Hello, everyone, and welcome to the 9.30 a.m. to 10.30 a.m. session of the 2019 Open Stimulator Community Conference. In this session, we are happy to introduce a presentation called Guinevere, Learn a Language Through Games in Virtual Worlds. Our speaker is Heiker Philp from the Guinevere Project, and Heiker is the CEO of Let's Talk Online, SBLL, an Immersive Education Specialist for Language Learning and Teaching. She's a co-initiator of the EU-founded Lancelot Virtual Classroom and the Avalon Virtual World and the Camelot Project for Machinima for Language Learners, and then, of course, Guinevere, the Games in Virtual Worlds. She's also the founder of the Virtual Roundtable Conference, and she co-owns Edgy Nation in Second Life. For our partners on this project, we're unable to join us today. That's Michael Thomas, Tansir Khan, Leticia Chiganato, and of course, Nick Zwart, and we heard from them last year. Please check out the website found at conference.opensimulator.org for speaker bios, details of the sessions, and the full schedule of events. The session is being live-streamed and recorded, so if you have questions or comments during the session, you may send your tweets to at opensim.cc with the hashtag pound OSCC 19. Welcome everyone. Let's begin the session. Over to you, Heiker. Thank you so much, Leah, for introducing me, and thank you everyone for being here. I'm very delighted. I'd like to welcome you to the presentation about Guinevere, an EU-funded project which has successfully finished last month, after two years of working with the consortium of five project partners to develop the expertise on how to build language learning games in virtual worlds. The project partners, unfortunately, could not make it, so I'm here to represent the team, and since we do have a little time spare, I'd like to ask the audience if – hi, it's lovely to see you – I'd like to ask the audience for helping me to brainstorm how to learn a language in the world. And for this brainstorming, I have prepared a document which I'm going to share with you in the audience now, and it's been also shared on the live stream. If you could help me, just answer a very few questions, a little survey, just like how many languages do you speak? You can also type here this in the text chat. How many languages do you speak? Which language would you want to learn? Yeah, exactly. And perhaps, why would you want to learn it, or how would you want to learn it? And then we will do a brainstorming session. Whilst you are filling in this short survey, perhaps even write something in the brainstorming session, I would like to present to you what Gwynethil was all about. This may take approximately 15 minutes, so you have 15 minutes to fill in this survey and perhaps, oh, we are speaking one language. Thank you so much. And then I will come back to your answers. Hold your answers for now, if that's OK. Hold your answers for now, because in 15 minutes time after the presentation, we will look at these surveys and do a bit of brainstorming. Is that OK? But you can write in the Google Docs already if you like. So back to the presentation. Allow me to present our project partners. We had University of Central Lancashire in the UK with really a fantastic project coordinator, Dr. Michael Thomas, and his team, Sylvia Benini, Crystal Schneider and Carol Vainbaugh and others at the University. And we also had in the project as our partner, University of Istanbul. The University of Istanbul had a special kind of set up with an English department and the computer department next to each other, closely collaborating on Gwynethil. Under the lead of Dr. Tundra Khan, Irfan Zimsek, Mustafa Ilkham, who is a fantastic programmer and an app designer, and Marilyn Tejula and others in the team, especially their many teacher trainees who learned to become English teachers. Then we were blessed with having the Italian University line with Dr. Letizia Tsinganotto, Andrea Benassi, Conchetta Russo and an incredibly well-trained team of teachers who are working in research of using Minecraft and OpenSIM.  And then we were really, really blessed to have Mick Swart work with us and his company is called 3D Learning Experience Services in the Netherlands. He's an amazing programmer, a builder, a scripter, an OpenSIM developer, and he's also helped to install and maintain our Minecraft server. I'll talk about the different environments in a minute. Finally, myself, Haike Filp, let's talk online. SPL and Brussels have been an immersive language learning expert for more than a decade. And I managed to co-initiate a total of four-year-funded projects since 2005. These projects focused on language learning in real time via the Internet using virtual classroom technology and virtual worlds. They're called Lancelot, Avalon, Camelot, and Guinevere runs in that line. It's important for the project description. And also I ran the virtual roundtable conference, been doing it since 2009. So, and now we get to, sorry, this is the next slide. So I hope you see it okay. We spent two years in the following three virtual environments, Minecraft. And because that's from six-year-old, OpenSIM learners from 10-year-olds and Second Life, which caters for learners from 16-plus onwards, as we know, and it's been a basic lead for adults. Until now, we were only able to cater for adults. But now these two new environments opened the way for younger learners. New to us was Minecraft. We spent extensive time in Minecraft. We also had a lot of fun doing it. There was more time spent in OpenSIM, and that was really a great experience because OpenSIM has improved so much in quality, and we were surprised how rich and beautiful it is. Nick Swarth built Guinevere Islands for us. He set up two regions, well, it was a total of four regions, sorry. He set up two regions with an orientation pass, some clothes, newbies, castles, roundtable halls, medieval village, a team game island, and some gaming analytics in the database of a team game island. He did fantastically. Also, these islands are hypergrid-enabled and still available until February 2020 under the following address, world.guinevereproject.eu, 8002, double dot, sorry, 8002. Afterwards, we will use the OAR fires, but we do not know where to go as of yet, but I do want to keep maintaining these beautiful islands. They're so wonderful.  On the Sky Deck, there were a number of scenes for machinima role-play, such as a bar, a catwalk for fashion shows, a theme park, an artistic workshop, airport check-in areas, and they were designed for machinima, but also for providing couplable objects for our trainees. Nick also for an hour, that's sorry if that was the slide too quick, rather. Nick also provided our Minecraft server, oh yes, sorry, that was Minecraft, so that's it. Nick provided the Minecraft server, and Euclain spent a lot of time on preparing activities for the kids. These included escape room type games, vital paths to pick up words of the week, roller coasters, et cetera, but, I'm saying a big but, sorry, not designed to grow that much, but the kids did not really take them on. We found that this did not really capture the interest of the kids. They preferred to build script, use potions, res, mine, and this had a pace and ingenuity which simply left us baffled. Some of the activities designed by teachers for the field tests were very successful. When teachers let the youngsters rebuild fairy tales, like Hensel and Grapple, or the three little piclips, which was greatly successful even with the young ones, the very young ones. And then, we did have a games park in Second Life. We also had some project partners who created special games for that, riddles, escape room type houses, et cetera, but the activities were very limited and only really taken up by the participants of the self-study course because for the teacher trip, yeah, escape rooms. So the teacher led course, we decided to stay in open sim. And now we come to the outcomes of the project. Your funding means that everything which has been developed during the project is really available. And I proudly provide or present these giveaways. Look, can you perhaps type this URL in the text chat? It's your guinevereproject.eu slash deliverables. And these are called IOs or intellectual outputs and some of them are really, really outstanding. One of them is a brilliant work done by Crystal Schneider who worked as research assistant for UCLan. She created a document called IOs for categorizing of games which where she lists numerous games with images of the in-world builds. Try it, yes, thank you. She investigates their goal, teaching objective, skills required, then she lists the CEFR framework elements like speaking, listening production, et cetera. Created a table with categories for listening, speaking, conversations, open productions like announcement of speeches, reading and writing, absolutely stunning. Very detailed, she also added, she looked at other categories like narrative, recounting something, guessing, questions and answers, socializing and collaborative activities for just for fun. This document alone, which spans about 70 pages, is a treasure and you get it from the URL mentioned above. All of them are outstanding, yes. There's fantastic documents on the IO2, IO1 theory of game design is a meta study on gamification studies. A game design of global dissemination, a village report, again with lots of games, but more of a historical document. Guidelines for language teachers on security, sorry, I've not actually listed them in the speak easy half but check it out. So now, this brings me to the highlights of the project, a teacher training course on how to build games and there is those two types of courses, one of which is a self-study course and the other one is a teacher-led course. The