I'm absolutely delighted to welcome back Brian Beatty. Brian's known to you, I think all of you, as the inventor of the term high flex, the first great theoretician of what it means. He's also a professor at San Francisco State University where he manages somehow to both support faculty, to consult worldwide, and to teach all the time and look incredibly calm while doing so. We've had them as a guest before. He's been a terrific, terrific person and I'm absolutely delighted to welcome him back. Brian, glad to see you here. Welcome. Well, thank you Brian for inviting me back again. I always enjoy being hosted by someone with the same first name, even though it's spelled it all differently. But it has been a kind of a wild ride, especially the last six months, both returning to faculty and kind of helping a lot of other people think about what high flex means and what it can offer them as they kind of consider how they're gonna kind of currently kind of grappling with the situation we all find ourselves in, so. Sure. You're world's guru for this right now. It's gotta be enormously exciting and a bit daunting at times. Yeah, definitely. And there are a lot of others who've been doing this mode or modes just like it calling it something else for quite a number of years. And I know they've been very gracious with their time too to help their colleagues, both inside their institutions and outside. So I know some of them are here in the audience today, so hopefully they'll get a chance to share some of their stories too. Oh, great. I'm just really, really glad to hear it and we're honored by your time. Just a quick question. I don't like to ask people to introduce themselves because as academics that will go on for a while, what I normally do is ask them what people are gonna be working on. And from what I can tell, for the next year, you're gonna be high flex all the time. You're gonna be teaching in it and advising people on how to do it, is that right? Yeah, I'm re-engaging in my teaching side of my higher education academic career and very excited about that and doing kind of what I call online high flex now because we're not allowed in the classroom. So that's in our, our system just decided to do this again in the spring and I guess we'll see what happens next fall. So there's that whole thing. The other thing we're doing is we're working on, more support resources around high flex. This open access book that's available free online spin out since October, that's getting a lot of attention. But there's a real need for more and a lot of individual institutions have faculty development centers and other places like that. They can provide quite a bit of a support. But I think there's a need for another kind of a general resource area, kind of a community site. And so we're working hard to kind of design that and start building it so that it's ready to go to support people, especially as they start working on their plans for spring and get prepared over the winter for whatever spring holds for us. Whatever spring holds up for us is quite a question. Just a couple of quick notes before we go further. People have been asking me, first of all, the open access ebook, you should find a link to it. If you look in the bottom of your screen, on the left side, there's a kind of tan orange colored box that says hybrid flexible course design. If you click that, that'll take you to the ebook. And again, thank you, Brian, for making that available. A few folks have had audio problems just refreshing this page usually does the trick. It seems to have helped more than a few times. And one more point, Nick and a couple others have asked, are we recording this? We are recording this and it'll be up on YouTube as soon as possible. That usually means tomorrow morning or so. Thank you for doing that. And hello to everyone else who's just piled in. We have almost 200 folks in here and I'm glad to see you. If you're new to the forum, I do very little of the way of actually asking you my own questions. I'm BMC here. So my job is to convey your questions. And before I can even say that, we already have questions. We have one from a medru community college professor, Sherry Chibangu. And let me just bring her up on stage right now. Hello, Professor Chibangu. No, I didn't mean to come out on stage. I'm clicking buttons. No problem. I just read and learned. And yeah, I've been clicking buttons. And so no, get me off stage, please. No problem. Welcome to the stage anyway, right? I'm glad to see you. If that's Monroe in New York State, I'm especially glad to hear you. So everybody else, if you have questions, you see how easy it is to pop on stage. Just click the raised hand button and the video works just like that. If you want to do text instead, just type in something into the question box. And we'd be glad, glad to hear from you. In fact, I think we've had a couple of questions that are already starting to come in. And the first one is one that, Brian, I've heard this from a lot of people, in fact. And this has to do with the question of equity. How do you see HyperFlex playing out in terms of equity? That is people who have uneven access either to the physical classroom or to different online technologies. Yeah, that's a great question. That's something that we've been really talking about lately, as a matter of fact, I did some work with colleagues on a white paper sponsored by a Canadian organization. And that was a main theme of it. We're supporting equity in this time of, kind of to use an overused term, unprecedented disruption in our educational system. And I think what it's done is revealed a lot of, it's revealed inequities. Maybe we didn't realize we're there or we're as critical as they are, but we're finding that every single mode we're talking about here, and in the HyperFlex conversation, we're usually talking about two main modes in the classroom or online, and oftentimes the synchronous and the asynchronous online. So we're really kind of talking about three modes. And so we've really had to become pretty cognizant of it. The fact that every single one of those modes has inequities kind of inherent in the design or the whole aspect of it. In the classroom, we know we can't serve all students who need access to education, actually whatever level it is, either because they can't get there, right? Or for whatever reason, or they don't have the time available. And so in higher ed, we've known about this for a long time, which is why we have all these online programs. One main reason, obviously, is provide access to students who couldn't be there for face-to-face programs. But we're also finding now, especially, even in our K-12 systems, our students can't get to the classroom now because a lot of times they're precluded from coming because of social distancing requirements or they're in quarantine or they don't feel safe or their parents don't feel safe. So there needs to be something for them beyond the classroom. And in many cases, there are issues of equity around that, even at that kind of the younger levels, not really lower levels, but younger levels. But when we move to the online world, I talk about designing for asynchronous first. Well, designing for an asynchronous environment, if that's done with a relatively weak pedagogy, there are inherent inequities built into that because they typically end up with a less engaging environment. Well, the studies I've seen and that I've worked with some doctoral students on, I have shown that those inequities are worse, the grade differential between oftentimes students of color and white and Asian students as a group, underrepresented minorities and others. That difference, which is problematic in the classroom, 10 or 12% maybe in some places, but it's often double online in asynchronous online environments, especially in the larger ones. And so there are issues of design that come out in this idea of online asynchronous environment, relatively easy to build online, but more challenging to facilitate an engaged environment. And it's harder to have that relationship. These ideas of presence online are really critical at this point. And when we don't address those well, we end up with inequities there. We may provide students with access to education that way, but if there's a 20 or 30% in the literature and in your databases in many of your courses, you might find this, that's basically a systemic inequity right there. Now we move to the synchronous environment, which most of us have done across the board, at least for a few months in the spring and many are continuing now, the predominant form is still synchronous online learning that I see at least. There are inequities built in there because of the access to the technology, for one thing, the bandwidth, just the network itself, the technology to use well at home and just having a home environment that's conducive to a study or a workplace. And so in my opinion, if we end up with just a single mode in any one of these, we're gonna disadvantage a group of students. And we've been doing that all along whenever we've done kind of single mode access. And so that's my real, that's my long-term kind of hope for this is that we can address some of these issues of systemic inequity by providing different forms of access to the kind of the same experience, the same courses, the same learning community, to the same learning outcomes. It's not easy, it's challenging. But I think in the long run, we'll find when we look carefully at what we're doing, we will be able to much better serve the broad part of our society that really needs the kinds of things that we can offer. That's a rich answer. That's a rich answer. You covered a lot of ground, especially thinking about the inequities over asynchronous versus synchronous. That's vital, very important. Yeah, we're having an internal debate on our campus and our faculty about which form of online, we're all doing, almost all doing online education right now, but there are elements within our organization that say, well, we should be doing asynchronous because of the inequities we see in the synchronous environment. And then there are other elements that know the data around asynchronous performance and the lack of engagement that's often designed into these courses and say, well, that's disadvantageous students as well. So we should be focused on synchronous. So my contribution is, well, we're disadvantaging people a little differently. It's often the same group that's disadvantaged. So if we offer, if we're able to offer both, if we can design for both and support both and prepare people for both, we end up having a lot fewer overall students who end up in where they have no choice or where they're disadvantaged in both ways. It's a smaller group of students, still not ideal. We do need the classroom too, of course. That's a powerful funding and a powerful strategy. We had a couple of remarks from the chat box. I just wanted to pass on. Sherry Pruppus says that she has found that more challenging than access to devices and Wi-Fi has been a place to learn as their homes are small with many people. Good point, Sherry. And Nicole says, as a learning community, human staff, teachers, parents, admin, students, we can demand reallocation of funds, e.g. from investments in private prisons to technology access. That's a good point. We have