So I wanted to get into this. You guys have been asking me to do like Maryland based schools and so that's what we're gonna be doing today. Tomorrow, Friday I think is what I said. I will be going live on GTCU to do one of the schools you requested. It's either gonna be Loma Linda or one of the Nova schools, probably one of the Nova schools since there's so many. So if you're interested in any of those schools then you have to join GTCU to see that one, okay? But let's get into it. Just again, I'm gonna go over to CASPA which is where you'll find all of the participating programs and you're welcome Ayanna because I know you've been the one that's been asking me for this program. Let me share my screen with you all so that you can see exactly what I'm talking about with respect to CASPA and then also the school that we're gonna be looking at today. So CASPA's participating programs, you'll see here it has all of the various different deadline colors and dates and what that means. So let's see, okay. So maybe, all right, so let's look for it. I think she called it University of Baltimore, let's see. It's still all the way down to the universities because I'm used to calling it Anarondale Community College. So yeah, so University of Maryland Baltimore is what it's called and that is a dual program with Towson I believe. All right, let's look at this, let's kind of search this. So I'm gonna copy this, I'm gonna put it into the tab actually and let's see what comes up, there PA program. And so I will likely switch the name of this because yeah, it's not the same thing. It's called something different, okay. So let me just search this really quickly. Oh, so there's two, all right. So you guys, there are two different schools that I'm looking at. So I'm doing today, actually I'm gonna be doing the University of Baltimore, okay. So like let's take a look at all of that because that's what Ayanna really wanted me to look at. So University of Maryland PA's programs and this is University of Maryland Baltimore because there's College Park, there's Eastern Shore, there's lots of University of Maryland's, okay. So I like this picture, everybody looks like they're having fun, 100. So this is really cool. I like the fact that there is like a program snapshot right when you get into it.    That's $100,000. So you just wanna make sure that again, you're paying attention to the cost of these programs because they can be very, very costly and attrition. Like we'll get into that right now as well. Okay, so let's just go down the line. Academics, again, I always tell you guys look at, oh, so here it is, all right. So it's the same thing, all right. So I wasn't like, I wasn't going crazy when I thought it was Anne Arundel Community College, okay. So it says the University of Maryland Baltimore Graduate School and Anne Arundel Community College promote excellence and education to foster the development of the component, is that competent, ethical and compassionate primary care providers. So their focus is primary care providers. It's a little bit confusing. So don't get yourself confused because they have their own aspect of a website for their PA program as well as Anne Arundel's. Anne Arundel has their own as well. And I wanna show you guys that too. So let me just share that part of my screen because I pulled it up just to make sure that I wasn't reviewing the wrong school. And I'm sorry, not reviewing, we're researching. There we go, because I'm not telling you to go here or not, okay. So this is Anne Arundel Community College's PA program site, okay. So same school, it says it here, University of Maryland Baltimore. We are now the University of Maryland Baltimore slash Anne Arundel Community College collaborative physician assistant program, okay. So long name, same school, we got this. All right, so let's go back to what I was looking at on that other tab for you guys. So academics. All right, so look at their mission, look at their vision and look at their goals. These are important things you need to know specifically what the mission of the school is, what the vision is, how you as an applicant can fit into that mission and the goals that the schools are trying to accomplish, okay. Curriculum for students. Okay, so this is how they have it split up. I guess you would take 86 at AACC and then 30 at UMB, okay. So that would get you your combined 116. I don't know exactly how it works. Like if you're actually going to each campus while you're there for different years, but that's, it's interesting, but it is a dual, like a hybrid kind of dual program with the community college and the university. So this just shows you all of the various different classes that you're gonna take. Clinical medicine is like what I did in PA school, we called it medical practice, but that's where you learn how to diagnose and treat the various different illnesses that you're gonna be seeing as a PA. Okay, so if you're interested in that, you can look there. Curriculum for prospective students. First year, all right. So again, just looking at that. Transcript and degree verification. Students who graduated in 2019 over four, please refer to Anne Rundle Community College office or I guess this is if you, students who will graduate in 2020. So this is if you need your transcripts, like from the school. All right, let's look at Artrition.  So class of 2019 to 2021, their maximum entering class size is 40. The students that they actually like allowed in. So again, they have the ability to have 40 students. Okay, 40 seats. Each year you see that they've kind of increased it to that max, like this class of 2021 has 40 students. Right now, the number of graduates is 39. So maybe someone decelerated or just, you know, dropped out. Well, got kicked out, you don't know. But showing you their Artrition rate, it was pretty high in 2019, lower in 2020. And obviously as of right now for 2021, it's significantly low, but you know, there's still time. So it's not to say that that is what it's gonna end up being, but it is important for you to know how schools are doing with their Artrition rate. Okay. All right, let's see, what else? Accreditation. They really, is this the same? No, I think, I'm like, they really like these like, black men over here, that's who they're like promoting. I guess they want like males or something, who knows? Let's, we can say that, but another picture of an African-American man wearing his short white coat, they have continued accreditation, which is good. Again, there's provisional, there's probation, there's continue, and then there's no accreditation cause you're developing programs. So they have continued accreditation, so that is good to know. Their next evaluation will be 2029. So that's also good to know, because you know that you're kind of set for the next few years. If for whatever reason, you do get accepted to the program, you have no worries there that, you know, the program's gonna get shut down or anything like that. All right, so let's look at their pants pass rate. Wow, they have a lot of guys in their program. One, two, three, four. I don't know if this is a guy or a girl's head. Five, six, seven, eight, nine, 10, 11, 12, 13. Wow, that's a lot you guys, because I mean, typically you'll have like maybe a third, if not like a fourth of the class is males and the majority is females. So that's kind of cool. All right, let's look at this pass-pants rate. Okay, so I'm gonna have to share that screen with you guys, because you're not gonna be able to see it because it popped into another window. So let me go here and share that. Hey, Logan. Logan said hello, you guys. Let's see, program pass-pants rate. Okay, all right, so they have the last five years, which most schools typically have it unless they haven't been in existence for five years, okay? So let's look at 2016. They had 36, 33 of them passed, okay? That's not too bad. Had 57, all of the class took it, 53 passed. So they've been kind of steadily in the 90s, which is an A, that's passing, that's actually pretty good. Looking at it in comparison to the national pass-pants pass rate, they're a little bit lower, but not significantly, so for you to be like, what's going on here? 2019, y'all, that was a bad year for everybody, okay? Look at the national, the national pass-pants pass rate was 91%, and they're here at 40, 94%, which is good, they did better. So of the 30 that took it, only one didn't pass, and then 37, oh, y'all, they got 100% pass rate for 2020. So that's like something to actually be really, really, really, really proud about, okay? So let's go to go back to the program and see what else they have to offer us. What else you guys should be learning about this? License disclosure, graduates of the University of Maryland are eligible to take, okay, eligible to take the pants. All right, this is what you guys came here for, admission requirements, so let's go. All right, so students enter the PA program in the summer term of each year. So this is a summer start, likely maybe May or June start, and then it's 25 months long, okay? So a little over two years. Therefore, a student should plan finances carefully, yes, indeed, the average GPA is a 3.0, that is your minimum GPA that you need, and all position students are required to have personal digital assistant email address and internet access, okay, cool. All right, admissions requirements. Okay, so this is the school, I don't know if you guys have heard me before, where I was like, one of the years I applied to these schools and I just was not paying attention, I was just kind of like, oh, whatever, I'll be able to get in, and there was a school that said the minimum, you could have nothing lower than a B, and I had a B minus, and I didn't get in, okay, because I had a B minus, because I didn't meet the requirements, and so this is that school, you guys, I have no shame in saying that, but it says applicants to the PA program must have a bachelor's degree or higher, they require the GRE, okay? Nothing said about the PA cat, so GRE is still king for this particular program, and then it says, a completion of the following prerequisite courses with a minimum grade of B in each course, not B minus B, okay? So just be mindful of that. So statistics, micro, anatomy, physiology, one and two, introduction to psychology or developmental psychology, general chemistry, OCam or BioCam, which is school they allow you to choose, prerequisites provided in the admissions information to ensure equivalency prior to submitting a CASPA application. This is also something to keep in mind that the anatomy and physiology courses are required to have been completed in the last seven years of the date that you submit your CASPA application, and so I know you guys have seen some of the schools that we did in the past, that I showed you in the past, and they don't all have like this year cap, but this one has it, but solely on anatomy and physiology.  