self-study course is freely available and modal and the teacher-led course will be offered commercially as from next year onwards. Again, learn.guineverproject.eu, if there's a chance you can paste this URL, sorry, being unprepared. Then we do have an app which is fantastic, developed by University of Central Istanbul, sorry, by Mustafa. It's called Gistory and it's not history misspelled, it's Gistory, sort of, yeah. The Gistory app is designed to take images that teachers provide and the images would be, images from in-world or other narratives or whatever and you can build little stories that are interactive which request or require the learners to, at one point, it didn't work, okay. It should work, it should still be around. Guineverproject, yeah, okay, thanks a lot. And the app itself is free, you can edit the app on the mobile device, add shots, add images, add activities, add little stories or chunks that could then be framed in an interactive story type app, beautiful. It will be out on the Play Store very soon and the Play Store will be the Google Play Store and the iOS version. Oh, thanks a lot. Thanks a lot, Steve. Yes, yes. Lovely, Lea. Lea Types, she wanted an interactive session, so you're doing well, contributing the links. Fantastic. So allow me just to spend a couple of minutes in showing you what kind of type of games were developed in the pilot project. So the one at the top left, the small image that you see with the poles, the UK poles sticking out, is a map of the UK with these poles indicating cities of the UK. The interesting thing about this, Lea was designed and created in Blender and then imported into OpenSim by one of our language educators who is here in the audience. And yeah, Lux, but yeah, amazing. She learned all this Blender stuff in crafts. Yeah, right?  Amazing, Lux. And what does that map do? The top of map is created in Blender and imported into OpenSim. The game is dynamic and the bumping into the cylinders triggers a script that names the city. Interacting with the map helps students complete these web-based activities. Clever, fun and effective, ingenious. Then we had an Alice in Wonderland hand and image sort. A wonderful Jesher cat-based hunt and image sorting exercise that tests understanding of the storyline. They're asking the students to sort the images from the original illustrations in order. Then we had a board game, a hand-drawn game with a variety of elements and this game is notable both for the hand-drawn board and the variety of different types of activities to engage the students in language practice. The variety of what they design tasks, including listening comprehension, using embedded video and audio clips would keep any class engaged. The bottom right, you see a mysterious forest maze. The mysterious forest maze is a great example of how important setting the stage is in a virtual world. This is a very inviting woodland walk, peppered with clues and puzzles to be discovered and solved along the way. The same puzzles in a more basic maze design without the forest theme would still be fun but probably not have the same impact. Then we see a memory game. This memory game is an example of what can be done with a traditional game in a virtual world that couldn't be done in the classroom. As soon as the student matches the correct image, the game tells the player in chat that is correct. If incorrect, the cards quickly revert to face side down to indicate the student needs to try again. And here at the bottom right, we see the Bank of Japan simulation. This role-playing game allows players to interact with bot tellers to ask for help and the right forms. To interact with the ATM machines to practice, recognizing which buttons need to be pressed to initiate different transactions. Which is a great reality-based simulation provides a wonderful practice opportunity. I also, sorry, I don't have an image for that. We also had an academic research game designed by two participants who were played by teams of player. Beautifully interesting was that, once it was in the language learning activity, it was based on a pyramid and you actually had to walk up a longer path to get to the very top. And the activities included several challenges but also fun stuff. Like sometimes the bot would actually just be allowed to stand and be animated for a dance. Most outstanding, and I tell you this was so impressive, we had unfortunately only one participant in Minecraft but that person seemed to have spent the nights in Minecraft. She designed a game in Minecraft that is almost on the basis of an adventure type game. It was, you had to, you entered a house, see that at the very top a little bit, you entered a house and in the house you had to really look for clues and the thought of it was that Dr. Morrell was missing but nowhere to be found. And eventually you could find some clues that would let you know that there is some location in the basement of that house. Now even to find the staircase downstairs which was under the carpet was not as easy. I think I would have spent a good hour just in the house looking for the next path which is what the idea is in an adventure type of game. Team playing game as well. So a escape room type of game, very good. So then you went into the basement of that house. This lab was filled with strange creatures. The whole lab was filled with mobs and skeletons and spiders and squids. And if you landed in the water you got killed. If you accidentally opened one of the creatures then you got killed. So the whole lab in the basement was so strange but it put you in the frame of mind that this Dr. Morrell had a strange way of working with these creatures or he was producing creatures or taming creatures or whatever whatever it was glorious can be. Now eventually after a lot of trying to search for clues you then would be led to again a ladder which goes way baby down. And in the last basement you'd find a portal to the nether. And then through that portal you ended up in Neverland and that's where you find Dr. Morrell sitting in a cage. The adventure type game itself was so, yeah, absolutely. And the adventure type game was so sophisticated and it also included all of these builds. So the house needed to be built, the basement needed to be built, the creatures needed to be rest or tamed or cored or whatever, whatever. The squids and it was so funny. It was absolutely stunning, absolutely stunning. This is the power of Minecraft we were at all. So this is just an impression of what we learned, what we had to, yeah, what we experienced in this virtual world and in the Gwinniver project. So what we have for you, the audience is a lot of giveaways with the deliverables, the IOS that you can freely download from the website. What we have for you is the self-study course. What we have for you is even an app and I invite you all to take it up. But now we'd like to do a little bit of a brainstorming session. We do have for this about 10 minutes, 10, 15 minutes to do. It was mentioned above in the one big, so if you go to the www.winniverproject.eu website and then click on deliverables. And there you will find the whole list of the so-called IOs, which are the intellectual outputs, starting from I01, which is the theory of game design study, a beautiful study, a meta study on a gamification document. So this starfarer asked, he says, I'd like to apply this approach to learning Icelandic and space pioneers grid with a pathway to old Norse. Now this brings us beautifully to the challenge, which I would like to give you, which is at Google Docs inviting you to think about how you would like to learn a language in virtual worlds. And I'm turning my attention to the Google Docs already and the first question that we asked was how many languages do you speak? And we see it's an anonymous survey, so we see that a three and a one and a one and a half, one and a half, that's lovely. Two active and two more passive ones, then we see a lot of one, one, one, one ones and one person put down the number four. So speaking four languages, that is amazing. And we see another number two. So that was just to get an idea of the audience of how many languages do you speak? Because we do have an American-based audience mostly, and if you did that survey in Europe, then you would come to different results. So now the big question is, which language would you like to learn? That was question number two. You wrote down, thank you so much for filling in this already amazing Spanish six, German two, Portuguese, oh, somebody's actually, somebody's actually collected already the subtotals. That's wonderful. So six people in the audience said they would love to learn Spanish. Two said they would love to learn German, one Portuguese, one Serbian, one Japanese, one Russian, one Hindi and one Icelandic. I guess that was you, Steve, that's the starfara. Sorry, starfara wants to learn Icelandic, fantastic. So why would you want to learn this language? Because China may rule the world is one of the reasons. That was important to know the reason for it. So, and near Mexico, that's why you would like to learn Spanish. That's fantastic. Another reason is mentioned because Austria is so close to where I stay, so some person wants to learn German. One of the reasons also mentioned was, I know many Spanish speakers, that would love to speak Spanish, fantastic. Another person mentioned to speak with family who lives in Serbia. And these ideas were written down from the beginning of this talk, basically half an hour ago. Thank you so much for filling in this Google Docs whilst I was presenting about Guadalajara. So another reason is given. I like to connect with people, ideas, cultures from around the world. And I just enjoy the process of learning a language. Oh, that's a lovely, lovely thought. It is one of the primary languages spoken in our state, which is the US. I have many friends and colleagues in Brazil I would like to do, to more easily interact with them and then when traveling in Brazil, so that Brazil is Portuguese. Spanish is becoming a de facto second language in the US to learn Old Norse, the Viking language. Brings me to the thought in Duolingo, you can learn Plingon, haven't you heard of them? To participate in, sometimes it's just fun, you know. To participate in diplomatic and scientific developments for the world's largest developing population in India. That's here, wonderful. And we're still, people still fill this in, that is amazing. I'd like to also encourage you to fill, well, to write things down if you want. Here in private chat, sorry, in public chat. I'm happy to read this for you. Hey, Heiker, we had a question from Lisa. Have you made considerations for people with speech or hearing disabilities in language learning and include both audio and visual cues for every aspect of the virtual world games? That is a fantastic question. Lisa, ask that, sorry, who asked that? Going to Dynasty. Oh yes, Lisa asked that.  