this season. I don't know if it's just me, but what is it about Disney and Christmas that just seemed to go so well together? Hit the like button if you love a Disney Christmas. And if not, let me know what your favorite Christmas theme is. But I guess both Disney and Christmas just have that magical feel to them. So in this video, we're gonna do a Disney Christmas themed puzzle. And this one is actually not in any of my haul videos, but was gifted to me by my husband. See, here's the thing. He totally had the nerve to send me a text message with a picture of a beautiful Disney themed holiday puzzle, knowing that I was gonna say, yes, I need to have it. So that's what I said. And he was like, done. So we are going to be starting the Christmas festivities with this beautiful puzzle from Disney's Thomas Kincaid studio. And this puzzle is called Cinderella Bringing Home the Tree. It is 1000 pieces and is 26.6 by 19 inches when it's completed. And this one comes with a puzzle poster, which is too exciting because I love this image already. And this one is by the company Seaco. I hope I said that right this time. And I really appreciate that one of you guys reached out to me and told me that I've been saying it wrong this whole time. So here's to hoping that I said it right this time. If I'm still saying it wrong, then that makes me quite pathetic. But anyways, now first impressions when I look at this image, I mean, come on, if you don't love this image, then I don't know what's wrong with you. For one, it's Thomas Kincaid. So this image is absolute perfection to me. The lighting is amazing. The details of all the trees, the house, the water, the sky, I'm in love. We got the prints in Cinderella. They just got there with their tree and presents. They're coming to visit me. You know, this is my cottage that they're visiting. I don't know what they're saying, bring Cinderella Bringing Home the Tree. She's at my house. Me and Cindy go way back. I don't know. I kind of feel like they should have called this puzzle Cinderella Bringing the Tree to Mandy's house. Why would that can't be her house? You have the castle in the background. I mean, isn't that where she moved to? That has to be my house. I mean, look how cozy it looks. You have the fairy godmother doing godmother things in the background. You have Jack and Gus Gus towards the front there. We got the bird friends. Look, you even got Lucifer behind the sled looking all creepy and stuff. Oh, even creepier. You have the stepsisters hiding in the bushes. That's weird. What else do we got here? There's always some sometimes you find some strange Easter eggs or some strange things going on in the Thomas Kincaid Studio images. If you look really closely, you got to find them because they're such small details, but usually you'll find some things in there. I can't quite make out what I'm seeing towards the back there. Is that Cinderella's dog drinking from the river? I think so. And oh my goodness, even creepier. You have the evil stepmother hiding in the trees. I don't know. This is kind of creepy. Don't you think? What's the matter with these ladies? Do they got nothing else better to do? This is very strange. This went from a festive looking fun image to a very strange, creepy situation. Nonetheless, this image is absolutely beautiful. I can't wait to put this together. Now, I can already tell what's going to be hard in this image. I know the sky is going to take me some time to complete. We have the snow. The snow obviously is all white and you have different tones in the snow. So that's going to be a bit tricky, I think. I'm pretty sure at some point I'm going to have to change my sorting midway as well. You know, the house is an easy detail. We have the Christmas tree. That should be fairly easy to be honest. We have the sleigh. We have the characters in here.  I'm already excited about it. But I'm also kind of feeling like this is going to be quite a challenge. Aside from the fact that it's 1000 pieces, you got a lot of areas that are kind of the same colors and tones and details. So this is going to be interesting. I'm thinking what I'm going to do here is I'm going to kind of go over what I'm doing along the completion process. Tell you which areas were difficult, which ones were easy, how I went about completing certain sections of the puzzle, and kind of like my, I guess, tips. I'm not an expert, but you know, kind of give you like my sense of how I kind of go about completing puzzles. And hopefully one of my ideas can help you complete your puzzle. We're all here to help. All right, enough chatting. Let's get this open and let's get started. All right, we're not going to get too crazy getting into this unboxing since we've done several of these Disney Seaco puzzles before. I already cut this off to kind of save time. Okay, we have our puzzle bag and our puzzle poster. Oh, too exciting. All right, that's going to be super useful as we complete this puzzle. Gives me some reference. Doesn't look to be too much puzzle dust in the bag.  Let's open this up. We've worked with this before. Nice image print. Let's see what the glare is. Yeah, we're going to get some glare on this. That's difficult. Anyways, guys, I'm too excited to start it. So let's get going. So I'm a sorter. Puzzle tray number one had edge pieces. Number two had sky pieces. Number three had pieces that had details like the sled, Cinderella, the prince and so on. Another tray had water. The next I put would look to be the trees. I had a tray for purple pieces. There was another for fairly dark pieces. And the last one had pieces that resemble the snow. And through my time sorting, I knew at some point that I would need to resort at least one or two more times. But if you have the space or the patience for that matter, you can sort each tray even further in the beginning. So after that was done, I started with the edge pieces and I do this 99.9% of the time. Then as soon as that was done, I went straight to the tray with the detailed pieces and tried to quickly sort it out a little further on my puzzle table. And with having the edges in place, I'm kind of able to map out where certain details go within the framework. So after I did my second sore, I started piecing together Cinderella, the prince, the sled, the house, all the pretty obvious details. And then I moved on from there. And that was when the real challenge started. Overall, I found the darker pieces much harder to solve because with the lighter pieces, you're able to see the differences in colors and tones much easier. Now something that I have been doing recently is I've been putting together sections of the puzzle outside of the frame. And I did this either on one of my empty puzzle trays or on the side of my table. And then I would add it to the rest of the puzzle. And this actually really helped me when I had issues with lighting. And when using the tray, I was able to bring it a lot closer to my face. So it was much easier to see. Let me know if I'm not the only one who does this, but I hate when I have a mess of pieces all over my table. And this always happens to me no matter how much I try to keep it organized. And obviously it happens as I'm resorting or grouping together common pieces. But anyways, about three quarters through my puzzle, I did a full resort of what I had left on my trays and whatever mess I had on my table. And this time it was by puzzle shape. Now this particular puzzle set had about overall I'd say eight general types of shapes. And they still had some differences, but it was good enough to at least get me to the finish line a lot quicker, especially for the sky and the bottom section of the image. Now a couple of negatives with this puzzle set. And I guess this is just a signature seco thing, but I did have that same issue again with popping pieces. I'd put a piece in place or pull one out and the ones around it will just flutter on the table. It was annoying, but I have to say for this particular one, it wasn't as bad as my Snow White puzzle. And if you haven't seen that video, I'll link it down below. There were some glare issues, but to be honest, with the overall tone of the color on the puzzle image, it wasn't that bad honestly. Now on a positive note, I was very surprised to find all of my pieces in very good shape. Previously I've had issues with the images peeling off the puzzle piece, and that wasn't the case with this one. And really, you cannot beat this image. This image screams Christmas. I mean, obviously, when you look past the fact that there's a creepy stalking situation going on here, I might have to have these women arrested for trespassing on my property. But overall, this puzzle was a lot of fun and challenging at the same time. This one took me about 8 hours to complete. I really struggled making time for this puzzle. I'm sure with most of you, the holiday seasons are a very busy time for you. Well, now I can finally start decorating now that my tree has been delivered. Now for my next puzzle review, I'm thinking about trying out a different puzzle brand. So make sure you're subscribed if you want to hear about my experience with that. Well guys, I wish you all a safe, happy holiday season, and I will see you in the next one.