If you took anatomy and physiology as a senior, then you should be good if you maybe took like one or two gap years, you're still well within that seven year period, okay? Applicants to the PA program must submit their application through CASPA, again, minimum cumulative GPA of a 3.0, no prerequisite minimum grade of like, and nothing underneath a B, UMB must receive the CASPA completed application by the deadline date of September 1st. So again, these dates are past, and I'll look at some of the schools to see if there's any schools that have these like December timelines or January or March deadlines, so that if you're still interested in applying to PA school, we'll have some of those programs there for you that actually like you can apply to still with the information that I'm providing, okay? So as foreign educated students must have their international college transcripts from all higher level institutions attended, evaluated by our WES, Spantra or ECE, which is cool. So they do accept foreign grads or foreign educated students.  I wanna study, you know, PA in America. Like this is one of the programs that will accept you. You have to go get it evaluated by one of these sites and see that you meet all of those very different requirements for the prereqs and then apply and that's, it's really that simple. Okay, applicants who use native language. Okay, so if you, if English is not your first language, then you would have to take the test of English as a foreign language, which is, you know, if English is not your native language, typically you've heard of this test before. All right, so that is that. What is this aspect, academic standards? So again, all PA students must receive a minimum grade of a C in each of your PA course. So nothing lower than a C, selection criteria. So these are the things that they look at, obviously not limited to this, but they look at your cumulative GPA, your science GPA, your letters of recommendation, which again are all things that you will be adding into CASPA, patient contact experience, community or civil service. Any of the recommended courses that they may have your GRE scores and then obviously your interview, that is like the final step to getting an acceptance. It says a non-refundable C deposit is required upon acceptance, but like most schools and no selection decisions will be communicated via telephone and or email. The decision of the PA admissions committee is final. Okay, so maybe they send out like, I don't know who uses like snail mail anymore, but maybe they send out like snail mail. It says it's not going to be communicated via telephone or email. I don't know if that's like, if you call them and you're like asking if you got in, like they're not going to communicate it that way, but they would reach out to you. I'm not really sure, but that's a statement that they've made there. Students who are provisionally accepted to this program study will be required to submit a health examination record. So you have to have a physical done. I had to have one done for my PA program as well and you have to have insurance. Also the criminal background check, that's also something that you'll have to have done and you'll need like ones with fingerprints because when you're doing like your Peds rotation, they want to know like, there's nothing in your background that would adversely affect any of the children that you will be essentially taking care of. Readmission to the PA course sequence. Students seeking readmission to the PA program are referred to the, okay. Specific requirements and eligibility must be met for readmission. The University of Maryland, Baltimore PA program does not offer advanced placement or a transfer and again, health insurance. So let's see if we can find this manual that they're talking about. PA admissions booklet, is it this? Yeah, I don't know if we can go through all of this because this is like 29 pages of information. I'm gonna look and see specifically if there's anything in here worth while but if you're interested in it, you can always go and look at this yourself. All right, let's just, let's just go, we'll look at that. Let's look at their manual, okay. All right, Ayanna has a question as well. Let's get that. I'm wondering what they mean by statistics, a math statistics or something else. So it was a math statistics that I did but this admissions requirements thing that I'm about to share with you guys, I think kind of goes into it a little bit more in depth. So hopefully we'll be able to answer that question for you. Okay, all right. So yeah, I'm right on the page. So prerequisite requirements, it shows you all of their six requirements and you see here it says B minus grades will not be accepted, okay. I did not see this when I applied like three or how many years ago, maybe four or four or so years ago. Maybe it was five. I'm not really sure how many years ago it was. It was a while ago, but I didn't see that. I probably like just glance past it and yeah, not accepted, okay. So that means it doesn't meet the requirements but it says statistics here. So it gives you all of the various different types of statistics, elementary statistics, statistics in social and behavioral sciences or bio statistics and that elementary statistics is your math, like your general math statistics, okay. We accept AP courses must be official from the college board for psychology, statistics and general chemistry. So they do accept AP courses for those three classes listed but clearly nothing else. So just keep that in mind if you are like coming straight out of college and you took like bio statistics or statistics or psych as a senior like I did for college credit, they will accept it but only those particular classes, okay. All right, so here, patient contact experience. It says a minimum of 1400 hours of patient contact experience is recommended but not required. And so again, if something is recommended, I highly, highly, highly suggest that you go after it, okay. Try to attain that with all your strength and your might because I'm pretty sure that people are coming in with like higher than 1400. So definitely shoot for that, okay. You're gonna have patient contact experience must be reported on CASPA, okay, great. And you'll put all that information in in CASPA. And if you haven't seen like CASPA and what CASPA is all about, I did a CASPA video a while back. So just search it in my channel and you'll be able to see that video and what like CASPA looks like on the inside and like where you would put all that information in. So that is a recommendation, you know, CASPA requires about three, I think it has less for about five maybe, I don't know, but it's like three, most schools require about two LORs. So that again will also be in CASPA and then GRE you will give them this code here when you take your GRE tests to have them send your scores directly to the program. So again, this is just talking about our foreign medical graduates, exemptions. So all of these different countries, like Trinidad and Tobago right there, that's my country, you guys. But all these countries have exemptions to the test of English as a foreign language because they have English as their primary language likely or one of their primary languages. So you wouldn't have to take it if you were born in Trinidad or from Trinidad, just saying. All right, so language must reflect a bachelor's degree, master's degree or doctorate degree. So you can, doctor of medicine degree, you can be like a foreign medical physician and then come and apply to Anne Rundle or University of Maryland Baltimore. And I guess just kind of like the PA name change, like don't use Anne Rundle Community College, call it the University of Maryland Baltimore. So I'm gonna change that in my title just so you guys can get used to that because it's essential for you to use the name that the schools are changed to. Selection criteria, so we kind of already went through this selection criteria and what they look at. Talked about the criminal background, the technical standards, health insurance.  What else? The Office of Accountability and Compliance is available to advise and assist all students, staff and faculty with their request for reasonable accommodation. So I think this is important for anybody that requires any type of accommodation with respect to test taking or getting in and out of facilities and just making things more amenable and better for you as a learner, as a student, so that you can actually succeed. So this is you, you should absolutely keep this link in mind if you do get accepted. All right, I mean, we're breezing through this. Sorry, prerequisite coursework description. So it just goes into more detail what they are requiring like in terms of those prerequisites. And so you can always, if there's ever like a question and this is like, you never really think about this when you're an undergrad, but it's really important to keep your syllabi. I kept like the syllabi to all of my, the different courses that I took and it was important because when I was applying to one of the California schools out West for my gross anatomy, which was mammalian anatomy by itself where we did like cadavers and nice sections into the cadavers, like they wanted to know that yes, we were still like learning like just basic anatomy essentially. And so I had to give them that syllabus to make sure that it met the standards. And so that's, I think something that's key that you guys should keep in mind is to keep your syllabi so that you can prove that it meets the standards that they are requesting. Oh, this is, I like this, this is my part. This is what I really want you guys to see as well, okay? So this gives you the makeup of the class over the last essentially like three years, okay? So for the class of 2020, there was an age range of 21 to 43, which is nice, very inclusive. The average age range was 26. There was 36% male and 64% female in states, 77%. So typically, and you can see that kind of across the board that about, well, I would say like, what three fourths of their program is in state residence. So if you are in the DMV area and you like wanna stay in Maryland, this is a good school for you to apply to. So there had, wow, somebody had their doctorate. There was eight master's degrees and they all have their bachelors, which is cool. And oh, and for class of 2021, they had two foreign medical grads. So that's actually pretty telling as well that it's possible, okay? Major field of undergraduate study, it was biology or exercise science was next, kinesiology and nursing, like to see that, like see nursing and kinesiology, like kind of not the typical norm for people. Other years, it's biology again, exercise science, genetic psychology, then biology coming in again, exercise science, public health and biochem. All right, so average GPA of the various different classes. So 3.49, 3.55 and 3.56. So you can see that the average GPA is about a 3.5, okay? So if you're trying to attend this program, you shoot for 3.5, 3.6, 3.7, because you know that you're pretty much on par with all of the other students that they have allowed into their program. Other average science GPA is also about a 3.5, so just keeping that in mind. And their common patient care experience hours is either being a patient care tech or CNA, medical assistant, paramedics or EMTs, PT techs, rad techs and ophthalmic tech, that's interesting. That's unique. I've seen like