We have not actually catered for what we call special educational needs, S-E-N. And in the project, that was never a topic. Basically, the answer is no. But I would like to check this out, Lisa. I'd like to sort of also perhaps consult with Crystal because she was the one who did a variety of games categorization. Perhaps she has come across some who would cater for one or the others, for those visually impaired or auditive impaired. Is that okay if I come back to you on this one, Lisa? Thank you so much. Now I'm turning again my attention to the Google Docs, but I would also like to, well, the next question was, why do you wanna learn a language was one of the questions, but the next question, equally interesting, is how would you like to learn a language? Now, immersion and lessons, immersion, books and videos is mentioned. Immersion, immersion with speakers. Immersion definitely is mentioned a lot through participating in 3D immersive communities. Immersion games and virtual worlds TV. With the immersion virtual worlds more practical. Immersion with speakers, my word. A variety of technologies, games sounds a fun way, but also with help. Awesome, awesome. And more is mentioned now under the brainstorming session, but let me stop this here and just turn my attention again to the public chat here in world to pick up some of the comments. Well, we're mostly talking about accessibility and then I repasted the Google Doc link for those who are joining the session in progress or you're on the live stream link and you're wondering where are we, we're looking at this shared document. Back to you, Hiker. And I think some of the volunteers in the background to also helping me collect this information from the live stream, because we want to also hear from the folks who might not have made it in work, but interested in what's happening here. Well, and I'm just picking up a comment in the live, in the public chat. When I visited Venezuela, I remember the signed alphabet different from the American Sign Languages Alphabet. And for the, well, the reason I commented that was Lisa was asking about accessibility and languages. And I know that in the Guinevere project, you were thinking you had a lot of diverse folks and languages. And I remember from the conferences, because I've spoken at the virtual round table conferences that what was beautiful about this is how culture and society and language and gaming and behavior all came together. So Lisa's question about accessibility is critical. And when I thought about something like the sign language for accessibility, and of course, one of my students worked on a sign language interpreter where you could gesture with your hands and a camera would connect essentially would interpret what you were gesturing. And then it would translate it over to an app that would then sign. It would do text messaging for you. And then he was working on a second life component for it or an open SIM component for it, because we were using open source. But the notion of bringing that into the virtual world. And of course, our challenge was having enough fidelity for the fingers, right? For the gestures to be able to do that. But so when I think of language, and I think of like when I traveled to Venezuela, I didn't speak the language when I went. And of course, some folks were a little hostile to Americans. So I had to be quiet, right? And I'm never quiet. Those of you who know me. So I started signing, not realizing that our signs are different. And of course they started teaching me, yeah. On the fly, because I was there for two months with no credit card and $75 in my pocket. So I was living with family and traveling across country and I had to be smuggled because of course, like I said, they weren't really happy. But I was determined to experience life and language at the heart of it. And of course, that was an eye opener. So for Lisa's question, even our sign language is different. And of course across America, every city has like two or three dialects. But even the basic language for the alphabet is different as we go to other countries. So I noticed that. And I think that's an important point. Back to you, Heiker. Awesome, awesome. What an experience. And thank you so much for just that thought sign language that can be interpreted lovely, lovely thought. I'm also looking forward to once the voice recognition is so far as that you can put a mobile phone on a table with somebody who's hearing impaired and the others who aren't. Like they're chatting, they're just talking normally. And then the mobile phone would just transcribe what it hears for the person who's hearing impaired. That's the one thing I was really also looking forward to. But let's take the thought of wanting to learn a language in an immersive environment. And here is what I would really, really like. This fantastic audience to help me create because the question of what next is very important. So I'm just going to show you what my dream is and I invite you to share your expertise. Now, this is, sorry, a broad image of the Europa Park in Germany and West. It just symbolizes the kind of, well, language games park that I would like to create in open sim. And a language games park would have like a corner for learning Spanish or a little tiny little village to learn Japanese or maybe a tea ceremony house through to learn Japanese. Or it would be a Chinese or the great world to learn sometimes just some visualization, obviously of the culture. But I can also imagine that this open sim community that I'm seeing in front of me, the fantastic experts in designing, creating, scripting, game design experts, likely. It's for example, and educators of a magnitude that is way beyond of what we language educators could even even dream about. Perhaps even AI programmers who could contribute some chatbots to this global village that I would like to create in open sim. So here's the image of the games park or the language games park that I would love to create for also perhaps in open sim to be something like a magnet for newbies, for the public, for people like who just want to be around and perhaps watch a film in Spanish. Maybe attend a tea ceremony in Japanese. Maybe learn some Spanish Samba or Brazilian Samba or Brazilian dancing or just do an also reading type of activity where somebody reads a book in English. So perhaps some of the librarian to present here would like to contribute their expertise to this village or global village or language games park to provide what's known as what we call graded readers or some publications that are suitable for language learners. We can all contribute if you would like to share with me in doing this our design thoughts, ideas, experiences. We could start building, yes, cyber serenity. And perhaps we all bring together that which in open sim, each of one has created as an educator and provided for their learners on their sims. These could be some chatbots, these could be something but something to learn a language. Thank you, librarian. Yes, culture, collaboration, but also perhaps simply something like get together. I would love to have this run events. So for example, imagine this, Monday is the Japanese day and then on Monday we have lots of activities to learn Japanese and in the afternoon, we learn Japanese and everybody who is in the Japanese region, you know, this area of that global village, is asked to either try to speak Japanese or try to understand Japanese and all the language that's spoken is Japanese if at all possible. Hopefully some translation tools will help us here. What about Spanish? Then on Tuesday, for example, we learn Spanish and all day we can immerse ourselves in this maybe Spanish village, in the global village and then speak Spanish, hear Spanish, listen to other speaking Spanish, watch some films during Spanish, listen to radio stations Spanish, speak with Spanish native speakers. Contact with the stone, yes, for funding, that's okay. Soon too, provided that thought. Are you wonderful? I hope you join me in building this language games part. I will invite the language educators in my team. I will invite those who will be the future trainees of Guinevere. I'll invite everybody who is in immersive to provide this cultural experience. So we are close to ending. So thank you very much for helping me to brainstorm this. If you could perhaps continue on that Google Docs and I would like to share then more links on that Google Docs that pertain to what we have already today. And this image should be a copyrighted image but perhaps just the thought. Now questions to you at the audience, please feel free to just mention what you think