All right, good morning everyone unfortunately due to a lack of quorum We're not going to be able to hold an official public safety subcommittee meeting In consultation with the city attorney and the city manager what we're going to do is our office of our OIR is going to give their report And we'll take public comment on that I as a council member cannot give any ask any questions cannot do anything about it It's just basically having an opportunity for OIR to give the report publicly Take public comment so that we can hear it, but we can't take any official action We can't do anything. This is not count as a an official meeting. So with that Chief do you want to facilitate? Oir given the report so do you want to? Madam city attorney, I think the decision was that all the only item that we will Unofficially take up is OIR report in order that that can be heard by the public But this is no longer and it's not going to be a public safety subcommittee meeting It is simply to hear the OIR report We appreciate that I'm sure I'm sure the chief will take time to talk to you after it if you have any questions All right, thank you councilmember Alvarez And so now we're going to move directly to the item on the agenda 5.3 with a discussion with the independent police auditor And the description is the Santa Rosa police department independent police auditor will discuss the 22 independent police auditors annual report and will solicit feedback on the program and methods to engage the Santa Rosa Community members so now we have joining us our independent police auditor Mike Janakko Steve Connelly who it does the day-to-day work working with our professional standards team and Their team member Brian course. I'll turn it over to them for further introductions and for review of the report Chief before we actually turn it over to OIR If you in the sake of transparency of this item since we do have a union representation And we also have a professional standards team if you want to go into questions maybe with individuals From the professional standards team and maybe our union representatives. I don't mind a little bit of back and forth This is a very important item. We do want to show Transparency and why we cannot actually ask questions from the dais and the public We do want the public to know that we take this item We heard your feedback. We heard the community support for this So we do want to be able to show our support and show our transparency So if you do have maybe some back and forth with the team on how you've engaged Please feel free to do that. Thank you. Okay, we'll turn it over to you Mr. Nako Thank You chief. Can you all hear me first? Yes great We are presenting our First report first annual report After year one of the work that you have been assigned us to do as the independent police auditor My name is Michael Chinako and I am a principal of OIR group and I've been affiliated with the team since 2001 I have Stephen Connolly with me as the chief indicated and we also Calling in remotely have Brian core of our team who was very involved in the outreach that we conducted last August and He will talk to you about that Look for appreciate the opportunity to present today Understand the circumstances Regarding this presentation But I'm pleased to know that we will actually have an opportunity to be With you all next week in person for various presentations including presentation to the full council next week Could we go to the next slide, please? As indicated Our team has over 20 years of experience in law enforcement oversight We do specialize in the independent evaluation of agencies and their internal review systems and what that means is Taking a look at taking a look under the hood with regard to the way in which the department responds When a complaint is received about potential misconduct how robust that response is how objective the investigation is and Whether or not with regard to outcomes whether the outcomes are evidence-based and principles Based on the information that has been to receive during the investigation With regard to Santa Rosa We have four individuals that are primarily assigned to the task As the chief said our boots on the ground at least boots on the virtual ground is generally Stephen Connolly He's been most involved in the work this year But he's received help from the rest of the team as well with regard to various matters Could we go to the next slide, please? This is a reminder to the public about the timeline that got us on the Santa Rosa planet We first got started in Santa Rosa in earnest as a result of a special assignment that the city and you all endorsed and authorized us to do which was an outside review of the investigations that stemmed from Uses of force and other concerns related to the demonstrations in Santa Rosa following the George Floyd murder and We were actively involved in that invest in that investigative process and what I mean by that is that We weren't brought in after the investigations were all completed and then asked to evaluate How the police department did that is how we operate in some of our jurisdictions, but not in Santa Rosa Instead the idea and the concept was that we would actually be involved During the development of the investigations themselves and by involved we're talking about involved in real time With regard to the fact collection process That model in the city of Santa Rosa and our work for the city is Santa Rosa Has continued on to our present Present responsibilities as well, but the advantage of having early involvement is that we are able to Interpose questions to help develop and shape the investigation To raise issues regarding additional Information that might be collected during the investigative process itself and not after everything's been Completed if you wait till the end then there is less ability to have any significant influence on that case because of timing issues because The paperwork has all been completed the employee has been notified and so this process that we have Undertaken in in in the demonstration cases as well as the cases subsequent Is an opportunity to be involved in shape the investigation in real time In November of 2021. We ended up going through the selection process Presenting an RFP response for your all's consideration, and we were delighted to be selected as IPA We got started around 2022 with regard to actually getting involved in the review and monitoring of cases Set up a process whereby the police department to its credit allowed us direct access to information including the body worn camera information the Database in which information about internal investigations are housed which makes it much more facile for us particularly since we are out of town to actually See what's going on with regard to any particular case whenever we have an interest in doing so And that has worked out extremely well in our view The city recognized that it was important for the city city residents and other folks connected to the city to have a better understanding of what we were about and what We had been asked to do and so after several several months of being operational through the city's assistance. We were able to facilitate and participate in various outreach sessions in the city of Santa Rosa in August of last year and Brian Corr will be talking a little bit more detail about that in a little bit here. Can we go to the next slide, please? In fact, this might be a good time to turn this over to Mr. Corr. So Brian assuming you are Hailing in from Cambridge or the Cambridge area on the east coast. I'll let you take over this piece All right. Well, thank you, Mike. I appreciate it and I'll just say briefly. It's very good to be here with all of you virtually It's been it's hard to believe it's been since last August But it has and I will say overall we have a very successful Community engagement visit. We had our four member team people that Mike told you about myself, Teresa, Nukula, Steve and Mike himself and We were in Santa Rosa from August 5th through August 7th So during that time we participate in a number of activities that city staff had organized and facilitated As it says on your slide there We had two scheduled listening sessions and two drop-in sessions and the distinction was that the listening sessions were more formal sessions with presentations Remarks from elected officials the city manager with the police chief was able to speak Briefly but really to listen along with us And then those were done in ways that we hope would really allow a variety of people from the community to come out We had one at the person wing Center and one at the Victory Outreach Church. I'm sorry. No one at the I should have had my notes in front of me when any of that I'll come back to that But the other sessions the drop-in sessions were less formal and they were really opportunities for people to Stop in and chat with us one-on-one. There wasn't a formal presentation One of those was at the Victory Outreach Church and the other was at the TM Rhea Penadriah, so those were both in An area of the city that you all know Rose land which is Outside the city previously and that really seemed to be a focus of a lot of the concerns and attention and During those sessions again, we got a lot of good information a lot of good feedback It's detailed in the report But a lot of what we heard was really about people's concerns generally around policing we work to Get people to speak more specifically about Santa Rosa Police Department But we heard a lot about both what's happening in Santa Rosa and more broadly the county One of the topics that we certainly heard a lot about was around the issues of homelessness and Enforcement how to support the unhoused people in Santa Rosa how to support the quality of life for Everybody in community and then certainly we were there just after the tragic shooting of Daniel playa's In Sonoma County, but that certainly had an impact and brought back memories for people But also there were a lot concerns about how will the San Rosa Police Department do the deadly force investigation of that shooting But again, I found myself in talking to the rest of the team that people were very happy to speak with us They were happy to share their perspectives and help us understand sort of the context in Santa Rosa the history But also the current state have we gone to the next slide, please So in our time there in addition to just informally chatting with people as we spent time in the city Which I was there's my first time to Santa Rosa And I'm quite happy to be there isn't a wonderful city you have the room forward to coming back again But in terms of formal meetings, we met with the police department that included meetings with union membership with leadership of the department and with the professional standards unit in Or to find out more about what they did to kind of see their day-to-day efforts, but really to have a chance to for us to have Interpersonal relationships really connect so that the work which already was going on could be done even more effectively and With that ability to really know each other the means with city leadership I thought were quite useful and those again were both formal and informal Number of people from city council did attend some of the outreach sessions But it was also a chance for us to get to know them as well and then finally right along with patrol officers which included for myself the opportunity to go out and See officers in action everything from traffic stops to an interaction with a person who was Apparently suffering from a mental health crisis and was Involved in both self-harm and being very disruptive in the environment though those I think were all very useful from our end and Feedback I got at the time I think again our whole team got was it those were very helpful for us to build those relationships I'm coming in as the new independent police auditor Of course, there's always concerns from the broader community from people who have more impact on