maybe two or three or met like two or three ophthalmic techs, so kind of pretty cool. But look at this, you guys. Do you remember what I said? Do you remember what their minimum was? Their minimum patient care hours was 1,400, not required, but suggested. But look at the average patient care hours that these people came in with. 4,500, 4,200 and 3,500. And that's telling, okay? And I keep telling you guys this in any time we have, I have like a consultation session with any of you and we're looking at the schools that you're trying to apply to. I keep it real with you guys that look, if you have like 700 hours, but this school's minimum requirement or the average is like 3,300, you gotta pick it up. You might wanna pick up some extra shifts or if you have the opportunity to do so, maybe you might wanna like take another year and actually just work and get more experience so that you can be more competitive. And if you have the time and the space to do that, I would suggest you do that, okay? So we talk about that a lot in our sessions. This again just kind of goes through the cumulative GPA. Again, talking about a grade of B or higher in these prerequisite courses, B minus is not accepted. Anatomy and physiology have to, they have to have been completed in the last 70 years. Lots of reiteration. If you do your research, you really should not make any of the like the silly mistakes that I made when I applied the last time. It talks about when their program opens, but look at this. It says when their deadline is, but it says it has strongly recommended that applicants submit their CASPA application by July 1st, okay? June, July, so that's like two months ahead of their deadline. Okay, July 1st to ensure that the application is verified because it can take anywhere from four to six weeks for CASPA to verify your application in those early like summer months. So again, yes, I like I say this again, but it's showing it here on their little booklet. Apply early as early as you possibly can.  After you've put in that information. So just keep that in mind. All right, are you a competitive applicant? Do you have a minimum of 1400 hours? Is it in any of these areas like EMT, CNA? Are you a search tag? These are all options. It says shadowing is not considered patient contact experience, okay? And volunteering will be considered as community service, okay? Is your science GPA in the range of 3.3 to 3.5? We saw that their average student had a 3.5.  You're sitting easy. So you shouldn't really be concerned. Let's see if they have something about their GRE, a personal statement consisting of 300 to 500 words outlining your goals. So you'll have to write a personal statement, okay, cool. Do you have community service? Do you have conventional fluency in other languages? So that's cool. If you have the ability to speak another language that can be a benefit to you, especially in healthcare. So keep that in mind. Do you follow the recommendations of anything with a B or better? B or better, not B minus. Those are what will make you competitive applicants. So it doesn't give like the average GRE score and it didn't show that in their class makeup. So that's something that you just have to determine for yourself, like what you're shooting for. I think anything over a 3.10 is really good for you to shoot for. So like 1.55 on each thing is, I think a decent thing to shoot for. So just keep that in mind but they don't give an average here. Talks about the CASP application process. And I like this, okay? Because so probably if you guys are watching this and you're like applying to other schools and you're like, oh, what should I do for my patient care experience? This program lays it out for you, okay? On all of the different acceptable like patient care experience, all right? So for sure, like if you are hitting any of these things like if you were an optometrist or an ortho tech, a paramedic, a PT aide, a PT assistant, all of these things are acceptable and likely it will be acceptable for some of those schools that you're applying to because these are like all pretty much clinical stuff. Things that are not acceptable, coding and billing, you're not really seeing patients like that. It's shadowing vet assistants or techs because you're dealing with animals, not people, being a chaplain, those kinds of things, all right? So I think this is a good list to kind of have in your back pocket if you're looking for what you should get your patient care experience in. And it just gives you information about anirunnel community college and where it's located and gives you some emails that you can hit up if you need more information like the registrar and what is this? Do I have to apply through CASPA? Yes, so frequently asked questions. Do my prerequisites need to be completed by the application deadline? All prerequisites, okay. So this must be posted with grades on official transcripts submitted to CASPA, okay. So there's nothing, no prerequisites can be outstanding. Again, we saw that with some programs where they will allow one or two to be like in completion but have to be completed by the time of acceptance. This program says they all need to have, they need to be completed and have their grades. So that is something to keep in mind. Does my degree need to be completed by application conferred degrees and date must be posted on official, okay. So you can't be like in the process of completing your degree, it should be done. Does my, does the type of bachelor's degree matter? No. If I retake courses, which grade will count for my GPA? For cumulative GPA and science GPA, everything is calculated through CASPA.  Do I still need to take the jury if I have a master's degree or higher? Yes, okay. Can I work while I'm in PA program? They don't recommend it, but you know, who's no one's really stopping you. Can I get credit for previous academic work? No. How often do you admit students? So only once a year, like this is not like a rolling admission where it's like three times a year, twice a year, once a year starting in the summer months. CASPA application sent in by July 1st so that you can have it within time for that September 1st deadline. They don't offer a part-time PA program as 25 months and they do allow foreign medical grads and foreign students to apply. We went through all of this. There are 40 C's available. Okay, so this is nice. Typical number of applications receive is 800. So I mean, there are some schools that receive like 1500, 2000 plus applications. This school says their typical, like their average is about 800 and maybe up in the years to come just because like the PA program, PA school is becoming more and more widely known and the profession is becoming more widely known. And so people really wanna become PA. So that may be up, but you're looking at 40 seats, possibly available, right? And 800 applicants. So that's like a, that's a pretty, pretty hard stretch. Like when you're breaking down like from 800 applicants to maybe like 100 people that you're gonna offer an interview to and then 40 of the 100 are actually gonna be admitted. So all things to keep in mind, but that is that. I think, I don't think there's anything else. Let's just take a look at their faculty and staff, okay? Jana says, is the introduction to statistics from community college enough to cover it? I think it should be, honestly. That would be something that you have to talk to the program directly about. So like just go to those various different links that they had for the admissions or the contact page and just ask them that specifically because they're there to answer those type of questions, but it really should. I don't see why not. My statistics, like once I retook it, no one had an issue with my statistics and I took it at a community college. So LaKeisha said, really appreciate all the care considering energy that you put into helping us. Thanks. You hear my voice cracking and my hair is crazy. I just watched it. So this is all for you guys. This is all for you guys. This is awesome. Thank you for this and on it. Oh, no problem. And Jana was just saying she was wondering the same thing. Let me just go back. I'm gonna share this with you guys really quickly before we end this video. Again, Friday I will be doing another live but it will only be to those that are on GTCU. So if you're interested in any of the Nova schools you should go check us out. All right, so I wanted to look at their faculty and staff. So this is Dr. Hendricks. She is the assistant dean and the program director. Kimberly Bizzle, Dr. Bizzle is the medical director for the program. Ms. Newman is the assistant program director. Ms. Aum, she is the academic coordinator and assistant professor. She teaches Dr. Archibald. What is she? Program director, research admin. Okay, so let me just... Okay, and it says Dr. Hendricks is the program director and associate professor. But then it says that Dr. Archibald is also the program director. So there's two program directors, I guess, which is interesting. Dr. Yang is a surgical PA with 20 years of experience and he is adjunct faculty. Professor Fleming, she's an associate professor. Dr. Galloway, she's an assistant professor. So these are all the people that will be your teacher, Professor Galvin, Dr. Magder, Dr. May. At least they all look friendly. Dr. Odeski. Oh, she's the farm dean. So she's probably teaching you guys pharmacology, which is cool. I love my pharmacology teacher. Professor Russell looks pretty young. All these people look really young. Oh, he graduated in 2017. What year did they graduate? Graduated in 2009. So it's very young professor here. Naya Ward, associate professor and program director, masters of science and health. Dr. Ward, not really sure what she teaches. Nicole Wooten is also an associate assistant professor. And then these are your staff. These are people who really do all the hard work, you guys. They're the ones that are like working behind the scenes, making sure that the program runs. So be kind to all of your staff. But that is that. I think those are all of like the important things to really look at. We already saw pretty much the costs, but let's give you like a full, I don't think it gives you like a full, it doesn't. It doesn't give you a full breakdown of what it's gonna be, but I mean, you can calculate it was about $100,000. So yeah, that's it. Okay, you guys, I hope you enjoyed that. If you have any other programs that you want me to review, please you guys leave them in the comment section below. Again, I'll be doing NOVA on Friday, one of the NOVA's because there's like a gajillion of them. And then join me again on Sunday for another video and back on Tuesday and we're gonna be doing it in the evening slash afternoon. I'm thinking more along the lines of like six o'clock rather than seven 30, just so that I'm able to accomplish everything in a timely fashion. But hopefully you guys enjoyed this. And if you have any questions for me, you know what to do, drop them in the comment section. Thank you guys so much for watching. Follow me on Instagram at AdanaThePA and on Instagram at Get That See University. I will talk to you guys next time. Bye. See ya.