about it. So Sun adds a comment about, this is why immersive learning may be the best for this. So now the question is, are there any questions from our audience or anything you'd like to add to this? Any thoughts from your experiences in the community? And while we're listening to our audience, I wanna thank you, Hiker, for a fantastic session. Did you have anything you'd like to close with before we wrap? Yeah, I'm just waiting for some comments from the audience. Immersive learning is what I'm imagining. It would be wonderful to have, say in the Italian part of that village to have some speakers in, some English speakers who want to learn Italian and some German speakers who want to learn Italian and then mingle, mingle in this area. Lisa, thank you for your input. Since I haven't talked to Rosetta Stone as of yet. No, but I might do. I'm quite good in getting funding from the EU so far. Let's see what else we can generate from the industry. Did you see that? Oh yeah, James asked a fantastic question. How do you think VR headsets would affect language learning? Well, if we could create these immersive experiences, so far I've heard yesterday that the possibility to export open sim to create immersive experiences in a Google cardboard type of VR headset are still not multiplayer. And for language learning, you need multiplayer surroundings. We need to communicate. We need to talk to each other, listen to each other. So I would like to work on bringing people together with the same goal, the same goal of learning a specific language. And if I manage that, I would be very, very happy. Sunsu says it would be a great way to get more people in these environments. And I totally agree. That's my goal. I would love to see a lot more people here in this conference who are just here for the first time. Yes, there's some on the livestream, but not enough. We want people to listen to us. And your translator and AIML server paths can combine Guimisa with Lisa. I don't understand that very much, but she'll explain that to me. We have one question. Oh, right. I think we need to wrap on this last thought here. Lux had asked about, since the Guinevere project is no longer funding, it's completed. What's in store for European teachers? Do you have an event that's coming up in January or February, or when's the next conference? Yes, we do have an event, and that's the Evo Sessions from mid-January until mid-February. It's called Immersive Language Learning in Virtual Worlds, and it's a tour through various virtual worlds out there with the goal of evaluating those worlds for language learning affordances. And we do tour all sorts from Minecraft, Second Life, OpenSim, various OpenSim regions, World of Warcraft, and even Fortnite. So, I hope you come and join us for the Evo Sessions more tuned. Thank you, Hiker. And I wanna thank you for a terrific presentation. As a reminder to our audience, you can see what's coming up on the conference schedule at conference.opensimulator.org. And following this session, the next session will begin at 10.30 a.m. in this keynote region, and it is entitled Into the Future Web-Based Virtual Worlds. Also, we encourage you to visit the OSCC 2019 poster expo in the OSCC Expo 3 region to find accompanying information on presentations and explore the HyperGrid tour resources in OSCC Expo 2 region, along with the sponsor and crowd-funded booths located throughout all of the OSCC Expo regions. And let's see. Check on the schedule just real quick to make sure I was correct on that. Actually, it's Dieter Hain. Yep, with Into the Future Web-Based Worlds. Thank you and have a great conference.


good morning guys happy february 20th it is a wednesday i'm about to head to my internship and i work until two and then later on my friends and i are going to wind down wednesday we're actually going to a different place we're going to selene um it's just a bar downtown but usually we go to i think it's called cella yeah pretty sure it's cella the selene's starting their wind down wednesday this wednesday so it's pretty much like the grand opening um and we have a sister who used to work there so she got us on the list for free cover the past weekend i had a couple people asking me where i got this wash band and i got it off of amazon and it was actually pretty affordable compared to the ones that they sell in the apple store um i actually got it tightened at a jeweler but it was only like five bucks um so i'll link this watch strap below and i'll link a couple other ones i got a lot of like apple dupes so they were pretty cheap they were like under 20 or something the other ones are more like sportsy this is like a band that i put on my watch when i'm like not working out when i'm just trying to you know look bougie and stuff so i did it i got ready within the time i actually got to ride a little bit later though like 30 minutes later we're actually going to go to our sister's 21st pregame before we had to selene wind down this is what i'm wearing in case i don't do a full ootd um i got this from forever 21 and skirt from boo-hoo we're at the chyler's pregame it's mangan's little so it's our first time i mean right now so here are our goats they're not on billy's there's a lot of them so um we're not on the stage i'm like i'm like i'll be done okay okay cool now there's a lot of them show your signs chyler's life saving 21st but i'm gonna need the light so you can see them up here it's all we've got we did it we did it so we're mouthing i like this kind of dress you're kind of similar like a minecraft right? yeah i like it i tried to really do tans but you look really good really? do you think it looks pretty tanned? i put some tanner on top of my old spray tan from this it looks good it's kind of like it looks like you just came back from the spring break or something my friends there um i'm gonna take some photos of them while they eat and just like you know some lifestyle shots to have for the app and the instagram um just get content and stuff like that so it should be fun and then i have to film which it looks like it's gonna rain and i wanted to film it outside so i should probably do that like should probably check the weather i have to do like a selfie video for an instagram post about seven days of giveaways for next week oh it looks like it's going to be sunny today but it's like literally the darkest clouds oh just kidding i see a little blue i didn't put on makeup for this just because i didn't have to be in the photos but later when i'm filming the video obviously i want to look good because um this video will be showing like do a lot of people winds up wind down last night was really really fun i got home and everyone was asking me like what would you choose like cella or saline i feel like i would choose saline just because there is like a rooftop so that's really cool and then they also have like a dj and a dancing um like dance floor um and cella doesn't really have that cella is like just more chill i don't know but like saline i feel like is a little bit more hype and they had so many cool things like cotton candy they had like literally so much food and i'm pretty sure they got it catered and usually cella does too but it's like bland ass pasta and like a wing and plus at cella they serve you so they are very stingy with the food that they give you but we served ourselves at saline so i guess we could honestly get as much as we want but if you guys do go to ucf or rollins or are in this area then i feel like you should definitely try saline's wind down it may not be like that grand because it was pretty much the grand opening so i don't know if they'll have all of that every single time um so i'm kind of curious to see like if they will because then i'll definitely go to saline over cella and also cella is like mainly outdoors and when it gets really hot it's kind of like uncomfortable because they don't have a lot of seating indoors and they make you like pay for tacos if you're actually getting a table and sometimes we would just like pay for a taco just to sit down so i don't know i feel like saline is better but i'm gonna go ahead and get all my weights kikis and meet my friends good morning good morning right kikis we're picking out what we want yeah all i hope to serve us some free breakfast hell yeah i think i'm gonna get the eggs benedict that's what i like usually always get and like all the um sweet stuff sounds really good but i'm just trying not to i already got you look at don't look at her jelly just talk to each other which would start again like a nice that's right everyone smile smile more take some butter okay i just got done with breakfast and i came home to an amazon package which is weird because i usually send all of my amazon packages to the amazon ucf store so i really don't know what i sent here but i guess we'll find out together oh okay well basically this is a graduation set so i can start taking pictures of people earlier than april because i think it's only maybe a week or two weeks i wouldn't even say two weeks before graduation that the seniors get their grad cap and gown but i'm personally graduating myself in april and i know i have a lot of projects in april as well so i don't want to do everyone's grad pictures just in april so i'm trying to do like majority of them in march so i bought a set so that we can start doing everyone's pictures in march so that's what this is i don't know why i didn't send this to the ucf store but whatever at least i got here i'm about to do my makeup um and just get ready for the day i have to film a set video like i said but it is so hot outside right now that i'm probably gonna die while i'm doing it but i have to do it like now so i can you know edit it throughout the day um it shouldn't take me that long but i feel like i always