their lives from policing and law enforcement and of course from those tasks with carrying out public safety law enforcement officers themselves and It was important for us to be able to have all of those opportunities to get to know people So I think I'll stop with that and I don't know if Mike or Steve you want to add anything on We'll go to the next slide So Yeah, if we could have the next slide, please that would be great And thank you Brian for for that summary of our trip to to Santa Rosa last summer and as Mike and Brian have both mentioned we are very much looking forward to being back in person next week and also happy to be here today to kind of preview that visit and to talk about our our first Annual review audit report in in this context. So thank you again for the opportunity So I want to talk a little bit in a little bit more detail about the the particulars of our role in Santa Rosa and the way that the contract was was initially set up the scope of work that the city established a year that the city council pushed for in terms of making sure that the oversight In the city was was robust and I think responsive to a new level of public expectations for transparency and accountability and law enforcement So I will tell you that we work in a number of jurisdictions and and we have different kinds of Relationships with different cities and different departments and different roles in some of those places It is a very very robust model that Santa Rosa has put together in terms of as that first First bullet point up top there talks about the whole idea of real-time review of all internal Investigations and civilian complaints is a very very significant Step that again a lot even jurisdictions that have some form of oversight It is very rare to have that level of Again real-time opportunity to participate and potentially influence those investigations We get notification of any critical incidents that occur. I am regularly in touch with with the Relevance team members in the police department. They have been very good about communicating and keeping me apprised of events they're going on and on a more day-to-day basis and We also have the responsibility of conducting periodic audits of Investigations and their outcomes and so that's where this year's annual report kind of falls under it It takes a broader look as opposed to the regular case-by-case operational Relationship that we have with the department and then part of our role again as defined by our contract in the scope of work Is to review and to make recommendations on on policy and training and we did a little bit of that in this report And we will talk about that in just a moment or two so next slide please So again, we have the opportunity as a Independent third-party outsider We review we can receive complaints from the public and have there are different ways that members of the public can get in touch with us And it hasn't been a very a really high volume But there certainly have been several occasions in which people have contacted us directly to kind of get information and understand a Little bit more about the role because they don't feel a particular or the comfortable going to the police Themselves at least at first and we explain the process and explain and try to make referrals over to the department to actually conduct the investigations while providing assurances that we will be kind of monitoring it and Participating in the process as it goes along our First annual report. Hopefully you had the opportunity to read it and I just it more we're looking forward to the opportunity to answer questions about that maybe next week and this Appearance today and next week is is our opportunity to report in Public and again to get that kind of direct opportunity to engage with with the council But also members of the public who are interested in in our work and in policing in Santa Rosa And then the whole community outreach piece is certainly part of what we were intended to provide and In terms of our profile in the city It's challenging when we are obviously geographically remote, but I have been in Santa Rosa on a couple occasions other than the August visit It's easy enough for us to get there when we want or need to for particularly significant events and We hope next week will be an opportunity to expand on our community outreach piece But we are certainly always available for interactions with the public and we have Had the chance to correspond and chat on the phone with people even when we're not there in person next slide, please So in terms of that the year one annual report There's kind of the occasion for for this meeting And again for our visit. It'll be kind of a focal point of our visit next week I want to provide a little bit of an overview of the process and that first piece I really want to emphasize because of how unique it is in our in our experience as as oversight professionals and obviously In the larger context of law enforcement oversight That the whole idea of the access that has been set up for us to the department's internal computer system We have full unfettered access I have the highest level of access that that the department allows for me to kind of be able to monitor and review anything that has been posted to the Department's internal database and that includes that the various Relevant reports police reports, but also investigative reports when it comes to a misconduct case investigations use of force reports and Perhaps most significantly all the body-worn camera The recordings that are relevant to the different cases that we have responsibility for monitoring So that the opportunity for me to go in and certainly other team members have this this access as well So the department has really literally kind of opened its books opened its computers to us and said hey You you are welcome to go in here and see what you need to see and we're not we're not walling anything off or keeping anything from you So that Ability to to see for ourselves what the the raw material is of these case reviews is obviously very very significant And I want to emphasize again. It's quite unique Next slide please So we talked a lot about the whole concept of real-time independent monitoring and that there are three basic phases to that one is the Notification we are alerted and sometimes, you know on the day that the investigation opens If it's a really significant case, but we are Notified early on of new complaints as they come in and new investigations the department may be opening We have the opportunity to actively participate in a variety of levels up to and including sitting in on the interviews and participating in the subject interviews of involved officers who have been the subject of a misconduct Allegation and then we can consult with the department in terms of the case outcomes what we think the Evidence is showing and whether the allegations were sustained or not and also the opportunity to kind of weigh in on potential disciplinary consequences in situations where it seems like that Policies have been violated and officers haven't met the department's expectations in some way So it's every phase and and again. It's a very robust interactive relationship that we're able to have next slide, please So just again in terms of an overview of our activity last year there were 67 separate matters that were investigated by the department 53 of them were public complaints and the other 14 were internally generated which means The investigations were begun the allegations of policy violations and the subsequent review process and Resolution that was all driven by the department based on its that the management's identification of a potential concern a potential policy violation a potential performance issue that it wanted to make sure It was it was looking into so I think both of those pieces are really Important to to make note of the idea that the there is a Vibrant complaint process that the public can take advantage of and does take advantage of is is that you could talk about? Wow, that's a that's a lot of complaints on the one hand, but on the other hand that it's a it's a sign that people are Confident in the system and feel like they will be taken seriously if they present issues to the department in that respect It's a sign that the process is working. Well, and then that the for the department to Investigate on its own initiative. I think it's also an important thing that sometimes gets overlooked with obviously public complaints are an important thing to be taken seriously and I think that was a big part of the genesis of Independent police auditor's role is to monitor those public complaints but the fact that the police department itself is is Identifying and taking seriously issues that it is uniquely able to to recognize and do something about I think is is also an important aspect of accountability to be sure Next slide, please So in again in terms of our involvement we can participate at lots of different levels including making sure that that all of the identified issues have been Framed so if a complaint, you know has four or five different elements to it We work with with the investigators to make sure that that each one of those things is sort of separately Identified and kind of grappled with in terms of the evidence collection and the the review process We participate in ensuring the thoroughness of investigations. We're able to to Monitor the progress of each case and again actively participate as needed and we can sometimes go back to the Investigator I am in touch with the the primary professional standards investigator Literally a few times a week and sometimes a few times in a day Just talking about individual cases and following up on particular things to make sure that investigations are appropriately thorough and that all the different Elements have been have been properly addressed and then our goal really does Obviously legitimacy of outcomes if you take a big step back that the public's hope and expectation is that our presence is going to contribute to their reality as well as public confidence in the legitimacy of the outcomes that that The department reaches and we are pleased to be able to say that that we have concurred with the department We don't always see things exactly eye-to-eye and sometimes that that tension or disagreement in different perspectives I think can can make for a better investigation and a better process, but we can say that we we do have a strong sense that the department takes these processes seriously that they have have Reached all of the outcomes in these cases in good faith and we are concurrence with the final results is is pretty much across the board and Then last but not least in terms of opportunities for holistic and intervention This is one of our big themes and in all the different work that we do with different in different jurisdictions when it comes to any kind of public feedback whether it's a citizen complaint and whether it's a particular use of force case that The department is going to be reviewing the officer's actions There's a couple different levels of it and one of them is sort of that bottom line question of whether a policy was violated or not And that is of course a very important one And it's probably the most important one, but it has been our experience and we think that the processes that are most useful and healthy and Effective are ones that don't just kind of narrowly look at that and stop and kind of discount other aspects of it But they see the the review process an opportunity to to really look at officer performance and policy and tactics and training and the way the Officers are doing things in the field and even if a policy An allegation misconduct is doesn't end up being sustained even if the policy itself wasn't violated There are often situations on the periphery of the case where you can say hey We get it that you didn't violate policy But we didn't understand why you chose this approach as opposed to that approach or we