Hello and welcome to the session. In this session we discuss the following question which says draw a circle with center O and radius 3 cm, draw sector having the angle 68 degrees. First of all let's recall what is the sector of a circle. The area bounded by an arc and the two radii joining the end points with the center is called a sector. This is the key idea that we use for this question. Now let's see the solution. For we will draw a circle with center O and radius 3 cm. So this is a circle with center O. O A is the radius of the circle where O A is equal to 3 cm. Next we need to draw a sector having the angle 68 degrees. To draw the sector using the protractor we will keep the protractor with its center point on the center of the circle and the base line of the protractor along the radius of the circle and we mark the point indicating the angle measuring 68 degrees. So we are drawn this angle AOB measuring 68 degrees. As we know that the sector of a circle is the area bounded by an arc and the two radii joining the end points of the arc with the center. Consider any point C on the arc AB of the circle. Now this sector O A CB is the minor sector and take any point D on the major arc of the circle. So this ADB is the major arc of the circle and hence O A DB is the major sector of the circle. Major sector is formed by the major arc of the circle and the minor sector is formed by the minor arc of the circle. So we have drawn a circle with radius 3 cm and having a sector of angle equal to 68 degrees. This completes the session. Hope you have understood the solution of this question.


Adam Pohl here with head coach Dominic Dawes and coach Dawes. You guys had a great effort out of the gate.  Tell us about your push in the first period. I mean, that was the game plan.  Pressure their D. They'll create turnovers. And that's what we did. And that's why we were successful. And they flipped the script on us after that. I know in the third period, many people will look to that. But giving up two shorthanded goals really hurts you. You had a great opportunity to get into that third period with the lead. Oh, that's huge. I mean, I don't know how many. I don't think we've given up two shorthanded goals all year. And then to give up two in the game is obviously a backbreaker, especially in a game like this. But credit to them. And they pressured us. And we turned the puck over and capitalized on our opportunities. You have to force getting opportunities on the power play, though. And late in the game, you were able to do that, get a five on three, which is so hard to do in the last five, six minutes of a game. And with that, you were able to get a goal to get back within one, as Davis was outstanding today. You had to be happy with how hard you guys fought down the stretch. It wasn't at all, to be honest with you. I thought we were awful. I thought we got outworked. And I thought that was the difference in the game in the last two periods is they outworked us. They beat us to pucks. They won physical battles. One of our big things going into the game was blocking shots. I haven't seen the final score sheet. But I know after the second period, 10 to 4 in favor of Utica. And I think that goes along with the hard work. So I think they outworked us and they beat us. Lastly, you got to turn around quickly.  How do you turn the page and get after it so quickly? That's it. I mean, I said what I needed to say in there. And now we have to turn the page. We've got to move forward. Tomorrow's the biggest game of the year. And that's the way we've got to look at it. And you've got to rebound and you've got to respond. Well, Coach Dahl's best of luck is you guys get ready for a big postseason run. Thank you. Final score, Utica 6 to 4. And once again, that is Coach Dahl's, as this is Stevenson Hockey.


Think Tech Hawaii, civil engagement lives here. Good afternoon. This is Business in Hawaii for Think Tech, and we're in downtown Honolulu on a hot day, the end of June, about a week before July 4th. And we're here today talking about issues and challenges of business leaders, specifically business leaders who are CEOs of organizations, trying to really be innovative, trying to push sales, trying to recruit and really develop line managers. The issues of CEOs are probably the same all over the world. And what keeps them awake at night, and how do they seek advice from other seasoned consultants and advisors? And that's the topic we have today on consulting, on traditional consulting, and the future of consulting globally. Welcome to the show. We have Jan Rumi, extreme left to me. Welcome to the show. Thank you, Ray. And we have Iqbal Ashwaf, just to the left of me. Welcome to the show. Thanks. Glad to be here. Great. Welcome by your esteemed backgrounds.  Okay, all right. That's a pretty interesting story. We did come here within a few years, a year and a half, I got married, and then I was driving through the licky, licky tunnel, and my wife was mesmerized with the beauty of Hawaii, and she just said, I mean, dear, can you find something over here? And then that's the end of the story. That's what we got to Hawaii. It's been about more than 32 years. Wow. So you've seen a lot of changes in Hawaii, especially in the business community. Absolutely. Absolutely. And I've heard that your background is in traditional consulting. Can you tell me a little bit about that? Yes. I've been in charge of consulting for Grand Thornton, local accounting and management consulting office of Grand Thornton International. And I've been there for 14 years, so that is consulting, you know, as everybody knows, consulting. But I think you will hear from Iqbal and I guess part of the conversation that once I met Iqbal, the light bulb went on, and then I said, this is the new way of consulting. I mean, you would say management consulting, that includes the big firms like McKinsey that's been around, or Deloitte, or Bain, or Boston consulting, and Grand Thornton. There's many firms out there that assist many big companies, and SME is a small to medium enterprises. And would you agree that consultants will advise and also solve problems for CEOs of these businesses? Yes, yes. They, primarily, the large accounting or management consulting companies, like you said, Grand Thornton, Deloitte, KPMG, you know, they have audit department, they have tax, and they have rest of their office here, which is basically to help out a given client. Anything outside of audit and tax, that's called management consulting. That's great.  How did you come to my life? Yeah, so I grew up in India, and you know, when I first moved to US in 2004, I used to work for GE, so I worked in many different roles, and mostly, I lived and worked in Milwaukee. And then at some point in my career, I just got sick of working in a big company, living in a cold place. I had visited Hawaii before, and I said, I'm just moving to Hawaii. This was in 2008, and the neighbor since then I have been here. So you've been here for 10 years, and working with businesses in Hawaii. And so we come to, very quickly, can you define, Iqbal, how you developed this idea, a new model of consulting, and how is it different than traditional consulting? Sure. You know, before I started working on GEALD in 2012, 2013, I used to run a company called Pro Accounting, which was owned by Pro Service, one of the larger companies here. And we were basically an outsourced accounting shop, worked with many small and mid-sized companies. And as a person running that shop, I would advise the owners. I kind of came to a realization that if you think 10, 15 years from ago, if you were a small retail shop in maybe Kailua, you would compete with a small retail shop in Kailua. But now the whole landscape has changed. You are competing with much bigger companies, internet business models. As really, it's an unfair playing field. So I wanted to give top notch expertise to smaller companies, but at a price that they can afford, and that was the genesis of this idea. So give me an example. You say that you're trying to help a local company compete at a larger scale or compete with advantage vis-a-vis mainland companies or global companies, and to shortcut how they would get there. Am I correct? It's like a shortcut when you think about it. Give me an example how you can, in a project or you've done, that really brought consultants or advisors to a small company that they would otherwise never meet and never leverage that expertise. Can I answer that question? Yeah. I mean, it really jives with the issues that I had when I was part of the large accounting and consulting companies. Most of the Hawaii businesses are not that large compared to the mainland companies. So we're talking about mostly a small and medium-sized enterprises. That's a me market when we talk about Hawaii. Under 300, right? Employees. Under 300 employees anywhere between $5 to $25 million business in gross revenue, the top line. So what they have had a problem recently is that when you are going to compete with Whole Foods, for example, they can employ the top-notch consultants with the top hourly rate from the best consulting that you can get anywhere. But a local business may not be able to afford it. And that's where the guild model, our company's model of growth-oriented, innovative consulting company comes in. And that's when Iqbal and I first met and he was explaining his idea, business model idea for the guild. I got hooked in right there and then I say, okay, I was doing all of that in the past, now I know for this time of a business climate, it got to be guild or guild kind of consulting companies that would be appropriate for the local businesses where we can get the top-notch expertise from our 8,000 point expertise who are as qualified as the expertise that you would get out of McKinsey or Deloitte or KPMG or Grand Thornton, but about one-third of the price. And how we are accomplishing that, I'm sure Iqbal can embellish on that, but that is what we are bringing to the market. Okay, Iqbal, can you give me an example for the audience? Kind of, I'll give you a specific example. So a large, 300-employee business-to-business company here is growing really fast and their biggest challenge is they are not able to hire, you know, in this climate employees fast enough. So they had this problem and everybody, you know, kind of, this one kind of relates to that problem. And they can approach it differently. They thought, oh, you know, Google and Facebook and all those Silicon Valley companies that we hear about, they have had the same problem. What do they do to solve the problem? So what we did was they called that project, Building a Recruitment Engine. And this company prepared a list of 15 questions. But they wanted to ask those questions at the head of talent acquisition in these companies that we named, very well-known technology brands. Fortune 100 companies that are recruiting globally.  And then we brought on from our 8,000 member consultants, we brought two people. One person was the head of SourceCon, which is the largest talent acquisition, you know, conference in the US, in the world. And the other person was the head of HR, recruitment specifically for many companies which had made, you know, gone public and all that. And through their contacts, we were able to interview the head of talent acquisition in companies like GoDaddy and Amazon. And this kind of projects, you know, kind of, and done at a price point, so that would have been unimaginable for this client. They would never have met those people and gain insights, the best practices, going on in Silicon Valley today. So they understood about what metrics they use, what is their process flow, what are some of the hacks, you know, how do they attract clients, candidates that they really want to hire, how to be a better, you know, employer brand, how to build that, what kind of applicant tracking system to use, all those, you know, kind of little secrets, they kind of knew in like a one quarter long project. But it's very challenging for a company in the Middle Pacific to identify that specific expert to solve their problem. That's correct. So with that, if I may add to that, that that's where the local growth partners like myself, or Igbal, or we have couple others in our business here, right here in Honolulu, so we are the project manager, or the conduit to do what we can do here within our seasoned background being a consultant. But we would bring in this point expertise, like Igbal mentioned, at a price point that is almost like one third, or let's say 40% of what you would have to pay if you go to a regular consulting or other marketplace that we have here. So how is that possible?  