a whole bunch of comments about this. Tanya Jusna has a question. She'd like to see the research on asynchronous creating inequity from lower reported engagements. Sure, I can share that with you, Tanya. It's an internal, like some of us have internal reports. It's an internal report on gray data from our campus from about a year and a half ago. Thank you for that. And that's the question. Tanya is a wonderful, wonderful researcher and a great person to know. So if you're not following her on Twitter, go do it. Tanya's amazing. We have a question, a video question, comes from Fort Lewis College. This is from Jennifer Ryder. Let's bring Jennifer up on stage. Hello. Hi, can you hear me? Beautifully. Hi, Brian and Brian. I think this is my first shindig event. I think I'm terrified to be on stage in front of 188 people, mainly because I have a million questions for Brian. So I'm gonna try and narrow it down to one. Okay. If you have about 30 seconds of context of our institution, it's about 3,500 students. It's in a Native American serving institution. We have over 50% students of color. We're one of the two institutions in the US that offers 100% free tuition for Native American students. And so we've had challenges in the past of student access, students coming from rural communities, students needing to leave for care of family members or ceremonies or things like that. So HiFlex has been on my radar for a while. I'm the director of teaching and learning. And so I try and invest in things like this that can help our institution. We have a pilot going this fall of 10 faculty doing HiFlex courses after learning about this model. And then COVID hit and we have kind of seen everybody doing HiFlex today in our teaching and learning committee. My team said, everyone's really doing a form of HiFlex. So I think my question is, how do you advise a small institution to adopt the HiFlex model, which is what our goal is, to adopt it as a formal model of instruction without overwhelming the faculty? So right now we've got HiFlex synchronous, asynchronous students saying, well, I understand you're allowing me to come synchronously, but I'd like the recording please. I need it because of this. And so students are advocating more for their needs. Faculty are feeling, I feel like we're at this point where we need to maybe reel it back to be successful and start small. And so what recommendations might you have to make sure that this is successful? So faculty don't go, wait a minute, this is more than I ever thought it was. Well, thank you for the question. I think that's an excellent question. It's actually one of the things I wrote down is to talk a little bit about if I had the opportunity, whether it came up in a question or not. But the way this has been done well in the past from my experience, and I'm gonna ask one or two people in the audience here to tell their story too, because I know they have a good story here, is that it's not, if it's coming top down, like the institutions making a strategic decision to do this, that it takes a couple of years really to kind of come up with a conception, what works for us, why are we doing it? Get that Y clear and get a small group of faculty trying it out. Maybe it's a single area, or maybe it's a faculty from across different areas, but you have a manageable approach, right? A pilot environment. And then as that has success, and if it has success to expand that, like you will with a lot of other kinds of things, but that's a two to three year process, probably at least, like most things worth doing in higher education. It takes a couple of years to get something off the ground like that. What's happening now, and we've all experienced this, especially when you hear high flex in the news these days, it's really usually, I see it's coming from really two different places. One, it's administrations or universities putting out public relations release to saying, hey, we're gonna better serve our students this semester by offering this high flex model, which often isn't even high flex, but it's like a multimodal model that kind of meets their specific needs. But there's never any talk from the faculty saying, hey, yeah, we're bought into this and we're gonna do this well. What we hear from faculty then is usually the pushback said, hey, they're telling us we have to do this. And one, I don't wanna be in the classroom or two, they're not giving me any time or support to learn how to do this. They're just expecting me to do this because they made this decision. And so that's what we hear. We don't hear the stories where it's actually working. Well, hopefully there's some of those out in the crowd, but to actually to talk about specifics, I wonder if I can recruit Kathy, Kathy Littlefield to tell her story. Cause she comes from, she can tell about a small school that made a strategic decision to do this and took a multiple year process to do this. So maybe Kathy, if you're willing, would you come up on stage and kind of share a little bit about the approach you took at Pierce College? I can bring her up. She's still here. Let me see if... I wonder if I might ask her to come up with us. Good. Hello, Professor Littlefield. She might be frozen. Her connection might be slow. While she's coming up, I'll also say I just recently heard about a story from the University of Southwest in Hobbes, New Mexico. I think it was an Inside Higher Ed. They had a podcast that was going on this week. And it was a provost of that, talking about how they made a strategic choice to adopt high flicks to address some enrollment issues they were having. And they took a, once again, they took a multi-year process to do this well, to get faculty buy-in, then to provide the supports they needed and to, and then to watch how it was doing and do some evaluation. They found that for them, it really worked well. They had, I think they quadrupled their enrollment, a small school and ruled, I guess, desertish almost, New Mexico, private school. So, very concerned about that. So, they, but they also took a multi-year approach to kind of build this idea that we're doing this because the institution needs us and it's gonna be good for students. And we're not just gonna throw you into this. We're gonna prepare you faculty so you can do this well. Hi, Kathy, I see you made it through. Here I am. I didn't know how to get up there. That's kind of interesting. My first shindig too, so this is good. Welcome. Thanks for the tip-off and for a great question. So, a little bit of background about who Pierce College is. We are in Philadelphia, Pennsylvania. We have a rich history dating back to 1865, but we are a small, nonprofit, non-residential institution serving primarily minorities. And we have always been dealing with adult learners. We have always been on the cutting edge in the 80s. We were one of the first to go with fully online and all of that. And we had, we came into high flex kind of organically and then all of a sudden I met Brian at a conference. I'm like, oh my God, you're the high flex guy. This is what we're doing. And it turned out that we were doing high flex and we didn't even know it. We have been four years now into integrating high flex. We call it PierceFit and we offer it as a flexible learning opportunity for the students where the students have the chance to go fully online for the week or in person for the week. And the reason we initiated high flex for Pierce, it had to do with being able to offer healthy course enrollments.  So a couple of faculty members and we got together and we said, well, what can we do? Well, let's see if we can combine them into one, have one course section that had a healthy enrollment and then we can divvied up, you know, how they wanna participate online or on campus. So we did a pilot with this and we initiated it with our graduate studies division which was small, it was just starting at the time and our health programs. So the faculty chair of the health program, Stephanie Donovan and I took this on for our two areas and we tested it and the students loved it. They loved being able to decide this week, am I going to be able to be in class or am I gonna be marked absent? We run accelerated courses, so courses are every seven weeks. And what we found is that we've had students that would tell us, you know, my husband is a firefighter. He doesn't get his schedule out but four weeks in advance and I never know if he can cover the children. So I had to take the course online but I'm really a better learner on campus. So our PierceFit model was perfect for students like that. So how did we do this? We took it to the provost, we took it to the president and the president jumped on board immediately. So we became a top down deployment of this. It became a strategic initiative because we were looking at a way to improve retention, improve attendance and we saw improvements with both of those and we've got some statistics if anybody wants them I can share that out or it's in that chapter in the book that Brian talked about a little bit earlier. So our first year of the high flex model, this was after we brought Brian to campus and kind of talked some of the faculty off the ledge of what he had happened to us do and they accepted it. After hearing it from Brian, they accepted it. We ran the first full year of converting all of the courses in graduate studies and health programs to this model. The second year we went across the curriculum and every other program went with this model. So we didn't do it on a voluntary basis. We did it across the board every course with the exception of maybe a few developmental courses or some of the law courses that had to be on campus because of ABA. So year two across the curriculum, year three, our LMS changed and we went to campus. So we had three years of mind blowing, faculty were ready to revolt on all of this because we had another change come our way. Everything happened fine. We got the canvas up and running, everything was good and then COVID hit and March 13th, we had the same situation that everybody else had. Our campus was closed. The city of Philadelphia was shut down. What do you do? It was simple for us. All we did is we took our courses that were already developed on campus and online within the same shell and we shut down the on campus piece. So then everybody became an online learner. We didn't have any hiccups along the way except for maybe a couple of students who had technology issues because other children were using that one computer that they had because everybody was online at the same time. Minimal little things like that. What we found was that the students were happy with it but there were still that small percentage that wanted to hear our voices and see our faces and we wanted to hear their voices and faces. So we added as of the fall a required synchronous element to it. It's required for faculty but it's optional for students. So we took our high flex from being on campus or online to be synchronous or asynchronous all in the same shell. And it has been really successful but we did the synchronous piece because the students wanted that. And we have a 90 minute requirement and I will tell you that for the last two, three weeks I've gone way over that 90 minutes and the students haven't bought one bit. And as you can tell, I can talk a lot. So it's not hard for