rk with them so that the energy use is minimized before we ever think about things like solar panels and other things like that. Of course, part of this process is a process of communication and presenting design ideas. So we sort of use effective presentation tools where we think of architecture actually is a process of communication more than anything. We as architects don't build buildings. We communicate what buildings are and so part of that process is presenting our ideas in graphic formats and we do that by engaging the community with compelling imagery. So imagery that really allows the community to step inside the building and understand what it's going to feel like and kind of answer some of their questions about what is this building going to be? Now it's really important as a part of the process, we don't just present, we don't just engage, we listen. So this kind of speaks back to learning about your community. Listening is one of the most important skills for an architectural team and we work hard to be active and sort of really careful listeners and in this process, one of the things that we're going to be doing is, many times community presentations are structured where questions for the community if the community has questions for the architectural team at the end, we actually often go into these community meetings with questions that we have for the community. So again, this kind of comes back to our kind of knowledge that the community are experts in themselves and often sort of getting answered about a successful building means reaching out to the community and asking kind of specific things that will help the design team advance the design in a positive way. And so here's some examples of that from the Garfield Park Library. What does that mean in terms of process outcomes? We have a couple of really important outcomes that we strive for. The first is fostering group dialogue. This is a communication process. It's a process of kind of meeting with neighbors and meeting with the different stakeholder groups and understanding what are very complex sort of goals for a project and how they all come together to make it greater than the sum of its parts. And that speaks to promoting stakeholder teamwork. We set that as a goal early in the community process that there's teamwork between the different stakeholders. During that process, we're doing a lot of listening. And one of the things we're listening for is because part of what a library is is something that tells the story of your community. So we'll be listening for those narratives that really reflect Santa Cruz. And then lastly, it's important that we develop community ownership. So that means that we work with the community through this process. So they see the project develop. They see their input and their feet incorporated with each round of the community process. And they really actually develop an incredible sense of ownership over the design because they were a part of that process and they contributed to it. So I wanna end by talking about values because it's really important for architecture, particularly public architecture and civic architecture to be grounded in values. One of the values that we hold very dear we know this is important to the city of Santa Cruz is sustainability. And we are thrilled that the library is targeting zero net energy. And that is something we will kind of be working on early in the process. And that speaks back to kind of learning about nature and thinking about passive design strategies. And then as well as working with a really talented technical team of experts about how we achieve kind of a very ambitious goal. Community is just a critical value for a library. Libraries actually phase are one of the preeminent community centers in America these days. And there's different ways to serve communities. It can be through a storytime event in a children's area. It can be through a makerspace where the teams are kind of showing off their technology skills. Or it could be for an outdoor gathering. Santa Cruz has beautiful weather and we love the opportunity to utilize some of those warm evenings for outdoor events. And it's also important that we have civic pride in these buildings. And these buildings reflect those values and the importance that they represent for the community. A library is an important building for any community and certainly for the community of Santa Cruz. And we design with that in mind that they have a prominence that respects and honors that civic pride. But it's not all about the big moments. It's not all about being on the street. It's also about the little moments. And we work very hard in our designs. We value this very much to create special moments that really are moments of kind of inspiration and wonder for when people walk into these buildings. Libraries are more than just a building. They are community spaces. They're spaces of creativity. They're spaces of learning. And this is an example of this portal to the children's area at the Half Moon Bay Library where you can see some of these early sketches of the idea of undersea bubbles becoming the children's sign and how that becomes a reality. And these special moments, they contribute to the memories of the community. The children are gonna come to this library. They're gonna read their first book there. They're gonna check out their first book there. They're gonna meet friends. They're gonna spend time with family. They're gonna grow the community. Years later, they're gonna have memories about this early experience they had at the Santa Cruz Library. And we are so excited to help create those memories with you. Thank you. Thank you, Abe and Katie. Really appreciate that. We need to see all your work all over. So thank you. Bonnie, do you have a wrap up? Yeah, so I'm going to go over actually to our interim library director, Eric Howard, who'd like to share a few comments. And then I'm going to wrap up with next steps after Eric. Great, thank you. Thanks, Bonnie. Good afternoon, mayor, council members. Welcome, Abe and Katie. One of the things that I really respect and admire in Abe and Katie is their humility and their willingness to learn and listen. I've worked with quite a few architectural firms for. And the three key things that I always look for is how responsive they are. Their experience and how innovative they are. And they knock it out of the park in all three of those categories. As you heard, where this is not an independent library, it's part of a larger system. And they have, even though they are really humble, they have an amazing amount of experience and Bonnie works and its culture. As they pointed out, our most northern branches and is in Boulder Creek and they're working on that now and completing that project. And our most southern branch is La Selva and they completed a beautiful remodel there. Not to mention Live Oak, Branch of Forty and Garfield. Their important piece of that experience is working with my staff. They have a really great understanding of how we work internally. They're really responsive to not just my needs, but to all the needs of the staff. In addition to the funders that we rely on too to enhance these buildings, while we rely on Measure S to make these really beautiful buildings, we rely on private donations to enhance these buildings, every single one of them. And Abe and Katie have been really responsive to their needs as well. When we've had donor meetings and they've given tours of these branches, I can't say enough how important that relationship is as well. So I just wanna thank them for their presentation today and for giving me the time to speak and provide a few words. Thank you. Thank you, Eric. Thanks, Eric. So I'm going to share just one last, or actually last two slides, which is on next step. And so just to wrap this up, to approve the contract today is for us to meet as a whole group with the design team and plan out sort of the timing and the stakeholder meetings. We're going to have October stakeholder meetings that we are hoping to kick off as well as workshops in November and December. And then we would be scheduled to come back to December. And I highlighted this a little bit earlier as well for a council presentation on major site design concepts. And then meanwhile, we'll continue working with the farmers market as brought up in our earlier presentation. We also have other stakeholders, including total fitness that we'll be working with as well on the site. And including in those stakeholder meetings, we'll be working with downtown organizations, downtown groups, as well as members of the community and interest groups. So they'll all be part of the outreach process and all of that will be presented and posted and noticed on our website. So with that concludes the presentation and we are happy to answer any questions that you have. Thank you. Great, thank you Bonnie. And again, thank you to Abe and Katie and good to see you Eric. We will go ahead and take questions from the council at this time. I do also just want to make an announcement for our next item, item number 25, because I do know that some folks will be joining for that. And I know four o'clock was sort of a time that had been put out there. I just want to announce we are not in, we will not be taking public comments this evening that item has, it is recommended to be continued to October 12th, 2021. I just want to make sure that that is available for people to consider. We will, the item will be heard, but we aren't anticipating having public comments this evening on that due to the continuation. So I'll flip back down to this though real quick and go ahead and take questions from council. I see council member Cummings, council member Golder and then council member Comtar Johnson. And thank you for that presentation on this item. Good to see you. And Katie, I had a question. I don't know who this should be directed to, but last year we had some extensive work done by group four to kind of come up with the design for the library mix use project on this site and put on different types of designs. And the council recommended one of the designs and that would have parking detached and try to maximize the amount of housing units. And so now with moving forward with Chase and Architect, I'm just wondering because of the fact that there was a lot of community input and there was a lot of work done and money spent on that group, how do we, or what's the plan for incorporating the designs that were brought for us from that group with kind of, you know, moving ahead? So. I'll start council member Cummings. And then, you know, Abe, you may wanna add on to that, but I will say that we took the site design and the specifics from the community outreach and the work that group four did. And that was included as part of the scope for their quest for proposals for all the architect teams. So all of them, when they presented their proposals, they presented it on the basic design that was the recommended design of group four that count proved that was based on the community outreach. With that said, you know, each of the architect teams, you know, did look at the possibilities for the site and there are some other options to consider as well that could result in potentially some more affordability, greater unit count and just some flexibility in the project. So we've encouraged them to make sure, particularly in the initial phase that, you know, pre-design conceptual that we are designing towards that direction that we had from council. But we didn't want to close off the possibility that there could be a configuration on the site that actually nets us more affordable housing and potentially nets us greater space for the library by creating some efficiencies from the integration of the project in a different way. And so we're going to be looking at that closely and but we're very aware of