feel like your communication could be better Or your coordination with your partner could have been better there are lots of things that that these cases offer as as opportunities for management to intervene not to nitpick or to undermine officers but to Really use those real-world experiences as feedback loops and a chance to get better And we really have encouraged the department to kind of lean into that a little bit more overtly And we'll talk about that more in the use of force review process as well next slide Critical incident review is also another part of our mandate in terms of the the Major critical incidents that have occurred since we got started that the one incident that we've had direct involvement with so far occurred in November of 2021 that was the death in custody of a subject In the aftermath of an active shooting incident that the police department responded to and there was taser use and other force and The subject ended up dying As a result of that encounter there have been a Criminal and administrative reviews of that process the district attorney has already Completed its review of that case as his standard practice and determined that the officers Did not violate any any laws In terms of their performance and the department has completed its administrative review We had an opportunity to actively monitor and participate in that process similar to the dynamic that we've talked about at other points of our Presentation and there's pending litigation in that case We have completed our work with the department on that case and we look forward to sharing more information about it publicly At a future point next slide, please Use of force review I touched on this earlier Our window into the department's use of force review process has been relatively narrow so far and it has been driven by Complaint cases actually that fall under our Bailey with a fall within our scope of work So a handful of the of the complaints that we received involved allegations of excessive force and none of those ended up being sustained That was a result that we concurred with but it also gave us a window into The department's kind of standard use of force review process any time there's a reportable use of force There's a certain amount of supervisory review and assessment that goes along with that And in our again limited opportunity to look at that process in the context of a few cases we found some Elements of it that we thought merited more attention by the department in terms of kind of ramping up some of the The documentation and the standard steps that we would hope supervisors are taking To again go beyond that that basic question of whether the force was in policy or not Whether it was justified in policy but to look at it more broadly and to to look for opportunities to improve officer performance Where where the situation warrants it next slide, please? So we had eight recommendations in this in this public report for our first year of work in Santa Rosa and They related to these these three basic categories with regard to the discipline process we have talked to the department about Making it more of a regular Event to interview subject officers in the context of these investigations. There are a lot of cases that are resolvable Just based on the body-worn camera recordings and that has been a huge change in in our profession as oversight folks that the the development of body-worn cameras and the the way that that has changed investigations by just providing so much direct evidence of What happened? Obviously, that's extremely valuable and we rely on that a lot But there are a lot of situations that we have seen where it would still be interesting to talk to the subject about mindset and What were you thinking at this point in time and there are some things that the body-worn camera? Just can't capture and we found that on some occasions the department was I would say You know reliant on the body-worn cameras to the point where they they didn't bring in the subject They didn't think they needed to but we feel like it would be more of it should be more of a regular event To to make that a regular part of the process and not have a stigma attached to it like oh boy This must be terrible because we're bringing this person in for an interview Something must really be wrong I think the opportunity to sit with somebody and to delve into the issues in a more thorough way again of this particular way Particularly with regard to state of mind issues would be a positive thing and we've actually already seen the department moving in that direction a little bit more in that the more recent cases from the last few months, so I think that's great and in terms of consequences our experience of the departments in those Those occasions when officers were found to have violated policy We are The department's approach to consequences in those cases is a little bit lighter and more lenient than what we are used to in other jurisdictions and we have talked a lot to the department about that and we Recognize that there are some cultural factors in Santa Rosa where you know what what? Might take a written reprimand or a day suspension to make an impression in one agency Maybe an evaluation note or a documented counseling is sufficient in Santa Rosa Just because of you know what the what that means to the officers and what the expectation is and it's obviously the goal of the Discipline process to correct behavior and to make the officers better as opposed to punishing them Again, unless it's an extreme case where the officers you know termination is probably the only appropriate option but when it comes to to Low-level offenses low-level policy violations We've talked to the department about just trying to get more of a handle on whether that the consequences are sufficient to the Violations that we've seen and so there's a little bit of recalibration going on there as well We I mentioned in terms of the use of force process the whole idea of holistic review and documentation the department has updated some policies and expectations to address some of the concerns that we had and Again, it's not because it was our sense that the force was was terrible or that they were finding things in policy That shouldn't have been found in policy But instead it's more about hey, let's let's look at this more completely and Talk to the officers about force options and techniques and strategies and Equipment choices and just ways that that you know we can better emphasize principles of de-escalation Or communication or other approaches that might minimize the need for force in particular contexts going forward and last but not least One of the things that we had the opportunity to do I went in in September to actually sit in on a Presentation of the department's implicit bias training that had been a big focal point of their their training goals for 2022 and the department Internally put together a block of training for every member of the agency on this topic that is of course a very A prominent one in law enforcement and really you know in a lot of different aspects of our society these days So we were impressed with the commitment of the agency to put something together And we were impressed with the sincerity of the officers who kind of designed their own Presentation after going to a lot of other trainings and meeting with people and learning a lot about some of the academic work in the field and We thought that it was an excellent start in terms of Showing a commitment a recognition of these issues a commitment to addressing these issues and and Our recommendations have to do with a couple things one is just hey Don't just say we've checked that box and we can all move on but keep it on the kind of the front burner as a focal point of ongoing Concern and updates and attention as far as the leadership of the department is concerned And secondly one of the things that was interesting was that it was department members themselves and There's some thought that bringing in some kind of outside voices and sort of expanding the lens a little bit There would be some Value to bring in some outside perspectives as well Even with the best of intentions obviously the office and I think the officers themselves had a certain credibility with their peers That I think was an important step, but obviously there are experts in the field and people from different life Circumstances who could bring a lot to that conversation, and we hope the department will keep that in mind on a going forward basis Next slide please Wow, I believe it or not. I really am gonna stop talking now and we are I know we're on a little bit of a Different format today just with the structure of the meeting, but again We are happy to have this opportunity to present and we look forward to engaging with with everybody in more detail next week So thank you Thank you very much to the entire OIR group team for that presentation as well as your patients Chief to you or professional services or our Union representative have any questions or feedback they'd like to give at this point No feedback, but other than this the chief of police We're really happy with this relationship and really it's been an opportunity for me to have that other lens of looking to what Can we be doing better at the Santa Rosa police department and and I think just one really crucial thing to Support what Steve Connelly was just saying of the absolute unfettered access that our independent police auditor has Which is quite different than what you see across the state of California across the nation and even here locally Of having that instant access of having the same login that I have as the chief of police to our internal process of reviewing every document The same with our body worn camera system And I think it's really important to us that our independent police auditor is involved in the process every step of the way from when We're crafting the allegations for our officers. They have the opportunity to be part of interviews If they believe that they would be able to support that Investigation and before I make the formal decision on what the Discipline is on more significant cases we're able to meet and get their feedback on those things and they really provide a great Perspective for me is the chief to be able to happen So it's been something that we're going to be carefully analyzing their recommendations and be moving forward With the areas that we believe that we can make some positive changes All right, thank you Any other comments all right with that we'll go to Public feedback since it's not an official meeting We'll still keep it timed at three minutes just to be respectful of everybody's time here So step up to the podium if you have something to say if you're here in person if you're online press star nine To or either raise your hand. I think we can do it that way Mr.. Dwight if you want to make your way to the podium. You're the only card that was submitted today so So we'll start with mr. Dwight and then we'll go with Anybody in the room that would like to say something and then raise your hand if you're on zoom or if you're on the phone through zoom Just press star nine to raise your hand and we'll get to you Take it away when you're ready mr. Dwight Thank you kindly. My name is Dwayne Dwight. I'm from Roseland and I wanted to first Thank you for continuing the meeting this morning and then thank the police department for the work They're doing for the city manager for the work She's doing and the council members for being on this subcommittee. It's a very important subcommittee and Wish the city attorney well as she moves on to her next adventure I'm glad she's been involved and I hope she tells the next city attorney That this is perhaps one of the most important subcommittees that the city can have and to make sure that there's a good Communicative activity between your office the police department and the community The police chief just mentioned a question. What can we be doing better? one