How can you charge $110 an hour? Whereas if you were to get that kind of expertise, it would normally, at the minimum, would cost you $225. Or multiples. Multiples of $100 an hour. And that's because GILT does all the marketing, all the project management, all other things that we don't have to pay a posh office, like a larger company. Like a larger consulting firm. But in order to understand the firm's issues and problems, the company has to have people embedded in the company to really learn about the issues and problems. Am I correct? That's right. And you're absolutely right. And that's where the project manager or the growth partner, like myself, are embedded in one of these clients. So we know the company. So when we are saying that, okay, this is a defined project, and we would like a point expertise who can solve specifically this particular segment of the problem that is growth oriented or CEO or the COO is trying to solve or look into an opportunity that the company is looking for. We have to kind of end there because we're going to take a break. And we're going to delve further into project management and growth partner and some of the details of what they entail. We're taking a break. Thank you. Truth is I'm impressed. I haven't been asked such intelligent questions in a long time. Thanks. My name is Stephanie Mock and I'm one of three hosts of Think Tech Hawaii's Hawaii Food and Farmer series. Our other hosts are Matt Johnson and Pomei Weigert. And we talk to those who are in the fields and behind the scenes of our local food system. We talk to farmers, chefs, restaurant tours and more to learn more about what goes into sustainable agriculture here in Hawaii. We are on at Thursdays at 4 p.m. And we hope we'll see you next time. There was an old woman who lived in a shoe. She had so many children she didn't know what to do. She gave them some broth without any bread and kissed them all soundly and put them to bed. Hunger is a story we can end. End it at feedingamerica.org. Welcome back. We're in the midst of an exciting dialogue with my two guests from Guild Consulting. And we're going to be delving a little bit further into how Hawaii firms in particular can gain access to global expertise and best practices in a way that won't break the bank like larger consulting models have done in the past. Jan, go ahead. I was going to point out that the hourly rate of our point expertise, the best of the best in a given targeted area specifically for that particular need of a given company, whom we can access out of more than 8,000 point expertise we have on our business model, they can come in and exactly do what we're asking them to do because they don't have to do any marketing. Therefore, there is no dollar expenses for them to do any kind of marketing. Any kind of office expenses for them or anything of that nature. They have been seasoned into large accounting and consulting or other big consulting houses themselves for many years. So therefore, when they're on our business model and available to our projects, all they're doing is what we're asking them to do. The social problem. Yeah, and therefore they can do at about 1 third or 40% of an hourly rate, a traditional consulting company would have to charge. And that's where the value proposition of guilt comes in. I guess maybe we should take a step back and explain what our business model is. So we have a really lean team of just four people here who are seasoned, generic kind of consultants. And we call them growth partners. You can call them project managers. And then on the other side, we have these specialists that Jan calls point expertise or subject matter experts. And they're all over the country. And they are specialists in any specific industry and in a function. So for instance, you can take the grocery industry vertical and inventory management. And we will have a few experts in that area. So when a client comes to us and says, I have this specific problem, we connect them to who is the specialist who has solved that problem like 200 times before. Somewhere in the world. That's right. There's been a little learning curve for them. And then we become like the translator, the person who does the legwork, everything in between. And we are also accountable to the business owner for the success of the project. So we are like the bridge between the expert and the person who needs their expertise. And one of the disadvantages in the middle of the Pacific for CEOs in Hawaii is that it's a market of 1.2 million people. There isn't a vast pool of consultants and advisors available to advise the CEOs in Hawaii. But at the same time, your best profile of a person who can take advantage of this new consulting model are CEOs who want to see growth in different. And tell me more about this profile of the person who really can take advantage and run with this model. Yeah, so we do two types of work. One is projects. Project-based, we do it for mid-sized companies and some smaller companies. These are mission-critical projects, big projects, where they need a specialist to come in. That's where we add value. The other is a specific service that we have launched called the Growth Partner Service. These are companies between $5 million and $20 million, where the CEO is really ambitious. They want to take the company somewhere, but they're just not happy with the rate of growth. And we bring in a structure for them where they can grow. And we become embedded in the company as a part-time general manager, kind of advisor, we show up multiple things. Then on a neat basis, we bring in specialists through us and we understand that company inside out and we know what is their budget, what is the problem that they're trying to solve. And we have several clients here who are very ambitious, who are thinking long-term, who know what the big issues are and they want our help and we work with them on an ongoing basis. That's right. CEOs want to be with people who have seen it before, seasoned managers, so not the fresh of the boat MBAs who may be set by larger consulting firms. I think that's a big difference right there. Jan, you want to add to that? Yeah, I do want to just add one thing is that when I was in Grand Thornton, a local company, when I would say that, well, I'm bringing in one of my consultants from the Wisconsin office or Chicago office or even LA office, San Francisco office, you know, a lot of time we had no choice we did. And sometimes it worked out, it didn't work out. And one of the big reasons it didn't work out is because that consultant may have been pretty good in the subject, but they didn't really know how to work with the local companies, local management, the local style of doing business. It's a whole culture. It's quite different than the impure area. Right, right. But that's where we come in. We've been here more than 32 years. I mean, I've been in charge of consulting for many years in Hawaii. I've seen all kinds of consulting both in the state government and a federal government, private sector, financial nonprofits, things like that. So we are the glue maker to define the needs of the companies here, both on a project basis, a specific mission-critical project, a growth-oriented project, or even to add the capacity of the existing employees. It's called capacity enhancement or capability enhancement. Are you talking about developing line managers to become... Yeah, I mean, they're good. These employees are good, but they probably haven't harnessed the rigorality of a seasoned way of doing certain processes. They're just missing a little bit. Discipline of large organizations. Exactly. So we bring in the discipline of the larger organizations to the SMEs in Hawaii. And if needed, as Iqbal said, we can bring in this point of expertise and bingo, we got it done with one-third of the price with the higher probability of success because somebody's not coming in from the mainland. We are the glue maker here and we are accountable to the CEOs and to the company. In fact, if Iqbal, you say some of the payment is also performance-based. That's right. You know, we believe in our model so much so that in many of the projects that we undertake, we peg part of our fees to performance to the results that the client sees. Because, you know, our clients, they are really not interested in a book of recommendations that other consulting companies might give them. They are interested in the execution part. They need help there. So we are very hands-on when it comes to providing. We are not just providing advice. And when they see the results, part of our fee is also linked to them seeing the results. You mentioned non-profit as you mentioned government. There's a diversity of the private sector in Hawaii from the hospitality, hotel, restaurant, IT, a lot of wholesalers. Is there any specific or healthcare, any specific areas, sectors that really are more demanding or that you really can solve problems across the board? I would say Hawaii is a small market. You know, when I was in charge of consulting of a Grand Thornton, I had no choice. I had to go for all kind of clients. You don't have a deep, you know, vertical industry that I can only focus in there and make the consulting fees. In Hawaii, it's a small market. So, GILT model works with all industries. It is not specifically for financial industry or non-profit or government as such at all. So, and therefore, this value of this, more than 8,000 point expertise out there comes so handy. We got the top expertise in inventory management for construction material suppliers or hospital supplier companies and things of that nature. But I want to go back to this thing I call performance-based pay. There, in my career as a consultant for more than, you know, 32 years, I have rarely seen a big consultant agree to performance-based fees. And that is hard to... Hard to not entertain if I were a CEO or owner of a given company. You know, to kind of answer your... The reason consulting companies specialize in industry is because they have limited number of people in their payroll. And they are specialists in this industry and they know how to work. In our case, we are a network-concerned model. We are not constrained by the number of consultants. It's membership and, you know, they're not on a payroll. So, we can be really agnostic to the industry. As project managers, we have general skills and we can work in many different. But real service delivery happens by these specialists who are from different industries and functions. So, we're really not constrained. That's right. It's a matter of partnering with the CEO to uncover issues and problems and then finding the right specialist out there. And you're correct. It is a new paradigm, a new model. The networked consulting firm may be the future of consulting in many ways because of the Internet that you can have access, like you said, to 8,000 different consultants globally which is quite different than a set of skills within only one organization. Each one of these consultants have been consulting on their own under umbrella of large organizations for many years. They're vetted as... Yeah, so in the last five years, you know, we have spent... So, we have criteria for each industry when we, like, these are people that we will invite to join us and we interview them at the time they become members. And then we only... We do a lot of kind of matchmaking. So, basically, you want, when the client tells us this is a problem they are facing, we want a person from a supply side who has solved that exact problem in a different context. Somebody who just says, oh, I think I can solve the problem. We will not even match them to that project. So, that really helps us take the risk out of a lot of problem solving that we do. And that's a good word to use because CEOs always look at risk as they develop their business and they want to minimize risk and to solve the problem in a most efficient way and get results and performance. And go forward, you just mentioned about project management. These projects, what kind of skills do you bring that really you think enhance or really bring good outcomes to these projects? So, if you think about Project Management Institute, you know, published a report and these are across many different independent objective reports, most projects fail. You know, you talk about IT project, HR project, whatever, most consulting projects fail. Some numbers are often quoted as 70%. And most common reason they fail is the person does not have the expertise to solve that specific problem. Maybe they oversold the client and then their communication breakdowns. So, we are just approaching our model by having the growth partner as a person who's in charge of communications and the person who's working the project has real expertise in solving that problem. And that is the way we are trying to de-risking the project. Does that answer your question? That's right, it's a very exciting model and we're also coming to exciting clothes. I just want to add one thing to Iqbal and your comment that even though we are project manager, growth partner, we're general, but being a part of Grand Thornton for 14 years or so, I have also been honed in a particular industry. For example, myself and each one of us, four of us in the guild, have deep expertise in specific area like a non-profit, financial sectors, the state government and things of that nature. Well, exciting to hear and I hope it's exciting for the CEO out there and what makes the CEO awaken night? All kinds of issues ranging from innovation to sales, but especially tied to growth. How do you grow a company? And this new model, the network consulting, may be the answer that could solve the CEO's nightmares. Thank you again for listening and watching Business in Hawaii and we'll see you next time. My name is Ray Tsuchiyama.


