a lot of people remember somehow, but because it was in some sense a very special meeting. It was a very special moment. So somehow we really, we sort of put a huge effort to have to make this happen. Manier had 11 PhD students. Some of those names in that list have people that have been particularly important to me. Obviously, there's the case of my older brother Miguel, who unfortunately is not here with us today because there is another conference honoring Ricardo at this very same time in Rio. But there you can find names like Kevin Enrich, who I hope he was around a little bit earlier. He was there, yes. Álvaro Robella, these are people that are actually taught many of us courses in mathematics. They are exceptional lecturers. And also, I mean of course there you can find Gonzalo. That has been a sort of huge influence for me. Right, so I'll do maybe a sort of quick trip down memory lane. So I'll tell you a little bit the first time that I actually met Ricardo. So the first thing to say is that I do not claim to have known him well at all. So I really got to know him towards the end of his life. But I got some glimpses into his personality and him as a mathematician too. So the first time that we met him was in the summer of 1986. So there was a big group of us. I mean, we were about at least ten, maybe, who's abbreviated remembers this better than me, at least ten that we were all essentially shipped from here to IMPA somehow. So this was towards the end of a very difficult period for Uruguay. The return of many mathematicians that were abroad happened maybe one or two years before that. And they came and they found a group of young people, I guess, who were very keen to learn mathematics.  That would be a very good thing for you. And indeed it was. This was a sort of amazing thing. I think it was ten year ago I was going to IMPA just at the same time during the summer of 1986. So among them were Beatrice, Alba Ruella, and my brother Miguel. So how did we actually make Ricardo? So Ricardo was a difficult catch. I mean, he wouldn't sort of show up. He wouldn't be at IMPA all the time. He was sort of well known that if he wanted to see him, he had to be after two basically, two in the afternoon. So we managed to catch him in the cafeteria somehow. And then, of course, he was sort of curious. I mean, he wanted to know who was coming from Uruguay. So sort of take these courses. So I went there with my brother, and hello Ricardo, come from Uruguay, blah, blah, blah. And then, you know, he seemed very friendly. And at the time we were taking a course on manifolds, a basic course on manifolds. This was being given by El Cidio Cilín's neto. And we didn't have really much to talk with him, right? I mean, this was around the time he has proved the stability conjecture. We were sort of little people. He was a big celebrity in some sense. So the only thing we could think of is why don't we ask him, you know, this very difficult problem that we cannot solve from the course, and we did. And he actually dispatched the problem more or less immediately after a coffee, a coke, and a cigarette. And then we sort of went away. So that was my sort of first encounter with Ricardo. So that was actually a memorable summer at INPA. A few months later, he came to Montevideo and gave an unforgettable lecture here at the email. So once again, I guess, I mean, my... Probably he wasn't coming that often before 85, essentially. It was essentially when Jorge Levovitz returned to the country that we started to see more of Ricardo, essentially. So he came and he gave this incredible lecture on geodesic flows. I really don't know why he picked that topic. He could have talked about the stability conjecture. He had lots of possible topics to talk about, but he decided to talk about geodesic flows. This was a couple of years after his work with Freire on Manifolds Without Conjugate Points. A kind of well-known term telling you that if you have a geodesic flow on a manifold without conjugate points, then the topological entropy coincides with the volume entropy that was defined by François earlier in the lecture in the meeting today. And he had just around that time, a few years earlier, given a new proof of a very famous term by Klingenberg that said that if you have an anosov geodesic flow, then you didn't have conjugate points. So conjugate points, as briefly as if you go to the universal cover, two points are joined by a unique geodesic. So if you have a manifold with negative curvature, this is obvious. But if you just assume an anosov, this is actually nontrivial. It's a nontrivial fact. So the proof by Klingenberg was a proof using the most theory of the loop space Ricardo gave a completely new proof and he had this sort of way of looking at the geodesic flows that we were fascinated with. At least I was. My first contact with the geodesic flow was essentially through Jorge Levovitz. Jorge had his own way of looking at things, but somehow seeing Ricardo lecture was unforgettable. I mean, it was not just the quality of what he was talking about, it was the quality of the delivery. I mean, you saw just a glimpse a little bit in the video how good he was at sort of explaining things. So his lectures