Hey everyone and welcome back to the YouTube video on PicoCTF 2018 and this video I want to take a look at the resources challenge It's only worth 50 points It says we put together a bunch of resources to help you out on their website If you go there you might even find a flag and here is the link to the page and it offers just a link You can click on right here. This challenge is a little trivial. It's not too hard Really, it's just look at this page and read through it You've got some links here to check out general skills cryptography web exploitation friends expiring reversing and a lot of other really cool stuff Honestly, I haven't gone through this yet We should they have a feature YouTube channel. So that's pretty neat. Oh totally want to take a look at that. Oh It's mr. Carlisle. He is fantastic I know him kind of personally through some of my stuff at the military academies So there's a lot of really interesting like content here that you can totally read through and I would recommend it And it's honestly just a good place to go to when you don't know the answer to One challenge or something that you may be looking at kind of under that umbrella of the category You know of the challenge that you're working on and it's awesome when you're doing that in CTF So this is certainly a good resource and that's important to kind of have in our back pocket at the very bottom Below this video tutorials here. It says thanks for reading the resources page Here's the flag for your time which you can copy and paste take note of and I'll actually do that I'm gonna create a flag dot text file as I usually do and We can go ahead and head back to the original page submit it for our 50 points We can put this together in a get flag script if we just copy the link address as we usually do I'm going to use curl which you may have seen or used before if not You can just pseudo app install curl if you don't have it installed on your system or whatever package manager that you need So curl will allow us to make a request to the web page and view the output of the page So like literally seeing the HTML source. You can see the flag right here in the output So what I'm going to do now is go ahead and pipe that to grep and a lot of times I've done this in previous videos So hopefully it's nothing new But if it's a new technique for you as you're starting to watch these videos for the first time cool. Hope you enjoy Grep grep will let us search at least when we're piping at least of the output that we give into the program And I'm using tack oh for only so I want to return only the search results that I return and Wanted to filter for to begin with and tack capital e to get regular expressions or extended regular expression support So that way I can use the flag format Pico CTF and then the curly braces And I'm going to use some regular expressions inside here to say period and then a star So period to match anything and then a star or asterisk to match multiple or like as much of you can of that So once I run through that it says a little bit of the curl connection stuff So I'm going to go ahead and make that silent with tack s and then I'm going to use tack tack color equals none on grep So we don't get that red color and that just that will return only the flag for us. So that's pretty handy Okay, I'm gonna go ahead and make a get flag script with that. So nano Been dashes a shebang line to pump that there mark that as executable It runs just fine and we can mark that challenge as complete All right, what do we got next these are? This are this is these are words Reversing warm-up number one 50 points throughout your journey. You'll have to run many programs Can you navigate to this on the shell server and run this program to retrieve the flag? So allows us to download the program? Let's go ahead and do that. I'm going to make directory for reversing warm-up number one head to that directory W get that file and If you have not used Linux before or you just don't particularly know how to run stuff You will want to dot slash and that's kind of a Term I suppose the colloquial name that I'm going to go ahead and use that I normally use Because you want to say in this current directory. So the period or the dot to mean the current directory Relative to it. I want to run this file or whatever program we want to run Except it has to be marked as an executable So the way you can do that is the simple chmod command to like change or modify make make Modifications of the file to add permissions to it and plus X that X or the executable bit will mark it as executable And we just have to supply the file that we want there So now if I run dot slash run Actually, if I were to check out LS, you can see it's highlighted green And let's take out you can see I've added the executable bit to all of the columns here So myself or the owner the group that owns it. That's the third column Again, I still me in my group that owns it and then everyone so everyone can run this now dot slash run and we get the flag so if we wanted to put that as get flag or redirect that to a static file and we can actually just move the program itself to named get flag simple stuff Okay Let's go ahead and submit this flag easy and As usual mark this challenge as complete Okay, next challenge reversing warm-up number two is can you decode the following string from base 64 format into ASCII? So base 64 is super duper common and capsule flag competitions. If you haven't seen it before can simply Google it base 64 on Wikipedia is a Type of encoding or a scheme of representing characters and data information in a peculiar way It is pretty easy to identify because it'll look like a lot of seemingly random like letters and uppercase lowercase letters with occasional numbers thrown in and The only other characters aside from that that are acceptable are a plus sign and a forward slash So those are the acceptable characters in the base 64 format and you'll see those just Maybe rarely but the most common stuff are seemingly random Uppercase lowercase letters more uppercase than usual sometimes and that's what makes it kind of easily identifiable the most important telltale about base 64 is that it ends the Like the very very end of the string or of the encoded data is a normally a set of equal signs It's it doesn't have to have a set of equal signs Because the the reason that the equal signs are there is because the length of this data has to be a multiple of four so if the encoded information like if the transformation of regular letters into their encoded form does not end up giving you a perfect factor of four like Multiplicant if that's a word multiplicant I don't know if it's not a multiplication factor or if it's not a multiple of four It will add these equal signs at the very very end as padding to make sure that it will eventually like it you'll have one two three or None sets of equal signs there at the very very end to make sure that it's a length of a multiple of four So peculiar thing in this case We don't have a equal sign of the very very end and okay If we wanted to you could just go an online tool to base 64 decode information There are a lot of these that are crappy and stupid and dumb and they waste a lot of time in my opinion I want to be able to automate this process I want to be able to do it from the command line or from Python or whatever that we're working with so there is a utility base 64 that you just have on your command line and Normally, I would echo stuff into this. I would just pipe it in and that will decode it for us just fine Another tactic that I've kind of seen which may be another interesting style is if you read it in at the very very end by using these Three less than redirection signs so just like that and you'll still decode it as you would expect Python can do this as well. You can just have a string and you can do dot decode Base 64 and that's the route that you should go another option is to import the entire base 64 module and then run base 64 dot b64 decode on it But I want to get in the habit more of just simply using the string Dot decode base 64 because you don't need to import a whole module and just seems to be a little little better a little faster Whatever nicer so that is the flag we can go ahead and actually make it specific directory for that Reversing warm-up to actually I'm gonna mark this as complete already since we know that we've got the flag at this point and we can go ahead and Do just that I'm gonna use Python to actually print out the Pico CTF portion of it that I want and Then I'll get the percent s in there and I'll percent it with our string that we have decoded from base 64 Okay Now we have a simple get flag script Not particularly necessary in Python because I did it from the command line one So I guess I don't know why I did that I'm using bash to just call Python, but simple stuff You could done that you could have done that in just Python if you wanted to and created a Python script just like that I I should have done that Cool, let's go ahead and run that redirect it to flag dot text Throw it in our clipboard so we can submit it for points and Keep winning cool. Hope you guys enjoyed this video. It's been fun I think the first set of the Pico CTF challenges are for someone that does a little bit of CTF stuff Like it is used to this kind of material this kind of content this stuff is pretty easy to run through and I'm trying to describe what I can and If you haven't seen before and hopefully I'm not jumping into too difficult of concepts or or being too quick on the keyboard for some Interesting things. Why is there a typo here? Krypto All right, I want to give a quick shout out to the people that support me on patreon. Thank you guys so much You're the best you are what keep me Motivated and a reason to wake up in the morning. Why does it always sound like I'm like depressed whenever I give this this? Thank you spiel one dollar a month on patreon will give you a special shout out Just like this at the end of every video five dollars or more on patreon We'll give you early access to anything that I release on YouTube before it goes live I need to be better, but actually getting some content backlogged and ready to be visible in there But hopefully that does not dissuade you from helping support I'm grateful if you did like this video, please you like comment and subscribe Link in the description is to join our discord server if you want to hang out with me other cool people It's really just a cool community full of CTF players programmers and hackers So if you want to hang out with any of us and tackle other catch-the-flag competitions Not just pico or even discuss more of pico now that the game is over It's a great place to do that. So thank you guys so much. Hope to see you on patreon. Hope to see you in the next video I love you. Bye


