Line from Orlando, Florida, extracting a signal from the noise. It's theCUBE covering Pentaho World 2015. Now your host, Dave Vellante and George Gilbert. We're back in Orlando, Florida. This is day two of Pentaho World, the second Pentaho World, and this is theCUBE, SiliconANGLE Wikibon's flagship program. We go out to the events. We extract the signal from the noise. Quentin Gallivan is here as the CEO of Pentaho. Quentin, great keynote yesterday. You must be excited. High energy. Thanks for coming on theCUBE. I am. It's outstanding. Thank you for having us. You guys do a great job here. Thank you. I love the fact that you're in the middle of it. You're in the buzz. We love being in the buzz. Yeah. Feel the energy. You know, it was so interesting here in the keynotes yesterday. You guys have a lot of substance. You've been around for 11 years. About the same amount of time as Hadoop has been around. Right.  So you've had time to harden your platform, and I think it really showed in the keynotes yesterday. I wonder if you could talk about some of the shifts that you see in the marketplace, some of the things you talked about yesterday in your keynotes, and how Pentaho has really capitalized on that. Right, right. What's really interesting is our second user's conference, customer conference. And very much the focus has been on around big data analytics, the Hadoop ecosystem, and really what's happening. And last year, you know, we focused a lot on the technology. And what's the technology around the Hadoop ecosystem? What do the pieces fit? What do the reference architectures look like? And then this year, because we had such a strong adoption, we really focused on the business use cases around Hadoop. And we're really starting to see companies take advantage of the technology where there's a return on investment initiative that's going to drive a revenue advantage, a cost advantage, or an operating advantage for customers. So the shift we've seen, really the kind of macro view is the maturation of the Hadoop market. So that's the theme of Pentaho World is putting big data to work. So as you saw in the keynotes, you know, a lot of discussions around internet of things, how are companies deploying it? How are they making money at it? 360 view of the customer, you know, big data analytics, how are companies getting intelligence about their customer in order to get closer to the customer to drive higher conversion rates on target offers and revenues. So what I like about the theme is really the maturation. It's really all about the business advantages, which is very different than a year ago. Well, the business value is critical.  What I heard yesterday from the customers that we interviewed is they're getting massive value, and the reason is you've actually put together an end-to-end pipeline. They're not having to spend 70, 80% of their time figuring out how to make all this stuff work. That's a critical competitive advantage for you, and it's unique in the industry. I wonder if you could talk about that. Yeah, I think one of the big, sort of unlocking the value of big data is that companies, there was a focus before around primarily just what data can we put in Hadoop, unstructured data in Hadoop, and that's an important component is being able to analyze this unstructured data. But what we've seen from the line of business trying to drive these 360 view of the customer initiatives or Internet of Things or fraud control and compliance is the need to blend that unstructured data with structured data or relational data data you already have in your systems about your customer, about the transactions, about all the ERP kind of activities. The key in unlocking is blending the unstructured data, which is really what are the behavior patterns, what are people doing on Clickstream, what are they doing around IoT devices, but blending that with the relational data, that's unlocking the insight. And so what Pentalo does that end-to-end platform, it automates the process, it takes friction out of the process, and essentially allows companies to unlock the value of big data. George, and I know you want to jump in, I want it to follow up on the whole IoT piece as it relates to strategy. I know Richard had a go, so I'll ask you the strategy question. Chris said yesterday, strategy should not waiver, should be consistent. Now that's not always the case, sometimes companies have to do massive pivots and change strategy. When you started the company, Pentalo started, there was no IoT, people were talking about IoT, and now it's like this huge tailwind for you, the Hitachi acquisition, and we'll talk about that, but so the strategy wasn't IoT. The strategy was around data, so I wonder if you could sort of summarize that strategy, because it's positioned you very well for some of the changes in the marketplace. Right, it's a great insight. When we started out really, we had two themes in the company, and we have been around for 11 years, that we've tried to be consistent to those themes. One theme is that we truly believe commercial open source is a way to innovate faster. So that was one theme we had from the very beginning. The other theme we had is that for companies to get real insights, you have to marry the ability to integrate data from all different sources, blend that data, and then easily put that into an analytical tool. So that's been our theme for 11 years. What's changed is big data. So big data has made those themes more profound. It's made those themes more relevant in the sense that the traditional data sources are still important, but now this unstructured data becomes very, very critical. And so for us it was easier to point the company with our themes at the bigger opportunity. Now as it relates to big data, so what we've been doing is really putting together an analytical platform that takes unstructured data, structured data, puts it into an analytical model, individualized it, that end-to-end pipeline. And so with big data we've been trying to find is what are the business use cases? And so IoT has just become another business use case that's getting a lot of attention, it's getting a lot of traction, and it's getting all this attention because you've got traditional, old-line, industrial companies that weren't really associated with technology innovation. They were associated with manufacturing innovation, supply chain management innovation, but now they're on the forefront of taking advantage of IoT as a way to transform these industrial businesses. For us it just happened to be right place, right time that we've been focusing on business use cases and IoT now becomes a very popular business use case. Lucky timing sounds easy, but a lot of execution behind it. Go ahead George. So I'm listening to two things that are related. One, it sounds like when you can unlock value across data silos and make it easy, you can capture a lot of the value that customers are unlocking and the rise of big data in a separate repository was a key part of that. Other than internet of things data coming from many different sources, how are you positioned to take advantage of that? I mean it comes in from so many more sources, it's continuously coming in. How do you work with that? Yeah, so there's a couple of key trends emerging around IoT, because IoT is a whole different game in terms of instead of a, you know, usual business communications is even about a person communicating to a person or a person communicating to a business. Now you've got people and things and people and systems connecting. Or things and things. And things and things connecting. And so from our perspective we're seeing a couple of key technology trends happening. One is the emergence of the cloud as a deployment model for big data, particularly around IoT. And you ask yourself, why is the cloud emerging as a deployment model? Or the reason you mentioned is that when you're doing internet of things you're basically capturing machine data from devices, from sensors. It could be 10,000 sensors, it could be millions of sensors on a global basis, sitting in a customer premise, sitting in a home, sitting in a retail shop. By the very nature, because of the distributed environment where the things are generating data, it makes sense to put that infrastructure in a cloud, a cloud environment. And so the cloud thing is an important piece. And the other important piece around the internet of things is the ability to capture data coming in very, very fast, coming in short bursts from devices and quickly move that into an analytical platform so that the analysis can basically capture the data and then review the health of that device. That's the main event around IoT is what's the health of that device and things like predictive maintenance are use cases where companies want to get ahead of the device failing in a customer's environment or on a factory floor is they want to see based on the health of that device with the machine data is telling them do something about it, do be preemptive, take that device out, remediate that device. That predictive maintenance piece is one of the key use cases we see around IoT. So my understanding then listening to you is you actually now have sort of pivoted like from the iPod to the iPhone into yet another super sweet spot that's actually bigger in the sense that as you say the internet of things sort of machine data is coming in continuously and very fast and so you need an end to end pipeline that doesn't get stuck handing off to different tools. That's one thing. And then you're also to some extent hiding the information processing layer in the form right now of a Hadoop ecosystem that does all these handoffs whereas you can sort of manage it at a higher layer. So in other words shorter pipeline, faster pipeline is that sort of a core of your advantage with the internet of things? Yes, because you are seeing what's happening with the internet of things is that it's moving away from a batch process of moving data to more real time, to more streaming of information continuously coming in. And so with Pentaho, we do have an advantage around the scalability of our infrastructure, the innovations that we're working on today and working on tomorrow to really go from that batch data movement to a more streaming data environment because that's going to be very critical and then also to your point is really take the complexity out of the process and that's the value that we bring is we try to abstract the complexity from the eyes of the customer and handle that end to end process in an automated fashion. So I want to bring in the Hitachi piece. We're talking about internet of things, obviously there's a clear Hitachi synergy there. One day we saw Dell announce an acquisition the largest acquisition in our industry's history of EMC, a company that HDS has been competing with for years. Interesting to note HDS, Hitachi going into finding ways to leverage internet of things acquiring a software company like Pentaho and you're seeing sort of these hardware companies consolidate. I wonder if you can talk about two things. One is what do you make of that? And two talk about the synergy with Hitachi and the IOT play I want to dig into that a little bit. One of the things that was compelling for me as the CEO of Pentaho to be acquired by Hitachi, what was my strategic rationale and really the strategic rationale for us was we saw a very big opportunity in just doing what we were doing. It was a 40 billion dollar opportunity, big data analytics and we started to see IOT this emerging use case and we have many IOT customers that aren't Hitachi customers. We'll continue to build more. But we're kind of on the outside looking in of the IOT tent. And what we saw the opportunity with Hitachi is really to expand our ambition expand the aperture and be inside the tent in terms where IOT is going. And what we liked about Hitachi's point of view is that if you think about Hitachi, you know it's an 80 billion dollar plus company and a lot of industrial businesses but it's also a very large I.T. company. And so we thought that being part of one of very large I.T. companies is also a very large industrial company. You're going to have domain expertise bringing IOT together and we wanted to be in the middle of all that. So that was part of the strategic rationale from my perspective. So that makes sense I want to talk about the go to market.  