From the CUBE studios in Palo Alto in Boston, connecting with thought leaders all around the world, this is a CUBE Conversation. Well, happy new year. One and all, welcome to 2021 and CUBE Conversations continuing our ongoing series. I hope your new year is off to a great start. And I know that the end of 2020 was a very good one for Avante. And Jim Shaper, who's the CEO, is going to join us to talk about that as is Nayaki Nayar, who is the EVP and the Chief Product Officer. So Nayaki and Jim, good to have you with you on the CUBE and happy new year to you. Thank you, John. Happy new year to you in 2020. I think for a lot of us couldn't get out of here quick enough, although we had some great things happen to our company at the very end of the year. So anxious to talk to you about it and appreciate the opportunity. Oh, you bet. So we're talking about some two major acquisitions that you made that both closed near the end of the year back in December, not too long ago. One with Pulse Secure, the other of Mobile Iron, two companies that provide you with additional expertise in terms of mobile security in the enterprise security space. And so Jim, if you would, let's first talk about just for the big picture the acquisitions that were made and what those moves will do for you going forward. Okay, great, John. We closed both acquisitions interestingly enough on December 2nd. So we've been fortunate to have them part of our company now for about the last 30 days. One of the things that we made a decision on a number of months ago was that we had a real opportunity in the markets that we serve to really build our business more quickly through a series of acquisitions that strategically made sense for us, our investors, and more importantly, our customers. And that really is why we chose Mobile Iron and Pulse for different reasons, but nonetheless, all very consistent with our long-term strategy of securing the endpoints on every network in every location around the world. And so consequently, when you think about it, and we've all witnessed here over the last 30 days or so, all of the security breaches, all of the things that go along with that, and our real focus is ensuring that every company and every individual on their network, outside their firewall, inside their firewall, on any device is secure. And so with these two particular acquisitions, in addition to the assets that we already had as a part of Avanti, really puts us in a competitively-advantaged position to deliver to the edge, and Niyaki will talk about this, the ability to secure those devices and ensure that they're secure from phishing expeditions or breaches or all of those kinds of things. So these two particular acquisitions really puts us on the map and puts us in a leadership position in the security market. So we're thrilled to have both of them. Yeah, before I go off to Niyaki, I want to follow up just on a point that you made, Jim, talking about security breaches. We're all well aware of the news of what we've been hearing from the federal level about the state actors and the kind of these infiltrations of major US systems, if not international systems. Some Interpol data, I read, 270 some odd percent increase in breaches just in the post-COVID time or in the COVID time the past year. That gets your attention, does it not? And what does that say to you about the aggressive nature of these kinds of activities? Well, that they're getting more sophisticated every day and they're getting more aggressive. I think one of the most frightening conversations I had was a briefing with our chief security officer about how many attempted breaches of our network and our systems that he sees every single day. And that we're able to identify what foreign actors are really trying to penetrate our systems. What are they trying to do? But the one thing I would leave you with is they're becoming much more sophisticated. Whether you're inside the firewall or whether you're on your iPhone as an extension of the network, the level of sophistication is startling. And unfortunately, in many cases, as evidenced by the recent breaches, you don't even know you've had a breach for could be months, weeks, days, and so what damage is done? And so as we look forward and as Nyaki kind of walks you through our product strategy, what you're going to hear a lot of is how do we self-protect? How do we self-learn the devices at the edge on the end of the networks, such that they can recognize foreign actors or any breach capability that somebody is trying to employ? And so yeah, it's frightening how sophisticated and how frequent they have become. I think the one thing that really struck me as I read about the breaches was not so much the damage that has been done, but the damage that could be done prospectively and about which we have no idea, right? You don't know, it's like somebody lurking in your closet and they're going to stay there for a couple of months and wait for a time that maybe your guard is even more down. So that's what shocks me. Nyaki, let's talk about your strategy then. You picked up obviously a couple of companies, one in the enterprise IT space, another one in the VPN space, adding to your already extensive portfolio. So I imagine from your office or wearing the hat of the chief product officer, you're just kind of licking your chops right now. You've got a lot more resources at your disposal. Yeah, we are very, very busy, John, but to Jim's point, one of the trends we are seeing in the market as we enter into the post-COVID era, right? Where everyone is walking from anywhere, be it from home, be it from office, while on the move. Every