And welcome to the CNTF End User Lounge where we explore how cloud-native technologies are being adopted by end user organizations across different industries. The CNTF End User Community consists of more than 145 vendor-neutral companies that use open-source software to deliver their products. My name is Cheryl Hung and I'm the VP of Ecosystem at CNTF. So in these live streams, we're very excited to bring along some of our end user members to showcase how their organizations navigate cloud-native and use it to build and distribute their services and products. And we are on every Thursday, sorry, every fourth Thursday at 9am PT. This is an official live stream of the CNTF and as such is subject to the CNTF Code of Conduct. Please don't add anything to the chat or ask any questions that would be in violation of that code of conduct. Just be respectful towards all of your fellow participants and towards the presenters. If you have any questions for us, then we will be monitoring them throughout the stream. Just ask your questions through the live stream chat. So this week, we have peritus.ai here with us. So before we dive into some questions, could you please introduce yourself? Thanks Cheryl. Thanks for having me here. It's pretty exciting because I watched the two sessions that were there in the last two months. And one was from CERN, other from Twitter. I have interacted with both organizations in a past life from an open-source perspective. So this is awesome to have a startup on this conference. Thank you. Yeah, I'm Santosh Srinivasan. I am the co-founder and head of engineering of Peritus.ai. So we are building out knowledge networks to help developer self-service where they work and this knowledge comes from experts they trust. All of our platform is built on cloud-native technologies. So this is a great forum for us to discuss this. Fantastic. I know that Santosh is your co-founder at peritus.ai. So maybe you can tell us a bit about the story of how you started this company. Why was this an interesting problem for you? It's a fantastic question. So just a little bit of a background about my own career. I started my career in Bell Labs Development Center. Later I went to grad school and landed up at Yahoo where we were working on what we used to call as large-scale data processing and that eventually became big data. I got lucky and I was introduced to the Hadoop ecosystem by a good friend of mine, Arun Murthy, one of the lead engineers on Hadoop. And that journey began in 2008, about 13 and a half years ago into open source. So in that journey, we built Hadoop at Yahoo for Yahoo. It was not commercial. It was not meant to be used by other people as is, but it was meant to foster innovation. And what we noticed was with open source, if things work, people pick it up and the adoption is really tremendous. I noticed two or three different flavors in open source where you can have viral adoption. One was the Yahoo flavor where we built something at rapid scale, massive scale, hundreds of millions of dollars. It was somewhat enterprise ready, but within Yahoo. And the other one is something like Mongo or Elastic where it's so easy to use and people gravitate towards it because they can use it and get to go without having to talk to many other people. The Hadoop ecosystem became so massive that entities started commercializing it. And I ended up in one of those entities called Cloud Era. So I went from being an end user, contributor, committer to a governance member in Apache to participating in a commercial activity at Cloud Era. And at Cloud Era, what I noticed being on the other side is open source is easy if you're a developer, but if your skill levels are below that of a developer, it's extremely challenging to use. And that's where the enterprise companies were forming. And this is the genesis of Peritus. How do you take technology and make it consumable by a large set of people who may not have the same level of skills as the creators of those projects? And that's why we are building out this knowledge network to help people get to that as quickly as they can. That's awesome. I mean, it's definitely something I agree with that if you are a developer, open source is pretty great. It's pretty fantastic. If you're not, there's a very high barrier to entry. So I'm excited to see how Peritus is going to help kind of lower that barrier to entry. Let's talk a little bit about your company, your team as well. So you're the VP of engineering. Is that correct? That is correct. Yeah. Yeah. So what are the responsibilities of you and your team now? Yeah. So one of the things about being a co-founder is my official title is co-founder of VP of engineering. I do a ton of things and sometimes people call you as the chief janitor as well. So you have to do anything that relates to the company. But my primary responsibility is to build our technology and product. So a significant amount of our engineering resources are built towards using the technology to rapidly build features in the product. So one chunk of the engineering org is for infrastructure because without infrastructure, we cannot build our product quickly. And when I first started the company, and since now, it's been about three and a half years, the challenge was I came from the big data scale out technology. And we are trying to try those technologies. And this is when Kubernetes was sort of taking off and it was not quite mature. So we tried a few things and finally settled on Kubernetes about two years ago. And we invested a lot of energy into doing both the scale out and also giving developers flexibility to spin up things on demand to do their own innovation. So that's one part of the organization, which is infrastructure. And we try to use multiple cloud providers because some of our customers tend to say, hey, just have to work on one or the other. And we wanted to be careful here because if you choose any cloud native technology hosted by the provider, you're kind of stuck in some sense. It's awesome. I would say it's the value is tremendous. But if someone else wants you to be on a different cloud provider, it's challenging. So we decided, okay, everything is going to be containerized. Everything is going to have REST APIs. And we'll use Kubernetes and then make sure it complies with whatever the cloud provider hosts. So it's easy to migrate from one to the other on demand. So we use a bunch of technologies from CNCF. The prominent ones are already popular, Kubernetes, Helm, use Keda, the cert manager, Prometheus. We are looking into using Falco for security purposes.  The list goes on and on. We are heavy into open source. Well, of course, I'm pleased that you use cloud native within your infrastructure. It would be quite funny if you didn't. And yeah, I'm also quite fascinated to hear that you look to the few different things before settling on Kubernetes. Is that right? That's right. Can you share some of how you thought and why you made that decision? It's just experience bias. So when I left the cloud data, we were trying to launch a cloud initiative to spin up clusters on demand to do scale out and Elastic stuff. So when we came in and we were saying, okay, let me first set the context of what's the problem we are trying to solve. We are trying to build out a knowledge network. So knowledge resides in multiple forums, documentations, KB articles, forum conversations, GitHub issues, GitHub PR comments, all of those things. So now we want this from everywhere in one central location. We have a knowledge graph which supports what we finally end up doing is provide recommendations to developers as they are working. So we have a machine learning team of a few engineers who are rapidly doing experimentation to try out the quality of these recommendations. We have the infrastructure team trying to help spin up, scale down and maintain stuff. And then we have the data crawling ingestion and organization team. And then finally, you have a full stack UI UX team trying to productize the underlying technology. So these are the four different components to the organization.  So let's just spin up things. Processing is interesting because it depends what you want to process and how. So since I came from the Hadoop background, we tried a few things there. It worked, but it was slow.  That's when we landed on Kubernetes. And it was challenging. The reason it was challenging is we are highly skilled engineers, people who have been at bigger companies with the same background. And getting to use technology is one thing, but if things don't work, trying to find out why, fix them as soon as possible without waiting on the community to provide a fix. And I've been on the other side providing the technology. Now I was consuming technology from open source while trying to have very fast product iteration. So that's how we landed on Kubernetes. And that journey began roughly two and a half years ago. And what does your infrastructure look like now? You mentioned you have multiple, you use different clouds. Can you give us an idea of the size of your clusters? Yeah, so we do things on demand. So what we have done is for production usage, we have a hot, hot setup. In case things go wrong, we can rapidly switch between two clusters and they're running their own namespaces and Kubernetes. We have somewhat of a staging environment that we prep before we go live on production. So we want to do testing and stuff. And for developers, they can spin anything on demand. So we've integrated right from the time you do a commit, your PR gets merged. You can get it deployed on the cloud almost within a matter of minutes into your own developer namespace. And you can create as many developer namespaces as possible because you're doing rapid prototyping. So let's take an example of you're doing a feature development. And feature development cuts across all of these four different teams, infrastructure, machine learning, data ingestion, and UI UX. So you want this subset of engineers working on a feature to work on a feature branch. And you should be able to deploy to the namespace for this feature branch from each commit to your own developer namespace. And when you think it's reasonably stable, you go through your PR review process, merge the branch to your main branch. And then the next release, we try to do one or two releases per week. It goes to staging. And then we promote it to production. So this whole life cycle has been built on the public cloud infrastructure. With some caveats we trained to use, let's say Jenkins. We didn't pick any of the build infrastructure in the cloud. Because sometimes when you want to do a build or builds happen within a minute, incremental builds. And most of these cloud native infrastructure, they don't give you that. They can go up to two minutes, not up to a minute. So we went for developer efficiency and speed as the first order for building infrastructure. Oh, very cool. It sounds like you have a pretty smooth pipeline then for the very nice developer