me to go on and on and on. But it was really successful and it has helped us with attendance and it has helped us with retention. Has it increased enrollment? I don't know whether anything can be attributed to where enrollments are because of where we are as a society but our enrollments have not declined which probably is a big thing in higher ed right now. Kathy, can I ask so prior to requiring the synchronous meetings all your faculty on campus were offering these high flex courses as asynchronous meaning the two pathways were either in person or a fully built out online course. Did that require, what did that look like for your institution to move all the courses to build them online? I'm thinking about we stipend for online course design. Yeah, that's a great question. So we gave every faculty member a course release for the fall term and a course release for the spring term to convert their courses. And we run under a model of course coordinators. So as a course coordinator you might be responsible for eight or 10 courses. So we had already online sections and on campus sections built. The coordination came to how do we combine them now into one shell? So even though it sounds like that's not much of a course release they weren't really redesigning they were merging the two into one course shell. And at the time we were with E-College and then of course we switched over to Canvas but the course releases helped. It was still a lot of work. It took a lot of training. We had a lot of faculty meetings that were working sessions where we could meet our deadlines because we all had deadlines that we had to go by. Some of them we missed a few of the deadlines but we made up for it. But the course releases really helped a lot with the workload. That's helpful, thank you. Sure. Thanks, Cathy. Yeah, so there's a few key things there, right? The strategic decision, the buy-in, the resources and support for faculty doing the work and the time it takes to do it well as well as responding to the needs expressed and perceived of students. And I think that's really one of the things that's really contributed to their success as well as the success of some other institutions that have been doing this well for a number of years. It's much harder to do this obviously when you're kind of thrown into them, it's thrown at you without any planning just like anything else would be. Why would we expect it to be any different? So thanks, Cathy. Sure, any time. Well, thank you very much, Professor Littlefield. You're welcome. And we have a whole stack of people who have more and more questions coming in. I wanna make sure they get a chance. Jennifer, did we help address your question? Thank you, yes. Kick me off stage. Well, we're glad that you made it here. Welcome, welcome to your first floor. Yeah, thanks for the question. We have a question from Mathieu Plourde at Université Laval. Hey there. There he is. Bunch of Ryan's here. Okay, cool, cool. So yeah, so my name is Mathieu Plourde. I work at Université Laval. I used to work at the University of Delaware 12 years in the US. Now I'm back in Canada, not a moment too soon. Anyway, my question was, anytime that you get a mixed bag of learners in a synchronous environment, either face-to-face or remote, I feel like the AV in the classroom is never good enough to actually carry the voice of everybody. It's like even when you're in meetings with other people, like for your job or whatever, and there's some people in a meeting room and other people are joining in remotely, I feel like there's always that disconnect that the person who's actually remote is actually somebody who's being kind of a second-class citizen in that environment. So I was wondering if you had any tips regarding this to make sure that we actually, because it feels like you're almost better off just having everybody on their computer, even if they're in the classroom so that they can actually interact with the live session or whatever is happening. So why do you even need them in that room, that physical room together at all? You know, that's a great question, Matthew. Thank you for the question and welcome from across the border that's still closed, I understand. That question actually came, one of the faculty I worked with in our college of education was teaching, high-plexed, just heard about it, new faculty come in and say, hey, I'd like to do this for my students because I know it's hard for them to get here. So she was doing online and her online was synchronous. So she had students in the classroom and student singers. After she did that for a year, she said, guess what? I don't see the value of having the students in the class. There's really nothing we can't, we're doing in the classroom, we can't do with the synchronous crowd. And for her, she said, I think it'll be better for me to focus on just one mode. So I'm just gonna do it all synchronous online and it didn't disadvantage her students because they were all able to join that way already. And so she moved completely into a synchronous online environment for that exact reason. I think for me, I found that I don't wanna get rid of the classroom component because enough of my students always come to class. Usually up to half of the students are always in the class. And so I know there's a value there. Sometimes it's a necessity, but oftentimes a value that they want and they need that. So I'm gonna continue to try to offer that. But to manage the synchronous versus or in-class versus online, that I think there's two things. One, the technology does have to support, maybe not excellent quality video or audio and video from the classroom, but it's gotta be good enough so that anyone who's online can hear what's going on in the classroom. We've come to finally got a solution where we distribute mics around the classroom and that works very well for us. But in the early days, this was the thing that was our biggest problem. And when we asked students, they loved the flexibility, they loved convenience, but when they were working online or trying to listen to a recording as an asynchronous learner, if we provided that for them, that was the one thing that they always talked about was, well, if I can't hear, it's no good to me. So that's a problem. So that's part of it. But the other part about not letting the students online feel like they're second class students is to intentionally engage the class with the online students as well as the students in the classroom. And that's primarily the responsibility I think of the instructor to make sure happens even though the instructor isn't always the one who has to always do the engaging. In the classes I teach where I have students online synchronously and in the classroom, I always encourage students in the classroom if they've got a device and they want to do it to also log into the synchronous environment. And so what they do then is what Brian is doing now for us is he's monitoring the chat. He's bringing questions up. He's telling me when, or they are telling me when comments are being made or they're just having their own conversations in the back channel of the chat or maybe some other technologies I'm not aware of. But that happens that way. And then when we do class breakouts, depending upon the numbers of students involved, sometimes we'll have class breakouts that includes students with technology in the classroom with students in the online environment. That doesn't always work well and it's not that well for all, works well for all students. So sometimes we'll have classroom only groups as well as online only groups. I'm not too concerned about interaction in that because they're interactive environments themselves. But then on me, my job is to make sure that what I'm doing some sort of interactive discussion, calling on students, looking for student input that I'm intentionally including the online students and not just letting them be kind of off to the side, maybe behind me on the screen or things like that. There are some institutions that put in some extra screens in their rooms where they're teaching in high flex so that the students who are online synchronous are visible to the faculty and probably to the other students all the time. That approach can certainly work well. It requires more investment. It's a little more complicated. But that's another way of supporting that process. Right? I think you've been at something like that, right? Like a wall of cameras of a participant. I don't remember what their room is called, but they have something like that where they can just teach from different rooms and whatever and have all these faces on. Yeah, there's a couple of pretty high technology solutions that one or two of them are in the book and the case studies. A lot of times they do that for research perspective too, to see, well, what do we have to do? The whole blend sync literature from the Australian project is great to talk about how effective those approaches can be. What I found in my work at my campus, I don't think I could ever get them to spring for a room like that and probably most of our schools couldn't. But the principles that they're bringing out I think are incredibly important for us to know a little bit about and to see how we can then apply them maybe with less technology. Maybe it doesn't take a $50,000 investment to do something that is engaging to students in both modes at once. One of the things that I had my, one of my previous employer buy was a mic ball. So I know that for a while, like people were talking about these things, just it's a ball that you just throw in the room. Throw it around, yeah. Yeah, it's kind of silly, but at the same time I feel like that could be like, if it works well, sometimes it's just a disconnect because it's Bluetooth or whatever. But I feel like that, there's something that can be done in that sense. I know that the way that I teach my class, I teach a class for a university of South Florida and one of the things I do for attendance, for live sessions, I think it's a fully distance class, but is I just give my students all their points at the beginning of the semester. So there's six points for attendance, whatever. If you miss a class, I don't care. You don't even have to tell me. If you miss two, then I'll remove a point from your bank and I'll ask you to watch the recording and send me two sentences about what you've learned or a question you have. So I just want to make sure that they actually stay engaged with the live session, but it's kind of a way to kind of avoid, if somebody really has a conflict and can't attend that live session, they can still take the class and do something. Do give them the point back when they send you the two sentences. I give them the point back as soon as they... Good. Right? Yeah. Those little threads. You don't shave off 10%, right? Yeah. Yeah. Well, we have some of our faculty who teach high flex also, even in our program have, like to emphasize the synchronous component. They don't mind teaching in class and synchronous online. They don't want to have students teach. They don't want to have to support students in the asynchronous because the way they're teaching, it's much more, they're naturally more engaging in a live environment and just a recording of that. They know, and I think we all know, it's not nearly the same as being