the community input to date and want to make sure that that's being carried through. Since it has been, you know, a multi-year process, there has been many touch points with the community over the years. And of course, the extensive work done with Jason in the past as well is also information on the project that we're carrying forward as far as the values and the input on the project to date. And so with that, if he may have some additional context to add. Thank you, Bonnie. So I don't have too much to add to that. I think Bonnie described it well, but essentially that's correct that our scope is basically defined by the, you know, previous iterations of community process that led up to this point. And we will use that as a start for our process and we'll be working directly with the city and the community to sort of further shape it to be the most successful project. And those are all the comments I had as was hearing some concern around, you know, are we starting again from, you know, step one with the library and just wanted to make sure that that was clear to the community that that previous designs from group four are being taken into account as we move forward. So thank you for that clarification. Council Member Boulder. I didn't have any questions. I just had comments and I just think that the designs that you shared are so beautiful and it was so inspirational and I can't wait to see this project complete. And I think it's going to be such a tremendous asset to our community. So thank you for all your work. I really appreciate it. Council Member Calantara-Johnson. Thank you. Yes, I would like to echo those sentiments. Beautiful job on the other libraries throughout the community. And thank you to the whole team for the presentation. I had a couple of questions about the community engagement process. It sounds like a pretty thorough process. My assumption is that I wanted to the notices of the workshops and focus groups will also be noticed and conducted in Spanish. Is that correct assumption? Yeah, we've been doing that on almost all of our recent outreach. So that's our plan is to continue that. Great, thank you. And how have we done outreach to the Latinx community in the city? What's our approach? Or what will be our approach? I haven't spearheaded that, but I have been engaged just in getting up to speed on some of that. We've been working with the city's liaison as it has been part of the process and the approach. And then we've been working also with some of our community partners that in sort of sharing the notices with them and making sure that they communication. Great. And then my last question is, I imagine that some of the efforts you've done here and elsewhere, the community engagement has been online given the current situation we're still in. Could you either Abe or Katie touch on how you have made these online engaged, accessible and interactive to community members? So I will actually acknowledge that we haven't done a project from the outset online, although we have done community engagement online. So this will be the first one where theoretically we may have kind of a multi event series online. On some level, I don't think the kind of approach changes dramatically. It sort of speaks to, we build the process up from the beginning. So we're not entering this process and then presenting a design to the community. That's not how we approach this. We engage the community in kind of listening and kind of information gathering first. And then we actually kind of take them along on the process of kind of learning about how we kind of think and in structure kind of design development. But similarly, it will be kind of structured regardless of whether it was online or in person. We will generally at the workshops lead with a brief presentation. And then we'll do breakout group. So Zoom has the ability to break out into rooms. So that we kind of try and break down the scale and people have a little bit more ability to dialogue with each other. And we kind of work with the community so that there's notes taken in that small breakout group. And then that small breakout group then can report back to the larger community. So there's kind of that idea of small group dialogue is present whether it's online or in person. And we will obviously adapt like everyone to kind of COVID protocols as we go forward. Thank you. And maybe just a thought or question for, I know that in the past when we've had community engagement efforts, we have, I believe we've opened up the library for those who don't have internet access or the capability to access these things on their own. So maybe that's something we can think about as part of this process. Thank you. Oh, yeah. Sorry, I was just gonna point out that as of today, we opened up reservations for our program and conference room. So we just went to the swing of that at all of our branches that are open right now. And then also just to try to answer your earlier question, we do have, we do outreach all the time, but beyond just, you know, not just to the city. So because this is everybody's library throughout the county. So we'll be doing outreach in Spanish and in English throughout the county to get feedback on this. Great. Thank you so much. I'm also really excited about it. Council Member Brown. Thank you, Mayor. And thank you, Abe and Katie for the presentation. It's good to see you. It's good to see your beautiful work. And I just, I wanted to ask a couple of questions about your, how you're thinking about described really, really clearly and, you know, vividly how you think about the experience and placemaking and showed us some beautiful buildings. And I just wanted to, so I have two questions. One is related to your role now being as the architect for a component of a mixed use project where the mass of the building and the height and all of that are gonna be dependent on, you know, broader set of goals. And so I'm just wondering how you think about, you know, that street level, engaging, you know, how people feel about the space of the library given that it's the most likely on the first floor of a much larger building. So just trying to think about like in those images you see the sky and it feels open and that's not gonna be the case in this case. So just how you're thinking about that. And then I think that there are a lot of variables and, you know, things that are gonna depend upon, you know, other pieces coming into place. What square footage do you have in mind at the moment? Are you thinking about that additional 5,000 square feet? I know as a member of the library subcommittee or the library subcommittee, excuse me, that we talked about that being a really big incentive for doing a project in this way is that we were gonna get significant more square footage for additional program space and other spaces. So are you operating on the additional 5,000 square feet assumption or are you trying to just figure out how to factor that in as we go along? First, thank you, Council Member Brown, nice to see you again. So first on the issue of the square footage, I'm very familiar with the kind of the different sort of calculations of square footage and the different studies that have been done over the years. What I'll say is we defer to the city in terms of setting kind of the programmatic targets. We're kind of familiar with the different categories and we're gonna work with the city about kind of where their goals are at. And obviously that'll be sort of a conversation done in tandem with the library as well. So I can't say specifically that we have decided to design to a specific target today, but what I can say is that we'll work with the city and the library and sort of build from that programmatic basis. In regard to kind of the library as a part of kind of this mixed use project, I think it's a really exciting opportunity and it's actually a programmatic pairing that is becoming more and more common, both with libraries and just kind of in general throughout America that these kind of libraries are being developed in tandem with affordable housing in many cases and in larger mixed use projects. So multitude of reasons for that. There's kind of synergistic reasons in terms of kind of the way different uses kind of reinforce each other, the idea that children who live in the building can go to the library. And there's also kind of reasons from a funding standpoint that they're being developed together, there's often an economy of scale of bringing the bigger project. In terms of design, so that's the other piece of it is kind of how does it feel comfortable in terms of the way we think of it is that the library and the housing are going to be friendly neighbors. So they're not the same building per se, even though they technically from a building code standpoint, it is the same building. But when we think about design, we'll think about kind of careful differentiation of the library from the housing in the way that they're having a friendly conversation with each other. So they're not trying to be the same. They're not trying to dress in the same clothes, to repeat each other like a parent. But they're in dialogue in a way that they feel comfortable next to each other. So obviously we haven't designed the building yet, but going in, I can say at the outset that that's how we'll be thinking about it is that the library will be in dialogue with the affordable housing and vice versa. And they will sort of at the kind of areas where the buildings kind of interact with each other, we'll think very carefully about those kind of moments of interaction so that they feel kind of carefully tailored and kind of give the building a sense of scale and friendliness. So hopefully that kind of answers your question about kind of how it will be integrated. And I just wanted to add Council Member Brown about the size of the building. As part of the scope, we're really looking at maximizing the footprint for the library and recognizing that there is a cost associated with that. So part of the direction and the exercise that we'll be doing and looking at the various pieces and programmatically the elements and the direction that we had previously from Council is how to most efficiently and from a design perspective, successfully achieve that. So when we come back to you in early December, we're really hoping to be able to show you a design, hopefully they get to that higher square footage for the library because we know that's a goal for everyone. And if we can do that, a cost effectively as well, we think that there may be a way to do that, you know, all the better. So those are our goals, that's what we're striving to achieve. Thank you. I see Vice Mayor Bruder, please. Thank you, U.A. and Katie. My questions, I also had questions on the outreach and engagement on the different components of the library and your presentation. There were great library examples and so in the timeline that is included in the packet, I don't wanna assume but with the engagement, how the housing parking library all fits in, is that all at once or do you break it down throughout the timeline? What does that process look like? I can speak briefly and then Bonnie, you may wanna ask, well, but I would see the development kind of happening concurrently to kind of Council Member Brown's question, the design of the library and the affordable housing they do need to be thought of together. So this is not two projects in isolation. These are programmatic uses that need to speak to each other and build off each other. We would definitely see that kind of moving forward together and we know that you can't have a community process for this project without talking about both components. It will be difficult to separate them out. So yes, I would see them moving forward together. Bonnie, maybe you can add to that. Yeah, I mean, absolutely, that's right. I mean, when we come back to you, we're not just going to be presenting the library, it's going to be the whole project and we're going to have at least one option that really close, almost exactly close the concept design where we had the council direction from last June based on Group 4's work and then taking those same programmatic elements and looking at ways we might be able to net more affordable units and more library. If there are other creative options to create that in the project, you're going to see that as well, but it's going to be for the entire project. We're really focusing and visually having, Jason's texture be the lead as a master library architect, they're still really engaged overall in the look and feel of the entire project and that's really why we have that forefront is also because it really is the library that is going to be visually what you're experiencing when you come to the project, particularly on the pedestrian level. And so we want to make sure that that's really leading the design, we move forward on this project, but the design elements on the housing, that's key too and because we have such a great team and they're going to be working together, we know that we're going to have a project that meets all of our goals as far as sort of just the overall look and feel on how it's integrated into the surrounding block and the neighbors. Thank you. Great. Thank you, everybody. I'm not seeing any other hands up right now. So I'll go ahead and take this out to the public now. And I see we have one attendee with their hand up. So this is for item number 24 on our agenda today. That's the contract for the mixed-use library master architect.  