experience, I could say. You mentioned some of the challenges as well earlier that you faced. So right now, what would you say are your biggest challenges when you're building infrastructure or you're managing deploying applications? So you brought up pipelines. A lot of the work is the workflow orchestration between different components, which are all microservices. So when we first started building pipelines, I have a lot of experience building pipelines right from a Yahoo days to cloud error days. And I built many execution engines to do that. So we picked some of those to start with. I'll just name a few for the audience here. We picked Airflow. I was the development manager for Uzi, which is incredibly difficult to use. Airflow was very, very simple to use, but it lacked a bunch of features. And we are trying to make a workflow engine work in Kubernetes. We looked at Kubeflow. Kubeflow was like very, very nascent when we picked it up. And we couldn't quite close the feature gap for us to be off to the races. A challenge we had when talking internally was understanding the mission on the vision of this open source project while you're trying to pick the technology is a challenge. If you end up picking the wrong one, you'll have to pay the migration cost later on. That's still within the company. The bigger challenge is if you hire someone, they may not even be familiar with the technology that you picked, even though it's open source. At the higher order stack, you have these angular versus react battles going on. So I have more of a core backend technologies, not a front end UI person. So as you go to the backend, these are the fundamental pieces you're building on. You can't change them quickly compared to the higher layers of the stack. So when you're thinking about this workflow thing, we tried a few. We tried Airflow. It worked initially, but it wouldn't work for us. Then we really explored to see, hey, have you built a Kubernetes integration that we can contribute to? It was not there. Then we looked at Kubeflow. It was too nascent for us to pick up. Then we said, okay, begrudgingly, we agreed, let's build something in-house knowing that at some point in time, we'll give this up or migrate to something which is more standard. So we have something built internally, which looks exactly like any other workflow engine, just that it works for us. And in the next two quarters or a year, we'll start migrating away from these. We are looking at MLflow and Kubeflow for the machine learning parts. Argo. Argo is something that we are very interested in because the activity in Argo started picking up last year. If you look at the commit history of Argo, I think the first official commit on CNCF GitHub repos is in 2017. The project itself was around from 2015-2016. So if we had known that Argo was active, that would have been a more natural choice for us to pick when we made our choices back in 2018-2019. Always very hard to know how things will turn out in the future, though, two or three years down the line. Yeah. Interesting to hear how you've had to make those decisions up once, how you've chosen to make them. Well, I had a lead come to me and say, don't build anything in-house. And the reason he said is we'll train people on a bunch of proprietary technologies and that skill is not portable. And when we hire smart engineers, we'll spend like a month or two training them on our technology. That's not useful to us either. He pretty much said it's a loose, loose proposition for us. Yeah, I mean, that's totally fair. I've heard this as well from other companies that one of the benefits of open source is that you don't need to spend time training or retraining people when they come in or out. Let's take a slightly different angle now, because I'd love to hear from both your experience and from what you've seen in the knowledge base that you're building out. I'd love to talk about some trends and predictions for cloud native. So just to start with, over the last, let's say, three, four, five years that cloud native has been around, what are some of the trends that you've seen? Yeah, so we actually did a deep analysis of CNCF. So I have that maybe we can talk offline about it, but so here are some interesting things I found that you may already know, right? So I looked at the graduated and incubating projects. Although we have used some sandbox projects, I just narrowed the focus to something which is well known. So there are 36 projects in that list. Just as a quick tidbit for one project emissary ingress, there was no reference to any of their activity on the main landing page for CNCF. So including that, I mean, there's no reference to any GitHub link community page or anything. Everything else is very nicely set up on the CNCF web page. I know where the GitHub repo is, the dev stats, and where the community is if they do have a community. So interesting stats. So now that you asked is 70% of them have a Twitter account. It's omnichannel. So they have to have a presence online. Two thirds of them are on Stack Overflow. Two thirds. Just north of 60% are on Slack, or they support a public Slack channel. And then after that it starts going down. Some of them have Google groups. Why is this important? For an open source project to be successful, you need a thriving community. You need people who can help answer questions so that both developers and end users can rapidly use, adopt and build out features and technologies. So what this tells me is if you take out Kubernetes and gRPC, they over dominate the activities going on in CNCF. So we actually did analysis saying with and without Kubernetes. Then we found out we have to also do with and without Kubernetes and gRPC. So what it told me is most of the action is happening on GitHub issues. Most of it. We also analyzed the Stack Overflow traffic for these communities. It's anemic. So they have overall a challenge of building out communities to rapidly evolve and move from sandbox to incubating to a graduated project. If you're mostly on GitHub issues, it means it's a developer-centric community. The end user community is somewhat missing in action. That's so interesting to hear actually because I assume that everything would be close to 100% on Slack and on Twitter. Actually, that surprises me that those numbers are quite low. Well, not low, but they're not 100%. Yeah. So if you really think about people who are using these technologies are complex. Let's first state that this is not easy technology. So people who are building it are very sharp, very smart. I'm talking about the after building out the technology or in the process of building out how do you get it off the ground? So you need to have an omnichannel presence. So most of them have that in place, but they have to be where the developers are. They have to be where the end users are. And for that, most of them use the technology on their computers. You're probably not doing something on your Kubernetes cluster on your mobile phone or iPad. Probably not, no. And so most of the action tends to happen on Slack because that's where you want to have a question. And there is this metric known as developer satisfaction. I ask a question, how many hours before I go and make my own choice before somebody has to respond? So if I don't get a reasonable response within my working day, and if you say, let's say I post a question at 4 p.m., then maybe the next day morning, I am going to do something on my own. So 24-hour window is kind of the sweet spot. So I am on several of the CNC of Slack channels. So I see this activity, it's very high activity, and these public Slack channels have a shortcoming because Slack doesn't give you free versions with infinite capacity. At 10,000 messages, you age out. People tend to ask the same question over and over again on Slack. So there's a gap here. So people who are building out the product, they are fatigued by trying to answer the same question. They have to dedicate time to answer questions on Slack. And you have to set aside time. So that's a challenge. You can't expect people to be doing product development and support and community building simultaneously. So that's an open problem. And I think we are working on a solution there. I'm happy to chat on how we can offer it completely free to all of CNCF. Oh, that would be interesting. Yeah, we can chat about this offline, as you say. Do you have any predictions that you think are going to come up in the next, well, maybe through the rest of 2021 and into next year? Always dangerous, I know, to make predictions. I'm not going to hold you to them. Especially when things are recorded. Just between you and me, nobody else. Well, I can give you an abstract notion of what will help make these predictions. And maybe then we can use that to say what might happen. I said at the beginning, what kind of open source technologies tend to succeed? Technologies that have been proven within an enterprise company that are being open sourced. And technologies that are easy to use. So these are two key factors that is just on the product side. And the winners are actually going to be people who build out communities where you can ask a question, get a response as an end user or as a developer. In the larger scheme of things, the half life of a project is dependent on the community. I've been in Apache where many, many projects have been shut down. They move into Apache attic. And that's a sad state of affairs. One really massive project is Apache Mesos. Very cool project. I've seen that they most have talked to one of their founders. It's a really impressive technology, but unfortunately they're considering moving into an attic, right? That's very sad to see. Very complex, highly useful project. So you have to build out your community and you have to build it out so that it sustains beyond the initial founders involvement and when it gets incubated or when it graduates. So based on these three things, maturity, ease of use, community, you can predict which of the open source projects in CNCF are going to be successful. Interesting to hear that. And also I very much agree with you that community building is much harder than it seems. It takes a lot of time, takes a lot of persistence, but it's the only way for the project to outlive the original maintainers. So what do you think is the most surprising thing that you've seen so far? Now that Perotista AI has been around for a little while, anything surprising that you've seen? So I've been on a lot of the Apache side of things in terms of governance and all of those things. And I am relatively new to CNCF, the whole model. I recently reviewed the due diligence document for Argo, which is trying to move from incubating to graduated. I was very happy to see the level of rigor that goes into declaring a project to be ready for the next stage. I was really impressed with the level of rigor. On the mechanics of how the