there. Is it enough to help students reach learning outcomes? I'd argue in most cases, yes, but it doesn't give them the same experience. So when the experience becomes one of the important outcomes from a faculty perspective, then oftentimes you'll emphasize the synchronous and let the asynchronous kind of be there as a backup to the backup to the backup, only if you have to kind of do that. It's still better than just being out of class for a week or maybe two weeks and not having anything, anything content related interaction to do or facilitated discussions or things like that. Yeah. Absolutely. Mathieu, thank you for the great question and please enjoy being to the North. Let us know when it's okay to visit you or when you can come back to bed with us. Yep, yep. And again, Brian, thank you for that meticulous answer. It is so helpful. Friends, we have a stack of questions and we're running out of time. So I'm gonna try to smoosh a few of these together based on where they've come from. And I think some of you who have put in text questions may have seen answers already. But let me bring up one right now. This is from Ellen Nuffer. She teaches in New Hampshire, but she's coming to us from the great state of Vermont. And she asks about universal design for learning. What are the links between the High Flex and UDL? Yeah, thanks for the question. That's a really important question too. We started, on our campus, we've been talking about UDL for probably as long as it's been kind of a thing, a recognition of the need for this as a way of usually through the lens of accessibility and providing fully accessible environments for all of our students by design as opposed to by accommodation. And then language is all in the message to faculty as well, if we design for accessibility and follow these principles, we're also designing for better learning for all of your students. Why? Because some of them learn a lot better from different forms of representation of the content that you're providing, as well as are much a better fit for different forms of representing what they know, right? So the idea of assessment options and things like that, or authentic assessments, which are all kind of engaged in the UDL kind of principles as well. So I think it's critical. When I do faculty workshops around High Flex, when we start talking about course design and content, that's the first thing I take them to is let's talk about UDL and let's review these principles because I wanna frame everything we talk about after that. How do we develop content? How do we develop assessment approaches? How do we engage learners? Through this lens of UDL as in options for students, different forms of representing information and assessment and things like that, they're not just good to support multiple modes of engagement and multiple modes of participation, which they do, but they're also good for students learning, right? And for the overall kind of the teaching process. So in the kind of the bigger picture on this was if you're gonna give them an in-class experience and an online experience and maybe two different online experiences, there's gonna be some differences in the activities that you do there around content acquisition, but also often around assessment and certainly around engagement. By giving them those different activities, you're kind of designing in a UDL-like approach because then they have some options to choose among those. And in my case, I use asynchronous discussions for all my students, even if they're in class, we take the time and part of their homework to prepare for the next class is to engage in an asynchronous discussion because of the different form of discussion because the discourse is different, the thinking is different. It's a different experience for them and I want them to experience that as part of their learning, their critical inquiry into the class and the topics. So yes, UDL is one of the major lenses that I use to kind of talk about designing this through. Thank you for the question. And Nick, you all said a question about that and I hope this is a good answer for you. And thank you, Brian. We have a very detailed question from Professor Denise Roy at Mitchell Hamline School of Law. And let me just bring this up. About small groups. I'm interested in how small groups work with choice to participate in or not class to class. I prefer preformed small groups that work together to build relationships over a number of weeks. Yeah, that's a great question. I'm actually, I do this in most of my classes. I have some sort of a group project that they work on for a number of weeks and sometimes a whole semester. And one of the challenges I'm relearning or re-experiencing as the faculty again is when I have half the students coming up in the synchronous session live, now we're not in classrooms, so live synchronous and the other students just doing it asynchronously. And so what happens to get a group started is a little more difficult because they're not always synced up on their communication, their synchronicity of their communication as well as the mode they prefer to communicate in. If they're all coming together synchronously in the classroom or online, not so much of a problem because there's a media there, either the class or the online media that you can use class time to have them kind of get together and figure that out. To get them started though, I found that it's been a little more complicated because even our LMS now doesn't show everyone else the other student emails. Some show up, some show down, some don't show up. So I found that coordination element to get them started better. Now I'm teaching adults in higher education and so I don't have a problem with kind of forcing the long-term coordination of the project on them, but I let them know that I'm here to facilitate. If they're having any issues, let me know and I can kind of help them through this process. I also let them know all the resources we use for the class including the live class link for them to use for virtual meetings is always available to them as well. And so they can always rely on the class media, whatever it happens to be, to do some of that coordination to get started. But they're working adults and so they have to be able to coordinate their own schedule. That's part of what they're learning, kind of the unwritten curriculum is learning how to work well on a team. Does it always work perfect? Absolutely not, right? I've never had a group project as a facilitator actually or as a student that was perfect, but they always find a way to make it work through. And yeah, so no silver bullet there, but... Oh, it's a good question. Thank you for asking and a really good candidate answer. We have another question from SUNY College. This is from Susan Werner, who asks, if an institution charges different cost credit hour for campus versus online course, where does high flex sit in terms of charging students? And if no difference about technology fees? That's a good question. Yes, well, Susan, from my experience in my institution, we don't charge technology fees per se for any students. And we don't charge differentially for online courses compared to face-to-face courses. We do have a few programs that charge differential fees, but it's for the whole program, not dependent upon the type of course it is. And so for us, when we teach high flex, we don't really have a structure to do anything differently about that. There are some institutions, the real challenge comes in, well, if we are choosing differential fees, what do we choose for a high flex course? Because students could show up all the time on campus. So should they be charged the on-campus cost or they could show up online all the time? Should they be charged the online course? In some campuses, the online course costs more. In some, yeah, the face-to-face course costs more. So I don't have a solution for that. I just know that it's one of those administrative things that has to be kind of worked through, which is why in a campus like that, even when you as an individual faculty would wanna start to do this, there's still an administrative implementation factor that has to be reckoned with and someone else has to help work through this, not just scheduling, but also on the fee structure. If anyone out there is doing it differentially and has a solution, I think it would be great to offer that because I can't offer the best solution for everyone. It just, I acknowledge the issue. Thank you for doing that. And that's a really good question. It's one that I think we'll be working through this year, especially with some student pressure. We have another video question coming in from Peter Wallace, University of Wisconsin, I believe. Let's see. Hello, Peter. UW Continuum, right? I'll give him a second here. You may have a connection issue. Hello, Peter. It's a movie now, yeah. Hi, Brian and Brian. Thanks so much for having me up. University of Washington, actually. Very good. I'm from Seattle. And we're seeing significant interest in high flex. The issue, as I really appreciate you outlining earlier, is that teachers in a lot of these cases don't have time to really learn how to do it particularly well. And it's resulting in potential inequities between teachers and between students. And one of the biggest challenges I've seen is kind of that balancing engagement and particularly active learning between the in-class and the online sessions. Any recommendations, anything you've seen done particularly well, especially where kind of doing active learning in-class online plus the online asynchronous, I think that's one of the really tricky things to design. And we're trying to come up with a short list of tips that someone who kind of feels like they are thrown into this due to the current circumstances can jump in and do without having to learn the full possibilities right off the bat. Thank you. Right, that's a great question. I think the way I address this with my own teaching is where I'll start from because I know that best is by designing an interactive online experience, asynchronous experience, which includes discussions but also includes other kinds of activities like working through a sample, whatever it might be. But you have them do something and create an artifact and post it and then use it in a discussion form like to comment on each other. And so that can be interactive. I mean, that is interactive, especially around the content and you can build interactivity around that for the social aspects as well as the teacher kind of presents aspects of that. And so if that solution is good enough then what I'll often do is I'm doing a similar activity in the class is I'll have the classroom students, when they're done with the activity we're creating some sort of artifact that then contributes to that activity for the asynchronous students who usually come in later in the week, right? So if we're doing some, maybe we're doing a draft of something, a list of things that are important or whatever it happens be. We do a report out in class but that report often is also captured in some way. It could be a document, it could be a video recording or something like that. That's there for the asynchronous students as well. It's not live, it's not as interactive clearly but it helps them reach those learning outcomes. The