Okay, this is Roberta Felicky-Conezzi and we are going to call to order the redevelopment authority meeting for the City of Sheboygan this Friday, March 27th. Let's do a roll call. Alderman Wolfe. Here. David Soxie. Here. Steve Harris. He is not present. David Gad. James Owen. Okay. Amy Horst. Here. And staff, would you identify yourself? Chad Peleshek. And Janet Dolman. And Janet Dolman. She's not on the speaker. Are you still? Chuck Adams. Yeah. Great. Okay. Let's pledge allegiance, I pledge allegiance to the flag of the United States of America and to the republic for which it stands, one nation under God, indivisible with liberty and justice for all. If we could look at the agenda and identify a potential conflict of interest, are there any conflicts of interest? Ms. Chair, this is Chad. I think James Owen is going to have to add stain and not even participate in the dialogue on the three sheeps brewing one. So he can probably, that's why it's at the end of the agenda, he can probably just sign off. Can do that when we're finished with discussion 3.2. You had minutes from the previous meeting from March 4th, Carol entered in motion to approve it. Please. Identify yourself when you do that. Wolf. Wolf moves to approve. Socks each second. Are there any additions or corrections? Hearing none. All those in favor say aye. Roberto, we need to, Roberto. We need to call a roll call. Roberto Flicky Pineski, Alderman Wolfe. Yes. David Soxie. James Owen. Sorry. David, David Soxie is Dave Gaston. Okay. Thank you. Thank you very much. We'll be done in a minute. David Soxie is Dave Gaston? Okay. All eyes. Oh Amy, sorry. Can you just say I? Thank you very much. Okay. If you recall, from time to time, when we have an outstanding loan, we are asked to subordinate that loan from some other manner than when we initially passed the resolution to supply that loan. Typically, it's a change of bank, but it comes to us periodically. And at the last couple of meetings, we discussed giving staff the ability to, in a pro forma manner, have those loans subordinated because it's basically a tactical thing. You have in front of you, and it was sent to you previously, the subordination policy regarding development loans from HUD. If you've read through it, does anybody have any questions about that particular loan, that particular policy? Chuck Adams here. I've made some edits to it since it went out to you. I'm happy to walk through those. We'll have to, when you approve it, we need to approve the policy as amended. No need for you to approve the form. In fact, I would encourage you not to approve the form because that's really, Chad can just change forms as needed based on your policies. Okay. All right. Chuck, before you start, the one thing that I noticed in number two on the policy, we won't agree to a subordination as the loan is in default. My question is, what about taxes if they are in default with their tax payments? So this policy only limits the denial, the automatic denial to a subordination request for a loan in default status. So taxes don't play a role in this policy. Let me give you an example. We could have a loan that was in default, a loan that was not in default, but they were in default for city taxes. We wouldn't have no authority about denying the subordination. So in that case, the policy would still authorize Chad to subordinate. That doesn't mean he has to. What this policy is doing is giving Chad authority to act. But he doesn't have to act based on it. What you're doing is putting a fence around how he may act. So you could narrow the fence by adding that provision in there. Or you could keep the fence where it is and Chad can at times when he sees that he's getting close to the fence and understands that the RDA might be concerned about it. He can still bring it to RDA. But if he chose to follow this policy, basically, you know, you don't have any complaints if he stays within the bounds of the policy and makes those calls. Okay. Does anybody else on the committee have questions about either the policy numbers one, two and three, or the criterion numbers one, two and three on that policy? Chuck, do you want to go through your final changes? Roberta, if you're ready for that. Yes, please. Okay. So the one change is very simple. It's just adding the word only in paragraph two so that the second sentence reads the redevelopment authority may consider a subordination request only if a loan has not been default status for a minimum of 90 days. It's just to provide some clarity. The other change is in the first paragraph right above the criteria. And the change here is mostly just for clarity as well. So that paragraph would read as follows. Assuming the subordination request complies with each of the criteria below, the director of planning and development shall be authorized to sign off on requests to subordinate the redevelopment authority of another lender. Chuck, I missed you with the dinging of somebody signing in or signing out. Can you read that again? Assuming the subordination request complies with each of the criteria below, the director of planning and development shall be authorized to sign off on requests to subordinate the redevelopment authority interest to that of another lender. Request to subordinate the redevelopment authority's interest in accordance with, okay. Any questions about those criteria? Any questions? Any, I would make a motion to approve. Second. With the amendment. Approve has amended. Okay. Is there a second? Second. Thank you. Are there any other additions, corrections, discussions? Okay. Hearing none. Yeah, if you want to read the rule. Yeah, Roberta Flicky Paneski, Alderman Wolfe, Dave Soxie, Dave Gas, James Owen, Amy Horst, all eyes. I'm also on the phone, so Steve Harrison. Okay, thank you. Thank you, Steve. We have a discussion on 3.2 ground determination for the blue harbor. If you would like to give us a background on this please. Sure. So this is in regards to the discussion we've had as it relates to the transferring of the conference center at blue harbor. And the city ultimately maybe getting the pentare property. This is an exhibit to that transfer agreement that has not necessarily gone to council yet. It's still being negotiated, but blue harbor is recommending that this assignment of the ground lease and the termination of the operating lease. So under the current terms of the contract with blue harbor. The city owns the conference center. The property all under the resort and conference center is ground leased for a dollar a year. And then there's an operating lease between the city and blue harbor