decision is made, it's so public, everybody can see the decision making. That's impressive because transparency means people trust the process. And the last part I find somewhat funny, but also I found I had a good feeling is everything was on git. For a developer, that's awesome. So for me, CNCF, and the last part I forgot to mention is open source is also all about licensing. I think 100% of CNCF projects are Apache software licensed 2.0. We definitely strongly recommend Apache. So that's very friendly, both for people contributing and when you import the technology in, you're fine in terms of a legality of using it. There are certain open source licenses where you have to think 100 times before picking it up because it triggers these things of, hey, if you're using it, you have to open source everything around it and it's too complex. Yeah, definitely. Open source licensing is before I joined CNCF, I did not have a clue how complex it can get. What more question for you about trends and predictions in cloud native? Is there anything that you're personally excited by and you think more people should know about? Security. I'm not from security, but the number of times you get asked about security when you go beyond proving value to getting adoption within enterprises. The first question you get asked is, are you compliant with X, Y and Z? So security projects, and I mentioned that we are considering using Falco. So those are things that I think people may not consider it as the first of the second project to think about when they're building out because you're just trying to prove value. So Kubernetes and security and cloud native and security will be an area which will get very hard soon. It'll get very hard. Can you tell us a little bit more about why you're looking at Falco? Yeah, so when we built out our products on cloud, we went to some enterprise customers and they asked, they would give us this huge checklist of things we had to pass before they would let us in. And some of these questions are like, have you had a third-party consultant certify that your product is secure? Have you done some kind of pentest? Have you done SOC2?  So some of these are compliance things. You do it at that point in time. It doesn't mean you're doing it every day, every minute, every second. So you have to be doing that. It's somewhat in the realm of observability and monitoring from a security aspect. So raw metrics and monitoring infrastructure engineers are awesome for debugging and things like that. Security is life and death for some companies. The recent ransomware that happened with this pipeline company, which carries oil, physical pipelines on the east coast of the US, that was alarming. First and foremost, I didn't even know this company existed. And the CEO of the company said this, we wanted to be nameless throughout our existence. We never wanted to be in the news. And they probably supply nearly 50% of oil to eastern United States, 45% to 50%. So when you build out these technologies, if they get hacked, then there is no recourse other than having to pay ransom and then trying to actively patch holes. And it's an adversarial game.  So for us, what it meant is you had to get ahead of it. Some of the cloud vendors have really good technology that supports it. They do port scanning. They do anomaly detection. But you also go deeper into your own use of the products and try to find out what else is happening. So in that context, we are looking into using Falco. Yeah, very, very interesting. I've forgotten about the oil pipeline story, but yeah, definitely something to be concerned about. Let's go talk a different topic again. You recently, or Perotus, I recently joined the CNTF and user community just a few months ago. So how did you hear about it? What got you interested to join? Two main reasons. One, we are using the technology piece by piece while not getting involved in the community. So one of our technical advisors said, hey, you guys have to be in CNTF. So look at all these other things that are being built. And what we are trying to build as a knowledge network, you have to do it for a domain, which is as it stands today, taking off or in common parlance hot. And you need to be aware of what's happening. So our technical advisor said, here is the community where you need to be there. Thanks to him, we got involved. We started building out our technology as a subset of that. Then we broadened the lens saying, what else are we missing? That's how Falco and other things came into the picture. And then we said, oh, if you have to build out a knowledge network, you really need to understand these technologies from an abstract perspective of what's happening, what are the gaps. So that was the second reason we got involved. Very cool. And what do you hope to achieve by being part of the community? Yeah. So our foremost objective was to understand and build, which is the main motivation. The outcome that we're hoping for is if we can give out a roadmap or a guideline to new projects and existing projects to say, here is a path to success. And we can help you get there faster, sooner, with little to no friction. That will be awesome. We want to provide the intelligence for CNCF based communities to do their job better. Developers can focus on building product and users can go on consumption. And we can take care of, let's say the community intelligence part at no cost to CNCF. That will be awesome. So we want to provide the community intelligence to CNCF. So that will be an amazing outcome for us. Super, super cool. I mean, I really look forward to seeing how we can collaborate a little bit further. I'm going to wrap up now, but is there anything else that you want to share with our audience before I wrap up? Oh, no, this is thanks for having me on this channel and it is phenomenal. I mean, I continue to be amazed by how well CNCF is run. It's kudos to all of you because it's a sea change from having been part of an earlier open source community. Now I've been on the outside looking in. So I hope to participate further and, you know, spend more time on the community side of things. I'm very happy to hear that. And it is a pleasure to have you in the community as well. So thank you so much today. And thank you everyone. Thank you to our audience for joining our latest episode of the Cloud Native End User Lounge. Again, we love having other end users to come and join us. So we really hope that you've enjoyed the interaction and heard about a little bit of something as well. We're going to bring the latest Cloud Native End User stories on the 4th Thursday of the month at 9 a.m. PT. And also don't forget to join us for KubeCon Cloud Native Con North America, which for the first time in a year and a half will be in person as well as virtual, which I'm very excited by. So if you're coming in person, it's going to be in Los Angeles. It'll be October 12th to the 15th. And you can hear the latest from the Cloud Native community. Also, if you would like to showcase your use of Cloud Native Tours as an end user, go to cntf.io slash end user to join the end user community. Thank you so much. And we will see you again next time.


Hello, welcome to this week's CMC markets currency snapshot with myself Jasper Lawler today We're going to be looking at the Canadian dollar specifically the USD CAD currency pair And there's been a massive spike in oil prices overnight with strikes in Yemen from a Saudi led coalition of Arab nations And so Canada is a big exporter of oil and typically the Canadian dollar moves in sync with oil prices So we want to see what they outlook for the Canadian dollar is here So as mentioned, there's been a strike in the Middle East And so there are some prospects for supply disruption of specifically Brent crude oil And so that scent price is higher That supply, you know, disruption may not actually play out Yemen's only a very small oil exporter And Egypt does tend to dominate the waters in that area Even though Yemen do have an important port Ardenne right at the beginning of the Red Sea which leads to the Suez Canal So nonetheless, this move in oil prices could be a temporary thing But we do want to see what the outlook could be for the Canadian dollar Which has not seen the kind of volatility that the oil prices have Economic data-wise, we've seen some fairly weak data from the US of late The strong factor there is the labour market with increasing employment Wages are looking a little bit sticky, not really rising as much as expected And retail sales and durable goods orders have been fairly poor in recent months So that is causing a bit of a pullback in the US dollar across multiple currencies We're seeing the Euro rally, the British pound rally And so the Canadian dollar is not quite reacted yet But if we are going to see some higher oil prices as a big oil exporting nation Canada could be the next one to benefit So let's just look at how this chart is setting up here with the USD CAD Because we can actually see there's an important support level Which could give us the clue as to where prices are headed Now this is a daily candlestick chart for the USD CAD And you can see that we've been in this range between 124 and 128 With that 128 formed around the 30th of January this year This 124 has been tested several times And we're right in around that area again now So should this floor give way, what we're probably looking at here Is a double top pattern And so that would then project us and the pattern would offer us an objective for lower prices And should the oil price sustain higher And should the US dollar continue recent weakness Then we could be looking down as far as 113 The peak reached in March 2014 just over a year ago So that's it for this week, CMC markets, currency snapshot We were looking at the US dollar CAD obviously And so this is quite a simple one, we're looking at that 124 support level And we're looking at oil prices And if oil prices sustain that 124 gets broken We could be looking at lower prices in the US dollar CAD exchange rate


Welcome to All Hands Update. I'm Petty Officer Ian Cotter. These are your headlines from around the fleet. The Navy Reserve celebrated its 100-year anniversary this month. Chief of Naval Operations Admiral Jonathan Greenert spoke at the Pentagon about how important the Navy Reserve is to the fleet. It's a diversity. It's the concept of diversity. What you feed us professionally, geographically, mentally out there is astounding and we thank you. The Navy Reserve was established by Congress March 3, 1915. The new 2015 All Hands Magazine Owners and Operators Manual will be available to sailors this month. The ONO is a resource for sailors and their families to better understand pay, benefits and the structure of the Navy. This year's ONO will be available in both print and digital formats. Your digital copy of the ONO will be available on navy.mil and ah.mil later this week.