This is for phone number ending in five, three, six, two. Go ahead, one more time. Go ahead for phone number ending in five, three, six, two, go ahead and yeah, there you go. You're ready to go. Okay, thanks. Hi, everybody. It's Judy Grenstra. I had thought of just presenting some other thoughts, but now I'll just go ahead. Council might not be aware that the library is embarking on a strategic process in the coming months. Doesn't it seem premature to have Jason design the interior spaces of the library before the strategic plan? An analysis of how much space for each of the library's services and programs would best serve this community. It was done by consultant Penny Hummel during the Nolan Tam process about four years ago. Now that was for a 44,000 square foot building, significantly larger than we'll be able to afford. In short, wouldn't it make more sense to design a building after the library has gone through this strategic planning process? Okay, now I'm switching to my latest reaction to what I've just heard here. So are you saying that the Abe Jason, which I greatly admire Abe Jason and Katie as a team. Now, my concern was about the outreach. Now that Bonnie has noted that the order of the meetings is different with the pre-design meetings now consisting of six focus groups and three workshops, which was originally scheduled for later. So are these two, is all this outreach, three workshops and six focus groups all supposed to happen in the week after Thanksgiving? Because that is really inconvenient timing as far as the ability of the public to participate because it's right around Thanksgiving and it's just too condensed. Okay, that was one point. The other one is, are you saying that this out, conducted by Jason, is going to include design of the housing components? Because I was under the impression it was just gonna be about the library because if you're including, it's gonna be way too much. Okay, thanks. Thank you. Next up, I have Krista. Thank you, council members. So this should be a pretty straightforward question, but I was looking for the answer. So the, an acquaintance of mine pointed this out that in the RFP for the Downtown Library Mixed Use Project, the project proposal must include a minimum of 50 affordable house above a new ground level downtown library. And then she also pointed out that the motion for approving this project was specifically for a minimum of 50 low income housing units. So I know that affordable and low income have different meanings and that those need to be, they have like very specific parameters. So I wanna ask, is it 50 low income housing units that are going into this plan or is it 50 affordable housing units? Thank you. We will try to clarify that as needed with the staff. Excuse me, other comments from the public today on item number 24, please raise your hand if you'd like to speak to this item. You can raise your hand by pressing star nine on your phone. I'm not seeing any other folks in the meeting today that would like to speak to this item. So I'll go ahead and bring it back to the council for deliberation and action. Vice Mayor Brunner, I see you and the member Boulder and then council member Watkins. Thank you. I know we received some information earlier. I wanted to just quickly ask Bonnie Lipscomb to clarify that there would be 107 housing units of extremely low and very low on the housing portion of this development. Is that correct? That's right. So it is affordable housing, but the categories of affordability for this particular project are very low. So at 50% or lower of area median income or even extremely low at 30% of area median income. So we're targeting those because that's the hardest to build affordable housing in our community and the least likely housing to be built without a public subsidy. So even affordable housing developers frequently have some challenge getting at that low unless there's a significant public investment. So we're really focusing there and it will also help us meet our regional housing needs allocation or renegals. Great. Great. I'm happy to make a motion to move towards awarding the contract for the mixed use library master architect to Jason architecture in an amount up to 2.289-550 or 2.9 and off 2.29 and authorized the city manager to execute an agreement with Jason architecture in a form to be approved by the city attorney. Thank you vice mayor. Is there a second to that? Council member Golder, I saw you. Okay. This is seconded by council member Golder. We have a motion on the floor then to go with the staff recommendation and is there additional comments from council members regarding? Go ahead, council member Brown. I'll just be very quick. Thank you. I find myself in a difficult position here because I absolutely support the Jason architecture being our architect for and to do the design for our new downtown library. I'm thrilled about the potential to get very low and extremely low income units actually built in our community. And I also am, you know, I have heard so much concern among community members about this particular site and the massing on this site. And, you know, and I just feel like supporting the things that I really want to support. I can't, I can't do that because I'm not going to be able to support that.  I can't support the, you know, the mixed use project moving forward on this site. So I'll be voting no on the motion but I do just want to say that, you know, I really have a lot of respect for, you know, Dave and Katie your work and I'm, you know, I'm looking forward to seeing what you come up with. And I'm glad you're excited and I'm glad others are excited, but I can't support it today for the bigger context. Thank you, council member. And I'm not seeing any other hands up by my colleagues.  We have a motion made by Vice Mayor Bruner seconded by council member Golder to award the contract for the mixed use library master architect to Jason architecture. And Bonnie, can we do a roll call vote please? Council member is Watkins. Hi, and I want to thank you for the presentation. Calentary Johnson. Hi. Brown. No. Cummings. Hi, and I'll just say for the record as well that we really wanted to see how this continues to roll out especially given that there's a lot of potential for affordable housing. And I know we need to really balance all the needs of the community. And I think that we have the potential in this project to really meet the needs of various stakeholder groups. And so, well, I'll be happy with the outcome. I think we're going to get a lot of positive community benefits. Golder. Vice Mayor Bruner. Hi. Mayor Meyers. That motion passes. And we had six in favor and one against. Thank you, everyone. And congratulations, Abe and Katie. We look forward to working with you a lot over the coming months. So, welcome back. Thank you. And we're so excited to do that. It's a privilege to work with you. We're very, very excited. Yeah. Knock my headphones out. Yeah. Whatever Katie said. Thanks, you guys. Okay. We will move on to item number 25 now. And item number 25 is 831 Water Street. And the purpose of this item was to conduct a public oversight meeting as according to SB 35 to assess compliance with objective standards criteria and accompanying density bonus requests for an affordable housing project proposed pursuant to SB 35. I just want to be clear for today, for the public attending today's meeting, this item is recommended for continuation to October 12th, 2021. This continuation is recommended to allow for our staff to complete further review of the revised plan submitted by the applicant on September 9th, 2021. Our staff to date has done an outstanding job on the review of this project to date, and this new information needs the same level of review. The October 12th, 2021 meeting will include a public comment period. And at this time today, we will not be taking public comment today due to this continuation of this item. And I would look for a motion to continue this item to October 12th, 2021 from one of my colleagues. And I do see Council Member Golder's hand up. I will move the recommendation to continue item 25, E3-1 Water Street to September 12th, 2021 for the public oversight meeting. I'd actually, October. Great, what did I say? I said October 12th. Okay, okay. And I will second that motion and we can go ahead. I don't know. My understanding is we are, I'm looking for Mr. Kandadi here a little bit. So we have a motion on the floor. Tony, deliberation by Council is, I believe to not be held today either, correct? That's right. The only issue before you is the continuance that Council Members can comment on the, on the continuance of the item, but substantive comments on the project or that sort of thing would be appropriate when the item is actually presented to you substantively. We have a motion for a second. So we're getting guidance from our attorney that comments on the continuance are appropriate. Other items, other comments should be held to the actual noticed meeting in October, October 12th. I mean, I will just add a few quick comments. Again, letting our community know that this is a very complex project. It's a very complex law. Both of these are complex laws and we, I just want to again recognize our staff. I think they've done a lot of work to try to really understand and look at the, the objective standards that we do have on the books with this project. So we look forward to receiving additional analysis by the staff for this. Council Member Cummings, did you have a comment? Yeah, I just wanted to appreciate the staff's analysis on the July 27th application for this project. And I fully support the initial staff recommendation for the now based on the analysis through the project's numerous inconsistencies with the city's objective standards. The applicant has legally agreed to an extension of the time period for consideration of his application to October 14th and has provided a letter which was circulated to the council to express this in writing. So I just want to make sure that members of the public know that this has been legally documented. And while my preference would be to deny the application based on the staff's analysis and require the applicant to submit a new application, I understand