were really sort of impeccable. So I guess those who have visited the institute here of Mathematics know very well of the informal gatherings on the corridor. So the seminar will always start late. I mean, you could not expect that it will start on time. It will have sort of, you know, it will start at time x, it will never start at time x. It will be sort of at least 30 minutes later. So here's a, so I went yesterday and took a picture of the corridor because I think I have this sort of wonderful memories of it. It looks a little different, I mean, in some sense it looks a little different today than what it did maybe 20 plus years ago. It looks a lot cleaner to begin with. But the seminar would take place in that room and then people will come out and sort of gather there, you know, classes of people and there will be conversations about more or less anything. The conversations will sort of move from sort of politics to football to mathematics. When Ricardo gave this seminar, he sort of came, sort of sat there on the corridor and we started chatting. So this was actually my first memory of a sort of kind of proper conversation with him in which I got a glimpse of his refined and lethal sense of humor. So his sense of humor was something that you had to be very careful about. And it's very difficult for me not to talk about Ricardo without mentioning Jorge. So I think when I sort of exchanged emails with Enrique a few days ago, he sent me some slides that contained that picture. I haven't seen that picture before. I don't know if any of you had seen it. I see Martin nodding. I've never seen a picture before of Ricardo and Jorge together. And I think this is a great one. Okay, so as I said, I never really got to know Ricardo that well. So I left in 1987 for my PhD and my further interactions with him were essentially in the sort of period 91, 94 after I finished my PhD. And I was sort of more or less like many people after finished the PhD without really knowing what to do and looking for a direction, looking for a bit of a future. And somehow things happened in such a way that I was sort of able to sort of interact with him. But this was also a particular difficult moment for him in which he was already suffering very much with his disease. During this period, I mean we sort of visited him with Miguel in his flat here in Montevideo. We had some sort of wonderful discussions. And I think one thing that I really wanted to say was that there was some sort of incredible moments, even during his weakest moments, you could see actually him switching the topic of the conversation to something that would be of interest to us. I mean that was sort of quite amazing. Okay, so I'd like to tell you a little bit then now about my own personal mathematical journey next to the ideas of Ricardo a little bit. Okay, so I would be touching upon his work on Lagrangian systems. So I will tell you a little bit about that. So in this slide I will just simply mention the three main papers that he published on that. So the first two were actually published in non-linearity. One actually, I mean the preprint was ready for many years but it was published one year after he passed away. And then the third one which is the one that I will really talk about the most was a paper that he actually never completed. So he wrote the paper and he wrote a series of theorems and wonderful conjectures too, I think. And the proofs were actually given quite a few years later by Gonzalo, by Delgado, another of his former PhD students, and by Renato Triaga, which I guess he must be also attending the other conference in Rio at the moment. So the paper was actually published twice. So it was published as a conference proceedings, I think edited by Francois here in the audience as well. Going back to that conference in 1995 and then it was reprinted a couple of years later in the bulletin of the Brazilian mass society with the follow-up of the proofs by Gonzalo, Renato and Jorge Delgado. So it's really on that sort of third paper that I would like to tell you a little bit about. Some of the ideas. So the first thing to say just before I go to the next slide is that again there is a sort of very, I mean in some sense a very kind of clear connection with the School of Engineering too. So I mean, so back when I was taking my courses at the School of Engineering, there were these incredible courses on mechanics. And there was Mechanics 1, Mechanics 2, and these were actually fantastic, particularly the course on Lagrangian mechanics. I did have conversations about these courses with Ricardo too, who found it actually very difficult. I mean there was a pretty tough somehow. And you could say that in some sense the work that he's done, you know, you could sort of trace a very continuous line from those courses immediately into his work on Lagrangian systems. We'll try to make a case for that in a minute. So I will mostly focus on this third paper and this is really an attempt to understand the dynamics on the various energy levels using variational methods. So I guess something that we are all very familiar with at some point, we must, you know, and I will go through that very quickly. The solutions of the Lagrange equations