organization, every enterprise is struggling with this, what we call this explosive growth of devices, devices being mobile devices, client-based devices, IoT devices, the data that is being generated from these devices. And to your point, the cybersecurity threats, right? It is predicted that it has been 30,000% increase in the cybersecurity threats that are being targeted primarily at the remote workers. So you can imagine whether it's phishing attacks, malware attacks, I mean, just this explosive growth of devices, data, cybersecurity attacks at the remote workers. So organizations need automation to be able to address this growth and this complexity, which is where Ivanti's focus in discovering all the devices and managing those devices. So as we bring the mobile line portfolio and Ivanti's portfolio together, now we can help our customers manage every type of devices, be it Windows devices, Mac devices, Linux, iOS, Android devices, and secure those devices. There's zero trust access that users need, the remote users need all the way from cloud access to the endpoint is what the strength of both mobile line and pulse brings to our entire portfolio holistically. So we are truly excited for our customers. Now they can leverage our entire end-to-end stack to discover, manage, secure, and service all those devices that they now have to service for their employees. Yeah, I mean, explain to me or just walk me through zero trust in terms of how you define that. I've read about, trust nothing, verify everything, those kinds of explanations, but if you would, from your perspective, what does zero trust encompass? Not only on your side, but on your client side, because you then want to give them tools to do things for themselves, to self-heal and self-serve and those kinds of things. Right, so I mean, zero trust is you don't trust anything, you validate and certify everything. So the access users have on your network, the access they have on the mobile devices, the applications they're accessing, the data that they're accessing. So being able to validate every access that they have when they come into your network is what the whole zero trust access really means. So the combination of Ivanti's portfolio and also pulse, that zero trust access all the way from as users are accessing the network data, cloud data, endpoint data is where our entire zero trust access truly differentiates. And as we bring that with our UEM portfolio with the mobile line, there's no other vendor in the market that has that holistic offering into an offering. You know, John, it's interesting, John, you talk about timing is everything, right? And when we began discussions with mobile iron, it was right before COVID hit. And we had a great level of expertise inside the pre-acquisition of Ivanti to be able to secure the end points at the desktop level. But we struggled a bit with having all of the capabilities that we needed to manage mobile devices and tablets and basically anything that is attached to the network. That's what they really brought to us. And having done a number of acquisitions historically in my career, this was probably the easiest integration that we had simply because we did what they didn't do and they did what we didn't do and then they brought some additional technologies with us. But what's really changed in the environment because of this work from home or work from anywhere as we like to articulate it is you've got multiple environments that you've got to manage. It isn't just what's on the end of the VPN, the network. It's what's on the end points of the cloud. What kind of cloud are you running? You're running a public cloud, you're running a private cloud. Is it a hybrid environment? And so the ability to and the need to be able to do that is pretty significant. And so that's one of the real advantages that both the pulse as well as the mobile iron acquisitions really brought to the combined offering from a product standpoint. Well, yeah, I'd like to follow up on that then just because the cloud environment provides so many benefits obviously but it also provides this huge layer of complexity that comes on top of all this because you just talked about it. You can have public, you can have hybrid, you can have on-prem, on-prem, whatever, right? You have all these options. And yet you, Avante, are having to provide security on multiple levels and multiple platforms and multiple environments and how much more complex or challenging is your mission now because of consumer demand and the capabilities that technology is providing your clients? Well, it's certainly more complex and NIACI is better equipped to probably talk in detail about this. But if you just, if you take a step back and think about it, you think about internet of things, right? I used to have a thermostat and that thermostat was controlled by the thermostat on the wall. Now everything is on Wi-Fi. If I've got a problem, I had a problem with a streaming music capability which infected other parts of my home network. And so everything is, that's just one example of how complicated and how wired everything has really become except when it comes to the mobile devices which are still always remote. You've always got it with you. I don't know what it was like for you, John, but historically I've used my phone for email, texts, and phone calls. Now it's actually a business tool, but it's a remote business tool that you still have to secure, you still have to manage, and you still have to find and identify on the end of the network. That's where we really come into play now. NIACI, anything you want to add to that? Yeah, so to Jim's point, John, and