to operate the conference center on our behalf with us transferring the conference center over to them as part of this deal that the city is working on. There would be a termination of that operating lease because they wouldn't need to operate on our behalf because we wouldn't own it. And then they would assign the ground lease under the conference center to blue harbor versus the city as part of that deal. This is really a just something blue harbor requested. I think Chuck could chime in and say that, you know, he's not sure that it's necessarily needed, but that they would like to see it in. And since the redevelopment authority was a party to the two agreements previously with blue harbor blue harbor is requesting that this be executed. So we're clarifying that the operating lease is now transferred from the city to blue harbor. It's a check items here it's actually the ground leaves. The operating lease was between the city and blue harbor and the ground leaves was between the RDA and the city. And now the ground leaves will be between RDA and blue harbor, because they are they will now be the owner of the property and it will make then that operating lease between it will terminate the operating means because there'll be no need for it. The other thing I would add is as Chad has pointed out, we're still in the process of negotiating. I, you know, I think it's, we're pretty close. We're just kind of waiting for some answers on a couple of things. And we're close enough that this exhibit is in final form. If you approve it, my suggestion would be that the motion would be to authorize Roberta and Chad to sign at, you know, at such time as the, the agreement is made between blue harbor in the city. We're going to sign it today. We want to sign it when we're ready to sign my question to you is, will we RDA be seeing a ground leaf between the RDA and blue harbor or is that already baked in. The ground lease is going to remain the same. So you, you have a ground lease with the city and that ground lease will be exactly the same with blue harbor. And so that's what you're doing here. It's just, you're agreeing that that that the city's portion of that ground lease is now moving over to blue harbor, but there's no change in the ground lease. Thank you. Are there any other questions? Okay, we are able to sign it at such time that it's appropriate to sign it. Was there a second? Right. Thank you. Any other questions? Hearing none. Chad, read the roll. Roberta, Alderman Wolfe, Dave Soxie, Dave Gas, James Owen, Amy Horst, Steve Harrison, all eyes. Motion is carried. We now have discussion and possible action on 3.3 from three sheets brewing. And as previously noted, James Owen will be excused from this discussion and his action due to a conflict. All right, so I will jump off the call then. You can. Thank you, James. Appreciate your, appreciate your attention. Thank you guys. Looking forward to meeting in person. Okay, Chad, did anybody receive the correspondence with with Grant Pauley? Yes. Okay, perfect. I would move to approve the action requested by Chad in his written. Wolfe's second. Okay. And what was suggested by staff is that we move to approve interest only payments. $5,471.17 for April, May, June, July and August and September. So for the next six months, and at which time he will resume normal principal and interest payments. Is there any further discussion? I guess the question that I have is for discussion is, what do you guys, how, how do you hand? How do you want to handle the principal payment? Do you want if they just stall it? And they, you know, I, I, the reason I recommended interest only is just to keep them on paying so that, you know, when we go back to principal and interest that they're still paying something. But the question is, is what happens to the deferred principal payment? Does it, does, do they just pick it up at the, we re-amortize or do they just pick it up at the end as a balloon payment? Or how does that work? Berda, is that something that we can leave open to the, to the, you know, to three sheets? I mean, I'm fine extending it because of the circumstances. I would say extend it. Just, just extend the principal payments at the end of the, at the end of the payment period. Berda doesn't, doesn't see, doesn't any of the, any, any company have the ability to pay it off sooner, right? Yes, we do. They do. So then really, you just have to make a motion that we're allowing them to extend it by this many months or whatever. Right. Check items here. The one thing you have to think about there is that you will still have a principal balance with some amount of interest at the end at that point. So the question might be whether the more appropriate action, what Chad has described here is just simply allowing them not to make those principal payments. And, you know, one option would be to just limit it to that and make determinations about how to handle, you know, the additional principal at a later date. If you do nothing, it would be the balloon payment at the end. But you can also, you can also delay making that decision if you'd like. And I don't know whether Chad had any conversations with Grant about this particular issue either. I talked to him about interest only payments and he accepted that because he said that's comparable to what the bank is doing, but he wasn't sure. I guess we didn't really talk in detail about the, the principal payments. So I guess you guys could make a motion to just defer the principal payments and maybe let the staff, you know, work through that piece as Alderman Wolfe just recommended and just have him continue to pay interest payments. And we'll figure that out given the timeliness of this. So what I'm hearing is that we are, we are in agreement for doing interest only payments of 547117. And that if need be at a later time, we determine what happens with the principal from those payments. Agreed. Okay. Carol, entertain a motion as such. I thought we did. I make a motion. Oh, and we had a motion to second it. Okay. Yeah. We have a motion and a second on the floor. Is there any more discussion? Okay. Hearing none. Chad called the roll. Roberta. Yes. Alderman Wolfe. Yeah. Dave Soxie. Dave gas. Amy Horst. Steve Harrison. Yes. All eyes. The motion carries. And that motion to adjourn when you're ready. Okay. I was just going to call for that motion. Alderman Wolfe moved to adjourn. Is there a second? Seconded. Are there any objections? Hearing none. We are adjourned. Thank you so much for the meeting. Thank you. Can you give me a call, please? Dave Soxie. Thank you. Get me off of it. Hi, everyone.