come essentially from a variation principle. And I think to sort of get into the theory, I will tell you right away the class of Lagrangians that Ricardo was discussing. So we'll not do it in the most general form. So for those of you that went to Gonzalo's lecture yesterday, there is a more general framework for this. You can take a convex, superlinear Lagrangian, blah, blah, blah. But I think, you know, the theory is already, and in some sense it's already a theory about that class of Lagrangians which in some sense are the most classical Lagrangians from classical mechanics. So you put kinetic energy and the kinetic energy comes in the form of a Riemannian metric. You have a potential, u of x, but then you also have a magnetic potential that comes on the way of a one-form theta. So in the velocities, so if you look about the, if you fix a point, so x is a point on the manifold and v is just a tangent vector. If you fix a point x, this is just a polynomial of degree 2 in the velocities where for high v's, the metric dominates, but for small v's, the one-form starts sort of getting into the way and produces some effects in the magnetic field, and this will come up in a minute. So that system, as you know, I guess I learned here, the School of Engineering has a first integral of motion which is the energy, which is just the kinetic energy plus the potential. That's the first integral of the system. So I wrote it in the most classical way because I could not resist switching to q, q dot, because I guess a few days before coming to the lecture, Martin told me this is a lecture potentially for a general audience. So I thought if I change the xv to q, q dot, I would be able to get away with it. And then I changed the theta to a because that's a physically relevant way of writing it for the magnetic potential. So that's the Lagrangian. So the action of a curve that actually Gonzalo told us about yesterday is just the integral of the Lagrangian. That's the action of any given curve.  The Euler Lagrange equations sort of pop up. Wonderful second order ODEs. Somehow they produce a dynamical system on the tangent bundle of the manifold. So the phase space now is positions and velocities. It's a space of all q, q dots. And the function E, which is defined on TM, is now a first integral. This is actually if you're working on a bounded space on a compact space, then this flow is defined for all times t and becomes a complete flow. And this is really the dynamical object of study. Now there's a sort of bit of geometry coming up that will be relevant in a couple of minutes. That is, again, very, very classical. So perhaps for this one, I might as well draw a little picture. So the geometry of those energy levels depends on the value, on the amount of energy you have, unsurprisingly. So if your energy is sort of very high, then the energy levels will project into the entire thing. But if you don't have enough energy, the energy levels might not project over anything, over everything, and there's this sort of threshold value, E0, which is the same as the maximum of the potential. And if you have energy more than E0, then you will project over everything. And if you don't, you will not. So I don't know if your money for LEM is just some sort of, if you like, some surface of hydrogenous. So remember sort of TM, you're looking at positions and velocities. So if your energy is less than E0, it could very well be that the projection of this is some sort of subset of M that doesn't cover everything. So the particles will sort of go, but then will reach that sort of boundary with velocities here, essentially, and then go back in. I will show you one very dramatic example of this, where the particles, you don't have enough energy and then the particles do not hit the entire configuration space. Okay, so let's keep that particular special value in mind because there will be now several values, special values coming up, associated with Riccardo's paper. Okay, so here's the dramatic example. This is my favorite pendulum. I don't know if you ever have came across this one. So this is called the Botafumero. It's a pendulum. Okay, so you have to be considerate here and sort of imagine that that rope is not bending and it's a sort of rigid rope, but let's assume that for the moment. Have you ever come across this pendulum? Okay, so this is, the story is very interesting. So this is in Galicia. The sort of idea is that you want to burn some incense and you want to distribute the incense all along the cathedral. So you have many approaches for this. You can burn many small little things of incense. Or you would have this amazing idea that the Galicians had, which is to sort of create this huge container with incense, hang it as a pendulum from the middle of this incredible cathedral and then make it swing in this sort of very dramatic fashion. So then the whole church and the audience will be engulfed in this incense cloud. Okay, so this is amazing, right? So the system of pulleys is from 1604 and they managed to push this thing to velocities reaching, you know, almost 68 kilometers per hour inside this very valuable cathedral. So that's a pendulum. Now fortunately that pendulum never reaches the entire