to your question also, as customers have what we call the multi-cloud offering, right? They have public clouds, private clouds, on-prem data centers, devices on the edge. And as you extend into the IoT world, being able to provide that seamless access, this is Zero Trust Access all the way from the cloud applications to the applications that are running on-prem, in your data centers, and also the applications that are running on your devices and the IoT applications is what that entire end-to-end Zero Trust Access is where our competitive strength resides with Pulse coming into our portfolio. Before Ivanti didn't have this, we were primarily a patch management vendor in the security space, but now we truly extend beyond that patch to this end-to-end access all the way from cloud to edge is what we call. And then when we combine that with our UVM portfolio in our endpoint management with Mobile Line, and also service management, that convergence across the people access where we truly differentiate and compete and we're in the market. Mayakhi, how does the internet of things factor into this? Cause I look at sensor technology, I'm just thinking about all the billions of inputs that you have now, right? With whether it's farming or agricultural inputs, business inputs, meteorological, whatever. So you've, I'm sure, you're considering this as well. It's part of a major play of yours in terms of providing IoT security. Absolutely. How more proliferated is that now and how much of that is kind of in your concern zone, you might say. Yeah, absolutely. So just taking this trends we have in managing the end points, you will extend that into the IoT world also, John, when we say IoT world, in the industry what it was like healthcare devices. So stay tuned in January release, we'll be releasing how we will be discovering, managing and securing for the healthcare devices like seamless devices, Bayer's devices, Canon devices. So you're spot on how we can leverage this trend we have in managing end points to also IoT devices, that same capabilities that we can bring to each of the industry verticals. Now we're not trying to solve the entire vertical market, but certain industry verticals where we have a strong footprint, healthcare is a strong footprint for us, healthcare is a strong footprint. So that's where you will see as extending into those IoT devices too. Okay, so in going forward, Jim, if you would just, let's talk about your 2021 in terms of how you further integrate these offerings that you've acquired. Right now all of a sudden you've got 30 days of, which is a snap of a finger. But what do you see how 2021 is going to lay out, especially with distributed workforces, right? We know that's here. That's a new normal with a whole new set of demands on networks and certainly the need for security. That's exactly correct, John. I mean, everything has changed and it's never going back to the way it was. Everybody has their own definition of the new normal. I guess my definition is at some point in time when things do return to some form of normality, a portion of our workforce will always work from home to what degree remains to be seen. And I don't think we're different than virtually any other industry or any other company. So it does put increased demands, complexity and requirements around how you run your internal IT business. But as Naaki talked about kind of our virtual service desk offering where you're not going to have a service desk anymore. It's got to be virtual. Well, you have to be able to still provide those services outside of your normal network. And so that's going to be a continued big push for us. I've been incredibly pleased with the way in which the employee bases of the acquired companies have really folded in and become one with our company. And I think as we all recognize cultural differences between organizations can be quite significant and an impediment to really moving forward. Fortunately for us, we have found that both of these organizations fit really nicely from an employee, from a values perspective, from a goals and objectives perspective. And so we did most of the heavy lifting on all the integration, shortly after we closed the transactions on the second of December. And so we've moved beyond what I would call the normal kind of concerns and angst around what's going to happen in this and that. We're now kind of heads down and what's the long-term integration going to look like from a product standpoint. We're already looking at additional acquisitions that will continue to take us deeper and wider into our three product pillars as Nayaki described. And that'll be an ongoing kind of steady dose of acquisitions as we continue, excuse me, supplement our organic growth within organic growth. Well, you got to answer my question that I was going to ask you. I found that the company four years ago, there were two big acquisitions back in 2017. We'd wait four years, Jim, until you get back into that poll again. So the plan maybe not to wait another four years before moving on. No, trust me, you won't be waiting another four years. Now you got to bear in mind, John, I wasn't here four years ago. That's right, right. Okay. Fair enough. Fair enough. Excuse me for your coffee. That's okay. I want to thank you both for the time today. Congratulations on sealing those deals back in December. And we certainly wish you all the best going forward. And of course, a very happy and a very safe new year for you and yours. Same to you, John. Thanks so much for the time. And so it was a pleasure to spend time with you today. Thank you, John. Happy new year again. Thank you. Thank you.