of the things that I see as a community member is that there's a lack of robust communication Now that word robust comes from jurisdiction agencies very few people say it out in the community Except maybe people at wine tastings The thing is There's not really a strong Communicative situation that goes on between the police department and the community in terms of just talking to community members They've how they've now had coffee with a cop. That's a good thing. I saw it at the cafe aroma the other day Thank you so much for being out there But that's not the ultimate way or perhaps the most optimal way in which you can interact with just regular folks in their community Beat cops that walk The walk that come out there and talk the talk also with the residents could be much more helpful This is the type of thing where it builds that trust and it lets people especially business owners know that they're being Heard is the term I think is best The regular folks that live in my neighborhood We got lots of issues going on We got what's considered a speedway if you will a raceway of young people Racing their cars breaking the law not caring about a lot of stuff when the police are there It stops but the residents don't know how to talk to the police to get this type of an oversight going So I'll leave you with the time that you just ask the chief of police and His public relations people to begin having more events in Roseland That are specifically geared towards walking and talking with the residents the citizens and everyone beginning of feeling of We're in this together and what can we be doing better? Right at three. Oh, wow Thank you so much Good morning. My name is Nancy Pemberton And I am a member of the committee for law enforcement accountability now and I want to thank the public safety committee oh, I are and the chief of police for this meeting for the hard work that's been done in the last year and I commend they're all I do have a couple of comments about the Content of the report one thing that concerns me is That there's no discussion of interviewing Complaints there is a great recommendation that more people more subjects should be interviewed before coming to conclusions But I also think that more complainants need to be interviewed the people who are complaining are not going to be the most articulate the easiest to understand and Interviewing them specifically about their complaint can uncover more information and I think that should be done more frequently Secondly there were a couple of descriptions of Complaints that it was not clear why the OIR group concurred in the exoneration Two of them were very minor and were actually pointed out in the in the narrative one having to do with a guy sitting on a Blanket and being approached and then finally asked for identification They said there was no violation of policy, but there's no explanation of why the guy was actually I'd asked for identification There's no explanation that he was doing anything that should have Permitted under law that put the police asking for identification the second one was a Guy sitting in a car. They receive a neighborhood neighbors complaint that there's but somebody Suspicious for sitting too long and again and the police told that the guy he had to move on There's no explanation of why he was told he needed to move on or quote encouraged to move on He had every right to be sitting there He and in fact they told him he was parked illegally and he wasn't parked illegally So I don't understand why there was no violation of policy or the law in that case so in both of those cases I think of if Bigs honorations were justified a better explanation is is required. Those are the kinds of Interactions with the police that cause People in the public to distrust police those are those small level interactions that are That that seem to be arbitrary Are the things that really raise people's hackles so I would encourage you to either relook at those kinds of things or Provide better explanation of why they should be exonerated. Thank you Hi, my name is can you hear me? Yeah, my name is a lot of Medina. I live in the first district and I kind of wanted to comment on On something that I heard recently In a conversation during a coffee coffee with a cup of aromas One of the issues that I brought up that was a concern to me was when it comes to SRPD the lack of support for civilian oversight much like a little at the county level and what was Mentioned to me is that one of the the things about the independent police auditors that these are experts that really understand the issues of How policies and and the laws around police action works and And and that was kind of brought up as I Said that in our in our justice system when people are being prosecuted they have the right To be judged by a jury of their peers, you know people that aren't necessarily experts These are people in our community that Sometimes don't necessarily want to serve in our jury But but I think that in terms of building trust Accountability is essential and I think civilian accountability Is something that that really could go a long way to better building that trust and and and I would hope that the city and The police department can maybe move more towards that model where a civilian oversight Is established that isn't you know necessarily just a paid organization But some of that is members of the community that participate in the community Maybe not experts but people that I think have a vested interest in making sure that we Have an accountable police force that's accountable to the people accountable to civilians of this community and the city I Think it's essential towards better relations and You know, I think we could all acknowledge that Our police department is essential and we want it to serve our people effectively We want to have good relations, but we do require accountability And so I just wanted to highlight that issue and Push the the city and the city council and the police department to to work towards that to a civilian oversight Of our law enforcement agency. Thank you. Hi. I'm Susan Lamont district, too I've been a regular attendee at the community advisory council meetings of Iolaro and I've become sort of a broken record there on a particular subject and I would also Want to reiterate it to this? this group in the OIR and that is Reaching out to the public to make sure they actually even know you exist because truly the majority of the public doesn't know and to find out keep them informed about what you're doing and Why it is important so I Know I know for a fact that Iolaro has had real trouble in the past with the press democrat getting the word out now we've Brought some pressure to bear and that has improved recently, so I would I would really like to see both OIR and Iolaro and the CAC and and the police departments to all approach all the media in in Sonoma County and Essentially ask but it's essentially would be a demand That there be regular coverage of what's going on that they would promise That they would do this now not everybody follows media but I Think it's in it's important that the public knows what you're doing and knows why you're doing it and knows what they can input We don't get it we don't get a lot of turnout back at the back when these organizations were first being started there was a lot of public interest because they were generated by by critical incidents and Now the public has sort of stopped paying as much attention and it but it doesn't mean that things are less important So I really would like to see in addition to being at Events and being out in the public and being out on the street that there really be a cooperation between these groups and And media because the public needs to know thank you Thank you. Is there anyone else in the room that would like to comment? I think everybody has All right, we'll turn we have one or a hand on zoom. All right, we'll turn it over to the zoom host to help facilitate that Thank you. Hi Jim. I've unmuted your permissions and you are now Able to speak Hi, this is Jim Duffy. I'm an oversight practitioner living in runner Park. Thank you for taking my comments It appears that the downtown enforcement team operates under different protocols From the rest of SRPD that governs the team's strategies and approaches the public safety subcommittee should host a presentation on these strategies and Approaches as they appear to result in increased citizen complaints Also, the city council should direct SRPD to adopt recommendation number one I want to echo what Nancy Pemberton was saying All these recommendations are good But this particular one recommendation one is critical to the integrity of administrative Investigations and complaints and not only all subject officers, but all complainants and all witnesses should be interviewed when there's a public complaint Creating effective any bias training is an iterative and difficult process And I command SRPD for for really leaning into this and I've heard really great things about How things have been going? I encourage you to continually to be holding these trainings as developed while working with your staff in the community to Continuously improve the trainings. Don't let the perfect be the enemy of the good Done correctly these trainings will continuously improve over time Cenerosis current oversight model of outreach Has or oversight model has outreach, but no community wide available community engagement function Outreach and engagement are different and are often confused Both are essential to a well functioning civilian oversight regimen I think you could start moving towards more engagement by having the CCAT host a couple of open town hall style meetings a year It's great that the CCAT will no longer be appointed by the chief I encourage you to consider community organizations doing the importance or a lottery system for the appointments to the CCAT There are many better appointment processes than using the agency executives or the city manager and OIR if you ask them they can help you think through these processes. They're really good with this stuff Thank you for taking my comments There any more hands on zoom? All right, that's all great feedback unfortunately because this isn't a meeting We can't get into it back and forth and ask follow-up questions On Tuesday the 20th, this will be going for the entire council and that's when we'll have an opportunity to address these things see cat oversight In general, so I encourage you to all show back up But as for now, I guess we will adjourn this informal Presentation of OIR if there's unless there's any Yeah before we adjourn. Thank you councilman. Oh, crikey. I just want to make a few announcements. So OIR will be here On Wednesday, June the 21st. Well, it'll be here Tuesday to present to city council There were all they will also be here from 9 to 11 at Tia Maria So you can do a drop-in meeting and if you have questions if you have questions about the report If you have questions about the process or how to make a complaint They will be there to have casual one-on-one conversations They will also prevent present to the community advisory team at 4 o'clock and from 6 to 7 There will be a community meeting So there's there's plenty of space available. We welcome all the public business owners And staff to attend Again, we want to make this process very transparent, you know OIR is here one to help us with accountability Accountability and transparency. We want to make certain that we continue to enhance our community engagement We want to build trust Are we do have a top-notch police department? They're professional. They're focused and they're focused on the community well-being That contributes to a safe and secure environment OIR also helps us with sometimes we have blind spots they point out professional development needs that we could also enhance And this is it's independent. They have their own autonomy So we want to make certain that you the public are aware that they're going to be here next week If you have questions, you can call the city manager's office as well The chief is also available for comments and questions. So thank you Thank you very much and with that I just want to say again Thank you so much to everybody for their time patience understanding During this non-meeting and we'll revisit this on tuesday. Thank you