I have, but let me show you how I do it. Here we go so I mean I So I spin the canvas like this. I did it on purpose, but I spin it and then I Mean it gets in my eye, right? So that's that's how that's that's Freak dude. I mean it burns a little bit, but that's that's how it happens for those of you wondering


Thank you for the introduction and for the invitation. So the plan is as follows, to give some motivation, some constructions following board shirts, and then my results. I'm just going to use the slides for motivation so that I can get the ideas across quickly. OK, so let me start by saying this. So if you like geometric representation theory or equivariant elliptic cohomology or anything vaguely related to that, and you're a young person, which is a technical term, meaning three years into your PhD or up to five years after graduating, then you should apply for the AMS Mathematical Research Community. So I'm organizing that with some other people. It's in June, so it will be, the focus will be on research. There'll be a few talks, but mostly we'll divide people into groups based on their expertise. We'll have some reading groups online ahead of time so you can learn more. You don't need to be an expert already. And the AMS has lots of funding for this, so if you participate in a mathematical research community and you're working on a collaboration, they have funding for the groups to get together in the coming two or three years. And so it's a good opportunity and you should apply if you qualify and you should encourage your young people to apply. OK, good thing I put that slide there because I would have forgot. And the deadline is February 15th to apply. OK, so let me start with the motivation. And so here's the context that I'm working in. So we have three categories of objects, which are of interest to people, some of whom are at this conference. So we have vertex algebras, chiral algebras, and factorization algebras. And these are factorization algebras in the sense of Baylentz and Drinfeld. So what are the relationships between them? So we have causal duality that says that chiral algebras on a space X are equivalent to factorization algebras. And I have some references there, so that's due to Baylentz and Drinfeld over curves and Francis and Gates-Goray in higher dimensions. All right. But vertex algebras are equivalent to translation-equivariant chiral algebras on A1 on the affine line. So that was known to Baylentz and Drinfeld, but the first it's written down carefully by Huang and Lepowski. And so if you want to preserve your equivalences here, I better stick the same modifiers on the right. So we have three categories, which are equivalent. So they're just different perspectives. Okay. So here's my notation for these categories. And in 1999, Borchard's, who was trying to make vertex algebras more accessible to a wider audience or trying to explain that the definition is well-motivated and natural, he came up with this other definition, which he calls AHS vertex algebras. So AHS and S are some input data that we're gonna discuss in some detail in the next section. And when he chooses a specific example, and I've denoted that by SB for Borchard's, he constructs a functor that goes from AHS vertex algebras to vertex algebras. And then he asks, so this is a paper from 1999, and he asks, he constructs certain examples of vertex algebras in this way, so lattice vertex algebras he can construct, but he can't construct everything. He asks, can we construct the virasauro? How far is this from being an equivalence? So I was trying to answer these questions, and I realized that we should modify his input data. So I call this S A1, and then there's a notion of translation equivalence, and I can provide a functor from there to chiral algebras. And it's not an equivalence, but it has a section, okay? So every factorization algebra gives rise to one of these funny vertex algebras, but there's more vertex algebras of these funny things, which get collapsed to the same element downstairs. So, and then there's a map from my category to Borchard's category. So in particular, his functor is essentially surjective, but it's not fully faithful. So why do I care about this? We have three perfectly good categories upstairs, why I introduce more complications. So here are some motivating questions that Borchard's was asking. These don't explain why we're interested in studying them, but they say some of the questions that I was looking at. So how far is this data from being an equivalence, and can we construct well-known vertex algebras in this category? So here's the reason that I started looking at this paper as I was talking to Dominic Joyce, and he constructed the following example. So let's start with a C linear abelian category, which has some conditions. So for example, modules over a quiver, or coherent sheaves on a nice variety, and then you form the modular stack of objects in that category, and then you look at the homology. And what Dominic shows is that it has a structure of graded vertex algebra. You have to shift the grading to make it work out, but he builds all the structure of vertex algebra, and he actually does this through Borchard's structure.  And so if one understands better how Borchard's definitions are related to the geometric picture, maybe when one can understand better how the vertex algebra structure on this geometric object has geometric origin, because in Dominic's preprint, it's just like a lot of formulas, like when you open a vertex algebra book, and so you don't really see what the geometry is. So the question is, can we use the geometric approach to understand this better? Could you indicate what the conditions are? I can't remember off the top of my head, but I can show you. We can look up a reference after, yeah, sorry. Okay, right, so that was the question that motivated me to read this paper of Borchard's, which I, to be honest, never heard of, okay. And another question, so actually Borchard's paper is called quantum vertex algebras. And so one of the advantages of his funny definition is that it generalizes very naturally to the quantum setting. So he's gonna define some category, and vertex algebras are gonna be commutative ring objects in that category, and quantum vertex algebras are braided ring objects in that category. So you have an R matrix, and then you have the usual braiding conditions. And so if you can understand how to relate Borchard's category to factorization algebras, then you can just transport those definitions over. So the answer to this question, I'm not gonna have time to get into it, but in brief, the answer is that you can adapt his definition, but it's not clear if it's useful yet. I haven't proven anything about it. So one thing that I've learned is that there are at least three different definitions of quantum vertex algebra, and it's not clear which is the correct one. So this might not be a helpful thing, but it is a thing. Okay. And let me just review, since I'm not sure what people's background are, just so you have an idea of the flavor of the categories upstairs. So recall that a chiral algebra on X, a variety, is a D module equipped with this Liebracket, which lives on X squared. So it's a map of D modules, and it satisfies the axioms of a Liebracket. And a factorization algebra on X consists of a bunch of left D modules on copies of X. So for any finite set, you take the product of that many copies of X, and you have a sheaf on there, and you have two kinds of compatibility conditions. So the first is Ron's condition, which says that if you restrict something on many copies of X to the diagonal, you get this thing on the fewer copies of X. So there's an example, the diagonal inside of X squared, and factorization isomorphisms, which say that if you restrict away from the diagonal, what you have on X squared, for example, splits into what you have on two copies of X. So you don't need to write these down or memorize them or anything, but I just want to do, to get the flavor of the sort of geometric objects that we're working with. Okay. So let me just leave that slide there so you can remember what we're working towards, and now I'll get into the details. Okay. Can people see the board or should we try to turn the light on? I don't know how to do that. Okay. So these constructions are mostly following board to its paper, but I'm gonna have sort of geometric interludes where I say if you're a geometry, you look at this and you say, this is what the algebra is telling us. So let me introduce the following notation. So we have two categories. The first category is the category of finite sets and then functions between them. And the second category, which is a bit more interesting, is finite sets with equivalence relations or partitions. And then morphisms have to be maps between the finite sets, which preserve inequivalence. So if two elements are equivalent under the equivalence relation in the domain, they can become inequivalent under the map, but it can't go the other way around. So let me tell you a geometric way to think of this. So let's fix X a separated scheme. A lot of Bortchard's definitions and results work in positive characteristic, but let me not worry about that because the whole picture doesn't fit together. So let's just assume we're over C. Okay, then what I can do is I can define a functor X bullet from this category of finite sets up into schemes. And it sends an object, so that's a finite set I, into the product of X with itself, and next by I. And it sends a morphism, let's call it alpha from I to J, that gets sent to a morphism of schemes, phi alpha from XJ to XI, and what that does is it sends the coordinates XJ, and we use alpha to tell us which coordinates to have. So if alpha is a surjection, this is a closed embedding, and if alpha is an injection, then this is a projection onto some factors. Okay, so what's the point? The point is that we can extend to a functor on this new category as follows. So we're gonna send I together with its equivalence relation to the set or the open subscheme UI, which consists of points in the product such that XI1 is not equal to XI2 unless I1 and I2 were equivalent. And so the condition on morphisms, so alpha from I to J, so this is just a map of sets, but if I and J have equivalence relations, then this preserves the inequivalents if and only if the following diagram. So we have our phi alpha, and inside of here we have UJ, and inside of here we have UI. And the condition is that if you apply phi alpha to something from UJ, you end up in UI. So now we have