say that and then it takes me way longer than i think so i'm just gonna try to do it now and then get to editing it so for the longest time i think it was like over Thanksgiving break and winter break i started using the l'oreal pro mat actually i feel like it's been ever since summer but i'm not really sure um and i decided to pick up the nars foundation i used to use the shear glow but i ran out and i wanted to try the the natural radiant longwear foundation so that's what i'm using today i do like the shear glow better just because i feel like the formula is um different like that one is just a little bit more dewy but this one is more full coverage so that's why i wanted to try it out so to make myself look dewy under this more matte foundation i use this um Elizabeth marten all over miracle ill and i just put it on my face before i put the foundation on so it gives me a little bit of shine just under it all right guys so i'm outside um i came back like behind to my sorority house so i'm currently facing like claire and my and the katie house is behind me um i wish katie like had one white wall where i could like film like videos and stuff but they don't um and i obviously don't want to film in front of like a green wall especially for like a zup video that's like not their color at all so i came to this pretty plant out here and the lighting's pretty good so should be a good video um it's a lot to say though so i have it all in a google doc right here and hopefully i can do this i get really really nervous a lot of times when i'm filming these videos where it's like scripted because obviously you want to say exactly like the script because you don't want to like mess it up or like sound like weird or like miss a word or something like that there's also a lot of people walking around which i didn't think would be a thing because i don't know i just didn't think that there would be so many people but it makes sense because all the classrooms are on this side and all of greed grows on this side so they obviously have to walk home but anyways i'm gonna start filming um wish me luck because i'll probably be out here for forever trying to get this done hey y'all it's nally from zep and i have some exciting news to share with you all the zep community has officially reached 7 000 zep members here at ucf and we are celebrating with seven days of giveaways seven days seven giveaways and more than 70 in savings for you and your zep member friend enjoy free food free cover and exciting surprises all week long exclusively with zep the celebration starts on monday with free burger pie be sure to share this post with your friends so you can enjoy the giveaways together and don't forget to tag us in your instagram stories when you redeem these giveaways thanks for being a part of the zep community if you love the zep app feel free to share it with your friends using the link in our bio all right guys it is 221 not sure when i started but holy shit that took forever this guy's hammering something there's like cars like driving all by me and buses driving on that road it's just not the best sound quality so i was trying to like wait till all this like died down a little bit but i don't know it just took me forever because i just kept getting distracted with all these people but i got this stuff got the content gonna go edit now i feel like i should go to the office but i also never like get to just chill at home and just like work on my computer so i might do that because that sounds you know like it's calling my name but we'll see hey guys happy friday today i'm in the same shirt um because it is a zep day again so i'm going to jimmy holis to get content for the app and the instagram and everything else um and then i'm also going to go to bento today to take pictures um but that's a little later so i'm doing this right now gonna meet up with my friend at meal plan come back to katie and get the day started so here with tiff love it's my roommate because in now um i'm going to bento to take pictures there and i didn't want to be allowed so i brought tiff they don't want to look weird because there's like a lot of people at bento like always especially since it's friday so yeah everyone's at happy hour and yeah they'll probably go after they don't want to be like who the heck is this up girl yeah i told tiff to wear her is up tank top so she could be a t-shirt model in the back we've been pretty like bed ridden all day we took naps yeah i did take a nap i wanted to take a longer nap but i was just like playing on my phone and i was like just take a 30 minute nap you never take naps so i didn't even like really like feel sleepy but i was just like i have time i guess so i just did you know we're trying to get things planned for like senior week and we usually have like a senior bar crawl and all that so like it's really scary because like it feels like i think it's like eight weeks away from graduation right now yeah it's like the beginning of the end it's so close so but like you don't realize that i know it doesn't feel like that yet it is not going to hit me until like neither is in another state yeah like moving home not even even then i feel like that's how everyone was like last year too like yeah no one started crying yet yeah like that because it's like until you're physically not all together yeah yeah yeah the next one it kind of hits you yeah and once we're like back in our hometowns that's probably when it's gonna hit me i know tiff's probably going to go back home right to tampa i'm gonna go back to tampa and we will see to be determined yeah to be determined hopefully freaking soon so i can start looking for a job so we're at bento right now we got the goods creamy chicken spicy noodle bowl sushi boba tea Thai tea we got it all and we're taking pictures outside because natural lighting is the best so it's really helpful when restaurants have outdoor seating so i can do that because then i don't have to worry about using flash because that's just awful i don't know food photography so doing this giving some contact good morning guys it is saturday and today i have a meeting with the ucf social media ambassadors so we're going to meet at the student union and talk about future projects and stuff like that before i go i'm gonna fill up this water bottle and i forgot about line bikes because i was like damn it's gonna be so hot i'm gonna be sweating outside i'm walking and stuff like that to the student union which it's not that far away but you still get really sweaty really fast here but i'm gonna take a line bike so i won't be outside as long it is three o'clock and the meeting is over it got out of like two-ish um and i'm sorry i didn't get any footage at the meeting i really thought i would but it just went kind of quick and the lights were off so i didn't really get that much or any but today was a big um phone calling day i literally called my whole family pretty much my grandpa my grandma my dad my mom um and kind of just updated them on some stuff um so every time like i would walk to or from somewhere like on campus i was like on the phone and i didn't have my vlog camera out because it was in my backpack so i tried videoing on my phone and it didn't work because like it doesn't work when you're on the phone so i was like damn whatever so i was trying to get b-roll but i couldn't i was planning on going to a coffee shop afterwards but i don't know sometimes like when i don't have like a buddy to go with sometimes i'm just like i'll just go home because i like to take advantage sometimes of working in my bed if i can um i know that's like not the best but usually i don't like fall asleep or like take naps that often so i actually like do good work in my bed i think i'm gonna do a little bit of editing because there are like i think three videos that i have um that i have not edited yet and i've had them filmed for like literally three weeks or four weeks or like two months i don't even know but i definitely need to edit those because i can just get them up real quick for you guys one of them is my assumptions video so hopefully that will be out before you see this video but no promises the last time i opened my assumptions final cut pro folder was February 8th it's currently February 23rd so that's awful of me gonna try to get this one done today um and then i'm gonna go get dinner with my fam later so you guys will see a little bit of that hey also it is currently 6 p.m and i'm waiting on my g-little to come pick me up um because she lives like that way and fresh kitchen is that way so i was like oh could you just slide on by and pick me up i could tell that like it's getting like a little humid on the camera oh i hate that during grad season like in the mornings it will be so humid that my camera has to like adjust to the humidity for like five minutes it's so annoying i'm actually really starving so i'm gonna eat one of these kind bars just to like hold me tight until we get there like it's not even that far but i feel like i'm just really hungry and i cannot wait any longer instead of editing my video i chose to kind of go over my resume and kind of fix things because my boss is amazing and she edited my whole resume and she gave me like advice and stuff like that i definitely need to add more and i think i want to make it cute because of a lot of the jobs i'm applying for are like more creative and not like you know business professional i don't know i've just heard that i should probably make it more cute if i'm applying for a creative job so it's been a while but this is my g-little and my gg's about to come join us in the car yet i'm hannah i've probably been on a couple other videos it's been a while yeah it's been a while we're missing a gap in the family my little is currently living her best life