Jag vill tacka alla organismer. Det är bra att vara här i ITS och för att sätta ihop en liten grupp av människor. Jag skulle också apologera på två siffror. En är att det har varit många år sedan jag jobbade aktivt på den här siffrorna. Min människa är kanske inte så fräst som det skulle ha varit annorlunda. Den andra är att jag hoppade att få den senaste veckan för att bli lite mer intressant. Men jag hade en kalld som du kan lära mig. Jag planar att fokusera mer på den spektralen av de människa människa modeller. Jag ska diskutera varför det är såklart klassiskt. Det är sida, kontum och de supersymmetriska människa modeller som kommer från människa. Planen är att ge lite mer av introduktionen. Vi har hört att många av människa människa fokuserar på att lära sig till att fokusera på de olika människa modellerna. Men det är inte svårt att få ut några extra saker. I den här videon har jag sett att många av de som inte är expert i den här människa människa fokuserar på det här. Det kan vara bra att förstå det i en mer detalj. Och fokus på spektrum och grannstadig konjunktur. Det är en avsäkterning om det är den sista människa människa. Det är en avsäkterning om att lära sig till att lära sig till den positiva människa människa. Det är en avsäkterning om att lära sig till att lära sig till den positiva människa människa. Och så ska vi diskutera varje avsäkter till grannstadig konjunktur. Det har varit många år sedan och det har varit en avsäkterning i några av dessa. Om vi recall, vi är considera en bosonic member. Vi börjar med bosonic case. Det innebär att vi har en invading av en människa människa. En världvolum i spacetime. Det är en avsäkterning om att lära sig till den positiva människa. Det är en avsäkterning om att lära sig till den positiva människa. Vi har en vänniska människa som är svarande i världvolumen. Sigma är fixat. Det är en avsäkterning om att lära sig till den kontaktiga människa. Vi har invading av ordentliga funktionser. Här arbetar jag i den liten människa människa människa. Även om invading i spacetime är r. 1 plus liten d är parametret i de här modellerna. Och en vänniska människa. D är essentiellt de transversal människa till människa. Vi har d är en avsäkterning av ordentliga funktionser. En avsäkterning av ordentliga funktionser. Det är en avsäkterning om att lära sig till den människa människa. Det är efter att lära sig till den liten människa. Och lära sig till den människa människa. Den här energi är byggad av Hamiltonian. Funktionen på spacetime. Vi har de x-kornet funktionser. Men också de konjugerade momenta P. Så det här är Daniels integral. Den här fixade särskilt. Vi ska tänka lite om det här. Vi har de momenta square. Och så finns det en Poissonbracket. Vi har Poissonbracket av ordentliga funktionser square. Det är en avsäkterning av ordentliga funktionser. Vi har två Poissonstrukturer här. En är givet av siffrorna. Här har jag sett den här normaliseringen. Men det finns fläktighet där. Det är en av de Poissonstrukturer som vi har. Det är en avsäkterning av ordentliga funktionser. Men också de dynamiska Poissonbracket. De här ordentliga funktionser och momenta ska vara kanonisk eller konjugerad. Det är en Poissonbracket här. Det har varit normaliserat. Och jag kan säga också att en av de detaljer som kräver den dimensionella reduktionen från den fulla teorien till den här siffrorna. Man måste också få ut några konstrainer och så vidare. Det är en diskussion i en paper med De Woll och Hoppe. Vi går över till den matrixkontexten. Vi har sett att de ska replacea de Poissonalibrar av funktionser på den här siffrorna. De har också varit normaliserade. Vi har sett att de är zero-min realvaliga funktionser. Vi representerar den Poissonalibrarna i terms av matrices. Vi går över till en algebra av traceless Hermitian- och biomedmatrices. Tracelessnessen är från zero-min och Hermitian- från de realvaliga funktionser. Det är bara n, det är matrixsize. I den här representationen representerar vi Poissonbracket- med konvitatorn av matrices. De intervjuar på surface och går över till tracelessnessen. Det är en fin fiktion att det finns en konvergen- så att vi kan, lite independentligt- av det aktiella topologin och så vidare- vi kan arrangera basis av traceless Hermitian- matrices, så att strukturekonstans- i den här basis är konvergen. Om du vill använda högre genus- surface för att parametra människa- hur kommer det att se upp på den visst sidan? Jag tror att du behöver skriva olika basis- som ger dig strukturekonstans. Jag tror att Jens är det mest... Det vi diskussade tidigare... Detta ansvar är den här. Det finns en abstract theorem. Många olika saker. En, för exempel, Bordermann Meinröngen- som provar att för någon genus- surface, den matrixalgebra- kan vara konverterat till den genus- surface. Men det vet inte vad basis- för högre genus- surfaces är. Detta matrices, i vilken du får- strukturekonstans- och A, B, C- är bara för Torai och Sphere. Så det finns en existens- av basis- och en strukturekonstans- i basis- så att du får konverterat. Det är lite mer trevligt. Men hela idéen- är att det respekterar- den här- repräsentationen. Det respekterar symmetrar- eller av konstrainer. Vi hade- i den originella- människa- difimorphism- invariant- på surface- och en- area-preserving- difimorphism. Vi vill- konserva den- area. Det här- i den matrixen- modellen- representerar- SUN- invariant. Så den- speciellt uniteria- för den här- area- konserva- konstrainer. Så- så vi har- den- Hamiltonian- som vi har sett. Det är nu en trace- över- momentum- sidorna- matrices- square- och sen har du- komiteter- square. Över- all- the pairs- of the matrices. Och- if you want to write this down- in terms of a basis- of SUN- and some standard basis- then you have just the sum of- and then we have- we have- the- the- structure constants- and then- so this will be the- the- the square. And then still- we have- we still have- so the canonical Poisson brackets- between the coordinate- and momentum variables- here. But now there's only- finitely many of them. So that's the whole idea- here that if- since we have a finite- dimensional system- we can then- quantize this- in the standard way- using the Schrodinger quantization. So- so we represent this- and set of- coordinates and momentum- on the square integrable functions- over the corresponding dimension. So we had the d- space dimensions and then- this is the matrix dimension. The basis- the number of elements of a basis- of this space. And then we represent- our Xj- as just multiplication operators- on this space. So we have expanded- in this basis ta. And while the momenta is represented- in terms of derivatives. So minus i times derivative- with respect to Xj. In order to- to represent the- the canonical commutation relations. So then our Hamiltonian that we had- the sum of p-squares- goes over to the Laplacian- acting on this space. And then we have a- scalar potential essentially. Which depends on the coordinates. And I will come back to- the details on this potential. But what we have here is also- symmetries. So we have- essentially the d- dimensional space. And the rotations- maybe represented- within this. Essentially Hamiltonian commutes- with such rotations. But it also commutes with- rotations in the- in the matrix space. Also SUN transformations. Which are then represented if you- in this basis by- orthogonal transformations as well. So what we have to remember is that we had- we have these constraints- of the thermomorphism invariance. So we still have that constraint- which we have to implement. So actually the physical Hilbert space- is not the whole space here- but rather this where I wrote- the sort of bosonic Hilbert space- physical. Which is then the SUN invariant states. So the SUN- so the generators of the SUN symmetry- can be written in terms of this basis- with the structure constant like this. And that acting on our states- should be zero. So that's how we implement constraints. And this is just amounts to the standard- direct constraint quantization procedure- that we still have some constraints. So we will look for- to solve those constraints on the quantum side. This is the constraint? This one is a constraint. So this is- at this point. I don't remember. Yeah. It could be second class at this point. So yeah, they have to- this is probably written in this paper. Okay. So- then we have this complication of- supersymmetry if you want to consider- the supersymmetric membrane. So the idea is to somehow add- spin degrees of freedom- and obtain a supersymmetric theory. So I will say something briefly- about supersymmetric quantum mechanics. Because it's not the full- supersymmetric quantum field theory here- but it's really a reduced thing- into the quantum mechanics. So then it can be more simply stated. So essentially a supersymmetric quantum mechanics- you can think of having a couple of different objects. So one thing is the- there is a Hilbert space. There is a grading operator K. There is a Hamiltonian. And then there is a supercharges- supercharges operators. So you have a Hilbert space. The grading operator is just an operator- upon the operator is going to 1. So you can sort of split the Hilbert space- into a positive and negative part. Or the eigen spaces of this. And you can term this- the even sector and the odd sector. And then this Hamiltonian operator. It should be even with respect to this grading. So it should map even to even. And odd to odd. And it should be a self-adjoint operator. But then you have the supercharger operators QJ. And if there are N- the curly N of them- that we can say that there is an N extended supersymmetry. These should be odd operators. So they are mapping the even to the odd. And the odd to the even. So they are interchanging these spaces. And they should satisfy- essentially the Clifford type algebra. That the square of QJ- should be the Hamiltonian. But they should also anti-commute. So this is the definition- of the supersymmetric quantum mechanics. And some nice properties that are implied- just by the structure is that- your Hamiltonian will necessarily be- non-negative operator. Because it's the square of QJ. I should say these are- in this formulation these are self-adjoint operators also. So the spectrum of the Hamiltonian- has to be on the positive real line. Then there is a pairing between- the eigenstates of the Hamiltonian. So if you actually have an eigenstate- with a positive energy of the Hamiltonian. So say that you have it- and you can use this splitting. So you can say that you have an even state- for instance, with positive energy. Then by just acting on it- with the supercharge we get to the odd sector. So you would have an eigenstate- with the same eigenvalue E. On that sector. So there is always a pairing- for the higher energy eigenvalues. But not necessarily on the zero energy sector. Because then you would annihilate the state- by acting on Q. So this is used for instance- in index theorems and so on. To spot whether there is a zero energy state or not. Okay, and then in this- in the supersymmetric formulation. What we want to do is somehow to- instead of having SOD- as the rotation group symmetry. We want to have a spin D- represented on trivially in our space. So we are considering actually- representations both- sort of spin representations- with respect to the RD space. But also with respect to the matrix space. And these should be represented- as some bounded- operators on some- folk space. The Hilbert space of the model. So we then have to go to Clifford Alibas- to construct such representations. So starting with the D- dimension space. And we're looking at corresponding Clifford Alibas- over D-dimensions. So