And you might have a slight advantage against the competition. And then you get bought by a big company and distribution changes. So can you talk about the go to market and how Hitachi will bring the Pentaho innovations to its marketplace. Right, right, right. So that was another strategic rationale for me is that if you look at the market opportunity Pentaho was targeting it's a big market opportunity and a lot of that market opportunity is large enterprises deploying big data solutions and buying the technology. For a small company like Pentaho we had to really work scratch and claw to get into those large enterprises. The synergy value of Hitachi data systems is they have a very large sales organization, they have a large customer base, existing contracts, really strong relationships. For me it was really a way to catapult into getting our solutions and getting part of these projects leveraging the large Pentaho go to market capabilities. So that's sort of synergy value one. So synergy value two is that Hitachi has a lot of software IP around technology around data management. One of the things that were very intriguing to us is that predictive analytics is becoming a very important part of all these big data analytics use cases, not just IOT. At Pentaho we have a predictive analytics capability and we have some data scientists. Hitachi's R&D has 500 data scientists and they're looking for problems to solve. So I looked at those 500 data scientists and all the Hitachi IP and said that's something that can be super helpful for us going forward. So tell us, Dave asked about sort of go to market. Let me ask about sort of go to market V2. Which is when you start leveraging some of their internal IP the data scientists and data scientists sort of this generation's professional services. How does some, how do some of Hitachi's businesses change and how does Hitachi sell to other industrial companies when they're sort of offering analytic data capabilities along with an industrial product. Right. So a couple ways that Hitachi's approaching the opportunity and I'll talk about where we fit into that opportunity. So even if you look around here at the convention center in the expo booth, Hitachi data systems has built big data analytical applications. Pentaho is more of an infrastructure end to end company but someone needs to build applications on top of that, our technology. So if you go around the expo here Hitachi data systems have built big data analytics for the telco industry in terms of network traffic analysis. They've built big data analytics capabilities for IT in terms of machine analytics. They've built big data analytics capabilities for smart cities. And so the Hitachi data systems already built a handful of really powerful big data analytics applications on Pentaho on top of Pentaho. So we're going to continue to be a partner there but we also work with a lot of other companies that are building big data analytical applications. 40% of our business comes from partners, many of those in the rooms many of those that you saw in the keynotes that build applications big data analytical applications on top of the Pentaho platform. Just to be clear 40% is it 40% of your partners build apps or 40% of your revenue comes from apps built by partners? Ladder. Wow. The ladder. That means you're one serious platform. So then a follow on to that is how do you think about capabilities that might belong in the platform but that application developers put in now that you know you have to trade do you step on them or do you broaden the platform? It's a great question so it gets back to the earlier one you had about so who are we? What are our themes? So our basic theme at Pentaho is commercial open source end to end analytical platform and be very extensible and be very about plugins. So our heritage has always been about having other companies, partners, customers build on top of the platform and because of our commercial open source roots they're very much an extensible API oriented platform. You can build plugins and that's been our community, the open source community that's been where they've really spent a lot of time is building applications, building visualizations building front ends, building back ends on the Pentaho platform. We're going to keep that heritage and that DNA so we allow companies like Hitachi to build applications on our platform and then you know the rest of the marketplace. So we've talked a lot about some of the exciting things IoT and let's close on sort of summarizing some of those things that excite you. You talked about telematics in your keynote you talked about O-Power talked about 5 billion devices 5 billion people, 50 billion things connected. We talked about cloud. Summarize Quentin some of the things that are exciting you you're head of a technology company what are some of the technology enablers that you see that are really exciting you guys? Right, so a couple things one is and again it's only been a year since we're seeing these dramatic changes and these shifts. It's amazing. But a couple things around big data that we think are really interesting both technology and then shifts. So one is we do think use cases like IoT are here, they're real, it's very transformative. We do think big data is getting cloudy right and not just around IoT but now you had FINRA on here and so look what they're doing in terms of that's very serious credible big data stuff I mean they're basically monitoring the capital markets in the United States looking for fraud as a regulator looking for insider trading 75 billion events or trades every day they have to capture and quickly analyze and looking for bad behavior that's serious stuff and they're doing that in the cloud they're doing that big data in the cloud so we think IoT, big data in the cloud and then there's all the cool stuff or the innovation that's going on in the big data space all these commercial all these open source activities like spark in terms of new trends that's a pretty exciting Apache project and you've got very fast processing in memory large data sets that could be part of a platform things like Kafka which is real time streaming message cues so there's all these components that make sense in terms of taking big data to the next stage what we're trying to do is that we want to be the heat shield for our customers around these components I mean we take these new technologies in we embed it in the platform then we harden it the exciting thing about these new technologies in open source is the innovation is dizzying the challenge is that it's fairly immature and fairly command line kind of technology so our job is to take those components in make our products faster more real time more scalable more performant and harden those and I think that allows a company like Pentaho whether pre Hitachi or post Hitachi to innovate dramatically fast because we are an open source company we take advantage of those technologies well you've made the open source angle work it's very hard it's obviously red hat huge success but a lot of companies struggling to do it why do you think Pentaho was able to be so successful with an open source strategy well we've been at it for 11 years so I think like anything else in business time and experience it allows you to it allows us to really shift our focus from yes we want to be an open source company but also where's the business value for the customers and so we've been very focused on keeping pace with innovation but where do we add value from a business and that's why we've really focused on these use cases that I talked about around big data I think the more that we can not only bring the technology but bring skills and expertise or cookbooks or blueprints around if a company wants to do IOT we've got a reference architecture for you if you want to do of your customer we have a reference architecture do you want to manage fraud from a big data standpoint we have a reference architecture for you so I think it's just a combination of technology plus business process skills and expertise well it's been an amazing journey so far sounds like a lot of exciting things ahead the timing has just been amazing to watch and you know I've seen a lot of exits in this business you guys aren't a lightweight tool or lightweight tool an acquirer has to then harden you guys have done a lot of hard work in doing that road map we're going to have some other guest on later today to talk about that and drill into that so Quentin congratulations on all the success and we'll be watching going forward thank you for all your support thank you for coming here and you sort of capture the energy of the moment here it's really been our pleasure so thank you keep right there everybody we'll be back live from Pentaho World in Orlando we'll be right back


Live from Las Vegas. It's theCUBE. Covering Informatica World 2018. brought to you by Informatica. Hello, welcome back everyone. We're here for exclusive CUBE coverage here at the Venetian in Las Vegas. Gay won, getting set up for the Solution Pavilion opening kickoff party. We've been here all day. For two days I'm John Furrier, host of theCUBE, but Peter Burris, analyst at SiliconANGLE, we keep on theCUBE. Our next guest, board member of Informatica for 10 years now. CUBE alumni, Jerry Held, industry legend, veteran, been there, done that, seen all the ways of innovation. Jerry, great to see you. Thanks for coming on. Great to be here and nice to see you guys again. 10 years at the board of Informatica. A lot, that's like, how many ways can happen in 10 years? What's been the journey? What's been your view? You and all the board means approving all the hires, the stock option grants and all the action.  What's the story? Well, it's been a great ride. It's an interesting company. I've been on a lot of boards. I've lost count of how many, both startups and then big public company boards. But Informatica's been a really fun ride. When I joined, we're going through super growth. My really good friend, Sohi Babasi, was running the place. He had a phenomenal 10 year run, like 36 quarters of record growth and profit. Just unbelievable. Look at from an ETL company back when it started to a full data integration company. Kind of went from the first phase of data to the second phase where it was more than just moving data to a data warehouse, but all phases of data integration. And that was terrific. And then we got to a point where it was time for another phase and a lot of things were happening. Not only in terms of where the company was going, but where the industry was going. And what year was that when that happened? So that was about two and a half, three years ago when we decided that the best route was actually to go private, because some of the transitions were going to be pretty profound. For instance, just the model of selling software going from license to subscription requires a dip in revenue. It requires restructuring your field. A lot of changes. A lot of product work. Yeah. So we did go very successfully. We went private and I don't know for some reason they asked me to stay on the board through that transition. And it's been interesting being on the private side. Now that it's a private company, it's run differently. We have some great private equity firms who are the investors, owners of the company. The board makeup is completely different. And we have a lot of people with the financial look at the company. But they're growth investors. There are some PE firms that come in and take a company apart and just try to get the most they can out of it. Luckily, the investors that we found believed in the future of the company. It's a growth company. It just needed to go through some restructuring. We're also really fortunate when SOHAB decided it was time to retire to promote Anil to be the CEO. And he's turned out to be fantastic. And we've had a number of changes really bringing in some fresh blood, new people into positions. Really strengthened the team. And in the last couple of years of SOHAB's tenure, he put a real focus on innovation. Because we had gone down a path of acquiring a number of pieces, putting them all together. But the innovation had sort of slowed down. Well, he started the process and it really picked up speed through this transition. So the company has come out with a series of really new, innovative products. So now Informatic is like one of the hottest pre-IPO companies in the industry. If you think about enterprise software companies. Yeah, we documented them. You've been here from the beat watching 23, four years ago. We talked to Anil before he was the CEO when he was running the products. They brought in some product people. They did the work. They buckled down. Okay, so I got to step back. Before you came on, you and I were talking about Waze. You've seen Waze, a relational database wave.  