that under SB 35, a developer has the right to revise an application and the agreement to the extension gives the city a reasonable amount of time to analyze the September 9th application. Given the decision has been made to not hold public comment, I'm prepared to... I was prepared to make a motion that has some amendments. So I'd send it to Bonnie and would like to see if either we could vote on the motion with the amendments or if we could vote on them separately. But the motion would be to move the staff's recommendation based on the applicants agreement to continue the 831 Water Street Project, October 12th, 2021 with the additional actions. One, the city council indicates its intention and support of the previous staff recommendation to have denied the July 27th application based on the detailed staff analysis of its inconsistencies with the requirement of SB 35. Two direct staffs to provide as early as possible before the October 12th consideration of September 9th application and analysis of it as detailed as the one that was provided for the July 27th application and three that since it's prohibited from conducting CEQA review under SB 35, the city shall not act as a responsible entity for the purposes of conducting environmental review of Section 8 voucher applications for SB 35 projects. Tony, Council Member Cummings, I don't believe we are accepting another motion. Point of order? I'm sorry, I'm going to load on for a, I'm just getting clarification from our attorney. Yes, that's what I like to say. That's all I'm going to do. I'm not going to present anything. It wasn't clear to me whether this was intended to be a substitute motion or a... Yeah, that was my question as well. A request for a friendly amendment. I would say, however, that I believe that it would be inappropriate for the council to take action on item number three. First of all, because I think in order to make a policy determination about how the city council would handle Section 8 vouchers for an SB 35 project in general, that's a policy issue. That's not before the council. Second of all, I think you would have to have public comment for that. And thirdly, my understanding is that projects that require NEPA review, the responsible agency for that is the agency in whose jurisdiction the project is located. So from a legal perspective, that's probably problematic as well. As to items one and two, I think, I guess I would just ask for clarification if this was intended as a friendly amendment or a substitute motion. I'm just not clear on that. Well, it sounds like that the friendly amendment wasn't going to be accepted. So I'm happy to move it as a substitute motion. So we'll take a vote on this substitute motion. Then Tony, is the substitute motion on second? Second. And can I just ask for clarification? Does the substitute motion also include item three? I would ask that item three be included for consideration on October 12th. If we can't make those changes today, then as these applications are coming forward, we need to understand what role the city has and since we can't discuss it or make any action on it today, then I think that it would be good so that the public understands what role we can play and we can have a determination of that when it comes to these NEPA reviews. I think what I would suggest, if the council wants to consider these items is that we proceed with a vote on the motion to substitute council member Cummings motion for the prior motion and just take an up or down vote on that and then the council could debate the content of the motion if it passes. So we have a substitute motion on the floor. So now I wonder you need to vote whether or not to accept the substitute motion. Exactly. And but I wanna make sure I'm understanding what the substitute motion is. Does it include number three? Cause I didn't get that wasn't a clear answer for that specific question. And what I would recommend is that we clarify that if the substitute motion is accepted. Okay, so we have a substitute motion on the by council member Cummings, seconded by council member Brown. And this would be to accept the substitute motion and correct the roll call vote. Council member Hawkins, did you have a question or comment? Sorry, I just wanted to get a question cause in terms of process, Tony, what I heard you say is that it's really about the continuance of the discussion just to continue the item but going into sort of substantive statements as sort of listed, that feels sort of not necessarily process, but I just am a little concerned also given our earlier conversation in close session. Yeah, I mean, I share those concerns and which is kind of why I'm suggesting that the council move forward sort of forthwith and decide whether or not to accept the substitute motion. So we'll go ahead and have a roll call vote, please, Bonnie. Council member Hawkins. No, and for the record, it's just because of the legal considerations associated. Is that okay? Council member Johnson? No, and I have the same concerns. Brown, Cummings, Boulder? No, and I have the same concerns. Vice Mayor Brunner? No, and Mayor Myers? I'm no also, and I have the same concerns specifically the language and the motion is inaccurate and it's based on our understanding, my understanding of SB 35. Okay, that substitute motion fails. So we will go ahead and take a roll call vote on the motion to continue. Council member Watkins? Helen Terry-Johnson? Cummings? No, and I just want to make sure it's clear for members of the public that I'm very much in support of the recommendations to deny this project based on the detailed staff analysis that came before the city council and it came before the community before it got changed yesterday at the end of the day. Vice Mayor Brunner? And Mayor Myers? Fine. That motion passes with five for the motion and two against the motion. Okay, we are currently with item number 25 and I did go out of order. I'm gonna go ahead and move to oral communications now. For members of the public who are streaming this meeting, if you want to comment during oral communications, now is the time to call in. Instructions are on your screen. Oral communications is an opportunity for members of the community to speak to us on items that are not listed on today's agenda. If you are interested in addressing the council, please press star nine on your phone to raise your hand. You will have two minutes to speak. When it is your time to speak, you will hear an announcement that you have been unmuted. We request that you clearly and slowly, state your name before making your comment so that we can accurately capture it in the meeting minutes. However, it is not required to state your name. Please remember this is the time for council to hear from the public. We are not able to log with each member of the public, but when we are able, we will address the questions raised after oral communications has been completed. You see that we have two folks in the audience regarding oral communications. I have phone number ending in 1810. Please press star six to unmute yourself. Yeah, how about blame shifting of his failed policies? Let's skip the previous judgmental errors of the lockdowns, arbitrary essential workers and businesses, facility science of cloth masks, and the many other ill-conceived mandates causing masks, casualty, economic health, and social chaos damage. I focus here on the continuous 100% policy bet on mRNA vaccines falsely promising a zero utopia in what has become an unfathomable monumental blunder using COVID fear porn at best.  It's go time against Biden and the like, not your neighbor if you ever wanna be a free people again. As to the policy error, it's plainly wrong to force every single person to undergo medical procedures with 100% informed consent for disease with such low mortality rate for so many people while denying treatment and de-prioritizing treatment research. Worse, the long-term risks are still unknown and available data suggests the vaccines aren't as effective, safe or long lasting as they need to be. The latest paper out of UC Davis finds 12 to 17 year old vaccinated boys are over six times quickly to develop a cardiac adverse event heart problem compared to unvaccinated children who required COVID hospitalization. Another finds COVID immunity for the recovered is 13 to 20 times more effective than mRNA vaccine immunity. Forcing something and discriminating inside other bodies is a risk.  Next up, I have phone number ending in 3585. If you could press star six to unmute yourself, please. If you press star six, you should be able to unmute yourself. Go ahead, please. Yes, my question is, will there be local hiring requirements on these projects for all the libraries so that taxpayer money stays within the community? Thank you, sir. Next up, we have item, or excuse me, phone number ending in 5362. Go ahead. Hi, again, it's Judy Grunstra. I'm following up on a discussion at a recent meeting about the fate of the River Street sign. Informal polling on Santa Cruz local showed a majority of people in favor of not reinstalling that sign, which is currently out of sight. Thank goodness. I believe Justin said council might discuss the sign with the public work staff. Please scrap the design, scrap the sign, recycle the materials, and get the arts commission and public involved in the design process for welcoming attractive sign or just install some landscaping or trees. Thank you. Thank you. Next, I have Krista. Please press star six to unmute yourself. Yes, thank you, mayor. So I just wanted to say that support, high density housing, bringing high density housing to Santa Cruz, especially low income and extremely low income. I think that's really important. And I think a lot of council members agree. I could support it much more and more vocally if I was confident that our, we had a plan for our water supply. A lot of the conversations I'm having with folks around this issue is mostly just really concerned about low, I don't know much about planning for long-term water supply, but I bet our interim city manager does. And I bet there are a lot of members in the community who have really good ideas about this. I know they sell, there's a lot of history with that. And I don't know if that's the right direction or not, but I would really like to see some really proactive action to concerns around water, especially when we're bringing developments. And I mean, I think housing is wonderful. It's kind of hard to support hotels when I'm considering the water shortage because visitors come in, they'll welcome you as much water as they like. And so I wouldn't support that, I would like to see some strong aggressive action on protecting our water. Thank you. Thank you very much. Okay, I'm not seeing any other hands up for oral communications this afternoon. And with that, our meeting is adjourned. Thank you, everyone.


AI is sometimes perceived as a quest to build an artificial human, and sometimes people talk about augmented intelligence. It's not unlike using a calculator or using Google. It's the idea that this technology augments our abilities and makes us better at what we do. And what it means to us is building computer programs that help society, help people, help scientists. A case in point we have a program called Semantic Scholar, which is revolutionizing scientific search. You know, scientists have their own specialized search, and like all of us, they're subject to information overload. They're drowning in a sea of scientific papers and so on. Our technology uses AI to help them home in on the right results, help them formulate better hypotheses so that problems like climate change, like vaccines for Ebola and Zika, all those things can progress more efficiently with the Semantic Scholar program helping the scientists. I am an AI optimist. I see huge benefits where AI can help us solve humanity's thorniest problems.