phase space. This is a spherical pendulum. The entire phase space will have been the entire two sphere and the Galician engineers have designed that so that that will not happen. So people will be safe. So that's an example where you don't have enough energy fortunately to sort of hit the entire phase space. You know, one idea that they haven't implemented yet if you really want to make it like the sort of Lagrangian system that I had before. So this would be purely kinetic energy plus potential. But you can imagine the sort of engineering putting some charge on that and then putting huge magnets on the walls of the cathedral and then it would be a perfect system fitting the theory as I wrote it before. Okay. So that fortunately has energy less than it does. So the cathedrals and the visitors are supposed to be fairly safe in principle. Okay. So how did Ricardo go into this Lagrangian system? So I think part of the story begins actually with a paper by John Mather from 1991 who wrote a foundational paper on the subject. So there's a paper and there's a title. And I think that paper had a very strong influence on Ricardo actually. So he actually came across that paper way before the paper was published and kind of decided to work on this somehow. I mean there may be other reasons that I don't know about but I know that this paper was a huge influence on actually Ricardo doing some work on these Lagrangian systems. So John Mather was trying to sort of essentially generalize his theory of twist maps on cylinders to higher dimensions and his model for high dimensional twist maps were exactly these Lagrangian systems except and it has to be said that in Mather's case he was looking at time dependent periodic Lagrangians. So they were not autonomous systems as the ones that had been describing but they had a dependence on time. So the main idea in that paper by John Mather is essentially to replace curves by measures and then rather than trying to minimize over curves you try to really minimize over measures basically. And then you would hope that the minimizing measures will be special and they will be giving you information about the dynamics of your system. This is essentially the main idea. So the action of a measure was also defined by Gonzalo but I remind you briefly you have a well probability measure on the tangent bundle you just integrate with respect to the measure mu. Now in my view Ricardo managed to bring this theory of John Mather to a completely new level with a completely new set of insights particularly in the autonomous case. I think he sort of picked up quite a few things that hadn't been picked up by John Mather mainly because I think Mather was actually interested in different things. I mean my understanding of this is correct. Mather always had an eye towards provisional diffusion and always saw this theory as a mechanism for construction. They saw it sort of going off to infinity basically in the time-dependent case. So this was an exciting time since more or less independently Albert Fatih was actually developing his weekend theorem. So there was a lot of somehow going on at the time actually Ricardo was working on this paper piece. So the paper of Ricardo has this great idea about these threshold values. These critical values which nowadays they are being named in honor of Ricardo they are called the Manier critical values and I will tell you about a few of them again they were defined in the lecture by Gonzalo earlier but I will remind you of the definition. It's a very simple idea somehow based sort of on the following fact. The Lagrangians that I wrote down have this very special form. There's a kinetic energy plus something linear plus a potential. So for each x-fix you can imagine these things they're just sort of parabolas basically. You can think of them. So they will have a minimum at every point. So if you pick your K large enough the L plus K will be positive. So if you take your K very large the L plus K will be positive and then the action of any closed curve will be positive. So then the idea of this critical value is really very simple. You say well let's try to decrease this value of K until somehow I kind of manage to find somewhere a closed curve that has negative action. Or you can go the other way. The way this is defined I sort of say it's defined by the infimum but you can also do it the other way around coming from the bottom. So you can just introduce in the paper this critical value. And it turns out that this critical value had all sorts of connections with methods theory. So one of the first theorems that is actually stated in that paper of Ricardo is a characterization of this very simple threshold value at C of L in terms of this sort of sort of invariant measures or the action of these measures. So he proved that another way by which you can recapture this critical value is as minus the minimum of the action of the Lagrangian running over all the invariant measures of the earlier Lagrangian law. And you can actually check it's easy to check from the definition that this critical value C of L is greater than or equal than this value E naught that I defined before. That has the property that the energy there was projected