challenge I find was finding the time to dedicate to the interaction with students throughout the week because my workflow as a faculty used to be prepare for class, go to class, do class. And if I didn't have an assignment they were turning in that needed feedback, okay, I don't have to think about this for a few days until I wanna make sure I'm prepared for class for the next time it met, usually the next week. What I've done is I've taken some time out of my face-to-face class and said all of you, it's gonna be good for all of us to use these asynchronous forums and some of that interactivity through this. And so what I would do is say, well, part of the time that's dedicated in class is gonna be for participation in the discussion forum. So you can sit here and do it now. You can walk away 30 minutes early and then do it on your own time but it has to be done. It's part of what's expected as part of your class participation. What that's done is that it created a much richer asynchronous online experience especially in a small class, 20 to 25 students. If I had most of the students in class in person, there might only be five people trying to do an asynchronous discussion. Not likely to be very interactive, possible but not likely. Now that I have all 20 or 25 in the asynchronous discussion it's much more worth, I feel a lot more value in the whole thing as an activity for students. And so what I do is I just kinda take, okay, 30 minutes, three times a week, dedicate that time in my calendar to interact in this particular forum for that particular class. I find that it took, so I'm shifting what I'm doing during the week, not necessarily doing more. So when I'm doing that in the forum, well, there are some other things I'm probably not doing as much. It might be administrative email or other kinds of things. You have to find that whole balance. But it's really, for me, more of a workflow change as opposed to a workload increase. When I first started this, it was obviously, it was a workload increase because I didn't get what I was getting into. And especially when I shifted all the students in that mode, I found that, boy, these people are really engaging in these incredibly complex conversations. And I find that I don't have to do a lot of facilitation. I have to, I watch and I read and then I add my comments where they're helpful. But they're learning skills and kind of facilitating their own discussions on there which is really rewarding as a faculty member to see. Thank you. And that makes me think about, it's not a high flex class but a class that I was working with or a biology teacher was actually writing a open textbook for an endocrinology textbook with her class. And very similarly, right? Okay, this is the class time that we're gonna spend in group work writing these chapters. Then she actually had more evaluation done by her students. So some of that feedback was coming from other students for exactly the reasons that you say, right? That just the amount of times you have to spend on feedback doing that. Right. Yeah, there's a thousand or a million great ideas out there. I mean, one of the nice things about being a teacher clearly is the ability to be creative and to engage when I invite students to the creative process, help them kind of shape topics maybe a little bit but they become this producers and consumers of content. Wow, it just becomes a pretty amazing experience for all of us. Thanks for the question. Thank you for the great question. And Peter, you'll notice give us the principle that only bearded people can be up here on stage. But actually we have, and Brian, thank you for this question. Your workshop's supposed to be fantastic. We have time for one last question and this is Daniel Tiriman coming to us from Denison, Ohio. Hello, Daniel. Hi, so I know we're near the end, so I'll keep a brief. So I work in educational technology and often I only have a few minutes with a professor and usually it's stressful because we're trying to do something with the technology. But sometimes I notice I'm not really engaging the remote students as well, sort of that second class thing we were talking about. When you only have a minute or two to just squeeze in some suggestions on just better engaging the class, what would you bring up? Yeah, well, when a lot of us, I mean I came into higher education from a K-12 background. So when I was learning how to teach in high school, one of the things that we learned in classroom management was to have a way to make sure you're calling on everybody and engaging everybody in the class so you're not what we would call teaching to the T, the people in the front row or the people in the middle right in front of you. And so finding ways to kind of structure that so you would keep track somewhere, however it might be. And I find that that's useful for me also in the online environment to have a roster that I can kind of check off on, okay, this person has contributed to the conversation or not. So if the faculty cares about that, that's an easy way to make sure that's happening to kind of keep track of that and just whatever is the easiest way for the faculty to do that. I think one of the challenges comes in when faculty aren't used to thinking that way because in the past, maybe they teach relatively small classes or it's a large class and so they're not gonna be a lot of interaction and they're just doing the natural flow who's got my attention, right? So that would be that there's a shift of perspective there that might be needed. I don't know, you're not gonna make that happen. Now, the other thing that is sometimes helpful is have students raise the issue of faculty. And if you see that happening and you don't sense that the faculty is kind of likely to be able to respond to intentionally, proactively doing this, it's possible they would be able to react to student feedback that's saying, hey, you know what, I feel like I'm not part of your class here. If there's a way to kind of engender that, not being in a technology support era, I don't know what access you would have to faculty that way or to students that way. But that's another way to get faculty to change their perspective is when their students start telling them, this is a problem, we need you to fix this. And it's within their ability and their range of responsibility to do so. I find that it's another powerful path for faculty change. All right, great, thank you. Daniel, thank you for the question and please say hi for me to all the good folks at Denison. I will do. Brian, I have to say the opposite of hi right now. This hour has just somehow flown by at a hyperspeed. I'm not quite sure how that happened, but you've been fantastic. You've answered all of these questions with just such a plumb and richness. I'm really thankful. Thank you very much. Well, thanks for the opportunity, I would appreciate talking about this and hearing the good stories of things out there too. So not just the kind of the negative stuff in the press. Well, I hear that. Well, friends, what I may just do is because we have so many questions, I may just copy these all out into a text file and then put it on my blog and then add the recording. We'll have to do that tonight and tomorrow to the blog so we can keep the conversation going. Just thank you, Brian, and all best. All best, you're a hero in these times. You've got a lot to do and we're really grateful for you being here. Thanks for what you do, Brian, also it's a really excellent forum. Oh, it's great people, my pleasure. But don't go away, friends. Got to point out a couple of news items for the next few weeks. And let me just thank you all for these fantastic questions. These are really rich, both practical and cerebral, really, really good at eliciting to a fantastic discussion. Thank you. For the next two months, we've got a whole bunch of other topics coming up, including faculty of color, augmented reality, virtual reality, extended reality, the work life COVID balance and crediting agencies and admissions. And on top of that, we have, of course, social media all over the place. Just use the hashtag FTTE, if you'd like to say more. If you want to dive back into the past, we have a ton right now, about 223 recordings. And we include Professor Beatty's first session with us, as well as sessions on other topics that we've addressed today. Just go to tinyworld.com slash FTF archive. And in the meantime, thank you all for coming. This has been a really, really rich session. I'm really grateful to all of you for everything you contributed. Please, everyone, this is a bizarre and extraordinary semester. I admire all of you for your creativity, your passion, your interest, your flexibility, and your hard work. Take care of all of yourselves. Stay safe, above all. And we'll see you online next time. Bye-bye.


this talk would be application of light from methods mostly to the, yeah, to the 5-4 theory on overview. First, I will a little bit remind this light front couple cluster methods and application this to the 5-4 theory as then some light from Fox state expansion results using symmetrical polynomial basis function. Also we're talking about this difference between light front and equal time, critical coupling value, then some sector dependent calculations result and of course some summary. So 5-4 theory, just some quick remind of course Lagrangian for the light front one plus one Hamiltonian does not have this one plus one there is no this kinetic term from the transverse direction. So we have just mass term and interaction term for the light front X plus equal zero mode expansion would be look like this.  For the Hamiltonian we have this four terms kinetic energy term, three to one annihilation of three particles creating one particle term, one to three annihilation of one creation of three and of course two to two. Now application of this I love CC to this 5-4 theory so we have this light front eigenvalue problem whereas the light front Hamiltonian applying to this eigenstate give us this mass squared expression. And without doing the four states truncation we applying this ansatz so whereas the state is really application of this exponentiation of the operator T to this valent state and this valent states usually include very small amount of particle so for the 5-4 it would be really only because we will consider only odd sector it would be really only one particle. It's differ from this really origin of this couple cluster methods from the nuclear physics and nuclear chemistry whereas really valent states are much larger and really for them they did not create more particles they just created excitations and this operator T is conserved or required quantum number included light front momentum and of course increases particle number. So if we really multiply both part of the eigenvalue problem by this e to the minus t we will obtain this Baker-Hausdorff expression of the light front Hamiltonian on the left hand side applied to the valent state and on the right hand side we have this expression and this guy really gain eigenstate psi. So eigenvalue becomes this effective light from Hamiltonian applied to the valent state and so from both side right now we have the simple valent state and now we do projections we project this on the valent state this equation effective Hamiltonian and we also project on