Is this the style of a guy that you might swipe right on? Yeah, I think so. I think we changed a life today. I really do. Yo, what's going on, everybody? Welcome to another special Fung Bros. makeover. I know you guys have seen us do this video before, but this one is a little bit different. We're actually gonna be asking random strangers to help vote on what kind of style and makeover this guy should have. Also, they're gonna be helping pick out what type of photo and what type of caption he should have on his new online dating profile. We got our man, Peter. Hey, Peter here. Yo, Peter, where you from? Tell them about yourself. Yeah, I'm an actor. Just moved here in December trying to get started from Oakland, trying to meet more people. What part of Oakland? The nice part? Go Warriors. All right, so what are you trying to do as far as like dating go? Haven't been too successful so far, so wanna see what real people think about my dating profile. Get started from there. All right, yo, Peter, you ready for this makeover? Yeah, I'm ready. Let's go. All right, real quick, before we get into that makeover, I gotta give a quick shout out. We partnered with Eastmeat East, the number one Asian dating app. Eastmeat East is a great way to connect with Asians from across the world doing all different types of things. They have this great live streaming feature. Even if you aren't single, you can join in on the fun. You guys got to check it out. So they're steadily growing up to 600,000 members, so we're gonna see how many of them will match with our friend, Peter, after we give him a new makeover and a new profile. So definitely check out this app by clicking on the link in the description box below. Guys, Eastmeat East, you know the name. Let's get on with this makeover. All right, real quick, before we get on this makeover, bro, I need to know your current style and let me see some pictures that you were gonna post. Suit, arm around your friend, so maybe let's not use that. All right, that's my Halloween costume, Asian tourist. Oh, it's your Halloween costume. I just thought you were using a selfie stick. Would you say your image is kinda like the awkward guy? It's kinda awkward, so I tried to make fun of it a little bit, so maybe if I take an awkward picture and I'm awkward, it's just funny, okay? First, we gotta go find out what people around LA think. Ready for the makeover, whatever they think on the count. Think on the count. What are some things that you've seen from guys that you liked and you didn't like, so as far as like profile photos and captions?  Stuff to show the personality, you know, like if she likes to go outdoors or she likes pets. One of the swipes I had to say no to was he took like a selfie in the bathroom with the toilet, like the lid, both of the lids were open and they were like right next to him. Oh, what are some bad captions? We told him to make it short and sweet because if you make it too long, no one's gonna really read it. I also like it when they add a little bit of humor to it, but it also depends on what kind of humor or girls are looking for, cause some people like the big bag theory, you can go for nerdy stuff. What kind of guy do you think Peter is?  You watch anime? Computer games? Activity, like badminton. Tennis? Yeah, tennis, like a tennis or a badminton player. Probably plays ultimate frisbee. Kind of like the term nice guy. Your bag does a nice guy, how does that feel? Is that a bad thing or a good thing? Nowadays, like kind of both. Like what kind of girls do you think he likes, style-wise? I think he likes like the nice, quiet girls. Late bag. Probably ones that are like genuinely intelligent and like he doesn't look like he's going for the ratchets, you know? As far as type of clothes, I have four categories. I have like streetwear, the preppy, kind of like Banana Republic. Rustic Americana, more like a denim jacket, and then I have the hipster. Let's go with the hyperfist, he'll look much better. I was thinking more of like the hipster look. Yeah, the rustic Americana, definitely. I could see him like in a jean jacket, like denim denim kind of look. Rustic, yeah. Yeah, I like that one too. Americana would look good on him.  The jean? The jean. The jean. Pompadour. Pompadour, semi-pompadour. A little pompadour. Yeah. Kind of caption, should he do the over the top funny? My tech company is worth over 15 million. I'm Mark Zuckerberg's brother-in-law, master Korean Mandarin in Spanish in two years. I'm a gold medalist, Olympic sharpshooter. I became a secret agent by the age of 19. I like this one. But retired by 20. Right now, I'm yachting my way across the Caribbean, sipping on a roasted Oolong milk tea. Okay, fine, I exaggerated a little bit. What's even true? I'm drinking milk tea while I write this, and I never retired from being a secret agent. Let's go save the world again. That one, that one, for sure. Absolutely. I love that one. That one's cool, but for me it isn't. Okay, what'd you think? Was that fun?  You got real feedback from real random people. Yeah, I learned a lot about what people thought. Okay. When they look at me. How did you see yourself before, and then how do you think people pretty much saw you? I thought I was just kind of like the awkward, you know, kind of nice guy. I got some of that. Surprisingly, you played basketball and football, but then they thought you just played tennis and badminton. Yeah, tennis and badminton, like ultimate. The results are in, and this is the makeover that people have decided on.  All right, so we're gonna try to make all that happen while we're out here, all in the next hour. Yeah, I'm really looking forward to this makeover, ready to look different. All right, so now we are onto our haircut portion of the makeover. We know we like to do this step first. So here we got Andy. Thank you, Andy, for doing this, man. Anytime, brother, anytime. The people have voted, they wanna see Peter here with a pompadour. Can we do that? Of course. All right, we got this, we got this. All right, man. To a good pompadour is just getting that volume when you blow-dry your hair and the product to use. The product is what's gonna complement that pompadour. Okay. Okay, so pretty much we were trying to acquire a high-volume pompadour, but his hair still needs more growth on the top. So we went ahead and just gave it a nice and tight fade on the sides, and we're gonna acquire that shape on the next haircut. Guys, even if you have short hair, you can achieve some volume. Okay, so we're gonna go ahead and do his eyebrows. So what I like to do first is go in with a one open and trim it down, and then come in with my straight razor and give it a nice, natural shape. This big a difference. Honestly, amazing. I think it's a lot cleaner, right? Proportions like long on top, short on the sides. It's perfect. It looks so good. All right, next up, we're gonna get you into your outfit that everybody voted on, the rustic Americana. I'm just waiting for Peter to come by. Hopefully the outfit fits. Yo, dude. How do you feel about this personal style? I feel very different. I've seen this look before, but now I can see it on myself. Okay, so you got the boots too? Those boots are actually really worn. I think we got those from the vintage shop. Are you ready to hear what people on the streets of Pasadena got to say? Yeah, yeah. What do you think about this outfit and does it fit him? I think it's stylish. It has its own little flair to it. I like to did them on dinner. I was wearing that yesterday, so I like that. Yeah. Question, does he look like he plays either tennis or badminton? No. Okay. I think it works for them. I think it's like the whole flannel and the jean on jean, and I really like those boots too. Okay. But old pair is really cool, man. That's something I would do myself, so I like the high fade and everything, and it kind of cleans everything up. You know? The whole fit overall, I feel like it's very...  Does he look like that type of guy? Not at all, man. Really? Not at all. Like, I don't know. The style of a guy that you might swipe right on it. Yeah, I think so. I like style on guys. I like when they dress for the hell of it. And I really like that. Does it look like he plays a lot of video games? I think video games, but I feel like it's more like a basketball video game. Okay, you might play 2K. Yeah, I think it's 2K. Help us come up with some photos to take around Pasadena. We're thinking about taking some in the alleyway, like something around some of the urban. There's like graffiti art, so it's like, that's really good to have. Where's the alleyway right here? Yeah, I just... You're talking about right here. Could you show us that? Yeah, I'm sure. Build you a new profile, man. You just moved to LA. Oh, you gotta get a date? Dude, don't look straight at the camera. Taking good pictures takes a lot of time and concentration, okay? This is huge. Cool, we got a couple good photos. Really give me like a good walk. Is that how you walk? Is that how you walk? Boom, who is this man? Who is this man? Different with that beanie on. I look like a cool Japanese artist. Now look more towards right above me, right above me.  So here, language you speak? Green, English. Age that you arrived, a lot of people are born in another country. You are too, right? Yeah. Okay, when did you come over here? When I was three. Education? High school year. High school, you didn't even go to college. You were pursuing your dreams, all right. Income, is this a scary one? No. The top one? No, no. Okay. For real? Inch sports? This is a funny one. Everybody thought you played badminton and tennis. No, no, baseball. Baseball? Soccer. Wow, you're getting your profile together. Now it's time to choose your photos. We got a number of photos to choose from. We're gonna pick one leaning, one walking and one beanie photo. What a journey it has been today, right? Yeah, I thought of myself one way first and then people in the beginning of today thought I was playing like video games and like badminton. And then I changed my clothes and now people think, you know, like me more than how I think about me. Like going out to bars and having fun with friends. You put on the rustic American look, which is what people actually voted on. Got a haircut, the hairstyle that people voted on. Look at your profile now, man.  We're using that funny long quote that everybody liked, right? To catch people. And then the photos are crazy. I mean, look at the photos. Yeah. You don't think that doesn't even look like you? No, it really doesn't. What can you tell people out there? Like, it does in a way matter. So I am the same exact person. I didn't change my personality or anything at all. Just my clothes and my hair. And people already see me so differently closer to how I actually am. Congratulations on the makeover. Peter from the Bay. Once again, everybody, thank you so much to our sponsor, EastMeatEast. It is a dating app. Focus on Asian singles, guys. You gotta check it out. They have matched over 90,000 couples. So they are doing a lot of great things for the Asian-American community. Your profile picture does matter, especially online, guys. So definitely make sure you get a fresh look. Take some nice photos. Put some thought into it. How you feel and how you look does change how people perceive you. So EastMeatEast is a great way to connect with Asians from across the world, doing all different types of things. They have this great live streaming feature. I put a link in the description box below. I think we changed a life today. I really do. All right, everybody. That's a fun girl's makeover. Let me know what you guys thought about his outfit and let me know if there was another outfit you would have wanted him to have. And big shout out to Peter. Big shout out to everybody that was in the video. And until next time, I'm out. Peace!