We're back in Las Vegas at the Aria for Falcon 22, CrowdStrike's big user conference. I'm Dave Vellante and you're watching theCUBE. Sven Krosser is here as the Senior Vice President and Chief Scientist at CrowdStrike and we're going to get a masterclass in AI for security. Sven, thanks for coming on. Appreciate it. So I love the title. Just I'm excited to have you on. I understand you were like employee number two or you know, really early on. Among the initial nine, yeah. 11 years ago and I think two days you started. What was that like? Was that, did you know George beforehand or kind of? Yeah, I knew George before, like not as well as I know him now. And it sounded like a pretty good proposition about what he was having in mind. Like things security-wise didn't really work that well back in the day. And we wanted to try something new, like cloud native, data-driven AI and use that to stop breaches. So yeah, like it was very exciting. Like you go there, you have nothing there. First day you open your laptop and you try to reinvent security. Yeah, so I mean, I know he never, he talks about this. I never said we're going to be an AV company. But of course, you know, you start with antivirus and when you're at an end point and known malware, okay, but unknown malware at the time wasn't really being addressed. And if I understand it, you guys brought in machine intelligence from the start. That's, that's right. And like the way we looked at it is, like back then we said you don't have a malware problem. You have an adversary problem. Just like recognizing that it's not malware, but there's people behind it that act on objectives that you need to, that you need to counter and you don't want to run after them. You want to be ahead of them. Like that was, that was the approach, like at a very high level that we were taking. And you know, now we have it a little bit more summed up and we say we stop breaches. So like that's the end result. So how do you specifically leverage AI? Which parts of the portfolio, is it across the portfolio?  How did it evolve? Yeah, we're very data-driven. So we're working hard to use the proper tools to work with data wherever we can. And AI being one of these tools that we like to bring to bear. The, the clouds, the cross track security clouds at the moment we're doing about roughly two trillion events with a T per day. Like that, that volume of data, like going through our platform, that's not something that you can, that you can work with manually, right? So we need, we need to bring the heavy machinery. Like that's, that's how we're bringing AI to bear. Two trillion events per day. I mean, there aren't a lot of organizations that see that many events a day. I mean, maybe, maybe some of the hyperscalers possibly. I don't know. That's a... Yeah, I think, I think it really allows us to get unprecedented insights into what's actually going on out there in the, in the landscape.  And that's why, that's why the volume is, is critical. And that's why we, that's why we, from the get go set out to build a cloud native platform so that we can actually aggregate this type of data and analyze it in one spot, basically where, where everything comes together that we can draw these connections. Will we ever see security without humans? I don't, I don't think so. This, this, this notion that machine intelligence is so intelligent that it just takes these jobs over. To me, it's more like a tool, right? Like these, these algorithms, they do need to learn from something. They need to learn from human expertise. The way at CrowdStrike we have things set up is like our, our human teams, our threat hunters, our MDR staff, our incident responders, like whatever they do, we're taking these insights and we're feeding them into the AI algorithms. So if there's, if there's a new type of attack and we have an incident response team on the ground and they find something that gets leveraged, put into a database and our AI can learn from it. I really like that in the keynote, Kevin Mandia actually talked to that, you know, like get the incident responders out there, get their knowledge, bake it into products and that's, that's the approach that we're taking with, with, with our AI. So in my head, I'm thinking, okay, what do humans do better than machines? I mean, humans are creative, right? Machines really aren't creative, right? I mean, and adversaries are very creative. So I guess flip side question, what does AI do? What does the machine intelligence do that humans can't do? Is it scale? Is it just massive volumes? Help us understand what humans do well and machines do well and how they complement each other. Yeah, so AI is very good at working with extremely large amounts of data. Again, like cloud native platform, like that's where you get this AI advantage. It can work with data that is a lot more complex, like more facets of data. So we talked about XDR here at Falcon a lot, right? Like you get data from all these different products from all these different angles. Like the more different facets you add to that, like it becomes overwhelming for the human mind. It's just like so much complexity that a human can put together in their brain. With AI, you don't have these limitations. It's just math. It's just like multiplying big matrices and you can work with a lot larger data sets, like those two trillion events that we do per day on the QuadStrike security cloud, but also data that is a lot more complex that has more facets, looks at the problem from different angles. That's where AI is especially useful. I want to ask you, as a topic I haven't asked anybody this week and I've been meaning to is, you know, there's this concept of living off the land, right, using your own tools against you. How are you able to detect that? Is that because of lateral movement? Or I mean, I'm sure there are many, many factors, but how are you addressing that problem that's kind of stealthy using your tools against you? Yeah, so adversaries, this is again, there's motivated humans behind that. They figured if they drop a malware file on the machine, that's an artifact, an indicator of compromise, right? And that can be detected. So they're avoiding dropping files on disk that could be detected or to bring their own tools. They try to work with the tools that they find on the machines. They need to act on objective though. There's something they want to accomplish. Like they're not logging in just to, you know, like do nothing. And this is where indicators of attack come in, right? Like we know what their objectives are and we're trying to capture this. We're describing this in an abstract way. What is it that they try to accomplish? That's what indicators of attack describe. And when they act on these objectives, then we can catch them. So I think that the term indicators of attack, you may have coined it, I'm not sure. I think there was an announcement at Black Hat. Those indicators are not static, right? That's your point. The humans on the other end are motivated. Are you, can AI help predict future indicators of attack? Maybe working with humans? Yeah, this is something that we recently rolled out where we're connecting our AI intelligence to our indicator of attack framework. Where basically the AI crunches the big data and then the indicators, the knowledge that the AI generates understanding the context of the situation can feed into the indicators of attack that we're evaluating to see if an adversary is acting on a specific objective. And then if an IOA triggers, that can feed back into the AI and the AI can use that information to derive from more precise results. We have a good feedback loop between these two systems and they're more tightly integrated now. As an AI expert, I want to ask you, is the intelligence, is AI actually artificial or is it real? Well, it is artificial because I guess we build it, like it's human-made. I think a lot of people get hung up on the term intelligent and it's not really intelligent in the sense that it acts on agency with agency, like you would look at a problem, right? It's good at solving specific types of tasks and problems that we can define in ways that these algorithms work on it, but it is not the same level of creative thinking that a human brings to the problem. And this is going back to the beginning of the conversation. This is why we like to have humans involved in the teaching of the AI. The AI can act autonomously in real time, stopping threats, but there's humans that take a look at what is going on to give the AI input and feedback and improvements because we are up against other humans, right? You don't want to have a human kind of press the buttons of the AI until they found a way around it, but that's called adversarial machine learning, a very real threat as well. We're looking at the problem as humans against humans. Like what tools do we need to bring to the battle to keep the adversaries out of our customers' networks? Okay, so my follow-up is, but there are systems of agency, fraud detection is an example, but I think your point is that that never would have been possible without humans. Is that right, or? Yeah, like on the one hand, these systems get trained with human knowledge. On the other hand, there are humans that take a look at if the systems give the right responses. Like there isn't, if you talk to your smart speaker, like for me, like I'm asking my smart speaker to turn a specific light on in my living room and it half the time doesn't work, right? Like that wouldn't happen with a human. There's a lot more context and understanding and humans are more robust. Like it's harder to fool a human. The limitation that we humans have is complexity, complexity and volume. So we're trying to make like a peanut butter and cookie approach, a peanut butter and chocolate approach rather, where we want to use the human creativity alongside the AI which can handle scale, complexity and volume at unprecedented scales. And when you bring it out to the edge, we were just talking to Stefan Goldberg about IoT and extended IoT. When you think about AI, a lot of AI today is modeling that's done in the cloud and then applied. But when you go up to the edge, you're starting to see more AI inferencing in near real time or even real time. Will that change the equation? What's the future of AI and cyber look like? I think it will be pervasively applied. So we're using it already on the edge, on our sensors but also in the cloud. On the sensor, we want to be able to act very quickly. On the endpoint, we want to be able to act very quickly without any delay with local information or if the system is offline for a period of time. So we have AI models running there. In the cloud, we have the advantage of being able to work with vast amounts of data without slowing down our customers' machines. So like models will be applied everywhere where there's data. That's kind of the name of the game. Like let's bring this type of artificial intelligence, this type of refined, digested expertise wherever the data sits. On the endpoint, in the cloud, where you have it. And CrowdStrike doesn't care, right?  The activity. So last question is how should we as humans prepare for the future of AI in cyber? That's a good question. I would say like stay creative and like figure out how we can get that knowledge that you have, like formalized into databases, right? AI, the way I look at it is an amplifier of human expertise. You do something at a small scale as a human. The AI system can do it at a big scale, right? Like it's kind of like digging with a spoon, whether it's digging with an excavator, with a backhoe. So I'd say stay creative and see how we can take things that we do as humans in the small scale and let's do it in the cloud, like with large data volumes. Great advice, good creativity, I think, is the key. Sven, thanks so much for coming on theCUBE. Really appreciate your time. Thanks for having me. You're very welcome. Okay, keep it right there. Listen, by the way, I meant to tell our audience a lot of resources at siliconangle.com, thecube.net, wikibon.com has a ton of research all available for no charge, no password needed. Just access that, check it out. We're live from the Aria Hotel in Las Vegas, Falcon 22, Dave Vellante for theCUBE. We'll be back after this short break.


I think it's really important to serve our community. That's been a high priority for me and it's the reason why I returned to school. I'm a former chef and I decided that I wanted to serve a higher purpose. It feels really hearty. The program is to teach people how to prepare food for themselves in a healthy way. So I get here early and I talk to the farmers and see what's good and then I go back, get my cart, come back and buy the ingredients and take it back to the library. We clean everything there and do a little bit of prep and then we wheel everything out here to the market and we're up and ready to go by 11 AM. So we are cooking kale today. So the recipe is on the back and then we have a selection of books that all have recipes for kale on the inside. I had been incubating this idea of wanting to get cooking into the library for years. I started a teaching garden. We taught kids about urban, organic gardening and on our first harvest, the kids tasted what they'd grown and were completely like their eyes popped and they were super excited and they wanted four helpings of salad and I thought we really need to get, make that connection between what they've grown and how to cook it. And I thought bingo, that's it. That's what we need to get a kitchen into the library. This program has completely blown my mind because people's responses are so positive and they're so excited when they see what we're doing and when they taste the outcome of the dish, they're surprised at how delicious it is. People do go home and make it and they've sent me testimonials of how it's changed their lives. A man said that as a busy professional it's lovely to have learned these simple recipes. He can go home and cook them and now he's eating vegetables that he never had eaten or enjoyed before and now he loves them and cooks them on a regular basis. And so all these folks are being introduced to the library's resources through this program and the featured ingredient, the vegetable of the day, usually sells out. So the farmers love our program because it's supporting them in their business as well. I do love it, yeah. It's really fun, yeah. And it's the little ways in which we change the world are what makes the world a better place.