That's never going to happen. It is going to happen. So I got to ask you, take us through what the wave is right now. What are you excited about? Because certainly there's no doubt that horizontally scalable cloud has opened up a new, kind of a new aperture, if you will, of opportunity. And it's impacting everybody. Data is not just a category. It's fundamental in the fabric of this next big wave. What is your vision of this wave? What's exciting you? Take us through that. Well, as we were saying, I've been in this data management business for 50 years now, so I've seen a lot of waves.  And I was there back at the birth of the relational database, the client server, and web, and cloud, and SaaS, and all of these. Each one, when they start, people poo poo, oh, it's very cool, but never take off. And there's a lot of people who miss great opportunities at the beginning of a wave. Now we're clearly well into the cloud wave, as I think most people realize it's for real and there's a lot happening. The one that I'm most excited about right now is in what I would call, you know, we've got had DBMS, database management systems. I'll make up a new term right here. I've never used this before, so this is the first on your show. So instead of DBMS, how about D-A-M-S? Data Asset Management System. That's what we need. We have got such a proliferation of data, relational databases, no SQL databases, Hadoop databases, we've got structured, unstructured, text, image, every kind of data. But it's proliferating at an amazing rate, right? We've got all kinds of types of data, sources of data, users of data. People now want to use data, not just the IT people, but end users. But it's out of control. We have this asset and everybody talks about it. You can see here at these sessions, what's going to transform your business? Data, data disruption. But it's out of control. Nobody knows where the data is. Ask the CFO where all the financial assets, they can show you the spreadsheets, they can show you the reports. Ask the Chief Information Officer, Chief Data Officer, they can't tell you. So what we need to do is manage the data asset. And how are we going to do that? As far as I'm concerned, the single most exciting thing coming out of Informatica, there's a lot of exciting things at this conference, far and away to me the most exciting thing, Enterprise Data Catalog. That is a data asset management system. It allows you to look across every type of data in the enterprise, on-prem, in the cloud, all kinds of data and get your hands around it. And you need to do it for two big reasons. One, risk reduction. And two, is reward enhancement. In other words, you have a way to reduce risk, improve governance. And boy, you can just look at the news every day, Facebook, GDPR, which is coming this week. This week is very timely. Europe is way ahead of us here. They're forcing companies to get their act together. But how do you do it? You need to get your act together on managing the data asset. It's not managing the actual data, it's managing the metadata. Where is the data? Who has access to it? What's the security? How many copies do you have? How many different views of a customer do you have that are inconsistent? The way you need to do that is through an enterprise data catalog. And Informatica has a super exciting product. The most exciting product, in the 10 years I've been on the board, is the single most exciting product that companies come out with. Sounds like you're bullish on this one, so who does a check mark on that one? Let me ask you a question, just to kind of take that to the next level. Jerry, what is this order of magnitude impact in your opinion? Obviously, it's a big wave. Can you kind of just give us a perspective? Waves have multi-year lives, sometimes 10 plus years. Pat Gelsinger, former Intel, always talks about waves. Sometimes they're 10, 20 year waves. What is the impact of this one, specifically around the catalog? What's it going to impact? Order of magnitude, share your color, commentary on how you see it shaping out. What's going to have these two huge impacts? Let's just talk about on the risk reduction side, on the governance side. Think about the potential impact to Facebook of losing controller data. That company could well get split up. I mean, there's a lot of talk about splitting up. How big an impact is that? Pretty damn big, right? Pretty big, yeah. I mean, it's huge. Yeah, billions, trillions. Yeah, and those kinds of risks are out there, and they've reached a point where the public, the government is no longer willing to put up with it. Now think about the reward side of it, the positive side. If you can get control over your data, and now you're doing all this great analytics, people create data lakes. You know what's in those data lakes? Most of them are data swamps. They put a lot of data in there, but they don't know what's there. If you could take all that data in the data lakes, plus the stuff you have in the cloud, plus stuff you have other places, and now you want to answer that hard question, get your analysts to be way more productive. How important is when you get that insight, how do you measure the business value? I'm sure on your show you have had dozens of people give you a specific instance of, oh, look what I did with Tableau, great product. I did all the stuff and I discovered this and I changed my business, right? You've had that. Oh, insights come out of the woodwork, everywhere. However, ask the question, how many insights didn't come out because these analysts didn't know where the data is. They didn't have access to all this data. They did find something, but think about what they could have found if they had a complete view of all the enterprise data and how it related to all the other data coming in from social media and everything. So what's the value of an enterprise data catalog? I think it's enormous, enormous. But Jerry, so I think that's an interesting, that's an interesting gain, you know, thought experiment. But if I were to combine that with another thing that excites me about what I'm hearing this week, the reality is there aren't enough analysts in the world to find it all. When we start applying machine learning to the process of creating, maintaining, sustaining the understanding of data assets, reforming, reforging data assets, ensuring that we are not dependent on manual processes in the catalog, it's that combination that makes it possible to actually augment the way that human beings look at these things. Ultimately, these types of systems are going to provide options to the business. Yeah, and you hit on an absolutely key point. What does it take to have a great data catalog? There are a number of companies that are trying to do data catalogs. Some are doing small pieces, cataloging, bits and pieces of the enterprise. Interesting, but the word enterprise is key. You need something that spans the entire enterprise. And when you get that complicated, the human brain can't deal with it. So you've hit on maybe one of the most important points. You must have an enterprise data catalog that's based around AI, machine learning, at least tool assistant. You're going to still have people that are going to be curating, you're going to have people that are going to be adding glossaries and all kinds of things. But at the core, there's so much data that you need to take the machine learning technology that's moving along quite quickly and try to figure out what are all these relationships? That is at a core component of it. So we talk, so I'm going to throw this at you. You tell me if you agree with me. What that comes down to is if everybody talks about AI, we talked about earlier, taking jobs away, doing the work. Increasingly, I think we're going to look at AI as a technology that provides humans options. Better forged, better formulated, well-structured options based on data. And that increasingly to think about creating data value is, is your system creating new classes of options for pursuing the value of data? And this combination of things, AI augmenting by presenting options to human decision makers so that they can look at all that range, all those possible vectors that they could be pursuing and choose the ones that are most attractive. Does that make sense? Yeah, I think there's two things. So there's two parts to it. One, you're exactly right. It can augment and give choices. But before it does that, it can eliminate a massive amount of just grunge work. Most analysts, this is a well-documented fact, most analysts spend 80% of their time in data prep and 20% in analysis. That's pretty well industry standard right now. If you're doing better than that, you're doing great. And what you can do if you do the right forum of catalog and get the data organized and then you use things like MDM and data quality to cleanse it, now you get to the point where the analysts is doing analysis and they're doing things, number one, that are more interesting, number two, that are more productive, and number three, that are going to have a bigger effect on your bottom line. Talk about the role of data when it comes to IoT edge, for instance, in the cloud. Okay, this is now, because of the scale, you mentioned scale with AI, that helps with the scale of data coming in. You get that. Now a customer's looking at an architectural shift with cloud, multi-cloud, and IoT, whether it's edge or whatever that's defined as. How does the cataloging and the data that vision you put forth impact by that? Accelerates it, does it change it radically for the buyer, the user, the enterprise? How does that enterprise customer think about? Well, it's another important source. So we have all these different sources of data and a growing source is going to be IoT data. And if it's streaming in, going into some repository, it needs to be cataloged and correlated with the rest of the data in your enterprise. Right now a lot of IoT data is just going into some system off on the side, not correlated with the mainstream data. The thing that I think is the big shift when you go from DBMS, database management system, we're focused typically on a single database, IoT data, or it could be accounting data. The focus was on just that data. The difference when data asset management system is think about your data as a whole, across your whole enterprise. A portfolio. The whole of your data asset, how do you manage that? It's not the bits and bytes, it's the overall thing. It's not the actual data, it's actually the metadata that you're managing. Or it's the data as it's being used and the metadata describes data that's being used. So data, like anything else, you apply it to work, it generates value. Metadata describes how it's being applied and then the underlying data elements are given context and semantic richness by the metadata. Exactly, exactly. All right, so here throughout the old, if I'm Joe Sixpack out in the street, I see, I hear catalog. He's talking about this stuff all the time. I go, whoa, catalog. In my mind I get a mental model of a centralized database, I think hacker. Because in government and all the hacks going on, decentralized data is probably better or de-distributed data. So I hear catalog, my mind goes centralized. Is that the right way to think about it?  