Thank you very much for this invitation. It's a pleasure to be there. It's late for me. I learned that for some of you, it's very early. Probably for some of you, it's a long time, but in fact, doing mass the day evening is beautiful. It's a nice place to discuss. So I prepared something, which is, there will be some serums at the end, but the serums are old, and they are not fully written yet. I mean, there is a small version on archive until you see the date. It's 2012, and we are still revising the manuscript and every time we revise it, it grows. So probably it's an end of the task. We'll see. And so what I want is to reach this material, but before that, maybe spend more time explaining why we're interested in doing that. So here is the abstract and I skip it. But in the abstract, you'll see that I'm going to discuss heights, a record of geometry, non-archiving geometries, which will be motivated by questions of archival geometry. And then the end is that real forms and currency, non-archiving geometry, so mixing real numbers and non-archiving numbers, and then a bit about mid-tride line models and complex geometry. So first is about height. So the height is sometimes described as naive. The height of a point is just a way of measuring its complexity. And you should take a point, a rational point of the particular space with homogenous coordinates, x1, xm, and you can choose them co-prime and integer, and then the height is usually just logarithm of the supreme number of those numbers. And with an unfortunate typo here, it's xm and not xj. One very important feature is the Northcote property that, once you bound the degree and the height, and you get only finitely many numbers. And for when the degree is one, it's very, it's obvious on the definition because you bound the homogenous coordinates. And one, one standard, which is built into the machine of heights is good functional properties, which at this level is very elementary looking that you take a rational map from a prototype space to another one. And it's given by a homogenous polynomial, f not fm in n plus one coordinates. And it's not always well defined because if a point cancels all of those polynomials and you won't be able to evaluate this, evaluate the map at this point, but otherwise you can. The first inequality is that when you evaluate the map at such a point, you just multiply the height by some constant, by the constant d, which is a degree. And maybe you add some error term. And if you have close to variety, which does not meet the determination locus. And if the bf is empty, then you have an inequality in the other direction, so the height of the image is greater than d times the height of the initial points minus some constant. Just let me mention that in some applications, it could be important to know something about this constant cf and cx, but for the moment I will contain myself with this inequality. So then what Veid did almost 100 years ago is to transform this weak functionality properties into a height machine that becomes quite more sophisticated. It's not obtrusively related to varieties in some project space, but rather to varieties equipped with a line variable l.  And then to do x and l, Veid defined a height functions hl on the algebraic points and for every morphism an equality of heights. So the height of f of x is the height of x with respect to the back line. Except that this is not true, because we had unspecified constants as cf and cx before. And so all these equalities do not really hold, they only hold up to a bounded function. And so these functional equalities up to a bounded error term. So for some applications, it's really innocuous, especially if you look at points of large height, it could be nice. But if you want to know what the height of some specific point is, then it's not sufficient. There were various ways in the second half of the 20th century to get rid of this indeterminacy.  And then there is a unique way of normalizing the height functions such that the equality for at least for this morphism is a precise equality. And in the case of dynamical systems, the interest of doing this normalization is that you get a characterization of the preparatory points, the point whose four orbit is finite, ultimately your cycle finitely many points, and then they are characterized by the vanishing of the height. So you should consider an abandoned variety and some morphisms such as multiplication by two, and assume that, for example, then what this function is, it's called a near and dead height. It's a positive quadratic form on the point of the abandoned variety tensile with r. And it's well known that this tool is crucial in half of the proof of the model Bayes theorem, for example. So the way where you see precise normalization is when you look at the mother measure of the point, so it's even more elementary than the previous case, you just take the point of p one. And you don't look at point of infinity, so you take a point of the former one with homogeneous coordinates which are one committee. The one that the height of this point is one divided by the degree of the minimal polynomial times the logarithm of the mother measure of the point. So you get an expression which is the other degree in the denominator and one logarithm of some integer leading coefficient. And the something which is the sum of all roots of a function which is essentially log of absolute value of the complex number if you are outside of the circle and zero if you are inside the circle. For example, on this formula, you see that from this formula, you can see that if the height is zero, then that imposes that the leading coefficient is one and then all the conjugates are inside the unit in circle and by the unit disk sorry. In this context, I should also recall the lemma conjecture, which makes sense because you have a precise normalization here, so the height of some point t should be at least some constant divided by the degree of the point of the degree of f. So it means that this should be universally bounded from below, unless the point is zero or with infinity. This conjecture is open but it's known that there are first of all a weak version due to the Rowalski up to some logarithmic additional term and there is also a recent version of an analogous inequality called a conjecture by Schindler and Zassenhaus and proved by Dimitrov. So, I missed the title. So, in this context what Fekete and Secker did is replace the disk by some compact set and replace this function log super number and one by the potential of the compact set. So this is a function on C which is zero on the compact, harmonic outside of the compact and goes roughly like an logarithm at infinity. And what it corresponds is that if you view, if you are inside the Riemann sphere and the north pole is a point at infinity, and then you have your compact set, what it means that if you are putting your your contact into some conducting materials of metal and the rest is supposed to be empty and you put a unit charge at infinity and then you get the capacity of this electric system. And from this function, what happens is that GK is very close to the function that appears into the definition of the matter measure so it would give another height function relative to the compact K and which would correspond to other geometric questions. For example, you could ask and Fekete and Secker asked consult whether you have infinity many points, all of those conjugates belong to the compact set K and which are also integer. And what Fekete and Secker proves is that if the capacity of the compact is too small, if it's more than one, then you're only are fine human points satisfying this condition. And if the compact has a great capacity greater than one when essentially you have infinity many points. It's another instance where having a precise normalization of the height allows to solve questions which makes number theory and geometry. Arachel of geometry was invented in the end of Arachel of this first work in 1774 and then it was in dimension one. Arachel was retaken by Fettings and Gillet and Soulet around 1985 to say 1995. And it furnishes a high tech machinery to specify the height in a fully functional way, but in a way which is also geometric. So, instead of looking at projective varieties and limelows, when we look at schemes over the integers limelows on that schemes and Hermitian matrix on the complex limelow over this meaningful. So the, the, the relation with the classical theory is that you could take X inside the projective space over Z. On this scheme you have the classical or one nine mobile. And X would just be defined by equations. Zero FN and the FG would be polynomial with integer coefficients. And on all of one, you also have the fubinister geometric, which is very classical object from complex algebraic geometry or analytic geometry. Which allows to measure the size of homogenous polynomial at a point X. So usually if you want to measure that, you could try to evaluate the homogenous polynomial at the point, but it doesn't make sense because when you multiply the homogenous coordinates you multiply this by the multiplication factor factor to the degree. So you just divide by say, say the norm of the point of the coordinates of the point divided by the degree of F. If you do something like that, you get, you have expressions which are well defined. And in some sense the classical theory of Bay Heights is just the particular case of molecular geometry with this, this functions except that the norm is not the precise norm. But it's a minor difference. This is essentially due to two things, that once you have such such shriples. So X and norms. There are functions which are absolutely well defined, and that apply to all close subskims of X. So you don't only have heights of points but you have the heights of everything lying on X. In a scheme of a Z, you have a classical definition that your scheme X over spec Z. Then you here you have the generic point of spec Z, which is spec Q. And then you will have a variety of a rational, but you also have a variety of two. And then you have varieties, which are in the language of the previous slide are just the variety of F2, F3, FB, etc, defined by the reduction module two or three, etc, of the polynomial that define the X. And then you have two types of tools. So you have two types of varieties, you have those which are fully vertical, such as a variety there. And then the height, which is defined in this matter is essentially the degree of the variety here. So you have a variety in some particular space of FB and that is the degree of respect to the corresponding language. And it's essentially the degree, you have just a multiplication factor, logarithm of one number. And in the other direction you have schemes which are this way, which are horizontal, they are subjective of a spec Z and they correspond to close the varieties of the generic fiber of a Q. And then what you get when you take the closure of something about the generic fiber, so something that will be horizontal. Then you get essentially the height, what we want to call the height of the generic fiber. And in some context, the height is normalized, so that's what you define by induction, something which looks like C1 hat of L bar to the power dimension of Z plus one, which is a notation like that, which is inspired by intersection theory. This would be this number, so essentially the height, and here is a degree of the variety in the generic fiber and this is just for normalization. So what perspective do we get during this, using this machinery, then we get that we transfer the question of having appropriate height functions into having appropriate models or appropriate metrics. And there is some hope that having a question of finding new models of varieties or good metrics and models is a question, which is of a more geometric nature and maybe can give a more precise answer. And in the context of a billion varieties, regarding the new haunted heights, the models are given by the number else and the metrics are classical that just a matrix whose first form is invited by translation and it's exactly the, the metrics that you can build on the line of all from the complex definition, complex point of view on a billion varieties and then I will not. For example, in the context of the appell, the bar theorem. Regarding the question of the KT as a really introduced a potential theory and cause and pay added capacities to have a question of conical type of a KT as a good type, but introducing compact sets at local places. And in algebraic dynamics. This business could be useful, but it's not so useful. Because it's very rare that you have some good reduction process that, for example, it would, it would be necessary that you really have a morphism over the integers and tending extending the morphism on the. Generic fiber and this is quite rare. And therefore, one still needs an approximation process of the same type as take, take, take process, and this is done by the theory of analytic metrics of chosen. And in some sense, this approximation process. It's, it's, it's very useful in practice, but still it may lack some geometric definition. For example, if you apply this geometry, this is the process on a billion varieties with bad reflection. It's very it's quite complicated to understand what to get. But if you do. If you look at the non-accommodian geometry on the non-accommodian uniformization of the other end varieties and you are supposed to see what happens in a cleaner way. Just to give for additional motivation of a record of heights. Statements which are impossible to, to give if you don't have those heights, except in particular contexts, such as dynamical dynamics. Is that you have inequalities that relate the height of the variety with the height of the points. So this is the height of points, small x, and this is the height of varieties. And this is a general equality. And essentially, essentially the, the, the height of the points of the variety are always greater than the height of the variety, except that they could be sub varieties, close sub varieties where the inequality doesn't, doesn't hold.  