say gamma matrices- satisfying the anti- computation relations. And then you take an irreducible representation- for these matrices. Or just- a certain matrix size. And I call this ND. So this depends on the dimension. And there is a certain natural- irreducible representation here. Then you construct- over this space that you got. You then sort of couple that- to these matrices. So the matrix degrees of freedom. And then you construct- a Clifford Alibas- on top of that space. And then you stop- in dimension a bit more. And then you consider the irreducible- representations of that algebra. And that will be even bigger. So then it's- the dimension is 2 to the- and then it's essentially this- dimension here. And D times N squared minus 1. And then half of that. And we will see explicitly how you construct- these things. In one way. Ja, så här- we consider actually a complex representation. But you can ask- whether you should want a real or a complex one. But typically- at this. So here it's the first stage. So it depends a bit- what kind of structure we can get. So I will come to this soon. So this real representation- in certain dimensions this turns out to be- actually a complex or a quaternionic representation. And then you can use that. So- but on this stage- you can also ask- should you have a real or not. But let's think of just a complex case. Otherwise it would be more complicated here. So- what happens in this picture is that we- so adding- to our bosonic Hamiltonian. So the- the kinetic energy is actually plus the- the scalar potential. We add this- so spin degrees of freedom or this- fermionic operators. The theta. And they come in with a- linearly in the coordinates- X. The rest is just this sort of- structural constants. And then it turns out that you can- write down a set of supercharges. So the number- of supersymmetries essentially is this- dimension here. And so you have a- linear in momenta. And then a- quadratic in the- axis. And then coupled to these- from variables. And then it turns out that- for certain dimensions these- satisfy this- supersymmetry algebra. That- the anticommutator of such- supercharges gives you the Hamiltonian. The physical Hilbert space. So this is just the- generators of SUM. So on the physical Hilbert space this- piece vanishes. So you have- it closes up to this- supersymmetry algebra. So in order to understand this- requirement. One needs to know a little bit more about- Clifford algebra and so on. But I don't have so much time to get to it. But let me ask- I. And then you consider the corresponding- Clifford algebra. And these are well known to be just- essentially matrix algebas or- a sum of two matrix algebas. But the matrices are- have a real or complex or- quaternionic structure. And so- this is just the dimension of- of the Euclidean space that we- construct this Clifford algebra over. And then this is the dimension of the- responsible representation of the Clifford algebra. And this you can read off from- this side. Then I have- essentially just written what- sort of the structure is in this- in these spaces whether there is an- additional complex or quaternionic structure. And then on the right- hand side here is what happens when you act- essentially how can- spin D be represented on these- spaces and then there is an- additional splitting into- either you have just- essentially an irreducible- representation or it splits into two. Either different or the same- representations. So actually you can see that the- special dimensions where you have these- supersymmetries, the case. So for my- label of D here it's the two, three, five and nine- cases. This is what I've marked with the arrows here. And it turns out so in the two- case essentially the structure is real, but in the three case the structure is complex and you can use that. And also in the five-dimensional case there is a quaternionic structure which you also can use. While in the highest dimensional case which is of the most interest is essentially a real structure but it turns out that there is sort of octonionic features in this case also. I have also- indicated this one here which is somehow a degenerate case, the one-dimensional case. So this is somehow- if you want some kind of zero- dimensional thing. So this is again related to the fact that you have- essentially the norm- division alibas are the real complex quaternionic and octonionic ones. And this is sort of the same thing which appears here which has to do with Clifford alibas. Okay, so I might come back to this- table. So now our full Hilbert space is then the bosonic one times the fermionic fox space where we have represented this Clifford alibas. And then again there is a physical Hilbert space which where these constraints vanish but now it's not only that bosonic sector but there is also the fermionic part here. So that's imposed as a constraint that we should be in the kernel of these operators but then you still have also a symmetry sort of a rotation- spin-d symmetry which is then essentially a rotation among the coordinates and then also rotation of these Clifford alibas or on the fermionic fox space. So what we would like to emphasize here is also how we can construct these fox space representations. So essentially the one way which was used by David Hoppe and Nikolaj is to essentially you pair up so given these stitas Clifford alibas you can sort of pair them up to construct creation and annihilation operators. So one way is just okay you take the first half and the second half and pair those up and then you have essentially creation and annihilation fermionic operators satisfying canonical alibas like this and what has been done essentially is to to split the space. So along with this pairing you use a splitting of the d-dimensional space into d-minus two variables and then the last two you use as a sort of complex variable you can take the real and the imaginary part of that. So I have here written X prime is the first set of variables here and then Z is the pairing of the two last variables d-minus one and d and if you do that this sort of goes well together and you can write down the Hamiltonian in terms of these creation and annihilation operators which involves these first variables here and so big gamma is the reduction of these gamma matrices in terms of this splitting and then you have the last part so this first part preserves the fermion number but in the last two parts you have a raising of two or lowering of two fermions fermions so in this sense the whole operator result of mix the fermionic sectors but there is this alternative in three and five dimensions which I'm not sure how much it has been discussed, okay it's also been used by Clausson and Halpern and then discussed this a little bit in my thesis that in these special cases since you have this complex or cotonium structure you can use that pairing which gives you a more canonical pairing of the fermions so that in that case your Hamiltonian can be written so using these other pairing you have essentially yeah so your Hamiltonian is then the bosonic and then you have a piece which conserves the fermion number and then the SUN and the bin D generators also sort of preserving fermion number then there was this degenerate model which essentially so it's one dimensional case which essentially is just a free Laplacian acting on the on the matrix degrees of freedom and then there's a piece which vanishes on the physical hyperspace so one way to the corresponding super charge so there's only one super charge in this case it's essentially just a theta times derivative so this is like a Dirac operator and its square is this Hamiltonian on the physical hyperspace but there's also here an alternative so either you sort of work with this or you construct and what you can call somehow a comological version which is so there's a way to also introduce fermionic creation and relation operators and then you have a Q which is not self-adjoint but you also have a Q star such that they sort of close up this supersymmetry algebra let me not spend too much on that so now we come to the question of what about the the spectra of this model so we have the classical side and just the membrane or its regularized version and then we have the quantum regularized membrane and the quantum super membrane and and one way to understand this differences is using toy models which has been very fruitful so if we start with the classical model we have this Hamiltonian again trace of this momenta and then the potential which we should note is a non-negative potential here and a toy model that you can keep in mind see if I maybe you can here so essentially we have a toy model potential which only depends on two variables so it's in R2 and it's x squared, y squared so the feature here is that there's certain flat directions so if we think about this toy model we have this in the xy plane then along the coordinate axis the potential vanishes but then it somehow increases rapidly in these cases so this is indeed the picture that arises here that in this matrix model potential you have vanishing directions where all of these matrices are commuting so it's essentially such a asymptotic direction so you can really go out to infinity while the potential vanishes but the important feature is that while you move in such a potential valley the valley also gets steeper in this in the transverse direction so because of this narrowing it turns out that you can actually there's a difference on the quantum side but if you just consider moving with a fixed energy in this potential well then you can indeed escape in the well to infinity so in this sense it's an assigned potential so on the quantum side so we are then considering this floating in operator essentially a little aplassian here plus this scalar potential and then again it's both of these operators non-negative but the important feature is this narrowing of the potential valleys here so we can again consider this toy model Hamiltonian so on the quantum side here so this is the bosonic toy model which is then just you know the Laplassian on the two dimensions plus this this potential and here you can use essentially this illustration but it's a little bit more complicated on the matrix side but essentially the same kind of computation that so considering this operator you use what is sort of happening along the valleys here to bound this operator from below by something which has a discrete spectrum so what you can do is sort of take you take half of your momenta here and you sort of put and you split your potential into two pieces and then you take also half of the x momentum put it here, half of the y momentum put it there and then you consider these two parts here separately so this if you recognize it's just like a harmonic oscillator in the x variable with a frequency y here so this is just bounded from below by the sort of zero zero point energy which is then the frequency y and the same thing here just symmetric in x and y so here we have somehow used that in such a valley there will be some kind of zero point energy due to the narrowing of this valley here which then depends how far out you are in the valley so so bounding from below with these parts you get in total an operator which has a potential which goes to infinity in all directions so because of this it has compact resolvent so it has a discrete spectrum and also it cannot have a zero you can see this for instance by sobel of inequality so this is the interesting feature here that we on the quantum side we get actually a discrete spectrum for this operator the same thing goes through as I mentioned with this more complicated potential so essentially you can parameterize this in a smart way but then everything changes on the supersymmetric side so we had this bosonic operator which we now know has a discrete spectrum but then what happened here was that we added this essentially a matrix piece here it's linear in the coordinates but then there is this matrix here also and what we already