over everything. It's again very easy to check. Now how does this connect with actually methods theory? Well, I can explain that sort of quickly. The theory has cages, naturally. What are these cages? Well, if you pick a close one form you can consider a new Lagrangian which is L plus omega or L minus omega. This would be exactly the same kind, right? If you just simply change in the one form by adding another close form. But of course if you think a little bit about if you have a close form you don't change the actual magnetic field. You're just changing the potential but not the magnetic field. So if you don't change the magnetic field the particle, the Lagrange flow is just the same, yeah? You have a slightly different Lagrangian but the orbits would be exactly the same. Even better, when you change the Lagrangian by a close one form it really only depends if you're looking in particular at these sort of actions of invariant measures and so on all the critical value it really only depends on the class of the form. Because if you were to change if you were to change the close one form by another let's say df when you integrate that df along a close two of it you get zero, yeah? So what is really relevant of a close one form is just the class of the form not the actual close one form. So this immediately gives somehow a function on co-homology on the first-term co-homology group. So if you define a function alpha of omega as this sort of critical value of L minus omega this gives you now a perfectly defined function from h1 into R. And it turns out that the previous term actually tells you that this is exactly Mathes' alpha function that plays a key function that appears in the paper by Mathes. Mathes' paper is about all this sort of alpha and beta functions of this one in co-homology and other in homology but somehow this definition of the critical value was capturing kind of immediately this Mathes' alpha function. So that was Ricardo's first theorem. There were many theorems in that paper but somehow also if you have that function on the co-homology classes and the theory has all these cages one thing that you can actually show which is, you know, not so hard to believe is that some of the sort of convexity of the Lagrangian is inherited by this alpha function and this function alpha becomes also convex and super linear growing faster than linear so therefore it has a unique minimum. So what Ricardo did in his paper is he said, oh well, this is a special thing somehow. I mean this critical value somehow doesn't depend on the gauges and you're sort of picking up one really now distinguished value associated to the system somehow. So he defined the strict critical value and C0L precisely says the minimum of this critical values of L minus omega. And this is very special. It has turned out to have connections with symplectic topology so there's a sort of wonderful kind of universe associated with this critical value which Manier was immediately sensing. I mean he was picked up various other things but I guess probably at that time he didn't picked up actually the depth of this critical value but what he did pick up and this he sort of mentioned immediately is that all these measures that were popping up in Mathis paper all these measures have to have high energy somehow. I mean so I remember actually Ricardo saying you know yeah and this you know what comes out of this is that all these measures by Mathis have to have energy, high energy energy at least is zero or higher something that was actually picked up by Diaz Carnero early on somehow that this Mathis measures had kind of special property related to the energy in the autonomous case. So then Ricardo had a question sort of tailored particularly for my brother and myself. So in one of the sort of visits that we made to his house he told us well he has a question for you too. So he said so I think this is very likely to be true. So if you have one of these energy levels in a Lagrangian system that is hyperbolic, there is an Osso in the sense that Enrique was telling us a little bit earlier it should have high energy. And I'll tell you in a minute why he was actually making that that sort of conjecture. I mean so he asked that question so we went away sort of thinking I mean this is great right? I mean this is a new problem straight from the master particularly tailored for us we got pretty excited somehow we got something that kind of nice that we could work on. So just before I tell you what it's so in some sense somehow the rest of the talk is a resolution to that question of Ricardo I think. So before I get into that I have to tell you a little bit about that there are actually many critical values. So this is a critical value C of L then you can change the L by L minus omega because of this cage then there is the minimum of that but then there are other things that you can do which are completely natural. So with Miguel we started looking at coverings and we said well why not? I mean this is a completely natural thing to do if you take just a covering of your manifold you can lift a Lagrangian and then if you look at the definition of a critical value you can define that the critical value on that covering. Completely