Because that's, security's critical on this. Absolutely, and so as you bring this view of data, just like when you have your financial books, where you have a central view of all of your financial assets, there needs to be security. You have to have, allow access for people for the appropriate level of information they're going to pull out. The data asset is no different. So you want to have a full view of all of your data and you want to have ways to allow and restrict access to the information. It's not the data, it's just where is the data and each of the data systems then have secondary. So it's not centralized, it's just metadata for visibility and auditing. I think there's an important point, I want to test this on you because you're asking a great question. The information model from IBM, we've had catalogs with databases, we've had catalogs all over the place. Highly stylized processes, stylized data stuck in a catalog. One of the things that's especially interesting is not the idea that we're going to start with a whole bunch of designs and put them in the catalog, but we're going to discover stuff about our data and the catalog will emerge out of the attributes of data and how it's working and how it's being used. If you, let's rewind back. So the answer is no, not centralized. Well, but it's not, Metadata may be so much centralized, but the data's not. We're not trying to do a centrally designed architecture, so let's rewind 50 years and go back to the beginning of relational databases. We had schemas. And back in the 70s, people were talking about, oh, let's come up with the schema for the corporation. We'll have one group go off and they'll design everything, failed. Then they had data dictionaries where they were going to put it all in place, failed. And all of these things where there was an attempt to centrally define and control the structure of data around the enterprise failed. That is not what we're talking about. Data exists in all forms with all sorts of schemas and definitions and all types of databases in Oracle and SAP and everything. All we're doing is taking the metadata and relating it and using it. Allowing it to merge. So that we have a view of where everything is. That data's different than this data. It's managed by different software. But we have one view so that now when an analyst wants to know how do I get the latest information on customer preferences for purchasing this, I can go here, here, and here and I'll correlate those and I'll pull them together with some too. Final question, and what do you say? Final question for you. If you take that to the next level, you're almost implying or actually saying that that philosophy of a catalog implies that it's okay to have a zillion databases. I might have a postgres database on this application. I might have an unstructured database over here. So in the future world where we're living in a tsunami of data, apps need databases. So the idea of, and they're going to be, yeah, data, different databases proliferating is not a bad thing under your model. Absolutely, we've tried having one answer, it doesn't work. And even if you could ever get a company, a large company, you can't do it, but if you get a company to get one form, then they do an acquisition and now they've got other forms. So that concept just doesn't work. It has to be a heterogeneous world and you have to have a way to pull a piece together. And that's why, just as a final point, I think what Informatic has done with this enterprise data catalog, which is a phenomenal product, still early days, but growing at a phenomenal rate, fastest growth of any product ever. You need a company that's independent, that's not a stack company. It's not an Oracle or an SAP. It's not a cloud company. It's not an AWS or Azure or Google. It's not a SaaS company. It's somebody who is the Switzerland of data who can take data from every place and just collect that metadata. And it has to be a company that understands machine learning and AI that can use it to pull it together. And they got to work with the clouds too. They got to work with all the clouds. And it has to be a company that has interfaces to everything, which is what Informatic is. So it's a perfect fit. And it's not going to try to then use that to exact significant control for how everything operates. Exactly. And it's not trying to sell you an application or a database. So you need that Switzerland. And I think that's why, to me, in the 10 years I've been on the board, I haven't seen a more exciting product, nor have I seen a customer reaction as dramatic as this. Every customer is talking about EDC. And if they haven't before this conference, they will after this. And the timing is critical on this too. Look, talk about timing. The tailwinds for this movement right now, more than ever. It's sometimes timing is- This week is, I mean, GDPR is a big deal. A big deal. And what's going on with Facebook and others is a big deal. So the timing is appropriate. And the product is fantastic. And I think it's going to be, when we look back next year, and we do this show- It's great. We have nine years of history. You can go back and say, hey, remember you said that, right? Data is the central strategic asset, not some corner case. GDPR is a signal to shot across the bow for all companies to get in the center. We coined the new term, database asset management system. Data asset management. We actually have research on that from a couple of years ago. Okay. We hear on exclusive on theCUBE here, data asset management system. Asset is data. It's going to work. It's going to be on the balance sheet soon. theCUBE is here out in the open. Informatica World 2018. Jerry Health board member bringing his insight. Thank you for sharing the data on theCUBE. We'll be back with more. Stay with us after this short break.


Hello everybody! Welcome to the MIT Scale Global Network poster briefing for next January 2019. We are going to introduce you how to be prepared for the research as for next January. So let me introduce myself. My name is Maria Kessoul-Sain. I am the incoming executive director of the blended master program here at MIT. And I'm really looking forward to meeting all of you in January. Hi everyone! I'm Tuva Sanmigil. I'm a research scientist at CTL as well. And we are very excited to have you here in January as well. And today, you all know that January will be a very crowded and busy period for all of us. So at the same time, you will have the chance to show your initial results about your projects in January at Research Expo. So we'll give some details about that Research Expo location and schedule and some points for presentation of the posters. Here today's agenda is including Research Expo location, setup and floor plans and schedule. And then Maria will tell about poster layout and we'll give some examples. And also we'll wrap up some important points to keep in mind. As you all know, Research Expo is a special event hosted by MIT CTL. And there will be almost 200 students coming all across scale centers. And these students will showcase their company sponsored projects to supply chain professionals. So this Research Expo would be the interest of both supply chain executives and recruiting professionals. And here you see that there is a small map of Cambridge including MIT buildings. E40 is the one that we are living as CTL people. And E14 is the medial lab building that Research Expo will be held on top floor of that building. So as a floor plan, it will be on sixth floor and we'll use rooms named as skyline room, winter garden and multipurpose room. It is dotted with the red line as you see and within that red line area on this day on Research Expo day, there will be some buffet tables, serving food beverages and some refreshments. And in the middle you can see that ePoster area to let you present your works. So for scheduling it is not certain yet. It may change, but basically we'll split the students into two groups named as A and B. And totally those groups will have one hour presentation time. In the first session it will be a 30 minutes presentation and the groups will switch to another one. And there will be a guest speaker and during that event there will be a voting process which will close around 7.30pm and at the end there will be an announcement on voting results for the last 15 minutes. Just this voting process is for the awards of the poster. So then be really prepared for, I mean sell your poster in that voting session. Thank you Maria. And from now on Maria will tell about poster layouts and will explain about some examples for some trees. Yeah, I think that this is important to highlight that you are going to be exposed during this session in front of different supply chain professionals and especially your network, your scale network, students coming from all over the world. So it's important that you show your work, the value that you are going to submit to your company, to the sponsor company. So this poster is like your business card in order to detect your potential. So it's important that you work in advance both from the technical point of view and also just to dress this technical work within this poster session. So this is why we wanted to have the same kind of format for all the students within the scale network just to show the same similar kind of element while of course all of you will customize all this content to your particular area, to your particular context. So in this format you will see different elements. Here for example the title, you can include a title that will be different than the title of your project just for focusing on the particular key elements. Also the students names, who is your advisor and if you can because maybe you cannot do it but if you can please include the company that is sponsoring your project. Here you will have, you will show yourself. So actually here you will have your names and the pictures of the project team members. So in terms of content, you will have different elements. So the format is important. So please keep the format constant in all your projects. So starting with the motivation. What is going on? How did you get in that way? So you already presented as deliverable. In most of the cases you have already submitted your motivation and your scope of your project. So this is something that you already have, I mean, done. Key questions. So go to the point, the main research questions. What is the simplest expression of your aim within this project? Relevant literature, keep the same format for all the different sources that you will include here. You don't need to include all of them. Only the most relevant ones. Central graphic is the focal point. So then usually you will use here some picture, nice picture that will catch the attention with different colors. And especially a picture that will summarize the main purpose of your project. You will summarize the problem. So yes, to highlight what is the main elements of your problem. The methodology here typically some students will see in a minute. Some students will use some kind of diagram with different elements, with some arrows. Yes, to show the progression, the spectrum progression of your methodology. How you are going to follow through the different steps of your methodology. Initial results, this is important, right?  The professionals that will see your work. Then you will show how far you have progressed with your project, with your work, right? So then you will need to synthesize what are the initial results that you have obtained through your effort. And expected contribution looking to the future. So what are the expected value that you bring to deliver to the particular company and also to the particular audience. Because maybe some of the results you will generalize in order to be able to make applicable recommendations to the industry. Or maybe to some group of companies, right? So this is the format that you need to follow, so please be attached to that. So we will see now some examples. Some ideas that maybe you would like to apply to your particular context of your project. So this is one example, so for example the title is quite short, but maybe it's too short. So the question here is this title describing the main aim of your project. Here then you will see, you will show a kind of figure, a kind of picture describing, but maybe this is so simplistic, I don't know. In terms of using some graphs, make sure that you include the label of all the two axis here. So here for example is not clear enough what are the units of these different blue and red bars. So what is the message that you want to show here? And especially how your readers will interpret that message, will be easy to interpret or not. Other examples that we will see here, this is very concise title, so five words, no more. This is perfect, describing exactly what you want to describe. So a catchy picture showing, related with the main aim of your project. So here a map describing the scope that the project aims. But for example I will include maybe here some short labeling about what are the different colors means. Here they are showing some quantitative results about the initial contributions in January. For example here I missed something about what are the different units of the different elements in this particular graph. More examples, for example this example is really nice, it's very quite balanced in terms of colors, in terms of content. Maybe the title is too long, so then please be careful with that because you need to catch the attention in the short bit of time. So the longer the title, the most difficult will be to catch this attention. They have a good combination between these two figures, showing here the methodology, so that they know what they are doing or what they are going to do in the future. So that they control the main work behind the project. So a short key question directly to the point structure test in order to highlight the different parts. So I particularly like this exposure. More examples here, please I mean if you would like to highlight something, let me know. Again this is a nice example with very good balance of colors, a catchy figure that is showing the different elements of the particular