know is due to the supersymmetric that this operator is the square of something of some self-adjoint operator so we know already that even though we added this part which is not definite it still is a non-negative operator and actually it's really important so for the supersymmetric it turns out that you will have a matching between you cannot just change any of these terms with some coupling constant or something because it has to match up there is also in this case a toy model so essentially it's this bosonic toy model with an additional piece so maybe it's useful to write it down so this is the supersymmetric toy model it's essentially the same thing of the R2 and then there is the identity matrix here and then you have a part which you can write so this depends on your taste but one way to write it down is in terms of two Pauli matrices so this operator is acting on so it's L2 on R2 just in C2 so you have a the Pauli matrices acting here sort of confused why you say minus okay exactly so I'm looking at this piece here which is sort of this is the one which is linear in the coordinates times the matrix and if I square that so the square of this part plus y squared due to the Pauli matrices matrices so that means that this operator is bounded from below by at least the negative square root of that so this is what you can use on this side then that whatever this okay it can become arbitrarily negative but it essentially if you go along a potential value so if if y is zero and you go along x here then you have just minus the absolute value of x along this value and this matches up exactly with this corresponding harmonic oscillator zero point energy so what happens is that there is this exact balancing out between the zero point energy of that oscillator and this fermionic operator here so it turns out now that this changes the spectrum again so it's no longer discrete spectrum but it's rather continuous spectrum on the positive real line for this operator of course depends on which operator we consider but this toy model has the same feature features as the real matrix models so it turns out that also in the full matrix models you can prove that this corresponding operator has a essential spectrum from zero to plus infinity so what you do is essentially to use this fact that so on the fermionic side yourself in where this is as small as it can be and in the bosonic side you take a state such that this is the smallest it can be and that there will be this balance between these and essentially you can construct then a sequence of states which sort of get pushed out into this valley and in this sense a sequence of while sequence of states so you can prove that there exists a sequence of smooth and rapidly decaying states I think maybe you can even maybe not compactly support well you can take them compactly supported and normalised such that for any lambda greater than equal to zero the Hamiltonian minus that states goes to zero so this means that that this point lambda is in the spectrum The theorem is for the full this is for the full exactly so this was in David Lyche and Nikolaj where they also used this toy model to illustrate the point so in the toy model case as I said this was size should correspond to putting yourself in the lowest energy here and then this phi is essentially the eigenstate in the transverse direction and then size is used to as a cutoff to move into the valley why does it mean that the membrane is unstable so in some sense it means that it costs zero energy to just to form everything you can move into this valley so in that sense so what it means in this valley if I understand correctly somehow you can form spikes of your membrane and so these spikes somehow you cannot see somehow the uncertainty principle is not there to stop you from such spikes forming so there is somehow som ionic degrees of freedom there is an extra it allows you to somehow fluctuate with spikes but I think in some interpretations then this is used as an advantage that you can somehow if you have a membrane it can somehow form a small tube or a spike and then it can maybe form a new membrane in some other section tube somehow you are allowed to change the number of membranes and these things that there is some kind of second quantized interpretation there that it can fluctuate in the components and topology and everything ok so then there was this conjecture concerning the existence of ground state so we should think about the case now that so concerning the spectrum of our operator so we know that in all of these cases the supersymmetric cases you have a spectrum which is on the positive real axis so this is the spectrum of the supersymmetric Hamiltonian and the question is really what about the point zero in the spectrum somehow so whether there is some stability in this sense that you would have a lowest energy state where everything can somehow boil down to or if it's just if there is no normalizable ground state there that somehow tells you that things are leaking out to infinity no stability so the conjecture was that in the highest dimensional case there should be a normalizable zero in the ground state so this point should be an eigenvalue and also that there is a uniqueness there so that there is only one such state while in the lower dimensional models there should be normalizable seriös state for any matrix size and also this statement was for all matrix size by the way you separated the center of mass motion the thing is yes so this is now so if I have a k square called zero ground state I would not see I mean if this is a master's ground state it cannot be I cannot go to the center of mass frame is it excluded by the formalism no I think that's just but I think that problem probably trivializes the center of mass problem is somehow you have somehow separated these things so I think this on the center of mass side this is probably just like a particle gauges for the string when one quantizes a string if you do it badly you eliminate the massless concept ok but yes so so this conjecture is then supported by various evidence so in the case the lowest the simplest case among the full matrix models so the two dimensional and two by two matrices there is a proof by contradiction due to your relation and the proof that there does not exist that there does not exist such a ground state and if I understand this correctly it's again has to do with some of the size or that we will come to this but there is sort of the geometry involved here whether there is you know whether these states are essentially decaying fast enough at infinity and this question was then addressed I guess it was discussed somehow in the Halpen & Schwartz but then Frölich, Graf, Hassler, Hoppe and Jao considered the asymptotics in the also in the n equals two case essentially studying what happens along these valleys and looking at the the equation I think that this is Serenius state with respect to the supercharge you can then see essentially what are the decay properties of such a state how is it decaying as you go out to infinity so the question is is it decaying fast enough to be normalisable or does it sort of maybe it does not even decay it could also blow up or stay constant and then you have to be you have to know also the size of these valleys and so on so there is a lot of interesting geometry then I guess Pillen G will tell us more about the Witten index approach however I should point out that in these models because of this spectrum being continuous and various difficulties of non non-compactness here one has to be careful when you make the index computations so you cannot just assume that you have a discrete spectrum and work on that so what I would like to point out though is the existence of embedded eigenvalues actually in the spectrum so it turns out using this the way we can define the model choosing our fermions so in the 3 and 5 case shows the fermions the way we did in this slide so since we could write down the Hamiltonian where the fermion number is preserved then we can work on a sector where essentially you have zero fermions so on that sector this Hamiltonian just reduces to the bosonic Hamiltonian so in these cases due to the existence of this complex structure you can actually just split so you use this structure to somehow split the Hilbert space into different sectors of fermion numbers and on one of those sectors the Hamiltonian is just the ordinary bosonic Hamiltonian and we know that the bosonic Hamiltonian has a discrete spectrum so in these cases there indeed exist points in the spectrum which come from the bosonic Hamiltonian so that proves that there exist embedded eigenvalues in those models but this was in these cases the three in five so the problem is in the in the say two and nine dimensional case we do not have this canonical structure and indeed essentially the best we can do is to have these non fermion number conserving terms which then mess up the whole picture so it's difficult to see whether there is such a reduction in that case I have to point out here that we can on the right focus space sector we have the same Hamiltonian here so another thing which is important to point out is in the three dimensional case you do have you can write down states which are zero energy states but they are certainly not normalizable so essentially what you can use in this case that the super charges essentially a direct operator but then conjugated with with a super potential which is of a cubic type so in the three dimensional case you have also a more canonical pairing up between all these volume form in the three dimensions taking these three matrices and so you use the anti symmetric tensor in three dimensions and then the structure constants forming a real valued function so indeed this also has some properties like certain valleys where it's zero certain directions where it's actually blowing up positively and then blowing up on the negative side so it's indefinite but if you just write formally a state where you have essentially zero fermions and then you multiply by this function then this is it's a smooth function and it's in the kernel of the super charge but it's not in the Hilbert space because of the indefiniteness of this and then you have a similar state if you just switch the sign and you take the full fermionic thing so in this due to the structure there exists such states but they are certainly not normalizable and they cannot be made normalizable just by changing you have to really change the the inner product of your Hilbert space a lot having exponential decay in order to accommodate such states and also in the one dimensional case there is essentially this you can think of as a plane wave model supercharge is just a derivative times a fermionic variable so again you can just take states which are constant with respect to that so so either you take zero fermions or full number of fermions and then acting with the derivative it's just zero but this is again a constant so it's not in the Hilbert space but it somehow is better than this case because then it's constant so if you just change your you inner product a little bit you can somehow accommodate for it so this is an interesting question whether one should somehow change this the normalization and play around with whether these types of states should be included or not okay so I will not go into so much of the detail on these different approaches but essentially one approaches by construction so you write down recursive equations on the different sort of expanding so one approaches to expand essentially Taylor expand the ground state around the point x equals zero and see how you can relate the higher order terms to each other so this has been sort of fruitful that we can find a unique state due to all the symmetries and everything you can find a unique value for the ground state at the point zero and then also I think to the first order but then there might be more possibilities in order another approach has been to deform the model