from theCUBE Studios in Palo Alto in Boston. It's theCUBE, covering IBM Think. Brought to you by IBM. Welcome back, I'm Stu Miniman and this is theCUBE's coverage of IBM Think 2020. It is the digital experience online. So rather than all gathering together in San Francisco, we're getting to talk to everybody where they are and we're happy to bring back one of our CUBE alums. It's actually been a little while since we've had them on the program. Willie Tejada, who is the general manager and chief developer advocate with IBM. Willie, so great to see you, thanks for joining us. Hey, Stu, thanks for having me. It's good to be back, it's been too long. So, you know, first thing, you know, obviously we're all together while we're apart because of the global pandemic. You know, developers, I've had so many interviews I've done over the years talking about dispersed development, you know, around the clock development. I had a great interview with, you know, head of remote work in the developer community at the beginning of the year before everything happened. So, you know, how's the community doing overall? And, you know, how are you seeing them react to what's happening? You know, in the developer community, I think one of the interesting parts is, one, developers feel oftentimes that they can actually make a difference to their work, oftentimes happens remotely. And so, one of the things that we've seen is a lot of the interaction that we have when we're doing our developer advocacy work has just converted to digital. And there's some interesting dynamics that kind of come about just even in that, where, you know, if you were doing something like a meetup in New York that was attracting something like 50 people to maybe a hundred, maybe the venue was limiting the number of people that you would actually have there if you had a popular topic or speaker. You know, we've had meetups basically be as large as 500 plus people when we went to digital. So, definitely some different dynamics as we actually talk about this new normal that we're in and everybody utilizing digital vehicles to reach the people that they want to talk to. All right, so I know last time we talked with you, a big topic we talked about is call for code and something that IBM has done different initiatives there and you've got a very relevant one.  Yeah, Stu, thanks very much. You know, the call for code initiative inside of IBM is now in its third year. We did it in 2018. The concept was fairly simple. Developers always love to solve problems. And we said, what if we challenge the 24 million developers to come and take a crack at society's most pressing issues? And in the first two years, we focused on natural disasters. You know, all you have to do is take a look at the coverage prior to the COVID-19 pandemic. And you had wildfires in Australia and in Northern California, where my home actually is based and you had tsunamis and hurricanes and floodings. And so the ability for us to actually bring the developer community to bear on some of these size most pressing issues was really kind of the concept up front. And IBM would help by bringing subject matter experts together, making available tools.  You get a expert on supply chain. You get a user of supply chain. You bring them together, developer builds these things. Well, not all the time can you get an expert in disaster, a first responder. So we actually created a lot of that fusion actually from there. Then over the first course of the first two years, we've had over 210,000 developers participate across 168 nations with over 8,000 applications submitted. So wildly successful. Now, this year, let's do to your point, we had something that we could really bear down on very heavily. We announced it that we were taking on climate change, kind of laddering up natural disasters was, let's look at the route, climate change. And then the COVID pandemic came about. You know, we said, let's tilt people towards that. And it's been a tremendous, tremendous outcoming for it. We've asked the developers to focus on three areas, crisis communications. You know, you may have been one of those folks that's on a conference call or emails and haven't been responded to on wait times forever. So those communication systems, how do we fortify them, get them to scale. The second area is remote learning. Really look at where all the students are actually these days and what they're doing there. Not just teaching, but basically, how do you give them entertainment? How do you actually provide them some little social interaction? And then the third area with the COVID focus is community collaboration. You know, we really want to try to get people, make sure people's spirits are up. And that really does require everybody leaning in. And again, you look at the news and tremendous examples of community collaboration and where technology can help scale or broaden that. That's really where call for code actually comes into play. Yeah, maybe it would be helpful. Tell us a little bit about some of the previous winners. You know, what would have been somebody outcomes, you know, more than just rallying the community, you know, what resources is IBM putting into this? So one of the things that makes it different is rather than it just being a regular hack, this is really a process inside of IBM that we developed over the course of the last three years where the challenge is one piece, the call for code challenge. We also developed and rolled out and committed another 25 million. With call for code, we committed 30 million over that five years. And then the following year, we recognized the need to see the solutions actually get deployed. And so we committed another 25 million for the fortification, testing, scaling and deployment. So when you win a call for code global challenge, you also get IBM support around deployment, fortification, some counseling and relation basically from development to architecture to even the business side of it. In our first year, we had a team called Project Al actually come out and win. And you know, one of the first things that happens, especially in hurricanes or these natural disasters, communication grids go down. So they developed a solution that could quickly establish an ad hoc communication grid. And anybody that had a typical cell phone could connect up to that wifi grid or that grid very similar to the way they actually connected to a Starbucks wifi system. And it would allow both the first responders to understand where folks were at and then establish communications. So that was in the first year. The second year was a team called Prometale. And in October, we selected them as the global challenge winner. And they were a solution that was built by a firefighter, a nurse and a developer. With this concept roughly of how do they monitor essentially a firefighters situation when they're actually in the heat of battle to best allocate the resources to the people who need the most. Understanding a little bit about their environment, understanding a little bit about the health that's actually happening with the firefighter. And again, it's one of those scenarios where you couldn't just build it from the firefighter side. You couldn't just build it from the nurses side and a developer would have a difficult time building it just by themselves. So bringing those people together, a nurse, a firefighter and a developer and creating a system like this is really, really what we're aspiring to do. Now, they won in October and in February, they're in a field deployment actually doing real testing in the field in some of the fields of Catalonia, Spain. So we've seen at firsthand exactly what happens when they win the Project AL team actually did some hurricane deployment testing in Puerto Rico that of course, IBM helped fortify and build connections between the Puerto Rico government so that we're really seeing essentially the challenge winners see this type of deployment. Well, I love it, you know, it's even better than a punch lot I could do. What do you get when you combine a firefighter, a nurse and a developer? The answer is, is you can positively impact the world. So, you know, phenomenal there. I'm curious, you know, where does open source play into this activity?  