natural thing to do that value would be defined and then the natural question was how these values were changing with the coverings so that these critical values were insensitive on the finite covers but they were going down as you were going up in covers. So you can naturally associate now two more critical values in terms of coverings because you know if you have a manifold you have all kinds of coverings of course but there are two distinguished ones there is a universal cover that we all know I guess is a kind of pretty well known covering which is the sort of abelian cover essentially given topologically by the kernel of the Hurewitz map from pi1 into h1. So naturally since the universe covers everything that's the smallest of the critical value but there was this other one from the abelian cover. And all these critical values are somehow always greater or equal than the critical values that the botafumero never reaches. It's important to keep in mind. So the resolution to Riccardo's question came in several stages unfortunately this was a couple of years after Riccardo passed away so with Miguel we first proved that this strict critical value that Riccardo had defined was quite naturally the same as the critical value of the abelian cover. But we managed to produce examples that somehow were giving a negative answer to Riccardo's question to produce an example of an anose of energy level with energy in between the critical value of the universal cover and the critical value of the abelian cover. And then one or two years after we somehow actually caught the right theorem. So if the energy level is an anose, then actually there is something going on exactly as Riccardo suggested. He just didn't quite give the right critical value. But I mean this is a really kind of minor thing in a way. So this is the universal there's a critical value of the universal covering, the one that has to that works for hyperbolicity. And then with Albert Fatih so this he kind of immediately realized that there was a kind of you know group theoretic reason for this to happen. This an anose of energy levels happens in services of hygienists in which the of course the fundamental group is not amenable. So somehow this sort of gap between the universal cover and the abelian cover only happens when the pi one is not amenable. A lot of this theory was actually being done on tori and of course on tori these two critical values are always the same. So that was the sort of the answer to the question. So now I'd like to tell you a little bit about why somehow Ricardo asked a question in the first place and this goes back to the theorem of Klingember and his sort of new proof of Klingember's theorem. So the key ingredients somehow to to produce this sort of phenomenon that the energy of an anose of energy of an anose of level has to be sufficiently high comes is at the heart of all this is this Klingember's theorem somehow. And it's something that I would tell you in a minute that which again I picked up from Ricardo and I have never forgotten somehow. This is like the essential thing that one has to look at. So the great theorem of Ricardo is the following. So it says that if a Jurassic flow admits a continuous environmental arrangement of bundle then the sub bundle is transversal to the vertical sub bundle. So let me just explain a little bit about this. So if you have an anose of Jurassic flow you have the stable and unstable bundles so the Jurassic flow is very easy to check that the unstable and unstable bundles are actually Lagrangian. So in other words this sort of symplectic form in phase space has to vanish on this sub space. And it's very easy to see because this two form is invariant so you just pick a couple of vectors in this stable subspace you let T go to infinity and that goes to zero. So the form has to be zero on any pair of vectors. So they have to be Lagrangian. So and in the anose of case of course they are just continuous so what Ricardo did was he sort of realized that somehow the only thing that actually mattered there in the closed case was not the hyperbolicity but just having this continuous invariant Lagrangian sub bundles and then the key property in clean and best theorem was the transversality of these sub bundles with the vertical sub bundle. The vertical sub bundle is just the kernel of the projection map. So it's essentially you stand on a point and it's just a fiber over the point. So the key geometrical property that a an anose of geodesic flow has is that this is stable and then stable bundles have to be transversed to the vertical. And I remember Ricardo clearly saying you need to forget about no conjugate points. This is really the property everything comes out of this. So once you prove this transversality of the stable bundle with vertical then the rest comes from student comparison ODE standard thing. This is the key property. And he gave a wonderful proof of this using the Maslow index. So he gave a kind of a very cool proof using the Maslow index and the Maslow cycle. Now his proof used the fact that the geodesic flow was reversible. So time reversible means that if you know if you go along the orbit and then if you reverse time you can come back also along an orbit. So this will happen for any classical system of the form kinetic energy plus potential but if you put a magnetic field the reversibility gets destroyed. Because the magnetic field twists kind of always in one direction.  