in madrid spain so it's so sad because it's like my last semester you know but like last semester was your last semester with her yeah yeah and it didn't hit me because i know she was saying that too she was like it's weird like this is my last semester with senali yeah like nothing ever hits me but i really want to come back for a one month recruitment so like like in august like this year yeah because i don't know what one else i will like see valentina and y'all again you know what i mean yeah like i feel like that would be that'd be fun to like reunite and stuff like that you should surprise her well i mean well i don't think she watches my videos yeah maybe she just like won't play this one or if she does she does but yeah try that'd be fine yeah i think i want to like do like a whole seniors like reuniting like i know it's gonna be like what three months after you graduate but like i think it'd be fun to like get an air bnb and like go out and stuff hello how are you good how are you i just want to go from a nap i'm amazing i'm carolina yeah and i'm hungry yeah i'm starving i just had to eat a granola bar because i don't think i could wait yeah i was like i had like a snack when i got home and i was like it's a whole meal for till dinner and then like 30 minutes later i walked right downstairs and i have to get another snack yum yum yum hey guys happy sunday it is currently 8 a.m and i am about to do my first engagement shoot ever this is honestly a really exciting day because i've been wanting to just dip my toes in just like the wedding industry as a whole i haven't shot at a wedding yet um but it's definitely on my to-do list like bucket list for you know my life um and i i don't know i just want to see how this goes and if i like doing couples portraits because right now i only really do graduation pictures that's super fun at all but i like barely have any boys on my portfolio so i definitely want to get more boys on there we're supposed to meet at nine at harry pilu gardens i think it's in winter park um and i've actually heard so much about it ever since special year so i'm excited to finally be going i still need to do my spring break shopping we're like two weeks out now three weeks out i don't know something like that and i definitely need to get on that i have so many things in my car like at every little store like nasty gal boohoo i even have some stuff on dope from like a bunch of stores i just can't get myself to like press the buy button because i don't know it's just like so expensive our clothes so expensive i just can't get myself to do it and i also am ordering like graduation dresses and stuff like that for grad pics and i obviously want them to be like nice quality so i'm like telling myself okay like it's fine if they're like fifty sixty dollars but that just hurts me so much inside but i don't know we'll see how they fit i mean i hope their return policies are good just because i don't know how it works on dope because it's a little bit hot out here it was definitely like perfect in the more early morning but now it's getting a it's getting a little hot this place is amazing if i were to get married in or i know this would definitely be my dream venue it is like this tropical wonderland it is beautiful flowers everywhere like so cute i'm definitely seeing the most perfect palm trees here she's so cool just wrapped the shoot i hope i got like a lot of footage of the garden itself because it was amazing it had literally everything you could think of like tropical palm trees the moss flowers like literally so much and it was like the most perfect place to take these engagement photos so i'm really excited to edit them follow my photography page if you want to check them out but right now i'm going to go to stardust because i'm going to film something for my sorority really quick and then probably head home after that just because i really wanted to take a nap um before chapter i feel like i feel like i need a nap


Before introducing the next speaker, let me make a very short announcement. So for speakers, please, in case of questions, repeat the question for the benefit of the online participants. With that said, it's my pleasure to introduce our next speaker, Josh Green, who will guide us from ball feelings to cube timings. Please. Thank you, Andras. Thank you all for being here. I think I've been more excited to attend this conference than any I can remember, at least in my recent memory. So I'm very glad to be here and to participate in honor of Tom. So the question I'll begin with is a well-known open-ended problem posed by Cassin and Herrera, I believe, from 81. And the question is, which rational homology spheres found in here and throughout the talk, I'm always referring to smooth manifolds. Which rational homology spheres found smooth rational homology for ball? It's pretty open-ended. The problem to take a rational homology sphere and determine whether or not it does or it does not, I don't know if that's a decidable problem. And directions usually given to this problem by focusing on a special class of three manifolds and attempting to answer a problem within that class. And starting point for the work I'll talk about today is a partial answer which Palleliska gave. Well, he gave a complete answer. So he solved the problem for lens spaces. And I'll quickly sketch what went into Palleliska's argument. If I have a lens space, it's the boundary of a plumbing manifold. So I take a linear chain like this and I put some integers greater than or equal to 2. And I'm taking the disk bundle of that Euler number over the two sphere and I'm plumbing a bunch of them together in a chain like that. And I get a compact, smooth, four manifold whose boundary, if I chose these according to the Hertzberg Young continued fraction expansion of P over Q, gives me a manifold whose boundary is this lens space manifold x. And if this thing happened to bound a smooth rational homology ball, then I could reverse its orientation and glue it on. And the result then is a closed, smooth, definite four manifold. So by Donaldson's theorem, I know what its intersection lattice is. Its intersection lattice is just a standard diagonal lattice. And it will have rank n, all of the rational homology is accounted for by the space x sitting within. And the intersection lattice on x, which I'm going to denote lambda x, therefore has an embedding into this standard diagonal lattice. So that places a constraint on what PQ can be. This lattice has to embed into the diagonal lattice. And if it doesn't, then you know that your lens space doesn't bound a rational ball. And that's practically a complete obstruction to a lens space bounding a rational ball. So this result, as far as I'm aware, was the starting point of a theme, which is that we have a problem at hand, say, to determine which lens spaces bound a rational ball. And there's a complete obstruction. Well, there's an obstruction which one proves is complete, which comes from an application of Donaldson's theorem and usually comes with a little twist. And the twist in the case of lens spaces bounding rational balls is that, although that's not a complete test, you have this trick of being able to reverse orientation on the lens space. And that'll bound a different plumbing. And then if it bounds a rational ball, then you're going to get a pair of lattice embeddings into diagonal lattices, a full rank. And it turns out that possessing those two embeddings is a complete obstruction to the lens space bounding a rational ball. So if it passes that test, then in fact, there is a construction to show that that lens space bounds a smooth rational homology ball. So that's a theme. And another aspect of the theme is that the examples that pass the obstruction, they tend to fall to a fairly simple iterative scheme or maybe not always so simple, but sometimes simple. And this was sort of the first instance of this I'm aware of. But it's a similar thing that comes up when you study which lens spaces arise by integer-dane surgery along a knot in the three sphere. And there the twist is different. It's coming from some information from the de-invariant floor homology. Another instance would be McCoy's work on alternating knots with a knotting number one. It gives a complete classification of those knots and a sort of a structure theorem for those knots. And it's again coming from an obstruction using Donaldson's theorem plus a little twist. And the result I'll describe today is a continuation of this theme. And in particular, I'm going to be interested in a broader class of three manifolds, branched double covers of alternating links. And I'd like to know which of those bound to smooth rational homology ball. So on to alternating links. Here's my main example for the talk. There I've drawn an alternating diagram of a link, alternating link L. And I can, this is supposed to be red, giving the diagram a checkerboard coloring. And I'm thinking of the red regions with the half twists between them as giving a spanning surface for this link. And I'm going to form the double cover of the foreball branched along a copy of this surface where I've let its interior sink a little bit into that foreball. So this is the branch double. I'll just think of it as the branch double cover of F. And what do I want to say? So that's a four manifold. And it fills the branch double cover of the three sphere branched along the link. And it's a very important four manifold. It plays for these links the role that linear plumbings do for lens spaces. And in fact, you can show, if you start with a two bridge link diagram, the four manifold that you get back actually is diffimorphic to one of these plumbings. So it is a strict generalization. And I want to understand this four manifold a bit, because it's such