so what you can do is somehow to single out some of the directions and make a deformation and then arrive at a different model which still has the same complicated spectrum a continuous spectrum but it has somehow reduced in complexity on some other aspects so this might be more amenable to computations and another approach is to somehow average with respect to symmetries so again you can view the model in a certain direction understand a certain region or selection of the coordinates as essentially also a harmonic oscillator type of problem and it turns out that if you take this operator which is then defined in this direction and you somehow averaged it over the directions you will find the full operator so the hope is to be able to use some averaging techniques to arrive at the model and then another approach has been to try to investigate this case whether the zero and new states just in the Hilbert space but maybe the sort of weakly in the Hilbert space so that if you just change your normalization a bit or if you allow for a slower decay or you know either just having constant functions or a slow decay that you might then spot these states and can somehow understand them that if you yeah that perhaps this is just a dimensional issue or that the decay is somehow there because of the geometry and then so maybe there is both in the two dimensional case and in the nine dimensional case there could be a ground state but it could turn out that it's in the higher dimensional case it's fast enough ok så maybe I just flash some things here this concerned the construction by recursive methods essentially expanding the state to higher orders in the coordinates and then considering the various conditions arising from it being a zero and new state and you can find that in the nine dimensional case with only well n matrix size is two then you can understand this essentially the value at the origin due to symmetry so it has to be a certain combination of states arising from the different representations here go into the detail of this and also Mikrochita and Chachilevsky studied the higher orders for this problem the deformation case so essentially it's a little bit related to this what happened in the three dimensional case that is somehow considered a cubic superpotential and then where we somehow use we single out some directions so let's say the last two directions eight and nine and also the indices eight and sixteen and then somehow you can using that choices those choices you can write down something which is nice and then you can somehow deform your model with respect to this choice and then you end up with so there is a deformation parameter mu and you end up with a Hamiltonian which then depends on this mu and in the case that mu is equal to one some of these terms drop out and you have something which you can which is in some sense simpler but you can still prove that this deform thing also has to the continuous spectrum then there is averaging or maybe not say so much about this what I can say you know so I have three minutes ok so maybe I can say a little bit about this weighted approach so as I mentioned the asymptotic analysis suggests to allow for more slowly decaying ground states so we saw already in the D was one this sort of degenerate model in some sense there was this ground state which is just constant so so the question is ok maybe it's just that it's not decaying fast enough so if we so if we change the Hilbert space a bit and we can accommodate for such states so here I change it by adding a weight so it's the original space so d rd times n square minus 1 with values in the form of a fox space but then I change the measure here a bit so I take this function raw alpha which is essentially just something which is decaying as x to the minus alpha so alpha is some weight parameter that can play with so in this so the new Hilbert space is just related to the old one with this function raw alpha so then we can define Hamiltonian with respect to the new space so h alpha but we define it just using the old quadratic form essentially it's still q times the q acting psi in the old norm so essentially you define this as an operator just say you start with the smooth functions with compact support and then you take this is a non-negative form so then you can take the corresponding fringe extension here but then there is an interesting ground state correspondence here so say that we had a state which is a ground so if it was a ground state of the original problem original Hilbert space and it's a zero eigenfunction of the Hamiltonian H but then since this deformed or this weighted Hilbert space it's just bigger you allow for more things here so then it will also be in that space and it will because it's zero eigenfunction here so it's annihilated by q so it's indeed also annihilated by this side so any ground state of the original problem is also a ground state of the weighted problem but on the other hand if you have a ground state of the weighted problem then you can you know that this is annihilated by q and you can use essentially elliptic regularity and these things so that you can conclude that this is actually a smooth function and it's annihilated by q so okay and it's also in that weighted space but it could be so you have essentially everything you want but it might not just be in the Hilbert space so it's a useful thing to look at this space instead to see if there's just some weakly bound states somehow in this problem so then what you can use is a certain spectral relation between the problems so if you want to see you know study the spectrum of the of the weighted problem it's the same as studying the spectrum of the original problem where you deform the Hamiltonian by say lambda times this function rho alpha so essentially if you want to see to understand whether this has a discrete spectrum then you just have to sort of look at the negative eigenvalues of this problem and so and also the question whether there is zero any ground state for the weighted problem is the same as whether this original Hamiltonian has a negative eigenvalue when you deform it in this way so you throw in a negative potential which has this decay so x to the minus alpha at infinity and you ask if there is always a negative there then it means that this weighted problem also has a ground state normalizable ground state so then you can sort of use spectral theory for these operators and so on so what I did was to look at the toy model again so this one and apply this procedure and I find that if the weight is large enough so if the decay is fast enough so alpha bigger than 2 then indeed this problem the number of negative eigenvalues is bounded by constant so this means that this in this picture that there is a discrete spectrum for this model okay so maybe I can I can sorry yeah so I wrap up maybe I can just say that in this weighted picture you can consider essentially a weighted index try to count how many more states do you get in this in this in a weighted case than in the original case so that's one possible approach so then there is just this final slide as I mentioned continue to construct the ground state to higher orders around the origin study this deformed operator there is also the question of the averaging of eigenstates the yeah so I have not proceeded yet with this approach to compute the weighted index for the toy model and the matrix models that would be interesting as well and then we saw that there are embedded eigenvalues in certain dimensions but what about the two and nine dimensional case at least in the two dimensional case I think there is some kind of reduction you can make also with respect to symmetries so that you can in some cases you can find I think you can in the two dimensional case also discover a sector of the Hilbert space where you have a discrete spectrum so thank you very much just a comment because it happened to be the end of your talk this D equals two case I don't remember so there is a paper by three former Soviet Union one of them is the mother where is Antal the mother of the woman who is faculty in Browen what's her name Arafi right I don't remember the time but a nice paper about embedded eigenvalues in D equals two this is exactly the one I was thinking of Arafi var koscheleven Medveten any questions, comments yes so this was very nice and a lot of information so what is the final message are you saying that this waiting could allow to find finally interesting ground states, weekly decaying I got lost what is the main message exactly the main message is that things depend on the dimension somehow it could just be that that even if there is no state it could still be that it's not normalised there is a state which is somehow decaying but it's just weekly decaying so then maybe you can compare the two in the nine dimensional cases so I think both in the I would somehow suspect but I don't know exactly what to ground it on but that both in the two dimensional and the nine dimensional case there is such a weekly such a weak ground state but that in the nine dimensional case it's not only a weak state but it's also normalisable with the original Hilbert space zero energy ground yeah, zero energy and that would also be embedded in still the continuous spectrum of the weak Nikolai yes, yes it's just in the end point of the spectrum one more question physics wise what's the message we have a sample of mass motion that is just inertial I guess and is it crucial to have a ground state or is it not crucial or what what's the physics message so this possibly someone else should respond to but I think yeah so I'm not sure exactly why you want to have a certain or what the motivation is to insist on a certain Hilbert space or if you have some interpretation if it turns out that your ground state is just not barely normalisable somehow that maybe you still have an interesting interpretation of it does it mean that there is for example a continuous mass spec that one I think is more in terms of this case that you can deform the membrane that you have these spikes and tubes and so on as I understand it this continuous spectrum indicates that you can easily move between different configurations but then I don't know I don't know exactly what if there's embedded eigenvalues this is somehow stable more stable but it seems it can still deform I think what you need in the end is really to just split up the Hilbert space into the different sectors and so you have some of these perhaps on the so we have the SUN symmetry but there's a constraint so everything should be there but then we have the spin D and that's not a constraint but a symmetry but there's also part of the conjecture is also what about the symmetry of the ground state so I think it is known that it should be a ground state should be spin D symmetric somehow so I think if you split the whole Hilbert space down into different sectors with respect to the symmetry then yeah somehow there's also a question whether these these spiky states these states you use to prove the continuous spectrum maybe they are not respecting the symmetry actually so maybe that's just a sector which you can remove completely last yes BFSS wanted the ground state same the ground state for some duality reasons but maybe Pilgen has the best comment you know these things although we motivated here as a regularized dynamics of membrane this also appears essentially the same thing but in the so called M-theory hypothesis there is 11 dimensional theory that reduced to 10 dimensional string theory and there is so called Kalluzer applying mode all along this compact circle so this in case of SUN N by N case this unique state you are looking for is exactly this Kalluzer applying particle so this conjecture I mean not only any 16 16 supercharge but 8 supercharge 4 supercharge come from essentially M-theory and type 2 super strength compactification so there is a large number of physics ideas that goes into this conjecture maybe we thank our speaker and I will continue