Okay, thank you very much. Well, I'd like to start by thanking the organizers for inviting me. It's my second time not at the ICTP and It's been really wonderful. It's everybody's good if not better than they the first time I was here Especially because this time I have a sea view last time. I was looking at the car park. So it's a big improvement So today I'd like to tell you about knots and liqueur crystals. This is all joint work with Tom Machin. He's up at the back there and it's Motivated in large part by Sobaland zoomers experiments at Ljubljana the stuff that he's been doing with his group and Igor Musovic's group that Created knots in liquid crystals for the first time about five years ago now. Maybe six for actually doing it and the question that I want to talk about is What on earth does it mean to have a knot in a pneumatic liqueur crystal? What is it like? What are its properties? so I'll start by saying a few words about liquid crystals and I'll repeat something that Randy said yesterday one of the ways of explaining to you all what liqueur crystals are Is to show something like this and say if you're old enough to remember this Transition then you have no excuse for not knowing what a liquid crystal is But maybe I'll say some things that are a little more scientific also So if you look at them under a microscope, this is one of my favorite ways of explaining to people what liquid crystals are Apparently this is what liquid crystals are And it's remarkable Randy talked about how you could extract Molecular size information from this picture. It's also the case that Back in 1910 George Friedel was able to understand with molecular resolution What's going on in this material just by looking at this picture? So I invite you all to think about how he might have done that apparently it was something that he learned in high school So I think that's another excellent way To convey what liquid crystals are but if you look in a textbook you see something different So here's a sort of standard textbook in the field And it will tell you that liquid crystals are composed of long rod-like molecules And then those molecules can do a bunch of things either they can be disordered That's an isotropic phase or they can all point in the same direction And that's the stuff that's in your displays or they can have these States with higher degrees of order in it like these smectic states that Randy talked about There's one other aspect that I like to emphasize Instead of talking about the way in which they're ordered. Maybe I'll go back a slide You can compare also this picture with the previous one and ask yourself How closely do the textbooks reproduce what you actually see in the real world? And one of the features of the sort of simple textbook descriptions is that everything is really perfect The layers are flat the molecules all point in exactly the same direction And so another characteristic feature of these materials and many others is to try to capture the essence of the defects in them Where the order breaks down in some way so pictures like this are extremely instructive for conveying what liquid crystals are You see locally you have an alignment of filaments and then there are these points There's a couple of them. I've highlighted there are a couple more that I haven't Where you can't assign any actual orientation to the molecules at those points and more than that You can characterize their character by thinking about how the orientation winds around them So these are called Disclanations and the main feature that this shows is that the rotation of the molecules around one of these points is not an Integer multiple of 2 pi but a half integer multiple of 2 pi and so it's telling you visually Directly without any other input that this is not a vector ordered material. This is a line field that you're looking at Okay, well, I'll say a few more two more slides with sort of general introduction to the theory of liquid crystals how to think about them and I wanted to say this because This way of presenting things has increasingly had a more and more profound influence on my own work It's remarkable. This is a paper of Charles Franks from 1958 Where he really set in stone the elasticity theory for liquid crystals It's one of the most famous contributions in the entire subject And it also happens to be the only paper that he published on liquid crystals So he did two completely seminal things in just one paper One of them was that he described the elasticity and the feature here the thing a contribution that he brought to it Was not to do it in some kind of algebraic fashion, but to think about it from geometric purposes So I want to describe the distortions of a perfectly aligned state in some geometric way I'll give you a little flavor of just one of these if I look at this bend distortion I can describe this as a curvature by saying well if I imagine the integral curves of The line field so that's some curve in space It will have some curvature and that curvature is exactly the bend distortion of the line field That's one way of thinking about the fundamental distortions that go on the other ones correspond to a mean curvature of layers that the line field is the normal to or a mean torsion the way in which things are twisting and the insight that he brought to this was that these ones were Somehow already known about from Osane, but by thinking about it in terms of curvatures He was able to realize that there's another curvature that he knows about which isn't on the list and which you can add to the elasticity theory, so of course there's also some analog of a Gaussian curvature for the line field and By thinking about it in the right way He could really get the right elasticity theory for liquid crystals So another feature of liquid crystals that I like a lot is that they're really very highly Geometrical and thinking about them in geometrical terms is really useful Yes, so if you if you take a curve whose tangent is everywhere the line field Then it will have some curvature and it's exactly this quantity actually as an aside Random aside just about vector calculus everybody in the field writes this band distortion as n cross curl n and I find that Obscures this geometrical interpretation whereas if I say that it's the gradient of the line field as I move in the direction Of the line field. It's much more obvious The other contribution that he made was a classification of the defects in the material He was thinking about a sort of simple situation where I have a two-dimensional material and there are isolated singular points Where the orientation is not defined and this is figure 2 from his paper where he drew all these examples And illustrated all the different things that can happen It's a line field So it comes back to an equivalent state in rotations that are half integer multiples of 2 pi rather than integer multiples of 2 pi But other than that it can rotate by any of those half integers whatsoever And those all correspond to different types of point defects in a two-dimensional or quasi two-dimensional pneumatic material And there's a slightly sort of fancier way of wrapping this up in terms of a lots of the groups that Randy talked a little bit about yesterday and one of the things that they're good for is That they tell you what the analogous classification the analogous to what Frank did is in three dimensions If I take line defects, and I try to classify them with the same homo to be 2 then The homo to be classification is just Z mod 2. There are exactly two of them There's a line that is no defect at all and there's a line that is a defect and Then it's interesting to look at this picture of the cross-sectional profiles And for instance convince yourself that there is a continuous deformation of something that looks locally like this picture Into one that looks locally like the minus one-half winding And if you haven't done that for yourselves, then that's another nice geometrical exercise that I encourage So this is a still from a video that I got from Miha Raunig at Ljubljana Of some of the experiments that were done there associated with work that he did This is a quench experiment. You take two colloidal particles. You put them in a liquid crystal You locally melt the material around it with a laser beam Then you turn the laser beam off it forms a collection of defects and they settled on into some nice Configuration around the defect and I pulled out a still before it settles to the final state to emphasize That these really are nice elongated lines and they have interesting shapes And what I'll try to do today is to give some kind of generic classification of the properties of such lines in pneumatic materials from a sort of a global Perspective of trying to characterize what they're like and especially what they're like when they're not simple loops But have knots in them this is just a sort of Summary slide to try to convey to you very briefly that Since the experiment came out of the Ljubljana group about five years ago There's been a number of people around the world trying to make similar sorts of things in liquid crystals So there's quite some variety of sort of knotted structures that you can study these days and there's quite a significant amount of Experimental work that is available where you can really genuinely make these things In the lab in some kind of controllable or reliable way by a number of different techniques So we want to contribute some kind of theoretical Understanding to the sorts of things that they're doing in these experiments and that's going to be one of the goals for this talk Now I want to give some kind of contrast one of the things It's wonderful about coming to seminars or workshops like this is the great diversity that there is in the talks You get to hear all sorts of things that are not in your own subject area and that's something that I like a lot So everything of course is about knots But there are many different types of knots.  I thought It hasn't really come out. I made it too Faded in the background, but in principle the background is this knot table from Tate's paper That a couple of other people have shown and I thought I would supplement that with another sort of artistic rendition of knots So here are some beautiful ones from the book of Kells, which is one of the ancient books in Ireland Trinity College Dublin And then there are a couple of flavors so that we've heard about knots in the first day about knots in molecules in molecular structures molecular ordering there are knots in DNA and then there are also these knots in Continuous fields like these vortex knots that Renzo was talking about and knots in optical systems That you might think of as being slightly different because they're not just knots in a little strand They're not in a continuous material and you have to worry about the entire field It's a random Specifying some quantum wave function or something like this. How are you supposed to do that? What does that mean? And so it's interesting even though you might always be producing the trefoil knot for instance Every time you see it it has a slightly different character and a slightly different flavor to it and you learn something new about it I thought I would show a little microcosm of this Again is a sort of general motivation for trying to understand what knots are like in different physical systems This is a recent one that I heard about when I visited Durham at the start of the year and talked with Paul Sutcliffe So these are two systems that loosely speaking are vortex knots They're slightly different one of them is the ghost pitaevsky equation that Renzo was talking about so that's like a Bose condensate or a superfluid vortex knot. The other one is a vortex knot in a reaction diffusion system It's the Fitzhugh-Nagumo equation So it's slightly different systems, but as a loose sense They're both vortex knots and the question is do they behave to see him or do they behave differently? So William Irvine's paper was exactly about The sorts of things that Renzo was talking about that under evolution you have these reconnection events There are pathways the knot type changes. He starts with a complicated 917 knot it goes through some sequence and at the end of the day you end up with an unknot or some collection of unknot So that's one way in which knots can behave in continuous fields And I think Paul Sutcliffe finds something very interesting. Here's his simulation with the Fitzhugh-Nagumo equation So it simplifies and simplifies and simplifies and you end up with the unknot So you start with something that looks complicated in both cases and in both cases It simplifies and you