a key tool. So before telling you more about that, I need to tell you about the take graph. So the take graph, I remind you, I am putting a vertex into each region of the surface. And I'm connecting an edge two vertices if there's a crossing joining those two regions. I could have drawn on the surface itself. It's a spine of the surface. So this is g. This is the take graph of this diagram. And I'll tell you a two part theorem. First, if I'm interested in the intersection lattice on this four manifold, which I am, this is isometric to the lattice of integer flows on the take graph. So let me explain that by way of example. So the flow lattice is just the cycle space of this graph, which in this case, I see it's two dimensional, generated by the classes of these two cycles. And this space inherits a natural inner product sitting inside of the chain group, first chain group of the graph with integer coefficients, thinking of edges as forming an orthonormal basis. So in this example, the flow lattice of g I can think about as being generated by these two classes, a and b. And a, paired with itself, is 5. It's a cycle of length 5. b, paired with itself, is 4. It's a cycle of length 4. And a, paired with b is minus 2 because they overlap in two edges, but they point oppositely around the two cycles. So that's a complete description of the flow lattice of this graph. So this, and a generalization of it, is a theorem of Gordon and Litherland, I think, from 78. That's the first theorem I want to tell you. And the second theorem is more recent. It's the statement that this four manifold is what is called sharp. So that's a definition. And also, this is a theorem due to Ohspath and Sabo. I can't remember when exactly, maybe 2005. But I'll tell you more about sharp manifolds in a moment. But the defining feature is that whenever you have a definite filling of a three manifold that gives you inequality of the de-invariance of the three manifold in terms of the intersection lattice on the filling four manifold, you have an inequality. And the condition to be sharp is saying that those inequalities are all attained by some spin C structures on the four manifold. So you can really read off the de-invariant of the boundary directly from the intersection form on the four manifold. But I'm not going to go any deeper into that. What's nice about this is that it feeds into a theorem from some years ago, which states that if ever you have a rational homology sphere and it bounds a rational homology ball and it also bounds a sharp four manifold, then one thing you know is that the intersection lattice on x embeds into the standard diagonal lattice with full rank. So that's just coming from the argument we gave before, if that's Donaldson's theorem. But something more is true, namely that every unit cube in I n, maybe to stress, I'll say, because of the pictures I'll draw, with integer vertices, really just a unit cube, whose points belong to this lattice, contains at least one point of the embedded lattice. So as an example, actually this link that I'm carrying around, the branch double cover of this example link is the boundary of a rational homology ball. And let me convince you of that by quickly drawing the picture. So there's my link. I'm going to attach a band to this link right here. When I make that band sum, what happens is that that ring becomes free. Then depending on whether you're looking up or down, you can cap that off with a zero handle after having done your one handle attachment. It goes away. And after I do write a Meister move and an isotope, this is the 2, 4 torus link. And I can do that trick again of adding a band. And I'll get then a two-component unlink. And I can cap those off with zero handles. And by virtue of this procedure, what I've shown you is that L is actually the boundary of a ribbon surface, R. So R is a ribbon surface with Euler characteristic 1. OK? And when you have a link which bounds a ribbon surface with Euler characteristic 1, that is sometimes what's called chi-slice. And it's a fact that if you have a chi-slice link, you take the branch double cover of that ribbon surface, then what you're getting is a rational ball, which fills the branch double cover of your link. Good. So therefore, our theorem applies. And we should be able then to embed the flows on this graph thanks to this part of this theorem into the standard integer lattice of rank 2. So here it is. I want to embed flows on my graph into the integer lattice I2, which I'm taking an orthonormal basis for, labeled E1 and E2. So it labels the axes this way. And A has to map to some class of self-pairing 5. And B has to map to some class of self-pairing 4, which then together have pairing minus 2. And one choice that works is to map A to 2 E1 minus E2 and to map B to 2 E2. And so I'll map where those points go. So that's where B goes. A goes here. That was the image of A. That's the image of B. And then I can look at the sublattice that they span. So I'm always allowed to go 2 up or 2 down from any point that I've already marked. And I can also make a night move in any direction. Got one wrong? 2 down, 2 down, 2 down. And I think that's everything that would fit onto this. So there's my embedding. It turns out that this is a perfect obstruction as well for obstructing lens spaces from bounding rational balls. So you can show that for the case of a lens space, having your linear lattice embed in Euclidean space subject to this condition is equivalent to having both the lattice and the dual, so to speak, linear lattice embedding into Euclidean lattice with full rank. But I don't know an argument which goes directly from this criterion to a reproof of Liska's theorem. So I don't see a simplification. This condition is going to continue with us. We call this condition cubiquity for the reason that the lattice embeds in a way that's sort of ubiquitous from the point of all the unit cubes. You hit each unit cube in at least one point. Pause for questions and to collect my thoughts. Yes, the question is what is the idea of the proof? Josh, the idea is that, OK, so you're going to get a bunch of spin C structures on this four-manifold, when you do C1 squared minus B2 over 4, you're getting V invariant 0. And this four-manifold's intersection lattice embeds into the Euclidean lattice. So you're thinking, which characteristic elements in the Euclidean lattice have self-pairing squared minus rank over 4 equal to 0? And those are precisely plus minus 1 vectors. And so the way the criterion comes out is you find that every coset, if you look at characteristic elements in this lattice, modulo 2 times this embedded sub-lattice, each one of those cosets has to contain one of those plus minus 1 vectors. And then you massage that into saying that actually every coset of the sub-lattice in here contains a point of the unit cube based at the origin. And then that ends up, I'm actually going to want to use that in a moment. And then that ends up being shown to be equivalent to having every unit cube possess a point of your embedded lattice. OK. So on the basis of that, the fact that it does what we want for Lenspace is we have a conjecture. So L is alternating. And if I don't say it, it would always be non-split. And if I'm ever talking about a diagram, I'm always coloring it according to a convention that the red surface at every crossing looks the way it does in this diagram. So I'm suppressing that. But the conjecture is that we have a complete obstruction. So the branch double cover of the link bounds a rational homology ball if and only if the lattice attached to the link which I never really defined. But it's this lattice on the Gordon-Lutherland lattice, on the Gordon-Lutherland manifold. Conjecture is that cubiquity is a perfect obstruction to bounding a rational ball, meaning admitting a cubiquitous embedding. But we don't know how to solve it yet. And what I want to do with the talk then is to give evidence in a special case. One special case is solved. Those are lens spaces. And I'm going to go to kind of an opposite extreme in a sense. So to get there, note, if I have a lattice which is already embedded in IM, is a sublattice of IM, if this is cubiquitous, then as I was explaining, every coset inside of IM has to hit the unit cube at the origin. So that means then the number of cosets is bounded by the number of points in the unit cube, which is 2 to the n. And this quantity is almost a quantity called the determinant of the lattice. The determinant of the lattice would be the index of the lattice in its dual lattice.  