Good morning, good morning. Welcome to the University of Michigan. I'm looking out at an incredibly talented, intelligent, creative group of people. I know that because we have outstanding faculty here. And our faculty have a very high bar for the students they consider and the students they admit. So congratulations on being admitted to graduate school here. And we're so delighted that you've joined us. I want to tell you a little story. It's a story about two graduate students and a professor who were walking across our diag one day. And they came across an oil lamp. And what do you do when you find an oil lamp? You rub it. And what happens? A genie pops out. So this genie pops out. This happens all dressed in maize and blue. And the genie says, you know, traditionally, we give three wishes. There are three of you. I'm going to give each of you one wish. And the first graduate student gets really excited and says, genie, I want to be on a beach in Tahiti. Genie says, sure. And poof, the graduate student is gone. So now the second graduate student gets really big eyes and says, I want to be hella skiing in the Canadian Rockies. No problem, says the genie. Poof. And that graduate student is gone. And the genie turns to the professor and says, what about you? What do you want? And with a twinkle in her eye, she says, I want those two back in the lab right after lunch. Now, like all good stories, there's a grain of truth to this story.  Your professors are going to push you. But they're also going to encourage you and guide you and help you and cheer lead. So work closely with them. And if you do that, what I can almost guarantee will happen is that you'll come upon what Richard Feynman, the physicist called the kick of discovery, that magical moment when you come to understand and see something that no one else before has ever understood or seen. And the rewards will be enormous. The other thing I want you to do, I want you to work incredibly hard, but I want you to remember to find at least a little bit of time for interest outside of your studies, for your family, for your friends, for outside activities. Even the professor in my story didn't have the students come back right away. She gave them the morning off. So welcome to Michigan. Work hard. Find that kick of discovery. And have a great time here. It's now my great pleasure to introduce the 14th president of the University of Michigan, Dr. Mark Schlissel. Dr. Schlissel, we'll talk to you for a second. I was going to tell you a little bit about him. He got his undergraduate degree from Princeton. And his MD and PhD from Johns Hopkins University, where after a postdoc, he was on the faculty. He then joined the faculty at Berkeley, where he became dean of the biological sciences and went on to Brown University, where he served as provost before joining us here at Michigan this past August. Today, he is not only president, he is also professor of microbiology and immunology in the College of Medicine, and professor of molecular, cellular, and developmental biology in LSNA. Please welcome President Schlissel.


L-literally. Okay, okay, stop booing. Ladies and gentlemen, welcome back to the channel and I'm so excited today because it is getting crazy. We had Sanji versus Virgo. We had Louvi versus Caesar. And we're starting to find out Law's true plan here and that's to get into whatever sad is. Because supposedly whatever is in sad or whatever sad is, is going to shake up the new world. And he's in the room with it right now.  Thank you. And let's get started. Oh thank goodness we start with this, bro. I mean, if this is just two episodes of him just walking through this room, I wouldn't be shocked though. What is sad? I'm still riding on the guess that D is dinosaur. Wouldn't be far off from dragons, man. And the question is, is it like a creature? Is it a gas? Is it poison? Is it just a gun? Imagine if it's just like a revolver. It's like the ultimate weapon. But they're not gonna get in. Yeah. Oh my, wait they actually didn't get in. Sanji! Oh my god, wait watch him kick through it. But then it endangers them. Let's go baby! When did he get through? Oh my gosh. Cutie San. He's lucky he had a badass moment last time. His leg. Oh shoot, he's like actually injured injured. I'm glad they're kind of hanging on to that though. Cause it literally cracked. That's what I said. If he kept biting he would have lost. Oh my god, it hurts to look at. Like my shin hurts. Can she explain to them what's going on? Like she knows. What? What is she doing? Maybe she thinks that this isn't the right scenario to tell them? I don't know. What's the point of lying? Make them fight for something and not question everything they've ever known? And now Sanji is like I'll just go along with it cause I think he knows the truth too. Like that's him. See now they stay inspired. Yeah, they will feel all dejected that everything they've known has been a lie. I guess that's smart. What is that? Oh shoot. Oh shoot. Oh shoot. The New World Dressrosa. Don't flab me. Go. Treat him as my younger brother. Yeah, I'm a rocker joker yet. Oh shoot. S.A.D. manufacturing. Oh, what? What the? What is going on? Destroy that. Is that what he's going to do? Who is this? What's happening here? Oh my gosh. Is her arm turned into the gun? He just took it. Kill Caesar? What? Oh my. Produce. Oh. Who is that? Bro. No one else. Oh, it's a gas. It is a gas. Ruin my business. Baby five. He's still just sitting there. There's so much happening. I don't even know what I'm looking at. Wait, really? Laws rebelling. I love Doflamingo's voice so much. Oh my gosh. So Doflamingo