project. Showing here a short title, here highlighting where and especially I mean where is the problem they are going to build with in terms of motivation and the background. I will advise maybe to change the learner size in order to be more homogeneous along all the different elements of the project. And so here with different diagrams they are showing the different elements of the project. I particularly like it. More examples, again nice pictures showing the main goals with different figures highlighting the different elements and here are some results. Oh for example here again right different balance between the different diagrams. They are concise they are simple but very easy to understand and including almost everything that they want to highlight. So here we are in this particular project and we are increasing the complexity of the posture. So then please pay attention to this balance so sometimes you want to include everything and you cannot include everything here. Why? Because then you will not be able to explain the main elements to your audience. Imagine the setup so you are going to be in front of different professionals who are going to jump from one posture to the other in front of a TV. So in a short period of time you need to highlight what you want to highlight. So maybe here maybe in some parts there is a lot of content for example here on the right hand side you see a lot of different figures. In one shot you cannot describe what it is so it needs additional explanation including all these two figures. Of course you decide and it is true that you want to show your progress but at the same time you want to highlight the most important part. For example here it is great that the students decided to use a map because it is a visual way of showing in this case the balance between supply and demand. But why not instead of using different figures maybe to use different colors. Going to more kind of soft colors to more dark colors in order to show the different grades in these different variables. So it depends the message you want to send but make sure that you are sending this message in the most efficient way. For example in another case this is a very long title here supply chain is repeated twice. You don't need to use supply chain term because we are within master supply chain management. So you don't feel obligated to use supply chain term. Here a lot of content is very difficult to read all these elements almost impossible that would say a lot of details. So you need to keep balance between direct messages that will be outlaw explanatory and also include the effort that you have been doing through all these different ones. So again they are using one, two, three, four, five different diagrams. So it's difficult to catch the attention without a focal point without a picture is really difficult. And I want to add something Maria as you emphasized before. You cannot put everything in the presentation you have to prioritize what you would like to show to the audience. For example for this slide it is very crowded. There are many words that no one can catch the real idea. So if it is possible to please use some catchy maps graphs or pictures and please explain your ideas with with the proper wording. This is too much to to understand the real idea. So yeah, I just want to understand. Yeah, we understand that you want to communicate everything that you have been doing because maybe you are really excited and you have really progressed along your project with the company. This is great, but then the risk of including all this kind of content is that you are not communicating anything right so be careful with this balance is important. And our advice will be to go to your advisor to ask their feedback, go to your mates, maybe to ask them, okay, what do you think? I mean, can you follow the main flow of the of the poster? Can you really understand in a sort of time where the main highlights, right? So yeah, be careful with that. Another example here. So then again, a lot of content here with all these different diagrams. A lot of, I mean, tests here, for example, the yellow part is not easy to read so a lot of figures and graphs. So it's good that you are doing quantitative analysis and then you are showing it showing your predictive analysis, but prioritize, prioritize the most important message you want to highlight here, right? And again, the same with the title, a very long title. Yeah, and and this in this case is nice in terms of balance or nice in terms of figures and nice in terms of the weight of test within the all these different sections, but instead of using a picture, they have decided to use formula here. I think you decide, of course, but I think it is better to cut the attention with a picture that will be autosplanatory. And then that the really the the the the formula is not so important because then here you have included some results out of the formulation, right? So it's most important results that the formula and one more thing I would like to remind you of students for the for the section names, please. Keep the original ones like background motivation problem, you may want to change like here. The titles the subtitles actually according to your thesis like full full search charge definition, but it is, it doesn't make sense to the audience. Okay, because you are using background motivation and then directly to full definition. You need to do that please keep your subtitles as in their original format that we are sending you in the layouts and then make your explanation use your pictures or graphs, whatever. And the formula is not the element that we would like to see in your sections, please be careful about that. Yeah, if you want to highlight some particular time, maybe you can do it within your text. Right, but keep the sections because it will be easier for the audience to follow the same kind of structure in all of you, right? Remember, then you need to pitch to solve your project in a short, very short period of time. So then the easier the better. Okay, some key points to keep in mind. Overall, clean, simple, very visual, including chart figures, photos, but, but especially thinking about the message you want to highlight and to keep the balance between the content and these kind of messages prioritizing the most relevant ones. One more thing I want to add here. And we cannot allow you to use YouTube videos or any sounding or, you know, any animation, any effect on in your presentations, please be careful about that. You can use some animations, they can move, but it is not allowed to use any sound or any videos. Actually, you will receive by email all the instructions, more detailed instructions from the different responsibles, academic administrations, and then you will see all the different details that you need to follow. It's not difficult, but you need to follow the different instructions just to be efficient because we have a lot of students and we have a lot of posters to organize, to schedule. So yeah, it's important that that you follow the instructions. Yes, also for, for, for making sure that you will send the right message to your audience. Yeah, in terms of title as we have already mentioned, clear title, impressive highlighting what you want to highlight. And please don't use vast words that maybe are very fancy, but, but they are not really representing what you are doing because we're also with that. So the, the, the content, the technical meaning is, is, is definitely very, very important. We will prefer five words, even fewer, ideally just to, to catch the attention in a short, in a short, very short sentence. For example, here you have four different very good examples from past years that they are using in this case for words, equal, miracle, chain fulfillment. So there is some kind of action here in the title fulfillment motorcycles for last mile delivery. Inventory efficiency versus risk mitigation. So clearly they are using this tradeoff between inventory and risks reduction of total life cycle time. So they are emphasizing the reduction part right while they don't use supply chain terms as we already mentioned. So it's clear they are direct to the point where they want to show up. More points. So the central picture that is in the focal point of the poster, again, keep it simple, keep it clean, high quality picture. Easy to understand, right? Compelling and it's interesting that this very catchy. No, we will not recommend to use charts, graphs, equation or a lot of words in the picture. So the idea is just to catch the attention. Graphs use large fonts and be balanced in terms of the text that you will include in the graphs, but also make sure that you label both axes in the right way, in a proper way, in a clear way. Make sure that you are attached to the explicit sections that we have included in the format of the poster. Yeah, and don't add any additional sections or change the dimensions. It's important that you are attached to the sections and to customize the different elements inside of each section.  So we'll have some recommendations about the center picture. So it is captivating enough. Easy to understand. The quality, clear, it's not fuzzy. The title short, five or a few words. Easy to understand, especially connected with the technical points, focal point of your project and something that will be interesting for the audience. Charts and graphs, again, easy to understand. Make sure that you do the labels and units, right in the labels and be careful with the font size. Text on the poster, be careful how you balance the different sizes. It was not nice to include big sizes in one size, in one section, sorry, and the smaller in the other, right? Because it is not showing a good balance, a good harmony along the different elements. Be careful also with the number of words, not too busy, but not too light. Check your grammar is very important. We are not going to do it. So then you need to make sure that this perfectly in that sense, overall, how interesting is the poster. You can talk with your mates in order to check again and make sure that you include relevant elements. Yeah, so very quickly, December the 3rd is like a first sub-deliverable, because you need to submit some information about your poster, all these elements. So the title, only the title, but remember that you don't need to include the same title on the project. You need to include top three choices for the category, because we organize all the different posters along these categories and these different elements. So make sure that you select the most appropriate ones. So this is the list here. You can come back to the PowerPoint later or please feel free to ask whatever kind of question with your advisor in terms of this classification. The third point is to identify four key words to be associated with your poster, with your project, among all these different choices. Why? Because again, we have a repository of different documents, different projects. So just for future readers, we need to make sure that the classification is according to the main topics of your project. And the fourth point, two, three sentences for the executive summary, describing those projects. Again, this is for December the 3rd. All these four elements are December the 3rd. And then December the 14th, you need to upload your poster with all this content. And of course, all these elements that are common to the previous ones, I mean, all these elements should be according to the poster you are going to include. So, for example, don't change the title because then the two titles should be the same. We have a question here. So let me see if we are able to submit an update in January. Imagine that we are having, I mean, dozens of posters. So then of course, then we are aware that maybe you will, I mean, would like to change some minor element. But the ideal is that you will not change anything. So make sure that you progress as much as you can till December the 14th. So this is a good challenge for you. I mean, to make sure that you progress till this deadline, this milestone. Yeah, because otherwise it will be difficult and complicated. And talk with your advisor, right? I want to add something that especially be careful about your final poster title because for marketing purposes, you are using this poster title in our flyers, in our advertisement to keep the attraction of supply chain professionals. So it should be matched together. Okay, please be careful about your final poster title. You can change some small points, some small mistakes. That doesn't matter. You can ask your advisor, but we prefer to keep the original poster title and many things we are going to stop here.