end up with the unknot. What's different about it is that this started out as the unknot There were no reconnections. There were no crossing events. It was nothing like this and I showed a movie for the unknot But this was true for actual knots for trefoil knots and higher type knots that they studied in this system So I think it's very interesting that although in principle they're both types of vortex knots they behave very differently Because of the physical system and I think it's a problem Well, I asked him if he had any understanding of this and at the time he didn't really and I think it's a wonderful question So I'm going to talk about knots in pneumatics with in mind a feeling for what does the pneumatic tell me about the knot Why is it what is special about it being in a liquid crystal as opposed to being a superfluid knot and The two questions that I'm going to focus on are a classification question I'd like to know what are all of the knots in liquid crystals I would like to come up with an analog of Tate's table some tabulation of knots I want to know how many different knots there are how many different pneumatic textures there are for each given knot type So what is the homotopy classification and the second question? Which I'll start with is a simple one. I've shown you already that you can make these Experimentally experimentally you can make knots in pneumatic materials Well, I wonder can I do that as a theorist? I don't have a lab, but I can think very hard. Can I do it for myself? So it turns out that they're doing it for yourself is not so difficult There's a small trick, but it's only a small one What you need to do is get yourself a copy of this beautiful book by John Milner and Read the first three pages So it's not all that hard and he explains in those first three pages the following construction for torus knots Arbitrary torus knots you take a complex polynomial in two complex variables with integers p and q that are telling me the type of Torus not or link that I'm encoding and Then if you look at the following thing if you look at where this polynomial is zero so where it vanishes On the surface of a three sphere So I have two complex numbers. That's four real numbers. I take the sum of the squares to be one That's a three sphere so on a three sphere I ask where is this number identically zero and then it's a wonderful Exercise to think about that and figure out that it's exactly a pq torus knot Now we want more than this. We don't just want the curve I want to specify the orientation of a liquid crystal molecule at every single point in space not just on this curve But Milner also tells me how to do that. He tells me hey look away from this curve I have this complex number that isn't zero and if it's a complex number that isn't zero it has a fees and the fees is an angle and you can point your Liquor crystal molecule at whatever that angle happens to be so there's a prescription for filling up all of space except for this Torus not curve with some angle which is the direction that you orient your liquid crystal molecules at So that's nice. It's a fairly straightforward thing. We use this to good effect for some of our early work It's also a little restricted He's able to construct torus knots and they're useful for many things and they come up frequently in many applications But it there's certainly not all possible knots So you might like to do other things and you can extend the technique a little bit and do some other knots And it you can go quite some way in constructing things that are geometric breeds But there again, you're a little constrained that the shape of the thing is a geometric breed and not an arbitrary curve And so I'll remind you of these images from the simulations that William Irvine and Paul Sutcliffe were doing These are numerical simulations, but they still have to start them in the right state Otherwise, you have no hope of creating this spontaneously So they managed to solve this problem of constructing completely arbitrary knots You just take a random curve and generate some field from it And I'd like to tell you about that because I think it's nice story And also it's one that at least in principle. We should all be familiar with So the idea is to use the Biosavar law Basically turn it into either a magnetostatics problem or I'll talk about it in the language of fluid dynamics and vortex lines Because well, I find that slightly more convenient for my purposes So what you do is you pick an arbitrary curve You imagine it to be a vortex line and exactly the way that Renzo described in the previous Talk and then you can construct from that vortex line what the fluid flow field is Absolutely everywhere in the material by some kind of Biosavar law So if it was a current loop, this really would be exactly the magnetic field that you would measure So that tells you about some vector field that's circulating around this line And then you ask yourself if you can turn that vector field into an angle That is winding around the line and that angle of course is the velocity potential or the magnetostatic potential associated with those fields So there's a fairly generic prescription that says start with any curve that you care to dream of And end up with some angle that tells you how to orient your field, your liquid crystal Or your super fluid or whatever it is that you happen to be working with And I'll show this just again to emphasize that in these continuous systems You really have to specify what's going on throughout all of space what the field is like absolutely everywhere And not just on some curve and of course, this is exactly what this construction does Okay, these things are kind of awkward to think about and visualize so sometimes it's nice to see that sort of hands-on description Okay, and we can of course you can Take this and just plug it in immediately to construct some director field that winds Around the curves and turns them into defect lines in the liquid crystal and you can construct a whole bunch of textures in this way There's only one little drawback from this construction in terms of its generality when it comes to applications in liquid crystals as opposed to in Superfluids for instance and that is that the director field that I write down The way that I write it down it has components in the x direction and in the z direction But not in the y direction So these are all completely planar textures the liquid crystal molecules live in this plane and they don't point towards you or away from you at all and Okay, you can do that But the molecules are allowed to do whatever they want so we should also be able to describe states where they can Rotate more freely if you like we need a second angle That will tell you the angle that they are towards you or away from you in addition to this angle in the xz plane so I'd like to think for a moment or two about how to do that and In doing it I find it convenient to translate the originals or BIOS of art construction into one in terms of Differential forms but the key part is that when you're trying to construct this angle that's winding any angle That's winding around some zero It winds by 2 pi and you have to decide Whether you want it to be between 0 and 2 pi and then there's a cut at 2 pi And you start again or whether you want it to be minus pi to plus pi and there's a cut between minus pi Plus pi or whatever it happens to be you have to decide to cut things on some cut surface In order to define a an angle in some kind of uniquely to single-valued fashion So the key trick in this is to introduce a surface whose boundary is the knot and Of course, there's tremendous freedom in the choice of exactly what that surface is and if you make different choices You might get different knots An example of that here's the simplest example of that. Here's the hop flink I show you the hop flink with two surfaces They look fairly similar But if you stare at them for long enough you can see that they're different and they really genuinely are different from each other One is linking number plus one the other one is linking number minus one and that's going to be a Topological invariant that will be preserved so long as you always have a hop flink So it really matters whether you pick this surface or that surface you get something different The other thing is that the surface helps us out in trying to choose or construct a second angle that will bring The orientation of the molecules out of this XZ plane to pointing towards you in some way And that's because it provides us with some additional structure to the space the space that is not this surface Is an interesting space it has all these holes in it that you can go through and come back up some other hole and so on So here It turns out there are there are two cycles the homology of the complement has dimension two so I show choice of bases for them here and What you can do is you can pick another curve So a second curve again completely arbitrary curve It could be a knot if you like and it should correspond whatever it is It will live in the complement of this surface and it will correspond to some homology class and again The homology class will be a topological property of the thing that you're constructing So it matters which class you choose other than that Doesn't matter so much Having done that you can then construct an angle that winds around it by exactly the same trick as I described previously So that now gives us two angles and if I have two angles that covers all directions on the sphere I ought to be able to get the molecule to point in any direction I want So that's the idea you use those two angles you write down a slightly more general Expression for what the direction of the liquid crystal is pointing in and then I Encode this second angle that I introduced by some kind of color winding Here's the schematic that tells you this color winding that's going from in this plane to pointing out towards you And you can construct a whole bunch of different things in this way But still there are questions about these things. There are at least two serious questions about this We can construct lots of things But you should still ask yourself. Can we construct everything is this really completely general and Are these all different from each other or? Some of these secretly equivalent under some appropriate Homotopy of the texture So it's nice to have a Robust I mean in principle this construction would give you a robust answer to that But in practice our knowledge of Cobordisms of surfaces was not quite strong enough to carry it out in this way So we had a slightly different approach They're coming up with a knot table if you like for textures in nematically crystals The approach is essentially Traditional calculation in algebraic topology using the methods of obstruction theory that I won't tell you about I'll just tell you what the answer is So the answer is that the number of different Neumatic textures that you construct with some particular fixed knot as the defect set is in one-to-one Correspondence with the elements of some group. This group is the first homology of the branch double cover of the link complement And then there's some equivalence relation that's associated with the fact that I have a line field rather than a vector field So up is the seam is done So that really the point about this is that having identified it this this thing This is a knot invariant and you can look that up in all sorts of tables and tabulations And it's not so difficult to calculate it for yourself by a variety of different little techniques And so when you've done this you can write down that if I have a 4-4 tourist link There are this infinite number of different things that I can do in a pneumatic liquid crystal There's not just one of them if I have this collection of three things a trefoil knot an unknot and a hop flink And they're all together in the same material Then there's this number of different pneumatic textures that I can make and if you make the baron man rings Then there's only 16 of them suddenly. There's a finite number And they come with some structure associated to that 16 of them To give you a flavor of the sort of variety that's out there and some of the things that we Find out about the properties of knots when they're in liquid crystals as opposed to other materials Here's a sample of the torus knots. So these are the PQ torus knots for P and Q up to 12 And I write the What this group what this magic number is that? Encodes the number of distinct pneumatic textures that there are And there are a few things that come out So one of the things that comes out is that some of them are completely unique