has known law for a very long time. Yeah, sure. Try killing law. That way he has his heart. That might be a little easier than I thought. Boy, Cisto is going for it. There's no way he makes her shoot herself. Oh my gosh. Dude, this is some insanely big scheme. Oh, huh? You best know. Higher caliber. He sees him as a higher caliber law just because of conquerors, Hagi. I mean, it makes sense because it's so rare. Caesar's like, I fought him? Bro, this is crazy. Baby five and Buffalo. Oh my gosh. Whoa. What is happening? What is SAD? And what's so Caesar's the only one that can produce it? So she produces snow or ice. That was like that wall of ice that she produced over Caesar. She just produces it? Like from where? It's not like coming out of her. Oh, snow snow fruit. Control snow. Yeah, but where does it manifest from? She just spawns it? Her voice actress sounds a lot like Nami. Snow snow. I mean, she's going to freeze him, bro. And when rubber freezes, it snaps. She also has like this advantage of being part bird. Like she can fly around. Control snow. I'm guessing she's relatively pretty much immune to like freezing or anything. Like she has like the best of both worlds, honestly.  We're just hitting every base, man. So that's why she said Doval Mingo would kill her. She let anything happen to Caesar because Caesar's apparently again, so important to this plan of Doval Mingo's. And she's not trying to defeat Luffy. She's just trying to like lock him down. And after finding out he's Congress hockey, I don't think she thinks she can defeat him if she wanted to. Is she gone? Oh, shoot. She's dead. That door is open. She's messing with them. Oh my gosh. Chopper in a freaking mocha. It's been so long. They're still just holding his door. He's got to keep those kids trapped for a little while. Let the effect of wire off more. Oh my gosh. Throw out all the candies. No option for them. I'm smart. Run mocha. Oh my gosh. They're like zombies. They're seeing how big they are compared to choppers. Terrifying too. Meanwhile, this ragtag group. Dude, this is so chaotic. There's so much going on. I want to go back to law, man. So labs going to blow up. Yeah. So I'm saying it's like chemicals and stuff and the gas outside like the whole island is just catastrophe. It's so chaotic. I love it. Can't hold my own. It's a grudge against dragons in general. Why? Oh my gosh. His attitude towards me. What? He's personally insulted. Robin just hates the yelling. Oh my gosh. Why does he eat dragons, bro? Watashi, Sisha. Oh my gosh. Nami is going to take it into her own hands. Oh my gosh. Never mind. Oh wait, she is. She's going to electrocute him. Nice, Nami. Hell yeah. Right. So can somebody in the comics explain the Watashi joke? Now the poor dragon. I hope they don't kill this one too. Long nose goblin monster. He's going to be terrified by Robin's powers. Cortison? I don't know what that means, but it's got to be sexist, bro. I love their competition to take down this dragon. I mean the question is whether or not Kinamon has a more valid reason to not like dragons than Brooke. I'm prepared for anything, honestly.  That is so sick. So what did Dofumiko do to that girl's boyfriend? We never asked that question. Oh no, they're going to kill this one too, man. Kinamon? I have a good reason.  No worse. It's going to be something stupid, man. It's going to be so dumb. Can we know why? Okay, of course not, man. They just hop right back on. Oh shoot, world's colliding. Oh chopper's all bloodied. Trying to hold him back. Hold the line, bud. Oh gosh. Everybody's getting closer and closer though. Oh, they're checking all of them. I wonder why they're checking their temperatures though. Just to make sure they're not sick. The boy? What? Secret room. Transform to do a small dragon? Wait! Kinamon's son! What? Wait! That is his son, right? Moronosuke. Wait, why'd she say he transformed the secret room where no one's allowed and transformed into a dragon? What? Okay, so he might genuinely have a reason to not like dragons. I'm so sorry. Okay, really quickly, I want to go back too. Dude, so we see Dressrosa, the new world Dressrosa. We got the pool, the ladies having fun, the old flamingo laughing. We have this girl who like puts a giant berry looking things on her hands and it eats them and has like an eyeglass booty. So I have treated him as my younger brother and watched closely of him as he grew up. So Delfamingo has known Law as a child. Interesting. I guess before we really didn't know anything about Law to be honest. So I'm guessing Law grew up in Dressrosa? That's where Delfamingo grew up? And Caesar is the only one that can produce sad. So if Caesar dies, sad is gone and his business is ruined. I love this guy's design. This guy, he looks like steampunk. He looks like a robot. He looks sick and it will ruin his business. Okay. I didn't really get the whole I didn't buy a camera and he's like, oh yeah, that's right. I don't know if that's just Virgo being a goofball. He did something to her boyfriend. She can like transform her body into weapons. Kind of cool. Kind of random. I don't know if it's a double fruit. And he said, I'm going to send baby five and Buffalo and then they all need to come to Dressrosa. So baby five and Buffalo are going to punk hazard. And he wants Monet, Virgo and Caesar to come all come back to. Okay. Get juicy, man. Next, next, next episode is Virgo. Yup. He's still going through. Please just let me find out what sad is. It's teasing so hard. Just put it in, man. Like how big is this place? Well, back to the room. Yes. D. Yes. Hold up. Dude, this is a giant chamber too. So don't let me go. Did confirm it's a gas. He is going to cut it. He's going to make a room first. But how could don't how could law use it? Because he said it's something we could use in the new world. Oh, shoot. And he has his heart still. Yeah. That's all I'm saying is full control over him. What, ego? Porement. Okay. That makes sense. Jeez. He wants to really like torture him like that time. What time? My guy is too fast for law. Oh, shoot. He said, I'm going to do this without using your heart against you. God damn. What's stopping law from making a room? Just having to get it off?  