So, uhhh the point I want to make is that if you compute this if you compute it and write it down you will get this inequality ok. So, let us compute it see what is uhhh so what is the expression for g. So, what is g of uhhh uhhh so g is like this g is a function of zeta and z is g of zeta alright and what is g of zeta g of zeta is just zeta plus z0 by 1 plus uhhh uhhh z0 bar zeta this is the inverse of g ok. You can check that this is the inverse to this alright and if you now now just differentiate calculate the derivative use using the quotient rule. So, you will get differentiate with respect to zeta you will get this is 1 plus z0 bar zeta uhhh whole squared uhhh 1 plus z0 bar uhhh z0 bar zeta into I differentiate this with respect to zeta I get 1 minus I keep the numerator constant I differentiate this with respect to zeta I get z0 bar and uhhh so fine.  So, I get 1 minus uhhh z0 z0 bar is mod z0 the whole squared by 1 plus z0 bar zeta the whole squared. So, you know if you calculate mod g dash of 0 which is what we want mod g dash of 0 you put zeta equal to 0 you will get 1 minus mod z0 squared okay that is what you will get for mod g dash of 0 that is the expression and then I will have to calculate what h dash of w0 is uhhh now. So, what is h of w0 h of w0 is uhhh this function uhhh uhhh so what is h of w h of w is neat it is this expression. So, h of w is just uhhh w minus w0 by 1 minus w0 bar w. So, if you calculate the derivative again by the quotient rule I will get the following denominator squared denominator constant derivative the numerator with respect to w it is going to be 1 minus numerator constant derivative denominator with respect to w is going to give you minus w0 bar okay and so expand it out I will get 1 minus w0 bar w minus so I will get plus w w0 bar uhhh minus w0 w0 bar divided by 1 minus w0 bar w the whole squared and these 2 will cancel I will simply get 1 minus uhhh mod w0 the whole squared because w0 w0 bar is mod w0 the whole squared by 1 minus w0 bar w the whole squared. So, mod h dash of 0 uhhh h dash of uhhh w0 and I have that is right I will I I should get this 1 minus mod w0 squared. So, you know now you plug in these 2 values in this equation in the in this equation and what you will get is I will get 1 by 1 minus mod w0 the whole squared that is the value of the derivative modulus of derivative of h at w0 and then I write mod f dash of z0 as it is I have to plug in mod g dash of 0 mod g dash of 0 is 1 minus mod z0 the whole squared this is less than or equal to 1 so that gives me what I want I get mod f dash of 0 is less than or equal to 1 minus mind you w0 is fz0 by 1 minus mod z0 whole squared okay and that is the uhhh that is the statement that is the that is the inequality of pix lemma okay. So uhhh and what you should understand is that uhhh uhhh now the of course this in when I do this calculation I have fixed uhhh I have simply taken z0 to be any point in the unit disc and I have taken w0 to be its image okay z0 is an arbitrary point. So, that that inequality holds for any z0 in delta and therefore I can I can replace instead of z0 I can put z by z belongs to delta and therefore I get the inequality of pix lemma okay. Now uhhh uhhh uhhh so the the only thing that I have to tell you is that you get equality if uhhh and only if f is a holomorphic automorphism of the unit disc. So, and that too for a single z0 uhhh if we get uhhh equality for a z0 then uhhh if you if you get equality if you get equality here that means you are actually getting equality here okay and uhhh but then you know in Schwarz lemma uhhh both the differential version and the original version of Schwarz lemma you always get equality only if uhhh the uhhh the automorphism is an automorphism only if the analytic function is an automorphism okay.  So, you see the uhhh what is the uhhh uhhh both the usual version of Schwarz's lemma from the unit disc to the unit disc and the differential version both are statements about inequalities okay both uhhh uhhh give you inequalities and they tell that you get an equality only in the case when the uhhh function that you are considering from the unit disc to the unit disc is an automorphism. You get equality only when it is an automorphism if it is not an automorphism uhhh by that if it is not an automorphism is supposed to be a self map okay map from a given set back to itself. So, if you have an analytic function from the unit disc to the unit disc uhhh which is not an isomorphism namely not an automorphism then you will get only a strict inequality at every point in the Schwarz's lemma statements okay and the Schwarz's lemma itself says both the differential form and the usual form of Schwarz's lemma says that if you get equality even at one point okay which is uhhh uhhh at at one point is is uhhh in the differential version uhhh if you get equality of the derivative at the origin with one modulus of the derivative at the origin with one then uhhh the function has to be an automorphism okay. So uhhh and also the earlier version uhhh the usual version of the Schwarz's lemma also says that that uhhh whenever you get an equality for uhhh point which is different from the origin okay then the analytic function has to be an automorphism. So, that condition will tell you that uhhh this h circle f circle g which is a function to which we applied the differential Schwarz's lemma that this will be an automorphism but then you can get f from this function by uhhh precomposing with h inverse on the left and post composing with g inverse on the right okay and uhhh uhhh uhhh and that is possible because h and g are of course Mobius transformations they have inverses and therefore it so this is an isomorphism uhhh this is this is an isomorphism this central thing is an isomorphism this is also an isomorphism composition of isomorphism is again an isomorphism. So, you will get f is an isomorphism so that proves Picks lemma okay. So, Picks lemma tells you that you will get equality here for a single z not if and only if you get equality there for all z for all z not for a for every z okay and that will happen if and only if the function f is an automorphism. So, if you uhhh so in other words if f is not an automorphism unit disc then there will be strict inequality here it will mod f dash z not is strictly less than uhhh this quantity on the right side okay. So, this is Picks lemma and as you can see it is just a generalization of the differential version of Schwarz's lemma because in this if I put z not equal to 0 I get the differential version of the Schwarz's lemma which says the modulus of the derivative at the origin cannot exceed uhhh uhhh uhhh uhhh uhhh uhhh you know it cannot exceed 1 okay. If I put z not equal to 0 and assume that f takes 0 to 0 that is if I put z not equal to 0 and assume that f of z not is also 0 then if you put that here you will get mod f dash of 0 is less than or equal to 1 that is the differential version of Schwarz's lemma. So, uhhh uhhh Picks lemma is just a generalization of the differential version of Schwarz's lemma okay but the point is that it is the key to uhhh so called hyperbolic geometry on the unit disc which is what we have to study okay. See so let me uhhh let me again remind you uhhh what we did earlier was that you know we were uhhh we are we are on our way to prove the Riemann mapping theorem okay and the Riemann map in the Riemann mapping theorem what we have what we are supposed to do is we are supposed to start with a simply connected domain which is not the whole complex plane and you are supposed to map it holomorphically isomorphically onto the unit disc. The first step that we achieved was to map it holomorphically isomorphically onto a sub domain of the unit disc okay. So, this was possible uhhh because uhhh it because uhhh the the domain was simply connected in the and it was not the entire complex plane okay. So, we reduced the mapping problem to a sub domain of uhhh simply connected sub domain of the unit disc okay alright. So, you have to now we are reduced to proving that given any simply connected sub domain of the unit disc you can map it conformally onto the unit disc okay. So, our problem is completely reduced to studying sub domains of the unit disc and so in other words you have to study the unit disc carefully and how we are going to do it or the way we are going to do it which will help us is study hyperbolic geometry of the unit disc and the hyperbolic geometry depends on so called hyperbolic metric and the hyperbolic metric the key to the hyperbolic metric is the Picks lemma. So, which is a uhhh nice generalization of Schwarz's lemma okay the differential form of Schwarz's lemma. So, you know that is how this enters into the discussion of the proof that we are looking at of the Riemann mapping theorem alright. So, now we go on to study hyperbolic geometry. So uhhh so let me do that. So, this is hyperbolic geometry on the unit disc delta. So, this is this is open unit disc centered at the origin radius 1. So, you know so you see so let us begin by uhhh uhhh recalling certain facts. You know if you have uhhh uhhh so suppose this is a complex plane and suppose you have uhhh an arc suppose you have a piecewise smooth arc or a contour which is just uhhh image of uhhh the unit interval uhhh or or uhhh any close interval on the real line by a function gamma which is piecewise a differentiable okay and which is continuous okay and such that the uhhh derivatives are also piecewise uhhh the derivative is also continuous okay. So, so if you take a contour from uhhh this point which is gamma of a starting point to gamma of b this is my path gamma or contour. Then you know how to get the length of gamma length of gamma and I will stress it I will say I will put in I will just prefix it by Euclidean okay because this is the length in the usual sense arc length. You know what is the formula for the Euclidean length of gamma or all you have to do is you simply have to integrate over gamma mod d z this will give you the length of gamma alright. And what is that integral I mean it is this integral is well you can also substitute you can this is from you know uhhh t equal to a to t equal to b uhhh uhhh modulus of d gamma t and that will be just uhhh that will be just integral from a to b uhhh mod gamma dash of t into mod dt okay and of course t is increasing. So, you do not have to put this mod here. So, this is the this is the Euclidean length of a of an arc okay. Now what we are going to do is we are going to take a special case uhhh we are going to look at this arc uhhh we are going to look at such arcs or contours inside the unit disc okay. So, you are going to have situation like this you have this uhhh closed interval a b finite closed interval on the real line and you are going to have this path or contour gamma and see the point is that this