the orthogonal to the valent state. And this second so-called auxiliary equations will determine us operator T in that functions in the operator T which is really showing distribution of the momentum and how much we will truncate we really of course will use truncation right now up to this point everything exact except of course higher for state wave function connecting to the law of state function through the sum soon again as soon as we do this truncation operator T then this connection between a lower state and higher state becoming already just some special way but it's still infinite amount of terms but now we also truncate this projection so for example if the valent state would be one particle yeah for the 5-4 theory here this if we keep infinite amount of term and we consider only odd sector so it would be time three, five, seven and so on so but because our real time we will truncate as many as we need so if we have I don't know time five function in the T operator we will truncate to the time three, five, seven, nine, 11 we of course will do much just to the one equation and yeah this effective Hamiltonian could be calculated from this Baker-Hausdorff expansion and it would be of course we don't keep infinite amount of term we terminate this when this increase in the particle number matches the truncation of this projection and in the previous talk yeah we were talked about the spectator depends on council divergences but we don't have here okay so for the 5-4 application of LFCC the valent state again it would be just one particle, one boson state and we take this simple contribution to the T operator which is really one to three so annihilation of one particle creation of three so it's really increase particle number by two and it's exactly what we want for the Laplace order because we wish we don't want to mix odd and even sectors and we really will consider odd sector function T2 will be symmetric in its argument and this projection on this auxiliary state this would be truncated to just the state of the three bosons because again it should be odd sector and we only need one function so we truncate to only one equation excuse me so far you started with this light quantization and then you propose an answer for the vacuum for the ground state that's what you've learned right no really we wish not to do a regular Fox space truncation so we still truncating but we truncating on the way how this higher Fox state connected to the lower Fox state but we still keeping infinite amount of the Fox state but you decided, well you started by deciding that you are quantizing your theory in the light form yes of course, yeah it's a light round sure, but did you say why you wanted to do that because I'm trying to follow, you know you can propose an answer for the vacuum then but it's not the vacuum, it's the massive state the vacuum is trivial I keep hearing that, I keep hearing that but is that, can you say something about that why is it trivial? In the light front? Because light front momentum, yeah light front momentum P plus it's always positive so we don't have, we never have positive we never have negative momentum so you cannot create vacuum from the I don't know, plus five and minus five, yeah there is no such thing, it's always on the zeros so the vacuum is empty state and that's it yes, of course, no I mean and now you're trying to populate it so now you're trying to obtain it no, no, balance states, these five states it's not vacuum state, it's just this state with a minimum amount of particles right, but this is an answer for what? you're trying to build a wave function yeah, we try to do five four without full space truncation in calculating a mass of states yes not the vacuum, the vacuum is trivial so just calculate the mass of states the one particle excitation one particle excitation so the vacuum being trivial you directly try to identify the side of the states for five four yes, yeah, so so again, because we truncated this projection only to the three states we terminate this Baker-House-Dorff expansion for this effective Hamiltonian also just one to three particles so creation, yeah we only keep these terms really who only create two particles, no more and this is really more efficient ways and instead to generate all these Baker-House-Dorff expansion terms just try to wait just to look what terms we really need okay, so how Valen's state would look so this kinetic term from the Hamiltonian add to this and this is projection on the Valen state yeah, we will have only one particle state so it's only two terms contribute kinetic energy and three to one and T2 operator this is again from the Baker-House-Dorff because this guy minus two particle and this is plus two particle so just really direct one to one and auxiliary equation again, which is cut to the only three states it has many more terms but point is that every term just create two particles yeah, two particles here, nothing here but this two particle here, again, nothing here and so we have really only two equations the equations for one function for this function, what is there known here? the T2 function we don't know T2, we extract T2 from this auxiliary equation exactly no to extract T to find T2 and as soon as we know T2, yeah, we can solve our eigenvalue problem we know T2, we can find physical mass okay, so this is Valen state equation after integration, so we have this T2 function from the T operator and it's really rescales again, these guys is a fraction of the Alangent-Hugh-Geno momentum so we rescales this and in order to express integral in this fraction and G is right now lambda or 4 pi mu squared so it's depending on the bare mass, yeah mu is a bare mass, capital M is a physical mass and this leads to the definition of this dimensional mass shift delta which will be talk about meaning of this shift later and it's of course through this shift exactly you also could say this mass renormalization is because it's physical mass how physical mass connected with the bare mass okay and this auxiliary equation it has so again, this is from the one to three term this is really wave function renormalization term and this is from some other terms in the Hamiltonian again from the Baker-Hausdorff expression and here we can see this non-linearity yeah T2 tilde squared no second order in T2 so this is so called loop correction so this is exactly coming from this infinite amount of fork state here because if we really expand this in the series it would be infinite series over coupling G starting from the first order in G so it's exactly how this LFCC methods implement this correction from all high order state okay and without really showing result for this light front couple cluster methods yet right away we wish to talk about just to compare with this fork state truncation where again we can see the odd sector and we just truncate up to three particles so again we keep one particle and three particle states then if we apply this light front eigenvalue problem in the one plus one direction then we will have in this case only two it would be coupled integral equation depending on the how many fork state we keep in here here we have only two fork states so it would be only two equations and this is really yeah it's already expressed in the ratio of the psi three and psi one and we can right away see that this definitely does not have loop correction in this second equation which is really coming from the three body sector it definitely does not have a loop correction which light front couple cluster has so it's simpler that does not include physics from the higher state and there's some description of the structure of the equation first is the same as a valence equation so this exactly the same as a valence state and LFCC but auxiliary equation it's for the LFCC it's contained five terms kinetic energy two to two time wave functionalization this vertical looks the most important and in comparison this fork state truncation to up to three particles only it has only three terms and does not have this loops correction also kinetic terms are not the same in the LFCC physical mass would be for all constituents but for this fork state truncation uses bare mass in three body sector unless of course we apply the sector dependent normalization and I already told that of course LFCC contains this vertical loops which is partial resummation of all orders now in order to solve really both with fork state truncated I give many problem and LFCC equations we use this fully symmetrical polynomials so they are this is multivariate polynomials of order n and x1 and x2 they are really domain is this triangle for the three particle yeah and of course because of the conservation of momentum yeah I remember that this x i's their momentum fraction so conservation of momentum it means that they all sum to one so we really have only two independent variables also it could be more than one polynomial of the given order so we're using second subscript to differentiate this possibility and again of course we don't take all to the infinity we truncate to some order n and for example this T2 tilde function could be expressed through this polynomials and this coefficient which we need to find and this is just for the convenience because equations both really LFCC and truncated they all contain this factor so we write a way to get rid from this factor okay so and this polynomials we did this work with our students so it could be shown that really all of them could be constructed from the second order and third this C guys right now is monomials and some general monomial could be constructed from the second and third order whereas they look this way and for example six order polynomial could be made to two ways either second order cube to the cube or this third order polynomial squared and it's of course we also really by hand using ground Schmidt we make them orthonormal for this truncated case or LFCC case and again it's much better than as again was mentioned in the previous talk much better than DLCQ okay so now if we take this life from couple cluster methods auxiliary equation and project them on this basis function expressed through these symmetrical polynomials we will obtain really matrix equation whereas what we are looking for is this coefficients A and this delta it's again the same shift it's expressed also could be expressed through this matrices and coefficients I will show this matrices on the next slide they are completely mostly computed by Gauss-Ligandre quadratures which is of course if you remember they give you exact answer up to some order and so really give exact answer for our needs so this is mostly a really overlap of two polynomials this matrices all these matrices all these numbers are finite there's no back originals no no everything fine yeah and now finally result so again we find we will find these coefficients A's and then we will find T2 this function T from the operator T and then we will put to this shift which is connected physical mass and bare mass and from here we can find again of course we first fix some G and then we will find this ratio and then we take another G and find another ratio okay so here really it result for the LFCC folk space truncation up to the three particles and also sector dependent mass did not talk yet but results here anyway and we can see that this