So, you know, where does open source fit in? 100%, you know, the amazing part about activating developers these days is just the broad availability of the technologies. And it's certainly stimulated by the community aspect of open source, this idea that they democratize access to technology and it's really community centric and folks can start building very quickly on open source technologies that are material. So, number one, all the things that is part of call for code and what we actually deployed are based on open source technologies. Now, one of, again, one of the thing, the differences is, how do we actually make those winners and those technology sets become real? And becoming real requires this idea of how do you actually build durable, sustainable solutions? So, each five of the winners every year have the opportunity essentially to go through the Linux Foundation and have their solutions established as a project with the idea roughly that people can download and fork it, people can actually fortify it, but it's available to the whole globe, that everybody in the world, to help build upon and fortify and continue to innovate on. So, open source is right at the root of it, not just from the technology side, but from the ecosystem and community side that open source was for. And so, we've seen as an example, the formal establishment of Project Al's software being open source by the Linux Foundation. And it's been fantastic to see both the participation actually there and see how people are basically are deriving it and using it, exactly what we intended to see in the vision of call for code and code response. Well, that's phenomenal. We're huge fans of the community activity. Of course, open source is a great driver of everything you were talking about. So, I'm curious, one of the things we're all looking at is where people are spending their time, how this global pandemic is impacting what people are doing. There's plenty of memes out there on social media. It doesn't mean that you all of a sudden are going to learn a new language or learn to play an instrument because you have a lot of time at home. But I'm curious from what you've seen so far, compared to previous years, how is the engagement, what's the numbers, what can you share of, is there a significant difference or change from previous years? You know, there's so much goodwill, I would say that's been brought about around the world in what we're seeing around the COVID-19 pandemic that probably the rate, the way I've described it is the rate of submissions and interest that we've seen is three X's above what we've seen in the prior years. Now, keep in mind, we're not even actually at the area where we see the most. So keep in mind, like right now, we tried to accelerate the time to highlight some of these solutions. So on April 27th, we'll be kind of the first deadline for COVID-19 challenge and highlight some of the solutions on May 5th, of course. Now, when we think about it, basically from that standpoint, you have, we typically actually see people waiting until that submission timeframe. And so when you think of it from that standpoint, you really oftentimes see this acceleration right at that submission deadline. But we're already at seeing three X's what we've seen in the past in terms of participation, just because of the amount of goodwill that's actually out there and what people are trying to do in solving these problems. And you developers, they're just, they're problem solvers overall in putting out those three areas, crisis communications, remote learning and community collaboration. They'll see examples of what they see on the news and think they can actually do something better and then express that in software. That's excellent. So Willie, one of the things, we've been talking to leaders across the industry and one of the things we don't know is how much of what we are going through is temporary and how much will actually be long-term. I'm curious if there's any patterns you're seeing out there, discussions you're having with developers, you talk about remote work, you talk about communication. Are there anything that you've seen so far that you think that this will fundamentally just alter the way things might have been in the past going forward? You know, developers are was actually looking for this idea of how they actually sharpen their skills or craft new languages that they actually know, new platforms, whatever it actually might be. And I think in the past, it was probably even from our perspective, this balance of face to face versus digital and a mix of both. But I think what we'll find going forward is a more robust mix of that because there's, you can't deny the power of reach that actually happens when you actually move something digital. And then I would say that, you know, think about how you at theCUBE have refined your studios and dealing with an interview like mine, it gets better and better, you refine it. You know, how you do an online workshop and how you do a workshop on Istio Service Mesh, you get better and better about how you engage from a real-time hands-on keyboard experience in what information, what chat, what community pieces do you put on the screen to stimulate these pieces. I think in general the industry and our company and our teams have gotten better even in the short amount of time. I think those things will be long lasting. I think we're all humans. So I think they still want the physical face to face and community interaction and camaraderie that comes from being in that physical energy. But I do think it'll be complimented by the things that we refined through the digital delivery that's been refined during this situation. All right, so Willie, final thing, of course, you know, this week you said that, think the winners are all being announced. How about, you know, people that are watching this and say, this sounds phenomenal. How do I learn more if I, you know, didn't get to participate in some of the initial pieces? What should I be looking for? And how can I, how can I contribute and participate even after, think? Well, number one, keep in mind that the challenge for the year will still actually go all the way to October and submissions for that poll challenger will actually go to the 31st. So that's number one. But number two, going to developer.ibm.com, call for code, you'll find all the resources. We have these things called starter kits that help developers actually get up and going very quickly, finding out more information about both the competition structure and really how you become part of the movement. Go there basically and answer the call. Awesome, love it Willie. Thanks so much, pleasure to catch up with you and definitely looking forward to seeing all the outcome that the community is putting forth the focus on this really important challenge. Hey Stu, thanks for having me, I really appreciate it. All right, be sure to check out thecube.net for all the coverage from IBM Think, all the backlog we had to see Willie a couple of years ago when he was on the program and check out where we will be later in the year. I'm Stu Miniman and as always, thanks for watching.


Okay, so welcome to this first course on algebraic geometry, so let me begin by trying to tell you what algebraic geometry is all about in the in its greatest generality it is trying to study the geometry of the set of common zeros of a bunch of polynomials okay, so let me write that down, so that is in one line what algebraic geometry is okay, so beginning with this let us try to take the discussion further, so when I say a set of polynomials of course I should tell you where these polynomials are from okay and then I should also tell you by that I mean I should tell you these are polynomials in how many variables okay, so you must have a fixed number of variables and then I should also tell you about the coefficients of these polynomials because of course for example we are used to writing polynomials over real numbers which means polynomials with real coefficients and for example also with complex coefficients okay or sometimes we also look at polynomials with just integer coefficients okay, so the coefficients usually come from a ring okay, so what is happening is that you see in this way the ring of polynomials in several variables over a given ring comes into the picture okay, so you see, so what you do is so we pick or rather we are given, I should not say we pick, so we are given a collection of polynomials, let me say a subset of polynomials, so let me write them as f sub alpha of x1 etc xn, s is the set of all polynomials f sub alpha x1 etc xn and this is each one of these f alphas is a polynomial in a polynomial ring okay, so this ring is the ring the commutative ring that consists of polynomials in the variables x1 through xn and with coefficients in the commutative ring r okay, so of course I will not repeat this often we are always going to be worried only about commutative rings and commutative rings are assumed to be with unit element that is with one and we will always assume that homomorphisms of commutative rings carry one to one okay, so r is a commutative ring with one okay and x1 through xn are variables n variables and this is the polynomial ring over r in n variables and each f sub alpha is a polynomial in this ring and you take some of these subset of these polynomials, so this is alpha is some indexing set let me put it as lambda if you want okay in which case I can rather change the index to small lambda for more coherence, so this S is a subset of the ring of polynomials in n variables over r okay and we want to study the geometry of the subset of the subset E set of S, the set of common zeros of S and that is defined to be the set of all r1 etc rn n tuples of elements of r okay, so this is just r cross r n times this is just the Cartesian product of r taken with itself n times, so these are n tuples of elements of r each one each r i is an element of small r i is an element of capital R such that the if you plug in xi equal to r i okay that is if you substitute for xi the corresponding r i in this tuple okay or in other words if you substitute for the tuple x1 etc xn the values r1 etc rn in that order then you will get a and when you evaluate this polynomial okay then you will get an element