There's just one single knot So all of this stuff that I told you of it whether it was planer or it had these funny windings And so on and so forth those were all equivalent to each other you could do that But as far as the topology is concerned those were all equivalent In other cases There is something funny that happens that I'll try to say a couple of words about in a few slides time Which is that the group that appears is just a bunch of different a bunch of copies of Z mod 2 And it turns out that the twos are important For some other property that pneumatics have so I'll come back to this in a moment But these these things where everything is just a copy of two So there are eight copies of Z mod 2 for a 99 torus link turns out to be an interesting observation from this table And the last thing is that some of times there are an infinite number of distinct textures that you can construct And I guess in a sense we were kind of surprised about I guess we would have been surprised either way if if You know, they had all been infinite and only a few finite we would have been surprised the other way around We would also have been surprised so we scratched our heads for a long time Wondering what was going on that give us these infinite numbers And then it was wonderful. I don't always think about liquid crystals. Sometimes I do experiments with soap films I persuade my students to take time off from serious stuff and do homemade experiments with soap films so I'm going to show you an experiment that Convays or explains why there are an infinite number of states in these systems so this is an experiment was done by Tom and Davade and Another one of my students. It's not here Dario Vasili couple of years ago with a rig that they 3d printed with the 3d printer that Matthew provided. Thank you, Matthew And set up this little experiment with a 4 4 torus link in soap and Then you try you create a surface on it So you create a spanning film then you have to pop some holes until it's a proper surface So that's what we do first Okay, so now we have a surface Whose boundary is the link and then you move the rings around and the surface changes and every now and then it's topology changes This is a real-time movie, so it's quite fast in real time and then suddenly this happens So what's happened here? It's maybe a little difficult to see it on this screen But if I tell you you might be able to pick it out What's happened here is that I know I have not one surface, but two There is a surface Here that connects these two components and that forms a hot flink With a nice little hot flink surface and then there's a completely separate surface here It connects these two components, but it's otherwise identical And so this is the magic fact that if you can construct a surface whose boundary is the link And it has more than one component Then it's Alexander polynomial is trivial and you can compute this group and the order is infinite So that's where the infinity comes from and it was really nice to see it in a home-made experiment So here's Some clearer pictures of the different surfaces the transitions that you saw in that video We started with this surface then it went to this one About halfway through and the end state was this one on the right This This one is with surface of over Okay, well, I gave a classification of what all the different types of knots are So it will be nice to apply it where possible to some experimental data The experimentalist can make these things it would be nice to say which one they made Of course identifying knots is difficult and identifying them in pneumatics is no less so But if it's simple enough then we know some things and we can Make some progress so one of the things it's simple enough this is a beautiful experiment of Liquor crystals that are embedded into toroidal droplets is done by even schmalyuk's group at Boulder And you have normal anchoring conditions on the surface of the droplets and they form defect lines in the interior because of those anchoring boundary conditions and they can make a variety of essentially tourist knots With this construction you have them in a tourist Geometry with the defect lines winding around and then it's a question of how many times they wrap over themselves as To which tourists not or link you end up with so they can construct trefoil knots and sometimes hot flinks And I'll tell you about the analysis of the hot flink So of course first of all I should tell you a little bit about how to think about hot flinks and Identify how many of them there are and how we'll try to identify them So it turns out that there are just two of them and there are two ways in which you can think about them and think About the differences one is in terms of these planar Configurations that I started telling you about things that just depend on one angle and have no Component that's pointing towards you And I told you there I showed you an example that there were two surfaces that you could choose one gives linking number plus one The other one gives linking number minus one and it turns out that that's a way of describing the two different states That exist in the system and usually I think about it in those terms so I'll map everything onto one of these planar Configurations and refer to the two different textures as being either linking number plus one or linking number minus one That's one way of assigning Another way of doing it would be to use this second angle that I introduced and have some winding around Zero line that links with this hot flink Okay, and I represent that angle winding that angle variation by some color That's going around a color wheel on the surface itself. Okay, so that's telling you what this angle is Just map it on to color on a color wheel And so you should ask yourself How can I relate one of these colored descriptions to one of the planar ones and there's a process? of Deformation that says well you can make the rotation very rapid you can collapse it Into a small region of space and have it more or less constant everywhere else. That's a continuous deformation And then I can think of this rapid little thing as just a little line a tether That connects one link component to another and then it's an exercise in visualization That I have never managed to do successfully in full three dimensions But you can do in a sort of a cheating fashion if you collapse things down to a 2d version of this 3d picture And see what's going on to convince yourself that you can move this tether around appropriately To change the linking number plus one surface into a linking number minus one surface By a process that only does singular things in the actual defect lines itself Which we allow for So something that has linking number plus one With on the surface, but the surface has color on it There is a deformation that will take it to one of these completely planar things with no color, but with linking number minus one That's the identification you should think of So if we go back to the experiment It's nice because the experimentalists used exactly this technique that I've been trying to describe to you of Measuring or plotting what this second angle that's rotating is and plotting it exactly as some kind of color function On their experimental data So you can read off fairly directly from the images that they provide you with what the surface is what the color winding on that surface is And then it's just a process of deforming it to see after the deformation when you make it a planar Configuration is it linking number plus one or linking number minus one and it turns out in this particular experiment They made the one with linking number plus one So that's at least Success in one case of course Applying it as a general thing to identify Completely arbitrary states for completely arbitrary knots is still something that's a long way off But in some cases we can really work these things out. So a second feature or property of these knotted continuous fields that I'll show for you is that They really depend on the entire knotted structure around them and not just on the Lines that you see not just on the link itself It really matters that it's in a field and this is an illustration of this So I show you something or if I only show you the lines themselves these look identical as identical hop flinks But if I let this system evolve Under relaxation of the energy for the liquid crystal This costs a lot of energy because it has high distortion and so it will try to reduce the amount of distortion in it and there are reconnection events that happen and You can watch what they look like for the liquid crystal and they're pure Relaxational dynamics. So here's a little movie that's showing you what it's like in these two cases And of course the point is that I'm not showing you the same movie twice Something different happens in the two cases. So the dynamics is different in the two cases And it's different for a reason Although they looked to see him at the outset when you just looked at the lines You have to remember this is in some continuous field and the structure of the field It's around these lines is important and it was different in a topological way in the two cases So you can go back and look at this and the movie on the left was a planar Configuration with this surface Associated to it and you can check that has linking number plus one and the one on the right was again a planar Configuration with this surface associated to it. So it was the other topological type with linking number minus one And their dynamics is sense. It really cares about this difference So I'll maybe try to say very quickly before I completely run out of time About one extra little thing that we find that's an interesting topological aspect of the behavior of of knots and links in liquid crystalline materials and that concerns when it's Possible to squeeze everything down so that the liquid crystal lies in this x y plane and Has no component that's pointing towards you For this hot flink example, I could always do this Any texture whatsoever it was possible to push it around Continuously to form it and turn it into something that was lying planar everywhere The question is whether or not you can do that in general and it's not such a Crazy thing to think about in a liquid crystal context This is something that at least in principle you could promote in an experiment by applying an Magnetic or an electric field that likes to align the molecules in particular if it likes to align them perpendicular to the field Direction and if I apply the field pointing straight towards you they will try as best as possible to lie everywhere in this plate with a few little Blips if you like so there are four different types of blips and now I have these little These little localized regions where it's pointing towards you and the question is can I move those around and Recombine them with each other and get rid of them. Yes or no And so there's an answer to this there's an answer to this again in terms of the topology in the topological Classification it turns out that you can do this if and only if That texture corresponds to an element in the order to subgroup of this homology group So there's some again obstruction theoretic calculation It tells you that this is true and what it says for instance is if I look back at these examples Then there are an infinite number of states on the associated with the 4 4 torus link But there are precisely two of them that you can realize in these planar configurations and only two and if I look at this Collection of a trefoil knot and on knot and on length and again They're in an infinite number of states, but there are only two of them that you can realize in this planar configuration And if I look at these Borromean rings There are 16 of them and there are four of them that you can realize in some kind of planar configuration So I think I'll stop here I think I'll go to my conclusion slide perhaps the last thing that I'll say is that this is still a mystery to me We have an understanding of what these planar configurations are for the hot flink That was a linking number story that I told you about it's fairly self-evident as Renzo said it was known even to Maxwell of course Maxwell was a genius of course it was known to Maxwell That that there are no linking numbers pairwise linking numbers for these Borromean rings So what's the analogous way of thinking about the four distinct? Planner configurations that are associated with pneumatics with Borromean ring defects, and I don't know that yet Okay, so with that I'll stop. I'll bring up my thanks slide. I was gonna tell you about cholesterics. Okay. Thank you very much