a functor on this new category. Okay, so that was our geometric interlude, and now let's go back to what Borchitz tells us. So he constructs the following category. So it's a category which he calls functors. It's fin in equivalent, A, T, S. And what these are gonna be, I'll explain the details, but the idea is that we want functors from, let's call them V, from this category into A, and for us, A is always gonna be vector spaces. So let me keep track of some choices that we're making along the way. So these definitions work in more generality, but the theorems only hold, and Borchitz examples and theorems only hold in these cases. So I don't wanna spend time on the things we don't need. Okay, so we're gonna have functors from here to here, and they're gonna be equipped with on, okay, let me put this in quotation marks. It's an action of a co-algebra. So what is an action of a co-algebra? I'm gonna have to tell you what we mean by that. So T is the co-algebra, and an action, not in quotation marks of an algebra. Where did that co-algebra and algebra leave? They're both functors. So I'm gonna explain in a second. Okay, so more precisely, in our case, so we need to construct this co-algebra, T. And the first thing we do is we're gonna set H to be equal to polynomials in one variable. So this is another choice which we're making, and the reason I'm introducing the notation H is because the category was called AHS, and this is our H, but we use it to build T. Okay, so we have this ring, and we make it into a co-algebra. So by saying that the co-multiplication of this element is the usual thing. And now we can define a functor T from finite sets into vector spaces that sends I to the tensor product I times of H. So that's just the same as polynomials in I variables. And this is a co-algebra because we can extend this. And this also gives us the functoriality. So I didn't worry about in equivalence, so if I wanna say what happens to a set with an equivalence relation, I just forget the equivalence relation. Okay, so that was T.  So we have a different compatibility condition, which I don't wanna say in general, but I'll say in a second what happens in our examples. Okay, so now we can. Everything's commutative, so. Yeah, but still, the edge of culture would usually put it something. I mean, I think, I don't know if action is really the right word, but this is what Borchardt's uses and this is the condition that he has. And in the examples that we'll see, it really is natural to think of it as a left action. So, okay. I think the comment is that algebras normally co-act. Yes. Which means that they're mapped from V to Z tensor. That's why I put it in quotation marks. This is an action, it's not a co-action. Okay. This is the source of S, I'm sure. Right now, yeah. So here's algebra object. So this should be S from, now it's important that it's defined on this whole category within equivalence. And it lands in Vect. And it should be an algebra object as a functor. So here, we're using that Vect is a tensor category to induce a tensor structure on the category of functors into Vect. So this is an algebra object and it should have an action of T and we have a specific example of T here. And so T should act by derivations. And that's the consequence of this condition star. So if I take an element of T and I act on a product of things in S, then I should get the usual formula. Okay. So let me give some examples. So the first example is in Borchard's paper. And so he doesn't call it this, but I'm gonna call it S sub B. And it sends a set I with an equivalence relation to the following algebra. So whenever I one and I two are not equivalent, we have their difference and it's inverse. So this is an algebra and it has an action of T by derivations in the natural way. That's probably why he picked that notation. Okay. Other questions about that? And it's a functor and for it to be a functor, it's important that maps from I to J preserve in equivalence. Otherwise we might get a zero here. And so then we'd have a problem, but we don't have to worry. Okay. So let's modify this example to get the version that I have in the slide up there. This is example two. So S a one sends the set I. So we had joined all the variables and then we invert the differences that we had before. So the observation is that these are, what are these? These are functions on a one without some diagonals. All right. Sorry, a to the I without some diagonals. And that's exactly this UI. We head over there. And so we can generalize this. So here's the generalization for X in a one. So any open, open affine curve with a fixed global coordinate, then I can take S X, which sends I to functions. And so the functoriality comes exactly because we have this map here. And so we can pull back functions. And the global coordinate is what allows us to say how, how these guys act. Okay, so now we have all of the pieces. And so a functor from finite sets with equivalence relations to vector spaces, which has an action of T and a compatible action of S. That is an element of this category. So let me denote it by C in equivalence. And so that's this category of functors. So now I said we want to look at ring objects in here. So we need to say what the minoidal structure is. So let me, there's actually two things we can do. And this is kind of analogous to the fact that if we look at D modules on the wrong space, we have two natural ways of making that into a minoidal category. So here's the naive thing. So if I have two elements, so these are two functors, then I can say that V tensor over S, W, sends I to VI tensor SI with WI. So this is an SI module. And TI can act because we use the comb multiplication to split it up into two factors, and then it acts on each factor. And everything preserves the functoriality. So that gives us an object again. Maybe you already said this, but do we want to think of S as being commutative always? Four, to get vertex algebras, yes. But in the quantum setting, it could be braided commutative. And Borchard's also has a comment. So A should be a symmetric minoidal category, and he has a comment what would happen if you took a braided minoidal category. I think you can make the definitions, but maybe you can't say anything about them. Or nothing has been said. OK, so that was the kind of boring thing to do, and here's the singular thing. So this is where the word singular commutative ring comes from. So the singular tensor structure is the following. So we're going to define it by saying that haums in this category from the funny tensor W into a third object, Z, these are given by, maybe I need more space. So these are given by compatible families of maps from the I tensor over C, or more generally whatever the tensor is in your category A, WJ to Z of I disjoint union J. And this is just my notation to indicate that I'm taking the disjoint union of I and J, imposing that I keep the equivalence relation on I and I keep the equivalence relation on J. And elements of I are not equivalent to elements of J. And so the fact that all the structure from S and T tell you that what the compatibility condition should be, and then you can show that this is representable. So you get an object B tensor W in here, and that's called the singular tensor product. So a remark is the following. It's that we can, well we have the forgetful functor from finite sets with equivalence relation to finite sets without, but we can do another thing. So we can say that we can embed functors which are only defined on finite sets. So let's call that category C. We can embed that inside of our C within equivalence in the following way. So let's send an object V to the functor V bar, and this functor is going to send I, so now I has an equivalence relation to, so I'm going to apply V to, I forget the equivalence relation, so I just have a finite set, so V knows what to do about that, S knows what to do, and then we tensor because S can also handle that. So every object in here can be viewed as an object in here, but if you take two objects in here and tensor them, you end up in here. You don't get an object back. So even if V and W are in C, this tensor product is strictly in here. Emily, does this answer product come from some sort of con extension or something? The formula with the compatible families looks like... Is it big convolution? Yeah, I mean... I think, I mean, it's really trying to do what the chiral tensor product does for factorization algebras, right?  But I'm not sure, probably you can... Okay, so the geometric thing to keep in mind in this situation when you have the case of Sx, then what is Vi? So V in this category C is its global, each Vi is global sections of a D module on some affine thing. And so it corresponds to some D module on X to the I, because we have the action of functions and then T gives us the action of the derivations. And then there's maps between them. And so when we look at V bar in the inequivalent thing, it just says that we should also remember, it also knows about the restriction of Vi to various UIs. But this guy knows about the restriction also. So it's not more data, it's just that our list looks longer. Things that we keep trying. Okay, so finally we can make the definition. So on AHS vertex algebra, a singular commutative ring object, V in C. So I wanted to live in this full subcategory. So what the multiplication map tells me is that I should have something from the singular tensor V, but I can only say that it's going to land in V bar. So in particular, if I take I and J to each be a point, I'm going to call the points 1 and 2, then I have a map from V1 tensor over C, V2 to V bar of 1, 2. Okay, and that's just V of 1, 2 tensored over so functions on X squared and then I allow poles. So that's the multiplication map. And then we can spell out what we mean for it to be associative and commutative and so on. And so the reason that we did all this work is because we have the following theorem. So given an AHSB vertex algebra, so that's SB right there conveniently. Let's call it V. Then if I apply this functor to the element with one point, which I'll call 1, so this is a vector space, this has a natural structure of vertex algebra in the normal sense. So this is how we get this theta B from that diagram, the blue arrow, from VA, AH, SB to VA. Other questions so far? So that's the end of the exposition, kind of. And so now I can say what is new. Actually, I'm going to begin with some more results of Borchert's. So the results are really asking how far is this theta from being an equivalence? And so the first positive result, so this is again in Borchert's paper, so let's let L, if it's a pairing, be an even lattice. And so then there exists some object, V sub L in this category of AH, SB, vertex algebra such that when I apply theta to VL, I get the lattice vertex algebra. So I think I have a few minutes, so I have some slides that sketch the construction. I don't want you to see the details, but I want you to see a few of the ingredients. So we start with our even lattice. Thank you. And then we construct this enormous vector space which you might recognize as the vector space underlying the lattice vertex algebra. And so it has a natural multiplication because it's a symmetric algebra. And we define co-multiplication in the following way. And it has an action of this T, and so that gives us an action of derivation. So we have a bi-algebra with a derivation. And we define the functor on finite sets by just taking the tensor product of this vector space. I think that upper L on the right should be a lower L.  