of r and that has to be 0 and that should happen for every lambda okay then and only then is a point of rn in this set okay, so such that f lambda of r1 etc rn is 0 for every lambda belonging to capital R okay, so maybe this I will just write it as such that okay, so you see so basically what is happening is that you already have 2 objects here on the one hand you have rn which is r cross r cross r n times okay and on the other hand you also have the polynomial ring over r in n variables okay and what is happening is that I am given a subset S of the polynomial ring and I am associating to that subset the set of common zeros of that subset which is a subset of rn okay, so and the purpose of algebraic geometry is to study the geometry of this common set of zeros okay, so this is the general picture so you can see that already there are 2 sides to the picture there is one side which is the geometric side okay where you have the space where you are looking at the zeros okay and you have here the algebraic side which consists of essentially you are looking at the polynomial ring okay, so you can already see that there is a there is a commutative algebra side and there is an algebraic geometry side, so algebraic geometry is all about going from this to that and that to this based on properties of both sides for example you could have properties of this set which are geometric properties okay and they would translate into some properties connected on this side and the properties that are connected on this side ring theoretic properties or which may be ring theoretic properties or they therefore they could be ideal theoretic properties or more generally they could also be module theoretic properties okay because modern commutative algebra is not just the study of rings and ideals but it is also the study of modules because module the notion of a module generalizes the notion of an ideal and also that of a vector space at the same time and this is more is more versatile okay, so the properties on this side are geometric properties the properties on that side are commutative algebra properties and it is this dictionary it is setting up this dictionary which is the subject of algebraic geometry okay and but of course there are several things that I will have to explain to you first of all I have not so let me write that here, so this is the geometric side and this is the commutative algebraic side and in some sense therefore you can say that algebraic geometry and commutative algebra are kind of married to each other in that sense okay there are two sides of the same coin okay, so but then I will have to explain to you what do you mean by what do you mean by the geometry of a subset okay because that involves several things but for example it is at the base level it will involve some topology and then on top of that it will involve further properties topological properties and on top of that it will involve some properties connected with manifold theoretic properties okay and so on and so forth which we will try to explain but let me at this point go to something else okay. So first of all you know if you give me an equation like this forget even a set of equations suppose I give you a single equation over a ring okay it might turn out that this set may be empty okay that is the problem this set if it is going to be empty it does not there is nothing interesting to study because there is nothing to study first of all. So that can happen very easily for example you know if you take the ring R to be real numbers and you know if I take something like just one variable okay and if I take the and if I call that variable so I just take real numbers with one variable X1 and if I take the equation X1 square plus 1 then you know that it has no zeros in real numbers okay because obviously you know because the zeros are non real they are complex okay. So it is very possible that if you work over a general ring okay this particular set the zero set can turn out to be empty and then you are there is nothing to study okay. So at this point this point there is a I should say a dichotomy the subject actually breaks into or rather can be divided into two parts. So there is one question that tells you that if you are going to work over rings such that this is never going to be empty okay then of course you have these are good rings over which you can do this kind of study okay. The other thing is the question that what do you do if this ring does not have those properties so the answer to that is there is an answer to both. So if you so the first question the first part is you restrict to rings which are algebraically closed fields okay if you restrict to rings which are algebraically closed fields then this set is never empty for decent collection of polynomials okay I will explain what decent means later and you can do geometry okay. So that is called variety theory and that is what is usually done in a first course in algebraic geometry then the other thing is what do you do with a general ring okay for example I would like to have I would like to work over the integers for example you know questions like Fermat's last theorem it also involves an equation in three variables it is an equation with coefficients in integers and then you are trying to ask whether there are non-trivial integer solutions apart from the easy solutions okay then you also need to solve questions like that and to solve questions like that of course there are equations over integers which do not have solutions for example x square plus 1 equal to 0 is very well an equation with integer questions and it has no solutions in integers it does not have any solutions even in real numbers so how can it have solutions even in integers. So the question is how do you deal with such things so there is a part of algebraic geometry slightly more sophisticated area of algebraic geometry which deals with such things and that is called scheme theory and the scheme theory is the it is a modern language of algebraic geometry and that is usually what is covered in a second course in algebraic geometry because it involves far more machinery okay but what we will be doing this course is that we will be safely restricting ourselves to the cases when this set is non-empty okay so what I am going to do is I am going to tell you something about I am going to tell you something about solving equations or rather okay zeros of equations so well so the first thing is you know as you would have come across in any first course in algebra normally the usually we start with integers and then you know you extend them to rational numbers well of course I could also take natural numbers before this okay you can well maybe I can even do that it is not a big deal I can take natural numbers then I extend them to integers then there are there is a field of rational numbers then there is a field of real numbers there is a field of complex numbers this is how it goes and every time you have a bigger number system and that is because essentially you want to solve equations so number systems become bigger and bigger because you have some equations for which you do not have solutions so you have to make the make the make your set of numbers bigger okay so you know for example natural numbers the counting numbers 1, 2, 3, 4 does not have 0 so an equation like x plus 1 equal to 1 which has a solution x equal to 0 will not have a solution here and an equation like x plus 1 equal to 2 or I mean x plus 1 equal to or rather x plus 2 equal to 1 which is a solution x equal to minus 1 also does not have a solution here so you are forced to go to integers and then you can have an equation of integers which does not have a solution integers which have a solution only in rational numbers for example things like 2x equal to 3 it is very well in equation over integers okay but the solution is x equal to 2x equal to 3 the solution is x equal to 3 by 2 which is a rational number so you have to extend so finally what happens is that you see that you come to fields and you come to field extensions okay and the point is that every time you ask the question when you get a bigger number system you ask the question well if I write a polynomial in that with that coefficients will the zeros of the polynomial always lie there and if the answer is yes at some point then that is called an algebraically closed field okay so the fact is C is an algebraically closed field okay C is an algebraically closed field. So and what does this mean that is so that is any polynomial in one variable with C equations has a 0 in C okay and in fact you know if a polynomial has a 0 if you call the polynomial as f of x of course it is one variable so I should just call it as f of x where x is a variable and if it has a 0 which means it has a value lambda such that f of lambda equal to 0 then you know x minus lambda is a factor of the polynomial and by the division algorithm you know that the polynomial becomes x minus lambda times another polynomial of lower degree of 1 degree less okay and in this way you can continue and well the polynomial of lower degree that you get that also will have a 0 in the complex numbers and you can factor that linear factor out and if you do like this what it will tell you is that finally any polynomial can be