So it means that this complicated to supine means that whenever you fix, you fix epsilon, there exists why such that for x in x minus y, the height of small x is greater than capital X minus epsilon. And whenever there is such an equality like this. You can use it as a variational principle, and Spiro, you know, Jean did that. And from this inequality proved liquid distribution theorem for for height of points, which are close to this law of bond. And, in turn, this could literally be a key distribution theorem, while the cornerstone of the proof by you more and John and the, of the Bookman of Conjecture, that says that that generalizes the monument for conjecture for sub varieties of varieties and roughly that says the monument for conjecture says that if you have a curve in its Jacobian, then you have only finitely many portion points on it. And one of the torsion points are exactly the points with neuronal height zero. And what the book of Conjecture says is that you have finitely many points. Whose height is what it says that away from those finitely many points, the height is bounded from below by a strictly positive constant, which is just the height of the curve. So, ending this this part with motivations for non-accommodian geometries. First of all, it could be just purely philosophical to put non-accommodian places exactly on the same footing as Archimedean ones. So this is what some people do, but in reverse, there is a lot of work trying to put the Archimedean place on the same footing as the non-accommodian ones and doing algebra, the skins of F1 and so on. So here I want to do exactly the opposite. I want to, I think that complex analysis and real analysis is much more developed than algebraic geometry. So one should be able to have tools from analysis to do algebra. It could be useful to do that when you have bad reductions and no good models. For example, one of my hosts is that it would be interesting to use non-accommodian analytic geometry on Shimura varieties to understand the heights instead of constructing in a difficult way models of Shimura varieties. So it could be interesting for, it's also interesting for distribution serums. And there are also other aspects of Archimedean geometry that lead naturally to non-accommodian geometry is that in some sense as you said, so for example, and Johnson observed, in some sense, the, the, the limits asymptotic limit of Archimedean geometry is non-accommodian geometry. So you could, one could understand the generations of, of Archimedean phenomena in a non-accommodian way. In some sense, this is what non-standard analysis claims from, from complex numbers you naturally build a field of non-standard complex numbers which is of non-accommodian nature. So let's discuss a bit non-accommodian geometry. There are building blocks. And I have two columns that explain the building blocks from the right geometry and those of non-accommodian geometry. For if algebra is usually algebraic geometry is about finding the general algebra of a field. And non-accommodian geometry looks at algebras which are questions offering of porous areas which converge with whose coefficients converge to zero. Algebraic geometry defines the space, the spectrum of an algebra and growth index, a set of all prime ideals with some Zaris ketopology and there is analogously an analytic spectrum of an affidavit of algebra. And which consists in, in multiplicative semi-norms on the algebra A. And another way to describe this, you can view prime ideals as equivalence classes of morphisms to fields. If you have two morphisms from two fields K and L, and if you can build a composite extension such that two morphisms from A to E coincide, then you claim that those morphisms are equivalent. And if you do that, you get precisely the prime ideals of A. If you do the same job by looking, with looking at morphisms to complete valued fields, because you are doing analytic geometry, so you need to work with complete fields, and then you will get the set of all multiplicative semi-norms. So what Berkowitz did is that defining the analytic spectrum, say all multiplicative semi-norms, so I just recall the definitions here to be clear. So it's just a function with positive values that the semi-norm applied in the sum is smaller than the sum of the semi-norms. It will become an Archimedean at the end, in some cases, and you will get a super-norm of P of F, P of G, but don't claim it is. The fact that it's supreme, the semi-norm is multiplicative, is that the semi-norm of the product is the product, and I think. And you also, during algebraic analytic geometry or K of some ground fields, so on the ground field, you ask that the semi-norm restricts to the absolute value that you're given. And on the set of multiplicative semi-norms, which is a spectrum of like in the Gelfand theorem, there is a natural topology, which is a topology of point-wise convergence. So you just ask that all evaluation maps from, so these are maps from whenever you have F in A, it's not F max, but P of F is P max to P of F. So for all F in A, you have an evaluation map from P, which maps a semi-norm P to the value of the semi-norm at F. And you ask that all of these semi-norms, these maps are continuous and it gives you some topology. And the point of view is to look at those semi-norms P, not as functions on the algebra, but really as points on space. And so one will view the value of the semi-norm P at the function F as the absolute value of the function F at the point P. So it is reversing the point of view, which will be important. So the, I skip a whole part of the theory, which will teach you how to glue analytics spectra together to get varieties which are not, which are more complicated than the varieties that analytics spaces built from affinate algebras, but it's not very relevant today with me. And I will also skip one important property is how to define new functions on your algebra, for example, analytic functions on the concept, but this will be enough for me today. So the interest of this, those spaces is that the topology is quite good. The spaces you get, we get, I will describe them in an example later, are locally contractible, they are locally compact. And if you try to do analytic geometry of the CP, for example, though the completion of the right closure of CP, then you get something which is definitely not locally compact and which is totally disconnected, so not locally contractible. We will see that there is an interesting interaction with the real numbers. And those spaces also have topology and also have a growth in the topology and growth in the topologies are is what happened when you try to glue compact sets. And when you want to glue open sets your topology. And it's useful to have to have both, both topologies. And indeed, there are many other theories. And so the naive theory has not enough local compactness in the. It's very good when you work over QP and do something which is relative to QP, but it's really insufficient here. The theory of state would, which only looks at CP points, but forgets about the topology and only looks about the growth in the topology has not enough points so you don't see really what happens. There is a theory by Renault built on formal schemes, but then one really lacks a space on which one can do analysis on geometry, the space exists, but it's not. It's not very visible. And there is also more recent theory by Huber, but this one has too many points for what to do. In some sense of the back of history which was developed roughly here is exactly what what we need. So just me let me give you an example. So we'll just the only example that people can do is they are fine. We want to look at some norms on the ring of polynomials in one variable. And so back of each claims that there are four sources of points. The first one are just given by you take a point in the, in the UK. And, and you look at some of them that takes a polynomial and takes the value of a and the absolute value. So you have the point zero, you have a point for one, and the other point for, I think I will pretend case QP bar. So we take point B here. Now what one can do is you can look at the point of the disk of center zero and register and you can look at the Gauss norm on this disk. And it will mean that you take P, Pd of F. In some sense it's just a supremum of f of a for all a there but you really need to take the supremum on the algebraic closure. And it's, if you expand this, the polynomial f, square efficient, Cn Tn, then it's just a supremum of absolute value of Cn all to the end. And it's not trivial that it is a, it's trivial that it is a semi norm, but it's an even norm is positive, but it's not trivial that it is a multiplicative and this is a content of the Gauss theorem. We have a lot of semi norms, and I will draw them. And we have a line of semi norms. And here I will write zero and one. And when one can go on with this line. In this line, I will use both rational disk and irrational disk according to R being rational, P to some rational or being really a real number. If you look at both points of both types, you get these segments, but you could also start from the point one and look at the disk from one, and then you have disks. You have disks at the point P, it's not, okay. And then you can grow the disk, but what happens is that when you, when you've reached the disk of center zero and radius one. It's not equal to the disk of center one and radius one because of non-accommodian property. And so you get that your line, which was supposed to go from one and meets the initial line there. And then draw the point P at some point. And when you start from a point P, it will do the same it will reach the initial line, but exactly at the disk of center zero and radius one of a P and then it will go. And so what you can also do that with this P squared, which I'm trying to do like this. So let's do P plus P squared will be there and P squared. And it will be disk of center zero and just one of a P squared. And you get something which is a kind of tree, and which is very branched because you can, you have a countably many branches, countably, countably down set of points. It's very, it's a tree, but it's very heavy. And here is a nice picture of this tree, when you draw it on the plane taken from the paper by Roschowski and Leuze and Poon. So here is the proof that this projective line, Bakovic, actually embeds in the plane and it's an object which is well known in topology. It's called the Roschowski dendrite. It's some kind of universal space which topologists like to study. Nevertheless, the point of view of Bakovic fits very well with Reynolds approach. For example, when we have a formal scheme or a scheme of a spec Z