Okay, so that's an object in C. And now I want to make it into a singular commutative ring. Well, it's already an ordinary commutative ring because it was an algebra. But we're going to twist that commutative multiplication using what Borchers calls a bi-character. So that's a map from v tensor v into, well, this is SB of one, two, disjoint union. So we can generalize those definitions and it satisfies some axioms. And then once you have a bi-character, you can twist, so this is, can people see the bottom row here? I can't. So this is a general formula that if I have a co-multiplication, a multiplication and a bi-character, I can twist. So I'm taking the two components of the co-multiplication of u, multiply that with the first component from v and then apply r to the remaining two components. And I get a map like this. So that wouldn't give me multiplication in the ordinary sense, but that's exactly what this map, mu, should be. So this is a general construction that anytime we have a bi-algebra with a bi-character, we can form a singular commutative ring. So the geometric analog that I haven't worked through in detail but that I want you to think of is that if you look at, for example, the classification of lattice chiral algebras, you start with a commutative algebra with derivation and then you have theta data which twists it and makes different kinds of lattice algebras. So that's what this r is doing and so we just have to work out how exactly to go from bi-characters to factorizing line bundles. So that's the kind of idea and the reason that I'm exploring this example is because this is also the construction that Dominic uses. So he starts with the the algebra coming from the homology of the modular space of objects and he defines a bi-character and his bi-character comes from a perfect complex on the product so I want to sort out those details but that's where this is going. Okay. So that's a positive result. We have some vertex algebras come or in the image of theta. Yes, please. Thanks. That's where we are. So here's a negative result. So this is due to me. So if you can construct the lattice vertex algebra, you want to construct it as a VOA. You want to see the virocyl. So the question is, from virocyl object mapping to this one and the answer is no. So there is no object A in Bortchard's category with a map omega from A into his what I called VL down there such that applying theta B gives the virocyl at level one. Yeah, virocyl with central charge one into VL. So this here is for the rank one case but you can generalize if you want to deal with more notation. Okay, so that's a problem because I mean that's one of the most important properties of this vertex algebra and we can't see it in Bortchard's setting. But we can fix it. So here is a positive result. Okay. So instead of using SB we use S of A1 or S of X more generally. So the first one is that there exists a functor theta X from VA of A8 SX to vertex algebras on X and so once you know that you have a vertex algebra on X you know by this is again for X open inside of A1 and Hwang and Lepowski that's equivalent to chiral algebras on X. And so you can just follow through so you get some formula here for the vertex operators and then you get some formula here but there's actually the second part of the theorem is that the chiral bracket, so let's say that this was V and then the vertex algebras is V of one and the chiral algebra is the D module coming from that, maybe made into a right D module, let me not worry about that. So the chiral bracket on V1 of R can be described directly in terms of the AHS data in the following way. So I need remember I thought I put the definition of a chiral algebra back up but so we need a map like this and it should end up over here and so the first thing we do is we use the this mu, this chiral or this singular commutative multiplication and we land here it's called an A suddenly this should be V, so V of one V of one V of one and if we we have this mu and mu lands us in V of one, two so mu actually starts here this is what mu does but then it's you can extend get a map like this so that's the first step and the second step so we use the short exact sequence for the this is the inclusion of the complement to the diagonal and then we have the diagonal so we are here we have a map here so this is from the short exact sequence and this last map here comes from the fact that we had a functor so we have a map from V one two to V one which comes from the from one two onto one and then and that induces this map here so if you follow through all of these computations it simplifies into this formula formula alright so now I have that functor well not quite I have it for a given X and then I claim that you can make it translation and then here's this thing which I called sigma so taking global sections so recall that part of the data of a factorization algebra is that you have a bunch of D modules on copies of X you take global sections of that and that gives you a V of a functor so taking global sections gives a sigma X from factorization algebras on X to VA AH SS algebras and it has the property that the composition from VA X to VA AH X is a section and so so Theta X is essentially surjective but this this kind of example of Borchards tells us that there's more things there's so I could take my lattice vertex algebra I make it into a factorization algebra make it into an AHS thing and I get an object there but it cannot be the same one that Borchards had because mine will have a map like this and Borchards won't so that's kind of a problem with Borchards category because it means you could think you've chosen a representative of the object that you want but it doesn't have the properties okay and so well let me just conclude do you know what happens with VL when you go around but you get a different representative for the lattice vertex algebra yeah I mean what is it I mean it's as explicit as the factorization algebra for VL is which is great so we can see how much it's different from Borchards example no so I do have a question that somehow what's going on is that Borchards data gives us a map all the way into here but we don't care about all of that data right so maybe there's a way of adding more morphisms like morphisms don't so the way I've defined morphisms in this category which Borchards doesn't define the morphisms but they're functors so I said that morphisms should be natural transformations but maybe they only need to be defined on some associated graded or something like that so there might be some way of loosening your notion of morphisms so that you can get a morphism here and basically because we've chosen these X's to be affine curves all of the UIs are affine and so all of the time we're just working with with global sections and so he's basically just dropped some of the axioms of a factorization algebra like some of the morphisms are not isomorphisms and so I don't really know that there's any advantage to working in that setting rather than just requiring them to be isomorphisms yeah Maybe you said this before but do you know how to see the Virisoro in this VA category in this AHSV category you just know how to see that I mean I do now because I have a section so I just I take my Virisoro as a vertex algebra or as a chiral algebra or as a factorization algebra and then I take global sections so this category here all of the objects except for Borchard's example and maybe Dominic's example the only examples I know are just global sections of factorization algebras and in the cases kind of my argument is that both Borchard's example and Dominic's example it would be better if we could find the expression that is global sections of a factorization algebra which I guess we can but just like tracing the diagram around I guess if we could see some geometric you know moduli space interpretation so the last remark that I wanted to make is that I didn't say anything about translation equivalence but it's pretty clear how you should define translation equivalence and so then all of the functors which I defined on X I make X equal to A1 and they are compatible with translation equivalence and so that's what's going on in that diagram that's all I want to say I was can you help me understand I'm a little confused by that negative result and the assertion of that theta X is a section for instance if you take what's written as W dot and translate it as a factorization algebra right so what happens is that VL does not go to this object it goes to something else and so that's what I mean that Borchard's he has a perfectly decent representative but it doesn't have the properties that we wanted to have so that's confusing do you know if these functors preserve certain co-limits or limits like this sounds like a localization kind of phenomenon right like you have some category and then you want to force certain things to be equivalences to get factorization I haven't thought about that I don't know I have to like my conclusion like I read this paper and I was like I want to understand and now my conclusion is like I think I was happy with factorization algebras but I somehow now have factorization algebras as a full sub category here so if I can understand quantum vertex algebras in Borchard's sense I know what the definition should be but I don't know if Borchard's quantum vertex algebras are interesting you know it's a full sub category not just the I think so yeah yeah I think so not 100% sure but any other questions sorry I did your job just


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