completely split into linear factors okay that is what it says and this is the property of the field of complex numbers which makes it algebraically closed and in general this is the definition of what an algebraically closed field is an algebraically closed field is a field such that you take any single polynomial in one variable over that field then all its zeros are in that field that it means that you can find all the zeros in the field itself you do not have to extend the field you do not have to extend your number system to something bigger where you will get the zeros okay. So basically what it tells you is that you know if you are so what it tells you if you go back to our setup what it tells you is that if I take r equal to c if I take my ring to be c which is in fact field okay and if I take n equal to 1 then I have c here and here I will have c of x okay polynomial ring in one variable and then it tells you that you would give me if you give me a single polynomial if this s is set s is a single polynomial then the zero set of that is non-empty in fact it will have the number of zeros will be equal to the degree of the polynomial but of course you have to count the zeros with multiplicity okay you have to count the zeros with multiplicity after all the polynomial may be x minus 1 to the power of 5 okay and then well if you want to if you want to count the zeros with multiplicity then you can think of them as 5 zeros but well if you think of it as a subset here you get only one point namely the point 1 okay. So what this tells you is if you are working on an algebraically closed field and there is only one variable involved and you are looking at only one polynomial then you end up in a situation where this set is non empty okay now the question is mind you our original question is we are not looking at a single polynomial we are looking at a bunch of polynomials okay and this need not even be finite this collection of polynomials need not even be finite and not only that we are not looking at a polynomial in one variable we are looking at a polynomial in several variables okay what the algebraic closure property tells you is that if you are looking at a polynomial in one variable and if you are coefficient ring is an algebraically closed field then if you look at the zeros of a single polynomial then it is not going to be empty okay but we want something very very gentle to happen okay the answer to that is so you might expect that should you put something more some more conditions than just the field being algebraically closed for such a thing to happen and the answer is no the amazing answer is yes the amazing answer is this itself will ensure that so long as the set S is good in a decent way if R is an algebraically closed field then Z of S can never be empty okay and this is a very deep fact and this is called the this is one form of the Hilbert Nullstahl and Salz okay so let me write that down so fact so if we take for R an algebraically closed field then for F in Rx Z of F is non-empty of course provided F is non-constant of course you know when you are looking at zeros of polynomial suddenly you are not looking at a constant polynomial what that means is if you are looking at a constant polynomial if that constant is non-zero then there are no zeros and if that constant is zero then the whole space satisfies the condition okay so if you take a non-zero constant and consider that as a polynomial then it has no zeros so it is zero set is empty if you take zero as a constant polynomial then it is zero set is a whole space okay so what it says is that if you take for R an algebraically closed field and this set S to be a singleton consisting of only one polynomial which is of course non-constant then the zero set is non-empty so you ensure that this is non-empty so you can do some geometry okay but then here is the important thing so what we want is not for one variable X but we want it for several variables and we do not want it for a single polynomial in several variables but we want it for a whole collection of polynomials in several variables okay so that is the that is our deep requirement and that is what the Nulstel and Schatz as it is called Hilbert's Nulstel and Schatz that is what it promises so let me write the following down so first let me say the following thing suppose so here is a very simple let me call it a lemma I will write a very simple lemma if the set S is such that that does not that does not exist a finite subset let me write f lambda 1 f sub lambda m and polynomials g lambda 1 g lambda m in the polynomial ring such that sigma f lambda i g lambda i is equal to 1 i equal to 1 to m then so I should say and only then so I should say the following thing so there is one part of the lemma which is very trivial there is the other part of the lemma which is actually the Nulstel and Schatz when R is an algebraical course field so let me say that correctly I have to modify this statement a little bit so let me make a small modification if the set S is such that z of S is non-empty then that cannot exist a finite subset such that this is equal to 1 so this is a statement okay so I am saying that suppose so you see the whole point is the following the whole point is we are trying to look we are trying to we are trying to study this set of common zeros okay we do not want that to be empty you do not want that to be empty and the statement I am making is that if it is non-empty then no finitely no finite subset of S can generate 1 okay no finite subset of S can generate 1 that means you cannot get finitely many elements of S and finitely many polynomials from the ring of which this capital S is subset of such that you take multiply them and then add them you get 1 that cannot happen that is obvious because you see if the 0 set is non-empty that means there is a value small r1 etc small rn in the 0 set and this value small r1 etc small rn when you substitute it in each of these f lambdas it is going to vanish okay so in particular if I substitute it in this relation on the left side okay the left side is going to vanish and I will get 0 equal to 1 and in a ring if 0 equal to 1 then the ring is a 0 ring okay it has only 1 element which is 0 ring and certainly we are not interested in working with a 0 ring okay so if the ring is not the 0 ring then what this tells you is that if the 0 set is non-empty this can never happen okay it is obvious this is a very very simple thing okay but the converse to this that the converse to this holds when the ring is an algebraically closed field is the is one form of the Hilbert-Nultz transfer so let me write that the converse is true if r is an algebraically closed field and that is that is the that is one form of the Hilbert-Nultz so maybe so let me keep it like this let me keep it like this let me not state it the converse will be that if the subset S if r is an algebraically closed field and if the subset S of polynomials in the polynomial ring over r in invariables is such that no finite subset of that can generate 1 then the 0 set defined by that subset is non-empty okay that is one form of the Nulstra Nsats which is usually called the weak form of the Nulstra Nsats okay so of the Nulstra Nsats so maybe I will write it down so let so what is that so if k is an algebraically closed field and S is a subset of polynomials over k in N variables of course small n is greater than or equal to 1 okay then such that such that that does not exist a finite subset subset let me write f1 etc fm in S and polynomials so let me continue here g1 etc gm so this is m again in the same ring such that sigma fi gi is equal to 1 i equal to 1 to m then the 0 set defined by S in kn is non-empty you can find solutions. See what you must understand is that the Hilbert Nulstra Nsats is a grand generalization of the property of being algebraically closed you know if I put in the Hilbert Nulstra Nsats if I put n equal to 1 then I am looking at polynomials only in 1 variable and if I take the subset S capital S to be a singleton set okay then this statement is obviously true if for an algebraically closed field see what you must understand is Hilbert Nulstra Nsats when you put n equal to 1 is true just by the definition of algebraically closed field because what happens when you put n equal to 1 and when you take the set S to be a singleton consisting of only one polynomial and then if you have this condition that then this condition will become that polynomial multiplied by no other polynomial gives you 1 which is the same as saying that that polynomial is non-constant okay then you are saying that there is 0 so that polynomial in k1 which is just k exist so you are just saying that every polynomial has 0 which is the definition of what an algebraically closed field is. So what you must understand is that Hilbert Nulstra Nsats is a grand generalization of the definition of algebraically closed and it is a very very important theorem and this is the theorem that guarantees that if you are working over algebraically closed fields then you can really do geometry okay. So and this is called the weak form we will come to the stronger form later on okay and I will see later on if I can hint at proof of the Hilbert Nulstra Nsats usually a proof of the Nulstra Nsats is given