gamma lines inside the unit disc. So, you know it is something like this. So, this is the unit disc delta and uhhh this is the complex plane again alright and now I am going to again this is gamma of a this is gamma of b and this is my path gamma. And what I am going to do I am going to something uhhh new uhhh instead of defining the Euclidean length of gamma which you know is this you integrate mod dz over gamma. I am going to define the hyperbolic length of gamma okay that that is that is that is only in the special case when the path is a path in the unit disc okay. So, so here is the definition hyperbolic length of gamma is you see what you do it is also an integral over gamma okay. See if I put integral over gamma and put mod dz I will get the Euclidean length okay if I put integral over gamma and and if I integrate mod dz I will get Euclidean length but what I will do is I will integrate mod uhhh I will integrate 1 by 1 minus mod z the whole square into d mod dz. So, I am I am adding this factor 1 by 1 minus mod z the whole square which is the uhhh which is the hyperbolic factor okay. So, this is called the hyperbolic length of gamma okay. Now what is so special about this expression the special thing about this expression is you see if I now take f to be an automorphism holomorphic automorphism of the unit disc that is it is a map from the unit disc to the unit disc which is holomorphic injective bijective holomorphic. So, it is inverse is also holomorphic. So, it is a holomorphic automorphism unit disc to unit disc and then you know so what will happen is this you know this this f will map uhhh so this is my uhhh so this is the map w equal to fz okay and uhhh so this is the z plane and here I have the w plane alright and what is going to happen is that because f is an automorphism uhhh one to one onto inverse is also holomorphic what is going to happen is that the image of this path is also going to be a simple path is also going to be a path inside the unit disc.   So, I get this so the path gamma is mapped by f isomorphically onto the path f circle gamma now now you see the beautiful thing you calculate the hyperbolic length of f circle gamma okay what is the hyperbolic length of of f circle gamma well it is by definition integral over f circle gamma of mod dw by 1 minus mod w the whole square this is the definition of hyperbolic length where I am using the fact that uhhh my my variable here is w and the variable here is z so I am using correct variable alright. But you see uhhh watch carefully what is uhhh uhhh so now comes now comes the you know importance of pix lemma okay now comes the importance of pix lemma you see what does pix lemma say see by pix lemma what you will get is mod f dash of z is is equal to 1 minus mod f z the whole square by 1 minus mod z the whole square for all z in the unit you get this you get equality in pix lemma because f is an automorphism of unit disc pix lemma says that you get the inequality of pix lemma will become an automa will become inequality if the map is an if and only if the map f is a automorphism okay you get this. But then you see see in this the in this integral you know I can make change of variable by putting w equal to f z if I make a change of variable then this integral is the same as integral over gamma okay mod d f z by 1 minus mod f z the whole square okay. But what is this this is integral over gamma uhhh d f z is f dash of z d z so I will get mod f dash of z mod d z by 1 minus mod f z the whole square this is what I get okay if I make a simplification if I make change of variable from w to z using w equal to f z I will get this. But what is this equal to by by pix lemma mod f dash of z by 1 minus f z the whole square is simply 1 by 1 minus mod z the whole square therefore what you get is this is the same as this these 2 are equal these 2 are this this this expression is the same as this expression because of pix lemma because of the equality in pix lemma which comes because f is an automorphism unit disc alright. So what is the moral of the story the moral of the story is the following the moral of the story is if you define the hyperbolic length of an arc or contour in the unit disc the hyperbolic length will not change if you apply an automorphism of the unit disc whether you take the hyperbolic length of gamma or whether you take the hyperbolic length of its image and an automorphism unit disc you will continue to get the same length the same hyperbolic length therefore the so we expresses by saying that pix lemma the equality in pix lemma actually asserts that for the automorphisms of the unit disc preserve the hyperbolic length the equality in pix lemma assert that you know automorphisms unit disc preserve the hyperbolic length ok. So let me write that down the automorphisms the holomorphic automorphisms of delta preserve the hyperbolic length so this is the this is a geometric you know statement concerning the equality in pix lemma ok and that is the importance of this expression instead of just integrating over mod dz which will give you the Euclidean length you integrate over mod dz by 1 minus you integrate mod dz by 1 minus mod z the whole square ok that is the that gives the hyperbolic length right. Now you know you know the hyperbolic length is I mean the unit disc is anyway as far as Euclidean space is concerned or the that is the plane is concerned the unit disc is bounded and you know if you take the ordinary length the ordinary length between any 2 points is going to be finite of course it cannot exceed 2 which is the diameter of the unit disc right if you take a straight line segment the length is less than 2 ok but what about hyperbolic distance so you know you can we can it is rather curious we can make a computation you know if you take the unit disc and you know take a point 0 take the point z ok take this straight line joining 0 and z ok and then try to calculate what this length is what is Euclidean length Euclidean length so you know to calculate Euclidean length first of all I need a parameterization I must think of this as a path so you know what I do is I just map 0, so if z suppose I call this point is z0 and z0 is r0 into e power i theta0 ok where r0 is this length which is actually the Euclidean length and theta not is this angle so this angle is theta not and this length is r0 from here to here ok then you know you know how to parameterize this path so this path can be parameterized as 0, r0 map to you just map 0, r0 to t well to the unit disc by simply sending t to t e power i theta not ok when you put t equal to 0 you will get the origin when you put t equal to r0 you will get z0 and you will get this straight line segment joining the origin to z0. So this is your path gamma now the straight line segment from 0 to z0 where z0 is a point of the unit disc what is the Euclidean distance Euclidean length of gamma is going to be integral over gamma mod dz by 1 minus mod z the whole square this is the sorry this is I should not put 1 by this it is just mod dz so what I will get is well if I substitute for the expression for gamma of t so z is gamma of t so I will get t equal to 0 to r0 and I will get here mod d of gamma of t but gamma of t is t e power i theta not ok and if I simplify this I will get integral 0 to r0 I have to differentiate this I take differential and the variable of integration is t so I will get I differentiate this with respect to t which will give me e power i theta not and then I will get dt and then I will have to put a mod and of course mod e power i theta not is 1 so I will simply get integral dt from 0 to r0 and I am going to get r0 which is what I expect the length of this straight line segment from 0 to z0 is r0 which is Euclidean length ok. Now let us calculate the hyperbolic length what is the hyperbolic length and of course I should tell you that of course r0 is strictly less than 1 because z0 is a point of the unit disc r0 is strictly less than 1 alright but what is a hyperbolic length of gamma hyperbolic length of gamma well it is integral over gamma mod tz by 1 minus mod z the whole square so this is the this is the formula for the hyperbolic length ok. So if you calculate that so you will get what is that so well I will get integral from 0 to r0 so I again substitute this I will get mod d d of t e power i theta not by 1 minus mod t e power i theta not the whole square this is what I will get so I will get integral from 0 to r0 as usual this is going to give me dt alright so and the denominator I am going to just get 1 minus t square ok and you know how to integrate this you split it as partial fractions you know it is 1 by 1 minus t minus 1 by 1 plus t if I am not wrong maybe I should put a plus here let me I will get 1 plus t plus 1 minus t it is 2 by 1 minus t square so I will have to divide by 2 so this is what I will get dt and you know what this is going to give me this is going to just give me so this is this is half 1 by 1 minus t is log 1 minus t so this is ln if you want ln of course t is less t is positive so this is ln 1 minus t into minus 1 and here I am going to get plus ln of 1 plus t and I am going to take limits from 0 to r0 so this is just ln 1 plus t by 1 minus t alright so I am going to get half ln 1 plus r0 by 1 minus r0 this is the hyperbolic length so the hyperbolic length the Euclidean length is r0 ok this is the modulus of z0 whereas the hyperbolic length is you have a fine expression it is half ln 1 plus r0 by 1 minus r0 and now you can see something the Euclidean length is finite ok it is bounded by 1 but you know if z0 tends close to the border of the unit disc ok if z0 gets close to the boundary of the unit disc then r0 gets close to 1 and as r0 gets close to 1 this approaches infinity ok I mean this denominator approach is 0 alright and therefore this quantity approach is infinity because r0 is going to tend to 1 from the left ok so this is going to approach 0 plus so this quantity is going to approach infinity plus infinity and ln of that is going to go to plus infinity so the moral of the story is the hyperbolic length will tend to infinity as the point z0 moves to the edge of the unit disc it as it goes to the unit circle ok so you know the so this is the beautiful fact about the hyperbolic length. The hyperbolic length makes this in as far as the hyperbolic distance is concerned this is not this is not this is not a bounded thing the unit disc is not bounded ok that is even the straight even the even a segment if you take straight line segment if you compute radial segment its length tends to infinity in the hyperbolic distance if the if the end point goes closer and closer to the unit circle so this is the point about the hyperbolic metric it makes the hyperbolic distance it makes this in the in the sense of in the sense of the hyperbolic distance it makes unit disc unbounded ok