God's can bleed. This is another endurance thing. Like just freeze Luffy slowly. She's not even trying to fight him. Just run him down. He is going to get more and more tired especially with the snow. He's not going to see through it either. He's just going to keep going. That's not Luffy's style to just sit down and look at the situation really. He's very straightforward guy. She's just still making more and more and more bro. He's going to run himself down this wall after wall up. My gosh. I'm being able to spawn snow is kind of crazy. 10 layer. Oh my gosh. How big is this room? Dude, she could do this and then someone just die inside of it. You would never escape. She's toying with him. Oh, I kind of liked that. She make like snow clones. Yeah. She knows especially because she knows about the Congress hockey now. Mmm. She's smart. Oh, she's freezing him. Whoa. Luffy, please. And why am I kind of jealous of a man? Just looks nice and lonely. Dude, these white screens are always like earth shattering. I see how much how dirty my monitor is. He's just going to sort of pass out. Someone's going to have to come for him. Damn bro. Monae's clapping her boys' cheeks man. Don't go into the light. Straight up just neutralized our MC in like 30 minutes, bro. Yes. Yes. I broke the floor. Oh my gosh. I love that. It was what Zoro just said.  Oh my gosh. It snapped them back. I love that. I got me hype. The garbage dump. Unless you can fly. He'll find a way out. Don't worry. This will work out somehow.  Oh my gosh. Oh my gosh. Why did they make the garbage dump look like this? Hold the line chopper. Hold the line. You can't reason with them. I love his antlers. Oh, this is so sad. He's too big and strong for his own good. What? He used too much energy. Trample him, please. Okay. Okay. He's fine. He's fine. Oh my gosh. My son was in danger. But he can try and bank on Moka having gotten there and throwing him out. Where's brown beard? He keep going. Yeah, bro. Can we talk about your son? Get him on. You've done all you could chop. Oh my gosh. She has them all. Oh, she has one. Okay.  This is like Black Friday, bro. And Moka's the retail worker. Oh shoot. Where they actually stopped them? Oh my gosh, bro.  Ants with pipes that hit you. She's only holding one candy, guys. Where's the rest? They're supposed to all share it. Yeah, bro. We either need to cut the law. Whatever the hell's going on with Kenamon's son because either lead is actually bonkers, man. Oh, oh. Now you got to cut your losses and just give them the antidote later.   Oh no. Wait, snow is Monet. I thought it was going to be a Caesar for a second. Where is Caesar? She snowed them in. Oh shoot. Oh, Caesar's probably going to the sad room to stop law too. Oh, it's sad that she looks at Monet and it's like she's like relieved. Uh, can the straw has just jump her please. Or she does this sorcery. I mean, this is kind of like this is not that that worry. I don't think I said the straw hats can just jump Monet. I think exam room. Oh, yes. Can we get more explanation? I was wondering why this scene was so slow like leading up to it. Like what do you mean transformed into a small dragon, bro? I hear on the ship with him. So Mononosuke may be a mythical zoan. Does it eat like the candies? The secret. What is the secret room then? Like did they do tests on him to transform into a dragon? Or did he just eat a double fruit for it? Let the master know that a kid knows. Oh, this is crazy. Okay. So obviously Caesar knows about Mononosuke. Oh, this is the secret room. Is this where he is? It was a vagapunk phone. A secret lab. He sees all of them. Law. Law is down down like straight up. This is an interesting looking room like the little DNA in the corner. Oh, he's just beating the tar out of him. It's not even a fight, man. Oh, this is sad. Is it? I mean, it kind of is. The fact that they've got this for in the lab is shocking. His heart. Hey, no cheatsy doodles. You said you wouldn't use the heart. Hey, Virgo. Hey, young man. Keep your word. What was all that big talk about not eating it? He's still trying to. And he still does. Wait. Oh, damn. Oh, my gosh. Kick this out of him. That was crazy. Boom. Oh, my God. Virgo is scary, man. Boom. Oh, Jesus. No. Oh, it's kind of weird seeing him without the hat. It's kind of wrong. It's like he's like naked. Oh, what's he doing? What is electricity? Excuse me. What the? How did he just do that? Did he have a room open still? Oh, damn. That hit him like straight on. Oh, well, it looks so different with no hat.  