like before, but I will do it over the I think of the valuation ring of the few K. Then assume I have a generic fiber, which is an antique space, but there is also a special fiber and there is a map from the generic fiber to the special item to the special fiber. And there is also a very important process, which is which has been understood by Bakovic. Which is very important, especially when you have that reduction, because then you would have a complicated special fiber with many, with, with many components and many interest intersections. But what Bakovic proved is that for each of these components, there is a specific point in the space. So here in my picture there are two points. And related to this intersection point, there is a real segment. So it means that from this picture and then if you had three by three intersection, you would have to draw two dimensional simplices and so on. So just from the combinatorics of the special fiber of this stuff, one sees in a very concrete way inside the analytics space of Bakovic. Some, some, some things, some object that is usually called a skeleton, and which is a polyetron inside the analytics space. And this is the one reason for which I say that those spaces have a nice interaction with real numbers, because we, we see real objects from topology, which are, which are nice, which are skeleton and also Bakovic proved that there is a retraction from the generic fiber, this analytics space, and to the skeleton. So this is why those spaces are well behaved. They are very hairy trees, but you can contract the tree. So the time goes too fast. Other than that, I've prepared too much stuff. So I will. Okay, that's really nice. Okay, in 10 minutes. Don't pay attention to the number of pages below. So now I think I can try to say a word about how to define real forms and currents in an archiving geometry. So it was on the implication, maybe it was on the implicit, but let me just say that, for example, a regular geometry is full of currents and real forms and differential geometry. So it comes from tropical geometry. So we have an analytics space of a field which always be cold care and will be assumed to be a normal Canadian and complete. I will consider tropicalization maps which are morphisms from X to to the tourists, which is the analytic tourists, but it's not necessary to pay attention to that is just given by and functions on X which are homomorphic in the sense I did not describe and invertible. And from this F, what I can do is I can evaluate the functions f1fn at some points of the space and can take the absolute value. And because we prefer addition to multiplication, I take the logarithm. And so I get one gets a continuous map from the analytics space to to the real real space. So this is something which is which was studied by delphan Capranoff and Zalevinsky of as a complex number called Amoebas. And here we have none of us. And it was shown by Gary Groves in the 80s and in this context by Capranoff and Eisenhower and Lint around 2000. And so if X is compact, then the tropicalization of X is not a complicated space is not a numberable like people have in complex German analysis, but it's a compact political subspace of and its dimension is just a smaller than the dimension of the initial space. And so it's another way of having interaction between analytics spaces and real geometry is just by looking at these tropicalizations and very useful. Maybe you've seen the definition of like Capranoff and you see that sometimes people don't take the F drop of X but closure of F drop of X, and this is because they don't use back of this space. So if I claim that those tropicalization maps are important, which I do. I will also use this to define smooth functions on an intake spaces. And the idea is that that moments are nice maps and antique maps in non-accommodation geometry. I will take the C infinity functions on the real numbers. And if I compose a C infinity function on the real numbers with the tropicalization map, I will claim that I get a smooth function. So, and there are a lot of smooth functions on spaces or ones are technical assumption that the space is separated and it's locally it's reasonable it has locally not philanthropic functions. I will not forget about this. And then there is a stone by a structure and this the smooth functions are dense in the smooth functions in the continuous function for for the compact open topology uniform components on compacts. And it's the same if you look at C infinity functions with compact support. And if the space is para compact, then you have smooth partitions to even up those partitions of unity. The compactness assumption is a bit subtle in back of its geometry. If the base field K is something like CP, if it has a countable dense subsets, then almost all spaces are very compact. But if K is the field of Laurent power series over the complex numbers, then if you take P2 and you remove one one point. You get something which is not not anymore para compact. So, anyway, this is an important assumption and sometimes it's annoying. We need differential forms and those differential forms are provided by the Bayer-Ezin Lagardex supercalculus. And so it comes from an analogy that on complex numbers, we have prairie subharmonic functions on real numbers, we have convection chance. On complex analysis, there is a mojampere operator and there is a real mojampere operator, which is slightly different. So here you differentiate with both the complex and the holomorphic and the anti-holomorphic variable, and then you only have the real variable. So here you have two n variables and on the real, you have n. And so while on complex analysis, you can do differential calculus with holomorphic and anti-holomorphic variables. You also need to develop some supercalculus, which means that you totally formally take the potential product of two copies of the differential forms. So it means that really what you do is you take one copy of the differential forms and you write them with D prime, and you take another copy and you write them with two different forms. And then you can do differential geometry, as usual, you can take D prime of this, you will differentiate the functions, and you will add some D prime in front of that. You can also take D double prime, you will add some D double prime, but you still will do different selection with the same variables. So it's very nice that if you do that, and you do D prime, D double prime to the end, you get exactly the real non-jamper operator. So this totally algebraic business that might look strange and unreasonable, but in fact it gives you naturally the operators that complex geometry, real geometry. From now on, we just take differential forms, super forms on the tropicalization and we pull them back formally on the space, meaning that locally I start from objects which are an open sets, a moment, and a superforms on the real space. I define a formally f of a star alpha, and then it's more or less standard to glue these objects into shifts. And the first proposition that showed that what we get is reasonable. For example, if you have two moments which have nothing to do, but f-trop is the g-trop, so there are two sets of functions which takes the same absolute values, then when you pull back the forms, you get the same thing. Also, if you pull back one form and you get zero, then essentially what you have to pull back was zero, so we don't lose anything. And just formally from the lag of that business, we get differentiations. One important stuff is to be able to integrate forms. And the idea is just to try to integrate formally back on the tropical side, but then it's complicated because here you have two n variables. And so you cannot integrate with respect to two n variables on Rn, so you remove alpha to them and you try to integrate. The problem is that this will depend on the choice of coordinates. And so one needs to add an additional structure on the tropicalization, which we call calibration, and which corresponds to the weights of tropical geometry. And we also have a balancing condition. So, from there, the machinery of currents begin as in analysis. We define the currents as a dual of compactly supported forms. Just by duality, we have differential operators and push forward because we can pull back forms. And because we can integrate forms, we have an integration current. And because we can also integrate forms on boundaries on subspace of some forms which have dimension n minus one n can also be integrated. And so this gives you different kind of integration. And as a matter of fact, we have a stocks formula. And we have also a formula, for example, it makes sense to take, if F is a neuromorphic function, it makes sense to look at logarithm of F. This will naturally define a current. And if we take the D prime, double prime of this current, we get the integration current on the divisor of F. And another formula, which I like to show, is that the analog in complex analysis of the formula that D prime, double prime of the, of the, this is exactly the potential for the disk of center zero and radius r. And when you do Laplacian of this function, you get zero outside of the disk. You get zero inside of the disk because outside is harmonic inside constants. And you get something on the circle. And it's well known that it's a pretty real measure of the circle in complex analysis, integration current on the circle of producer. And in our context, you get, we get something different. In some sense, the boundary of the disk or this R is simply the Gauss point at the other one, which was related to the semi norm P, D zero R, and we get the integration on this space. And it's an analog of this function in works. So I've skipped my time over by more already two minutes. So, I will just tell you what I wanted to don't don't try to read this. So, just to show, I will show them but in from this, once you have forms and currents, you can define a matrix on nine walls, just by copying the definitions from a 19 geometry. In the next nine walls, we'll have coverage of forms. And because of the point career and formula, when you integrate products of coverage of forms. We get the degree from algebraic geometry, from algebraic geometry when the situation comes from algebraic geometry. The more interesting and more difficult is that when we take, when we start from a natural matrix format for metrics which are natural for from algebraic geometry but given by models like in a record of geometry, those metrics are not smooth. They are out corners are defined by some maximum functions. And so when we take the, the churn form we don't get a form but a current. And for for the same reasons that we can, we are able to define products of those currents and and to give formulas for for for the for the products of those currents and in fact, we recover exactly what is given in a record of geometry by formulas which are natural from from the point of view of geometry and which allowed me 15 years ago to define measures on on back of each faces. So here we don't in the end we don't have only measures that we have measures for matrices and goals that we have forms and of all types from for for these matrices and goals. Also, we are able to understand the positivity we are able to understand the intermediate currents and the positivity. So this is just the starting point of business. It promises to be useful and we hope it will be. What is remarkable for us is that it has been used in many works. Meanwhile, so our paper is not yet finished but people have done interesting stuff with it. So, so for example, gobbler and Kuhneman should gobbler and Kuhneman have shown that something is making a lot of noise is my my efforts. So gobbler and Kuhneman used it together with other ideas from tropical geometry to to define quite a full set of geometry in the moment setting you and Mikami have shown a relation of the natural geometry groups that can be defined by these forms with child groups and K theory. It also appears more recently in a work by Ducro Ruchensky and Leather, who showed that Archimedean integrals naturally converge to non Archimedean integrals in the sense that I described. So, I think it's a last slide. There are a few three additional slides that are empty in order to be able to write something. If I need it. So, thank you very much for the attention. I'm sorry to be slightly overturned.


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