the view is doing exactly this folk space truncation up to three particles it's doing the views LFCC coming really approximately 1.5 for the G and sector dependent doing better closer to LFCC so how expensive is this to perform these calculations for example if you were to include one more term into this the five particle term in LFCC would it be feasible or is it becoming quickly LFCC would be yeah because of this non-linearity T2 squared term yeah it's difficult so this is the reason why we really did not expand LFCC we did a folk state truncation except instead of just to the three we did up to nine I will show next but yeah LFCC expensive but doable so it's exactly really what would be my summary is that because LFCC really we will see later doing views then truncation to for example time 579 state folk state truncation exactly because we included only one this T operator just annihilation of one particle creation of three particles no really just adding two particles so we exactly thinking about adding another term to see how much better it will do so summary for LFCC at this point so again it's models relatively simple but require numerical techniques in comparison with folk state truncation shows introduce physical mass for kinetic energy terms without use of sector dependent renormalization and again it's doable yeah particularly using this symmetrical polynomials and these folk states this low folk state truncation up to the three particles definitely are doing views now what about extended folk state expansion so here for the odd sector we will go up to the ninth state and for the even sector up to the eighth state so now Eigen state of this fully Hamiltonian with interaction of course would be expressed through this, through this folk state and so really every physical state we include time ideally infinite amount of the folk state and of course it's normalized and now just again this Eigen value light front Eigen value problem just yield us this coupled system of equation where we really can see that wave function of the sector M it's connected with itself also with the two up states and two down states which is of course nothing surprising so it's preserved with either odd sector or even sector okay and for this kind of to do numeric here we needed polynomials extended to the not just to the C body but to the N body and right now this polynomials it's again it's product of these monomials whereas this powers of course summing up up to N and it started from the second power because of course first power because of the constraint it's really equal to one yeah because again domain okay so now using these multivariate polynomials we again obtain just matrix equation whereas what we're looking for is this coefficient C and we have this different matrices here like overlap of non orthogonal basis function in time given sector and here we don't do grand Schmid because it's produced so terrible around of error so we really did this using single value decomposition as usually through this U matrices and diagonal matrix matrix of the eigenvectors of the B and diagonal matrix D and also in U we only kept column associated with eigenvalues above some positive threshold according to the Wilson and of course we can define some new coefficients and new matrices. So finally we have this again ratio of the physical mass to B mass squared relative to this critical coupling and this is of course interpolation again odd, oh no maybe this for this without sector no without sector dependent really odd we went only up to the seven particle sector and for the even to the eight and here we also plot in four times odd why because there is no binding state for the even sectors yeah so really two odd will give us one even so this is some sort of like check and we can see really that even and for odd they relatively close to each other no except near critical coupling which is nothing surprising. So here as they intersect mass equals zero and few different points which is really taken as the error estimation and we take in your critical coupling is 2.1 plus minus five hundredths. How does this result compare with LFCC? LFCC was going to the 1.5 yeah it was going this way no I mean a little bit higher than 1.5 so this truncation up to the seven and up to the eight for odd and even really doing better again we- I thought that if the LFCC mass is smaller it means that it is a rational approach it means that LFCC is better is LFCC a rational approach? Yeah LFCC giving you physical mass yes for the constituents but because we're including only one T operator only what this what adding two particles T operator one to three this is not enough but it's still a very rational approach right? Yes yeah you're adding all this contribution from the high order So what I'm going to do my question is the follow-up I do a calculation I see two values for the mass one from this approach and one from LFCC and I see that LFCC value is smaller Shouldn't I conclude that I should prefer LFCC way function because since it's smaller and if the method is variational whatever is smaller means that I'm doing a better job. Why are you saying that this is better than LFCC can you explain? No, I'm thinking- Well the LFCC calculation there breaks down close to the critical coupling. Well I don't understand what does it mean that it breaks down it gives you some answer for the way function No, there are no solutions to the non-linear It's becoming he at this point it's becoming complex Okay but let's look at the last point which is not complex It's lower than the Fox state location point Doesn't that mean that I should prefer the LFCC point or is there some other problem which I'm not aware of? I would just add more terms to the LFCC Why should I add more terms? It's already a calculation it gave you a way function If normally if I'm doing if there are two different groups which provide two different variational answers I look at whichever answers gives a smaller energy I say well that group is doing better period You can of course add more terms but even without adding more terms they are already doing better So is this correct logic or not? You jump ahead to the plot that combines light front cover poster and the- But I think this without combining this question should have an answer Another one, there So we have everything light front and Fox space truncation and also sector dependent Fox state truncation So but this is the last point of the light front So up to this point it's just yeah it's numerically just becoming complex numbers here Okay so it's not much different up to that point The goal was really to obtain critical coupling value We did not look for the best wave function we looked for the critical coupling value so we were doing this Fox state truncation high and higher order in order to see this convergence and for example we can see that five and seven almost identical and sector dependent require really nine but Yeah I understand but this whole curve not just the critical coupling this whole curve is an interesting observable We heard in the talk of Marko Cirogna that he can compute using Barreira summation this whole curve so this whole curve contains a lot of information not just the critical coupling so it would be interesting to know eventually not just the critical coupling but the whole curve as a general comment Okay so in any case so this light front extended Fox space truncated give us critical coupling at 2.1 Now let's compare for the equal time again we really have to do this rescaling because different people using different for the G so now it's all in this G bar and we can see that light front guys always has lower critical coupling than equal time there is a systematic difference and so these brought us to the idea I mean we were talking with some patriarchal the light cone Masai Burkut and in 1993 he did this work which connected BMS of the light front with the equal time BMS through these really tadpole contributions if calculated in the equal time again light front there is no vacuum to vacuum contribution in the light front but in the equal time there is this tadpole contributions and of course clear why it couldn't be in the light front because we go from zero to four particles and then from four particles to zero which is impossible unless one of the light front momentum would be negative and we cannot have We asked maybe a stupid question but I could use a little bit about the sign maybe just a question of convention why is the plus on this side of the equation and not on the other side of the equation because I would have thought that precisely because you're missing this on the light front you should be shifting the light front to give you the equal time and not get it around probably better question to directly to the Masai who has much higher there are two minus signs in there actually this represents the negative of the tadpole oh ok maybe there are some yeah at some point it would be because you're missing a piece that's positive no these backing expectation values are proportional to the tadpole contribution that's Matias' work to show that correspondence and that's where they're at the minus sign it would be negative yeah it would be negative so it would add exactly because after adding this stuff to the light front we will come approximately close to the equal time oh so basically the way that you've defined some prevention this thing is actually negative yeah yes yeah yeah yeah yeah yeah of course yeah yeah no we would not present this if it would be these graphs are calculated in which theory the equal time Masai is Matias Burkart he did this in equal time and we did this in the light front and this is some sort of like that they equal so for the equal time is the tadpole for the light front it's c2 p3 no from 3 to 1 so some sort of agreement that it would be the same in both equal time and light front so equal time so he was calculating these guys we were calculating these guys yeah we're together so now the question was how to calculate this so this is the expectation value vacuum expectation value of the square of the field in the interaction full theory with the direction and this is in the free theory so in order to calculate this like in any time quantum field theory book we're doing this point splitting so we're shifting light front time and light front momentum by the epsilon so we separate from the zero and we also inserting using fullness completeness of the state of the Hamiltonian we insert this one here inside and so now we have to calculate two matrix element right one and left one and of course a joint representation for this operator shifted by this in this joint representation so right this sandwich could be calculated and of course left also could be calculated and for the free state and by the way because here we have only time creation annihilation operator we really because remember this is the eigenstate of the full Hamiltonian so each eigenstate including all infinite number of the Fox state but it's really for each state only one particle will contribute because of course here only one operator in the five field and for the one particle free state because really it would be right now free theory free Hamiltonian so we really just have this annihilation operator here and for the left creation operator here so it all could be