Dude, why? You know what he kind of looks like he's related to Luffy, like without his hat, his hair. It's kind of bizarre. Like, I see it, man. It's weird. Oh, bro, I could die, man. Oh, wait, he's going to try something. Oh, maybe not. Oh, my God. Oh, and Caesar's going to show up, too. Oh, wait, no. Caesar went to that secret room. What? Oh, he is here. Oh, I forgot about Smoker. Oh, damn. Oh, damn. Oh, my gosh. Oh, my God. Oh, my gosh. This is crazy. Oh, my goodness. Okay, so more questions and more answers this episode. I don't think the room that Caesar went to is the secret room where Mononosuke is or was. But now, like I said, the question remains is, like, what, I guess, gripe does Kenomon have against dragons? And it's probably somewhat related to the fact that his son turns into one. So I'm assuming he already knew that. Like, prior. This isn't like a new thing since he got to the lab. So, yeah, wait, I just kind of just broke that down. I don't think any testing that Caesar did while the kids were here turned Mononosuke into the dragon. So it may have been a devil fruit before he even got to this island, before he was even taken to Plunk Hazard. So maybe they wanted him to test on him because he's able to turn into a dragon mayhaps. And honestly, that might be how they produced more, maybe? I don't know. Either way, dude, like every time it cuts to something else, I'm like, oh, this is going to be crazy. Oh, this is going to be crazy. Oh, this is going to be crazy. Like, the four episodes of them running from the smoke was worth the payoff because this is insane. And now they're just all in that room with Monet. Like I said, I don't think it's that big of a deal. Like, I think they can take her down pretty easily unless she just traps all of them. I really don't know. I don't see that happening though. Luffy's in a garbage dump. Like I said, I think he'll find some stupid, obscure way to get out of there. But yeah, dude, just like the, it's the intrigue mixed with the hype fights that just, it makes the whole show. Like guys, that's been it for my reaction to One Piece today. I hope you did enjoy. Drop a sub on the channel if you're new, so you don't miss any of the rest of the craziness. And I'll see you in the next one. Peace, peace.


will talk to us on bettie cones over fiber products. So thank you for the introduction. And first of all, I would like to thank the organizers of the school for giving me this opportunity to present my work. So today I will be speaking on bettie cones over fiber products. So this is a joint work with Rajiv Kumar and my PhD thesis advisor, Anand Narayan Hariaran. So this is the outline. We'll define what graded bettie numbers are, what bettie tables are, and see some examples. After that, we'll review some known results. And finally, we'll come to some of our recent results that we have obtained. So throughout the talk, I will be assuming that k is an infinite field. R will denote a standard graded k algebra. And all modules will be finitely generated. What are bettie numbers? So suppose we have a graded module, m over standard graded k algebra, r. Then the ij graded bettie number of m, one way to define that is, it is dimension as a k vector space of the jth component of tor i mk. In other words, what we are saying is that if we have a graded free resolution of m, f dot, then the ith free module that appears in the resolution has beta ij many copies of r shifted by degree minus j. So we tabulate these bettie numbers into a table, which we call as bettie table. And so the ijth entry of this bettie table is beta i, i plus j, and not beta ij. So in the previous talk, Professor Deepankar defined regularity. So we can read regularity from the bettie table as the index of last non-zero row. And similarly, index of the last non-zero column gives us a projective dimension of m. And one thing here to notice is that I'm not assuming my rings to be polynomial rings or regular rings. So regularity of modules, so projective dimension of modules need not be finite. So bettie tables are in this case infinite matrices. So let's see some examples. So if my r is a polynomial ring in two variables, and if I take these two ideals, they are generated by regular sequences, of course. So it's graded free resolution will be given by the Kozol complex. The only difference is that we have to take care of the shifts, depending on the degrees of the generators. And these are the bettie tables. For example, we can say that regularity in this case is 2, in this case it is 3, and projective dimensions are 2. Let's see a few more definitions. We say that the module m is pure. If for every i, beta ij is non-zero for at most 1j. So what this says is that if you consider a bettie table, let's say let's consider this bettie table. So here you can see that in column index by 1, there are two non-zero entries. So this is something that is not a pure module. Whereas here, it's a pure module because you take any column, it contains at most one non-zero entry. A pure module is said to be linear if the non-zero entries appear in a single row. So for example, this table is a bettie table of a linear module. And a standard grade k-algebra is said to be Kozol if the residue field has a linear resolution. So for example, this bettie table will look something like this, with this entry being equal to 1. So what we do is we generate a cone of all finitely generated, bettie tables of finitely generated graded R modules, so which we call as bettie cone. So it is all non-negative rational linear combinations of bettie tables of finitely generated graded modules. So the CIs are rational numbers, non-negative. And we have it subset, namely bettie cone of pure R modules in which we consider linear combination of bettie tables of pure R modules. So we can see that this is clearly a subset of this set. And the natural question that one can ask is when does the equality hold? In other words, when can I write bettie table of any module as rational linear combination of bettie table of pure R modules? We have some results like Eisenberg and Schreyer in 2009. They proved that if your