So it's not reversible. So Ricardo wanted to know I mean and this was sort of with the clock going back a little bit in time at sort of 1991 wanted to know well I mean there had to be a cling ember theorem for this more general class of Hamiltonians where my proof using the reversibilities replaced by something else. And this was another question that he posed earlier to Miguel and myself and when I when I came back from my PhD that I came straight back here to Uruguay my first project with Miguel was actually to look into this come up with a new proof of this that didn't use the reversibility. And I think this is perhaps maybe this is a kind key point of the lecture I guess today this was a wonderful moment I will tell you in a few minutes why we came up with this proof this was a proof that we gave it was published in 1984 but somehow we started working on this in 1991 a paper that I'm very happy with and somehow I do have wonderful memories of discussing this paper with Ricardo and Miguel and Ricardo helped us a lot with the writing somehow he kind of liked the sort of idea he liked the project and then you know there we felt his sense of humor as I will try to show you in a meaning his lethal sense of humor more than once he volunteered at some point I had to write the introduction for you and then I'll show you how to do it he did it and it was actually way much better than the ones we wrote and so there's a sort of I did check this with Miguel so at some point in the paper emails going back and forth this was the early days of email and at some point we needed to deal with the muscle of cycle which is not quite a manifold but it behaves as if it were a manifold it has some singularities it's stratified the bad part has clearly mentioned 3 so it almost works as if it were a manifold but you know we needed to get the technology right so at some point you know we needed to give the right reference and we sort of inserted a phrase in the paper you know saying that this is a you know this was a stratified cycle in the sense of with me or something like that and then Ricardo came back with the following comment I thought it was great I did check I did check with Miguel I mean this is yes yes no don't know he said that yes he did so so I went back I read the paper again it didn't look too bad I went to listen to the symphony again the fourth movement it's not pedantic it's majestic actually which I'm not saying that the introduction or the phrase is majestic in any form but again I think Ricardo in some sense at his best I mean his sort of sense of humor was sort of spectacular he was very fond of music too somehow he was really incredibly knowledgeable you could sort of switch the conversation very quickly from mathematics to music he would do that more properly with my older brother who was much more knowledgeable than me in classical music but that was sort of wonderful wonderful to see and there were many sort of exchanges of these sort of nature somehow kind of private ones but they were really very good so the actually just before I go into this this is something else that didn't impress me I mean his command of English was remarkable I mean we actually saw it in the video how well he could explain so he he read huge amounts so he was some sort of anglophile in some sense and his knowledge of the English and sort of American literature was extensive and deep I mean actually quite remarkable so he was he was different really many levels the the transversality of the stable and unstable bundle with B already forces the energy to be bigger than A0 and this was actually in some sense our first observation that we told Ricardo oh if you since we have this new proof in the transversality of the stable and stable bundle this is actually telling you that the energy has to be high enough you cannot have an an awesome energy level that will produce a sort of hills region like that and Ricardo said oh really yes you can't and he he really liked that sort of observation somehow he said oh I thought if you sort of you know put a system there with enough balls bouncing against each other like those sort of systems in mechanics that we saw the school of engineering it had to be an awesome no it can't it can't because the once you hit the boundary the vertical vector field kind of becomes vertical and if you are looking at the transversality if you prove the transversality of the weak stable bundles with the vertical you violate exactly that if you had a something that projects that didn't project over anything so that kind of made not just our day but our years to come in some sense you know the fact that Ricardo found this interesting made us incredibly happy and now you can see why he asked us that question early on so once he came up with these critical values and these critical values were bigger than E0 then he said oh I have a question special for you too so why don't you now try to prove that this is also an energy level has energy even higher