so that is one fact that you have to notice alright so well now you know I have to so I will tell you that what is what is it that we need actually we are looking for a statement like this we are looking for a statement which says that if you take any analytic function from the unit disc to the unit disc then if it is not an automorphism unit disc then it acts like a contraction ok so what I have defined so you know to define the notion of a contraction I will tell you what a metric what a metric is because you know a contraction map is defined between metric spaces it is defined from one metric space to another and a mapping is said to be a contraction map if you know it decreases distances you take two points in the in the source space they have certain distance but you take the images and then you measure the distance the distance becomes smaller so if this happens for a map it is called a contraction map and essentially the statement that I need for the proof of the Riemann mapping theorem is a statement that if you take a analytic map of unit disc to itself which is not an automorphism then it will necessarily be a contraction map but contraction with respect to what metric it is with respect to the hyperbolic metric which I am going to define now ok what I have defined so far is just hyperbolic length of an arc in the unit disc I am going to define the hyperbolic distance between two points in the unit disc ok so let me do that next so so hyperbolic metric on the unit disc so here is the so here is the definition of hyperbolic metric so here is my unit disc ok and of course here also I should have marked this as 1 here I should have marked it as 1 as well this is the origin alright so you know take two points in there in the unit disc alright take two points in unit disc and what you do is the following for z0 z1 delta define the hyperbolic metric so hyperbolic metric or hyperbolic distance function the distance from z0 to z1 and I am using the symbol rho ok to be you know maybe I will use rho sub h to insist that this hyperbolic and you know what I do I do the following thing simply join from z0 to z1 you choose any path contour gamma measure its hyperbolic length and then minimize over all such possible paths so the hyperbolic distance from z0 to z1 is the least is the least of hyperbolic length of paths from z0 to z1 various paths from z0 to z1 inside the unit disc you measure their hyperbolic lengths and then you take the minimum you take the infimum in fact ok so here is the definition this is equal to infimum of hyperbolic length of from z0 to z1 in the unit disc ok so this is the this is the this is the hyperbolic metric so in other words this is infimum over all gamma such that the hyperbolic length is given by integral over gamma mod dz by 1 minus mod dz the whole square this is the hyperbolic metric where of course gamma of such that gamma is a path in the unit disc from z0 to z1 so this is the hyperbolic length ok ok so you know I am taking of course all all lengths all these integrals are non-negative and you know so this infimum does exist right but what is it what is this infimum and you know does the infimum the infimum value does it correspond to actually length of a particular path that is the question and the answer is yes given any two so here is the important statement about hyperbolic geometry so given any two points in the unit disc there is a special path from passing through from this between these two points which is called hyperbolic geodesic it is the path of shortest hyperbolic length from I mean between the two given points and what is that path the answer to that is the path is a circle passing through those two points which is orthogonal to the unit circle ok so that is the theorem so the theorem is here is a very important theorem the theorem is for any two for any two points z0 not equal to z1 in delta the arc of the circle through z0 and z1 and orthogonal to the unit circle ok is the unique path of minimal hyperbolic length from z0 to z1 so this is the theorem so the theorem is that what is this hyperbolic distance it gives you see the hyperbolic distance is defined by some minimization it is the minimum you are supposed to take all possible paths inside the unit disc from z0 to z1 measure their hyperbolic lengths and take the minimum ok which seems a very it is not a it is not a definition that will help you to make calculations because you have to find minimum but the theorem makes it clear it tells you what is that path which will give you the minimum hyperbolic length that path of minimum hyperbolic length is nothing but the arc of a circle passing through these two points and which is orthogonal to the unit circle namely it is where it hits the unit circle it will hit at 90 degrees ok you know two you can also talk about the angle between two curves at a point at an intersecting point it is by definition the angle between their tangents at that point so we say two circles are orthogonal if they intersect at say two points and at each point of intersection the tangents to the two circles are perpendicular to each other alright so you know so the picture is like this you know if I take the unit circle if I take the unit disc you know if I take a point if I take a two points like this ok then you know my hyperbolic geodesic will be something like this it will be this will be the geodesic from here to here and that is because this is the circle which passes through these two points ok and which hits the unit circle at 90 degrees so you know so this is z0 this is z1 and at this point if I draw the tangent to the given to this circle and the unit circle this will be 90 degrees similarly here if I draw the tangent from here and here this will be another 90 degrees so this will be the hyperbolic path and the beautiful thing is that you know if you draw all these hyperbolic paths of paths of minimal hyperbolic lengths which are called geodesics you will get things like this see so you know if you you know if you take if you take two points along the along a diameter ok then the hyperbolic geodesic will be the diameter itself any diameter is a geodesic because if you take two points if you try to find a circle passing through two points which lie on a line in principle there is no circle but you think of it as a circle with you think of also straight lines as circles with the third point at infinity ok so if so the point is that the geodesics will look like this you know this will be one geodesic any diameter will be geodesic then you know if you go a little to the left the geodesics will become like this and you know if you go get smaller the geodesic will be smaller this is how the geodesic will look like ok. And the fact is that you need a diameter will be a geodesic ok and the theorem says that these are the paths of shortest length that is how you get the paths of shortest length so this is a theorem that we will have to give a proof of and we will do that in the next lecture. So let me write let me add here paths of shortest hyperbolic length are called geodesics for the hyperbolic metric and so let me finish with one important statement you see if you are looking at the Euclidean distance Euclidean metric okay then the geodesics are all straight lines okay if you take any two points in Euclidean space what is the shortest what is the path of shortest length it will just be the line segment joining those two paths straight line segment. So the geodesics in the Euclidean metric they are just straight lines okay alright and straight lines are important for Euclidean geometry right in the same way these geodesics that we get for the hyperbolic metric okay they will play the same role as straight lines play for Euclidean geometry okay so all the axioms except the parallel axiom that hold for straight lines I mean parallel axiom also holds for it is also taken for Euclidean geometry but this all those axioms will work with the geodesics for the hyperbolic metric except that the parallel axiom you have to throw out the parallel axiom okay all other axioms that you have for straight lines okay the same axioms will hold good for the hyperbolic geodesics so the so all these curves on the unit disc they are the analogs of straight lines on the Euclidean plane the analogs of the straight line on the Euclidean plane which are important for Euclidean geometry the analogs here are these curves the hyperbolic geodesics and you know you can check a lot of statements like you know if you take two lines if they are not one and the same and of course you know if they are not parallel then they will intersect at you know one point one point in the finite plane and of course if you think of infinity as a point then they will also intersect infinity alright and the same way here also you can check that if you take two geodesics which are not you know one and the same they will they will hit at one point okay and if you take three lines you can use three lines to form a triangle and every triangle is formed by three lines okay which are the lines are passing through the lines the sides of the triangle in the same way you can also define hyperbolic triangle a hyperbolic triangle will be something like this you know so you know I can so if I draw a hyperbolic triangle it will be like this it is given by three hyperbolic geodesics so one like this one like this and one like this so this is a hyperbolic triangle okay and you know that in Euclidean geometry the sum of three angles of a triangle is equal to 180 degrees what will happen in hyperbolic geometry is that the sum of three angles of a hyperbolic triangle will be less than 180 degrees okay and so you will have all these nice things happening differently from what you know in Euclidean geometry so hyperbolic geometry will give you new set of properties okay and the basis for all this is the so called hyperbolic length which is defined for a for an arc but the key to the fact that the hyperbolic length does not change under an automorphism of the unit disc is the equality in pix lemma okay so pix lemma the equality in pix lemma is a bearing point for a whole geometry okay and what and now I will now let me tell you if you take this hyperbolic metric then if you take any automorphism from the unit disc to the unit disc any automorphism unit disc to the unit disc will be an isometric with respect to the hyperbolic metric okay that is what you will get okay so the whole beautiful point about pix lemma will be that you know any automorphism unit disc will actually be an isometric of the hyperbolic distance of the hyperbolic metric and any map which is not an automorphism unit disc will be a contraction with respect to this hyperbolic metric and that is a statement that we need to proceed with the proof of Riemann Riemann mapping theorem okay which we will do in the next lecture.