ring is a polynomial ring, then the equality holds. In other words, every bettie table can be decomposed into bettie table of pure R modules. And using this, they resolved the multiplicity conjecture of Herzog, Funnich and Srinivasan. So the statement was conjectured by Weisen-Solderberg and they had also provided a proof for D equal to two. So this result is for polynomial ring. So after their work, several people tried to analyze this bettie cone for other classes of rings. For example, this paper studies bettie cone for KXY modulo quadric, convenient stamp studied for rational normal curve, Georgia Tand Sam studied for three non-colinear points in plane and let's see one result from this paper of Anand Narayan and Kumar where they consider Cohen-McCauley standard graded K-algebra with this special Hilbert series of dimension at most one. And they prove that in this case also the bettie cone and pure cone are equal. If you see both the results, we have put some condition on the ring and we are trying to look for this equality. So natural question to ask is what about the converse? So suppose you know that this equality is true, what can you say about the ring? So we started with looking for converse of this result in particular and we started from the case of bettie cone over fiber product. So I'll define what fiber products are and we'll see that converse of this result is true in some case. What is fiber product? So suppose you have two standard graded K-algebras with the same residue field K, let pi one and pi two denote the usual projections then as the name suggests the fiber product is defined as all ordered pairs where a comes from R1, b comes from R2 such that pi one of a is equal to pi two of b. And this fiber product fits into this Cartesian diagram. Let's see an example. So if R1 and R2 are these two polynomial rings then the fiber product is you put together all the variables and go more by all products Xi, Y, J. So you can see that these two are domains but this is not even an integral domain and that is some of the properties as follows. So if R1 and R2 are standard graded with maximal ideals M1 and M2 then M1 direct sum M2 is maximal ideal of the fiber product and we have M1 into M2 equal to zero. We have the short exact sequence of R modules and from this it follows that the depth of the fiber product is minimum of one depth of R1 and depth of R2. So we can see that depth of R can take only two values either it is zero or it is one whereas the dimension is maximum of R1 and R2. So if one of the R1 or R2 has dimension at least two then these are never cohen, these are not cohen Macaulay, the fiber products. So in order to understand the Betty cone one has to understand free resolutions and for that we'll have to understand how the scissor g's look like. So that's where we started and we have this result that if R is fiber product and if we consider a finitely generated R1 module not an R module then we can think of this M as an R module and considering M as an R module its first scissor g module is isomorphic to this isomorphism is a graded isomorphism. So it can be decomposed as some copies of M2 with some appropriate shifts that come from generators of M and first scissor g of M over an R1 module. With some more work we were able to show that if you start with any R module then it's second scissor g module can be decomposed into an R1 module and an R2 module. So we had to analyze first scissor g of module that is a sub module of a free module because first scissor g of M is a sub module of a free module and once we have this decomposition we can use this lemma to get some information about higher scissor g's. What we were also able to show is that if R is fiber product and suppose there exists a pure R module of infinite projective dimension then first of all such a module should have linear resolution and existence of just one module like this forces the ring to be causal. So we know that there is this result of Audemars-Weisenberg and Piwa which says that ring is causal if and only if k has finite regularity if and only if regularity of k is zero or equivalently every module has finite regularity. So in case of fiber product we can add this statement to the list as an equivalent statement that existence of one pure module forces the ring to be causal. And in particular it follows that in case of fiber products suppose we have this equality then it forces the ring to be causal. This is the converse that we have obtained. So suppose R is a fiber product with depth one and if we have the equality of bety cone and pure cone then we do get that the Hilbert series of R should have this form and in particular it forces the ring to be Cohen-McCauley. So just in case you are wondering about depth zero case because we know that depth of R can be zero or one there is a partial converse that was obtained by Rajiv Kumar and Anand Narayanan. Yeah. So what this result says is that it gives some characterization in case of bety in case of fiber products for Cohen-McCauleyness in terms of this equality. So how much time do I have? Yeah, so this is a sketch. So what we do is because depth is one we can pick a non-zero divisor from each RJ then we consider this ideal because of this equality we can decompose this module into pure modules where this M zero has linear resolution then we analyze this M zero to conclude that the ring should have dimension one. So in particular it is Cohen-McCauley and then we write Hilbert series of R in this form and show that this F of z should be a linear polynomial so that it has this form one plus N z. These are some of the references.