calculated and this final expression for these two sandwiches and we also can insert in this free guy just to have the same because again our free theory really can't each only contained one body state we now can really come to representation of the modified Bessel functions for this difference and argument of course has to go to zero so when it's go to zero it's really have this logarithmic form and also this earlier factor and so really this difference equal to this sum and as you can see it's negative there is a really probability of one body state in every eigenstate and this is of course would be logarithmically divergent if we approaching critical coupling when physical mass goes to zero and this how we define this shift so shift really become positive because we put in this negative side here so we either can say that life around it's equal time minus some shift or we can express this as a ratio or we can express this as a coupling constant for the equal time through the light front coupling constant or we can express this as a ratio of the physical and bare masses for the equal time through this ratio in the light front whatever necessary just to see that there is some convergence we looked at the relative probabilities for this odd sector again it's only up to seven body but what we see right away is that each next sector becoming ten times at least order smaller than previous one so there is convergence definitely contribution from the highest sector they becoming less and less probable so this is a good point but the bad thing that near critical coupling at two point one there is no kick because has to be divergence there because again physical mass goes to zero but this guy doesn't go to zero unfortunately so we don't see this kick growth we would expect that probability near critical coupling somewhere here has to suddenly increase particular near critical coupling higher foxtade we expecting would be more and more important but delta should remain finite unit critical coupling yes but it's unfortunately they will yeah because when this goes to zero this guy has to go to zero and in our calculation it didn't go to zero didn't go enough to zero so this is the reason why we started to do sector dependent hoping that invariant mass I mean higher foxtade will not be suppressed by this invariant mass so what is your interpretation of this I mean your interpretation is that you just you just need more states is that you need higher particle number states to be able to actually perform this procedure that is the problem is that you just don't have enough particles we see that in this regular foxtade truncation because invariant mass still quite high so this higher foxtade they still suppressed as a contribution of this higher more excited foxtade has to grow near critical coupling it has to become more and more important you would expect near critical coupling and it means that really probability of the one body state has to go to zero no I mean it has to become smaller and smaller near critical coupling and we don't see this unfortunately but from convergence point at least this plot of probability some sort of encouragement that each higher foxtade sector becomes less and less probable and now this is a plot of shift relative to the critical coupling whereas the points obtain extrapolation in the basis side and these two curves this is a linear and this is a quadratic fit which is really view constructed only up to g equal no I mean taking data from up to critical coupling equal one and I will explain why this into the next slide but in any case shift is relatively good because when we add this shift to our light front mass critical coupling we have equal time critical approximately coupling or do you have agreement in the full mass curve because also the full mass curve has to be ratio of physical mass to equal time mass we can see that there is a problem arise after g equal one so this is the reason why we only used instead to go down down it started to grow and this is the reason why we used for this shift calculation only point up to g equal one but before g equals one you get good agreement yes, yeah so this is again the suppression of this higher foxtade they don't exhibit themselves well enough because it's still probability again for the one body sector still staying up high does not allow them to expand to give more probability for the higher foxtade I don't understand this point because the m squared has to go to zero and here it goes to point 84 and then starts shooting up yes, yes, yes so this is we consider this is why for example foxtade truncation is a bad thing to do or we have to include much more many state not just on 7, 9, 8, but more no, I didn't say before you show the plot where the mass was going through zero before previously you had a plot before you started discussing this mass change you had a plot which had a mass reaching zero yeah, but it was a light front yeah, and now it's equal time this is using the correction this is divided by the bare mass of the light front so the correction between equal time and light front is diverging once you get to near the critical coupling and so the connection is breaking down that's why this swings up here at the larger G yeah, so this is the bare mass for equal time well, this is straight here we have some unpublished results about how this behaves when you compute the correction in equal time and there you can swipe yeah, there's clearly something wrong in the light front calculation near the critical coupling that's the bad news in this because of this yeah, so again this probability of the one body sector in the really some sort of lower state doesn't go to zero as we wish so then this expression which is really expression for the shift will diverge but if we use points up to G equal 1 to estimate shift then we would obtain this kind of value and from the which is half equal time value for the critical coupling with some sort of relatively close to each other keeping in mind this error again, if we don't use data too close to the critical coupling which is 2.1 and this is why we try to use this sector dependent scheme in order again to avoid this because sector dependent in the higher so if we truncate up to the three particles you will have only one body and three bodies so there is a self energy in the one body but there is no self energy in the three body sector and because of this I mean every constituent will have physical mass here so it means that higher fork state is not suppressed by this invariant mass invariant mass again this is really result of the application of the kinetic energy operator on the state this is what is so called invariant mass so I will not go to the detail of the sector dependent calculation in any case you are giving physical masses for this higher state whatever it is up to three particles or if we really did this up to nine particles and each previous for that particular truncation we calculate the masses we just use some special scheme from the sector dependent calculation but in case there is this plot is the result with this new scheme sector dependent scheme which is supposed to give more room for this higher fork state and again because convergence is slower here we have to go for the odd case up to the nine body sector and really this is a good thing I mean this is what is expected and again estimation for the critical coupling about 2.1 they really only three some sort of little bit different but five, seven and nine relatively agree with each other and now this is a combined result whereas this open symbols it just for state truncation from three to seven and then close them dark figures it's the sector dependent scheme up to the nine truncation and also LFCC result for this critical coupling and what is there could be extracted from this so the sector dependent and standard fork state truncation they some sort of agree with each other and critical coupling from both cases coming to approximately 2.1 sector dependent converge more slowly and this is really expected because we expect that higher fork state should become more important so it doesn't converge so quickly and also there is this plot of these probabilities again we will hoping maybe here we will have this increasing of the probabilities near critical coupling again for the but at least we see that sector dependent probability is higher which is again dark figures higher than the regular space fork space truncation except of course I mean when we go to the highest state they almost the same but we still don't see this a growth of probabilities near critical coupling and some sort of summary out of this there is convergence we definitely see that probability for the highest state is smaller than probability for the lower states and that also this sector dependent probability they are higher than regular fork state truncation probabilities which is again good indication that in the sector dependent approach higher fork state becoming more important but we expected more rapid increase near critical coupling we did not see this so this hypothesis that this high invariant mass suppressing this higher fork state it's really was some sort of incorrect so we wanted to go to some coherent state approach or to add another term in the LFCC just hope it will resolve this issue to see this growth really of this higher fork states near critical coupling thank you for your attention I have a question I did not understand it seems to me you are saying that you are expecting to see that as you are approaching the critical coupling the high occupation numbers will play more and more important role and you don't see is this a message that I should this we consider as a problem so something wrong here because of this because we expect critical coupling is exactly the phase transition so this higher fork state they have to play more important role so their probability has to be higher in equal time this happens so something wrong with the light front something we don't take into account one slide we forgot to add is that LFCC does show an increase but because the calculation breaks down before you reach the critical coupling it's not clear this was another positive point about LFCC I just did not put this slide LFCC probability would grow only they started to grow somewhere okay LFCC we stop some sort of a 1.5 so they grow near this guy so really we just wanted to add more term to LFCC and see what happened because maybe exactly the main point it's exactly truncation and LFCC I mean truncated but just truncation of the way not the truncation in the states one possible problem with the LFCC calculation is that we start with the valence state just as the one particle state and that kind of implies you're keeping that as too important and you probably need to expand the valence sector to include more states so that the one particle state can disappear it can't disappear completely from the current on-sauce because that destroys everything but if you include a more complicated valence sector we have more freedom and then presumably we could reach the critical couple in recalculation that's one of the things you want to try thanks more questions from the two or three people in the room who actually did two light front perhaps some questions well then let's postpone questions to lunch and thanks again