somehow which is higher than this sort of threshold given by the critical value story there so this was really made us very happy for a long time it makes me happy even today okay so to get the stronger property that K is bigger than Cu one has to combine the transversality of the weak bundles with a topological argument and somehow use a little bit more and then once you know that these are actually the grangians you go to the universal covering and then the whole proof kind of unfolds and this will somehow what we did later on with Gonzalo we will not do okay and this is enough to give K bigger than Cu just before I finish I think I have just wanted to slide more quickly and I will be over there is still an open problem here which is actually quite interesting we still don't know and this is kind of natural now in the context of Lingon-Basthen whether every energy level K less than Cu have gone to be points right so I think I will finish just with two slides because I think it's quite I feel quite fitting to finish with this for reasons that you will see in a minute so Ricardo had did a lot of work on the on these Lagrangian systems from the generosity point of view and he introduced the right notion of generosity which is perturbing and this is complete I hope it's completely natural by now at this point perturbing just with potentials functions that depend only on the point on the point X because if you do that you will not leave the class and he proved an exceptional theorem in this direction again was published in 86 but it was proved quite early on Gonzalo mentioned this theorem a little bit earlier mentioned this theorem in his lecture and he said that there is a generic set such that if you have a potential in that generic set and then the Lagrangian L plus Phi has actually a unique minimizing measure and in addition that unique minimizing measure is uniquely organic so his view was that somehow if you were allowing for generosity properties you can make all this theory all this sort of math theory very very sharp and you will sort of start kind of getting a very very clear picture of what was going on and in fact he conjectured and this was a wonderful conjecture in that one of those papers that for every Lagrangian you can find a generic set such that that unique minimizing measure is actually supported in a periodic orbit and when I say periodic orbit I mean periodic orbit and sort of a clearing point as in Gonzalo's lecture and again I guess I'm putting the most expensive conjecture there because it's free at this point I guess as Gonzalo said so it was also known from quite a few years ago that the unique measure if it is supported in a periodic orbit then generically the orbit will be hyperbolic I think the Gonzalo and Renato did that with these sort of canal interpretations that Gonzalo explained in his lecture and I think I would like to finish and leave you with this which I think is a very fitting final to see one of Ricardo's PhD students after decades of spectacular work including his conjecture for surfaces in the sea to topology thank you


We have a question about the Treasury bonds. I want to get these up here to take a look because we've been waiting for this pattern to complete. It came within about three pips of making the exact 1.618 expansion down there at 1.5803. The low we got to is 1.5806. And we've now rallied up to the 1.59 level. Today we sold off to the 78% level of yesterday's low, which was right around 1.5812. We're now back to that 1.59 level. We should get a move equal to what we had during the 23rd of October. That move went from 1.59 up to 1.60 and a half. So that would take you up to roughly 1.5919. That would be a 61% retracement off of that move. Folks, there's a problem in the bond market. I mean, we really, it's not being talked about very much. We see it in the repos occasionally, but you stop and think here. We've got the stock market at all time highs as we come into today. And the Federal Reserve is thinking about dropping interest rates. Folks, do you realize how weak the Geistar and economy must be for the Federal Reserve to do something like that? What am I missing in the thought process here? You know, I'm not the smartest knife in the drawer, but for heaven's sakes, I wasn't born last night. It was three nights ago. Something is not right here. And I don't know what it means. And the problem is in the bond market. I've said that for a very, very long time that it's not the stocks that is going to be heard here. It's going to be the bondholders. So I don't know what's going on. I know there's pressure from the Trump, I don't believe that for a minute, Jim. I think that's all cannon fodder.   So he's doing what he thinks he should be doing. I don't think he's yielding to pressure, but you know, again, I don't really know. All I know is it doesn't make any sense to drop interest rates here, you know, and the interest rates are really not. I mean, if you can't get people to do something at zero, what are you gonna give them? They're gonna have to give them two toasters, I guess. I don't know. Negative interest rates has never made any sense to me, and it's on a global basis, so that's my opinion, and I'm sticking to it.