in a course in commutative algebra but then there is also a way of looking at that proof completely in algebraic geometric terms. So this is something that keeps happening that you must always keep at the back of your mind there are many things that can be said in this on the language on this side this is the algebraic geometry language in this there are the same things can be said with the language on this side this is the language of commutative wings and modules and ideals and things like that okay. So proof here will involve you know ring theoretic arguments ideals and homomorphisms and modules and things like that whereas the same proof when you translate it here it will have geometric meaning and it is this it is trying to go from one to the other that really enriches both the sides okay. So okay so incidentally I should tell you what this Nulstra Nsats is so Nul this is German you know Hilbert was a German mathematician of course one of the greatest of all time and Nul stands for 0 and Steyler stands for position or point and Sarts means theorem or statement so it is actually so if you translate it properly it means Hilbert's theorem on zeros of polynomials of a bunch of polynomials okay fine. So okay so what we are going to do is so from now on now on we will always work over an algebraically closed field K that is that is that is we take R equal to K so if you want for convenience you can even think of the algebraically closed field as complex samples so that you know if it makes it easier for you to think about things and visualize things okay. So what we are going to do so our picture becomes so our picture goes from that generality into something more concrete so we have the following picture on the commutative algebra side we have K of x1 etc xn this is the polynomial ring in n variables and on the geometric side we have Kn which is k x k x k n times okay. Now well how do you think of Kn you are used to Kn from linear algebra I mean the always one would the simplest way one would look at it is a vector space of dimension n okay for people who have done module theory Rn can be thought of as the n dimensional free module over R okay so in fact we do not use the word dimension for modules so I should amend my statement to Rn is the free module of rank n over R okay. So dimension is usually reserved for fields so Kn is an n dimensional vector space over K a module over a field is a vector space okay so but it is not the vector space properties we are interested in so you see the vector space the properties of vector space are you have the 0 vector and then you know you have addition of vectors and so on and so forth. So in that sense you know the vector space studying the vector space properties is literally studying linear algebra but that is not what we are interested in is actually trying to study the points of the space okay without any regard to the vector properties okay so you so it means that all points of the space are alike I mean if you take the plane and throw away the vector space structure that means you take the plane and how do you get the vector space structure you have to first have an origin because for a vector you need an initial point and then you need a terminal point so normally what we do is we have an origin and every other point to every other point we associate the vector which starts at the origin and goes to that point we call it the position vector of that point and then we study all these position vectors and add them as usual with parallelogram law and then so on and so forth. But what we are going to do now is not call any not worry about doing all this we are going to think of all points as equal as one and the same so think of Kn but do not think of the axis do not think of the origin as the origin of the vector so you just think of it for example when is equal to 2 think of the plane but without the 2 axis there is a point called the origin but that point is not you do not try to for every other point you do not try to draw position vector and think of it as a vector. So you know this process of trying to think of Kn as a space not of points but not as space of vectors is what makes it into what is called an affine space okay so the affine space Kn is different from the vector space Kn in the affine space you are only worried about the points not about the vectors okay so you will see often in algebraic geometry people use the word affine and that is the whole point okay. So the first important thing is do not ever think of these vectors okay though it is a vector space of dimension Kn but that is not what we want right so well so this is the affine space literally and given a subset S to get the 0 set of oops yeah that is right here so here is our this is the picture we are going to look at and we are going to see what is there on both sides okay. So the first thing that I am going to do is so that brings us to the following question that brings us to the following question what are we going to do with this set we have thrown away the vector space structure is just a set what are you going to do with it so the first step is to give it a topology okay and that topology is called the Zariski topology okay so I will explain what that topology is so well so let me write that so let me write the following thing Kn along with the Zariski topology is called affine n space over k and denoted Kn okay so the first thing that we do to get some geometry on the left side is first of all have at least a topological space okay so we make Kn into a topological space what does that mean it means that you have to specify a topology on it and specifying a topology on it means what you try to give a collection of subsets which you make all as open subsets and this collection has to satisfy the axioms for a topology and what are the axioms for a topology the whole space should be an open set the null set which is the empty set should be an open set an arbitrary union of open sets should be open a finite intersection of open sets must be open so these are the four conditions for a collection of subsets of a topology of a space or of a set to make it into a topological space okay so so what so I saw that explain what the open sets are okay but then you know in when you go to topology there are there are two ways to approaching a topology one way is by open sets the other way is by using closed sets okay because closed sets are just complements of open sets so I can also give a topology on a set by giving a collection of subsets called closed sets but then the conditions will be complementary okay because of D Morgan's laws so the conditions will be that the whole space is a closed set then the empty set that is the null set is a closed set any if you take a finite collection of closed sets their union is again a closed set okay and if you take an arbitrary collection of closed sets their intersection is again a closed set these are just translations using D Morgan's laws for the corresponding axioms for open sets so basically what I have to do is that I have to tell you either I should either give you a collection of open sets or I should give you a collection of closed sets which satisfy the corresponding axioms and what happens in geometry is that is easier to begin with by looking at collections of closed sets and guess what what are going to be the closed sets the closed sets are going to be just common zeros of functions of this type so you see the so the idea is the following you look at this space the look at kn think of these as functions on kn of course you take any polynomial here and you take a point here if you evaluate the polynomial at that point you get a value so certainly a polynomial the elements here which are polynomials are certainly functions on this space and what you do is you call a subset here to be closed if it is the in the zero locus common zero locus of a bunch of polynomial functions which is exactly what this is okay so the moral story is that if you declare subsets of kn of this form zero loci of a bunch of polynomials common zero loci of a bunch of polynomials call them as closed sets then you get the Zariski topology that makes this kn into Zariski topology so what that will tell you is that what are the open sets open sets will be loci where certain where functions do not vanish the loci where the functions vanish for example the loci where locus where a single function vanishes is a closed set and the complement of that locus where the single function does not vanish is an open set okay and this is in tune with our common sense okay because if you take a real valued function on some subset of Rn or you take a complex valued function on a subset of n dimensional complex space Cn then the set of points where the function takes the value zero is going to be a closed set provided the function is a continuous function because it is a point is always a closed subset and if a function is continuous the inverse image of a closed subset is closed therefore the set of points where the function is zero is exactly the inverse image of the point which is zero and that has to be closed okay. So it agrees with our usual intuition so the idea is to give the Zariski topology in that way okay so we will look at that in more detail in the next lecture okay.