So this index is actually going to be the square root of this determinant. So that means if I take the determinant of lambda and I divide by 4 to the power of the rank, that's less than or equal to 1. It has to be a somewhat dense embedding. So this is a quantity that just kind of naturally pops up for us. And it probably needs a better name. But for purposes of this talk, I'm just going to write it like this and think of it as kind of a renormalized determinant of this lattice. And yes, what is the index in that example? Anybody care to answer? How many points per unit volume are there? There are a couple of ways of proceeding. You see in every unit cube, there's actually a unique point. So that's suggesting maybe the answer is 4. And you can confirm that by taking the gram matrix. The way you calculate the determinant of a lattice is you take a basis for it. You make the matrix of inner products of the basis elements. And then you take the absolute value of the determinant of that matrix. And that's 16, which is indeed 4 squared. So this is kind of an extremal example, which will where we're going. And so based on this, if I have an alternating link L, I'm just going to define the normalized determinant of the link to be, well, just the normalized determinant of its associated lattice. And in terms of the picture of the link, well, so this is the link determinant, but then it's divided by something which is kind of not really a good invariant of knots or links. This is going to be the number of red regions. I'll try to write it a little bit bigger. It's the number of red regions minus 1, 4 to that power. So it's very sensitive to the coloration of the link used. If you take the mirror link, you'll get something different because there's no relationship between number of red and black regions in general. So there's a little corollary, then, that if you looked in some link tables and you wanted to know which branch double covers of some low crossing alternating links bound rational balls, one thing you could do is to calculate this normalized determinant. And you see that if that normalized determinant is bigger than 1, then there's no way that that branch double cover could bound a rational ball. So it's kind of a simple numerical test. Not a complete test. So for example, the normalized determinant of our running example link is equal to 1. Also, the normalized determinant of the pretzel, 1, 2, 4, 4 is equal to 1. And in general, it can be practically anything. It can be less than 1. It can be bigger than 1. It can be equal 1. And notice that lambda, if we have a cubiquitous lattice, so if lambda is cubiquitous and it has normalized determinant 1, this happens if and only if lambda is equal to the set of center points of a tiling of Euclidean space by cubes of side length 2, or 2 cubes for short. So I'll highlight those cubes. I can't stop drawing. There, you see the cube tiling staring at you now. And wouldn't you know? But there's some interesting results about tiling of Euclidean space by equal sized cubes. So it had been conjectured by Minkowski, 1897, and then proved him by Hayosh, 1942, that in every lattice tiling of Euclidean space by, it's a redundant to say this, but congruent, cubes. There always exists a pair of cubes which touch along a full facet of each. And since it's a lattice tiling, any cube really looks the same as any other to translating. So it suffices to look at the cube centered at the origin. And of course, you see the one just above it touches it along a full facet. So the separation in dates and Hayosh being one of the giants of geometry of an era suggests that there's some depth to this result. In the end, an elementary argument involving bases of finite Abelian groups, whatever that is. But it's a hard argument to come up with. It's an easy argument to read. And then it's an easy argument to forget. And Hayosh himself apparently was, so this was his second attempt at writing a PhD thesis. The first one apparently wasn't good enough for Bayer, was it? Yeah, so OK. So he had to go back and work for three more years before he got it. And he was like, OK, he has a 45-year-old conjecture of Minkowski. That could be a thesis. And he never felt comfortable with the proof of this result. Well, anyway, there are other stories you can tell, but I'll just stop with that. Great, so we can actually buy something from this result. And I guess it's time for me to tell you what the main theorem is, which is going to use it. Well, the slightly darkly humorous thing is that he finally decided later in life he would give a seminar where he'd exposed the argument at last. But then he passed away shortly before he could do that. The theorem, the L is alternating. That's one of these extremal examples. And D is going to be alternating diagram of it, which is colored correctly to make. So the number of red regions is raised to the valve that fits this formula. Then the following are equivalent. One is that this link L is chi ribbon, which I showed you by example earlier, what that is. Chi means Euler characteristic 1. Two is the link is chi slice. So if you know about slice ribbon, this is a slice surface with no closed components with Euler characteristic 1. So if you understand the definitions, this is supposed to be obvious. Third is that the branch double cover of L bounds a rational homology of all. This is more or less a classic result of Cassin and Gordon, as I understand. The fourth is the result I told you before, which is that the lattice attached to L is chi decodis. All of these things we've seen. And then the final thing is where the meat of the theorem lies. And that is that this diagram you've represented your link by belongs to a certain explicit class of diagrams called denote curly D, in which I'll now describe. And by the way, once I've described it, it'll be fairly clear that being a diagram in that set implies that the associated link is chi ribbon. So you complete the chain of implications. So it certifies the conjecture that I'm erasing in the extremal case where normalized determinant is as large as it could be. So here's D. Again, it's this kind of simple iterative scheme like I was alluding to earlier in the lecture of the kind I was talking about earlier in the lecture. So it's the smallest set. And they'll necessarily be colored, alternating link diagrams, such that first the round unknot diagram. And I hope this is the right convention. This crossing, one crossing diagram of the unknot line D. And I guess I do need to tell you how the colors work, at least in this one. I think it should be like that, if not the other one, which is also closed under a certain composition. So here's the composition. I take a pair of diagrams, D1 and D2. I expose a crossing from each one. Maybe I won't put in the coloration because it gets a little noisy. But the coloration on this won't really match the one here. It's not that there's going to be a consistent color on this region, because the crossings, it wouldn't look right. So the composition is you take those diagrams and you join a cross in the way that I'm doing. You take that little composition circle and you enlarge it and put it right here. So that's the composition law. And that's the set D. Yeah, you almost see direct some of the intersection forms.  Well, there's gluing. But I don't think that that's what that is. It's sort of vaguely reminiscent of two or three sum and graph theory. But maybe there should. OK, I'd like to know the word. OK, so about as clean as structured theorem for link diagrams as you might hope for. And as far as five going back to one, that proceeds basically like as in the example. You pick a diagram from this set. And if it's not one of your seed examples, then it looks like this.  And I put in a band and it pops off. And then it simplifies down to a connected sum of things that were already in D and induction. You prove that the link represented as chi-ribbon. So examples are a running example of a diagram is certainly in this set. You can check that directly. And the standard pretzel diagram, although this has the right normalized determinant, this diagram's not in this. I have five minutes. All right, so all the work is in now showing that four implies five. So it issues quickly from Hayosh's theorem. So you suppose that lambda is cubicotis. So you suppose that lambda is a two cubed tiling lattice. And then what Hayosh will tell you is that there's a nice presentation for this lattice that find a lower triangular matrix with two's on the diagonal, zeros and ones below it, so that the column vectors form a basis for lambda. We call it the Hayosh basis. And it's a very nice basis. So if you take any one of these basis elements, or if you take the difference of any two of these basis elements, these are what are called irreducible elements in this lattice. Meaning you can't write it as a sum of vectors of non-zero vectors with non-negative inner product. Parse that. Kind of like root vectors in a root lattice. Sometimes they're called simple elements. OK, so you've got a two cubed tiling lattice on your hands. And you're wondering, could lambda be actually isometric to the lattice of flows on a planar graph G? Well, there's a nice fact, which is that the irreducible elements on the lattice of flows on the graph, these are one-to-one correspondence with oriented cycles in the graph. So you know that these standard basis elements must match to some cycles in the graph. And the fact that differences are irreducible also tells you that cycles that touch each other can only do so in a very simple way, in a way that their sine sum also gives an oriented cycle. So there are a lot of tricks like this going back and forth. And in particular, this last column, which is a vector of self-pairing four, what that's going to find for you in your graph is a four cycle. And you're going to find that this graph decomposes. So I have a bit of graph going from one vertex to the other in my planar drawing. And I have a bit more graph going between the opposite pair of vertices. I'm not telling you what's happening in these looms. But that's the kind of structure that the graph has. And that four cycle is the take graph echo of this decomposing cycle circle here. So what you can do is you can do a decomposition and see that the graphs that you get, again, have lattices of flows, which are two cubed tiling lattices. So you kind of decompose and you induct. And then what you find is that G has to be the take graph of a diagram D inside of this set script D. So that's how the proof that goes. I'll leave that up, but I'll just close with a conjecture. So maybe a remark and then a conjecture. We can go a little further. So we've got this whole class of links now. We know their branch double covers bound rational balls. And we can study the relation of ribbon rational homology co-boardism between elements of this set now. And we have a complete understanding of how that works. So if I have two of these links with a ribbon rational homology co-boardism between their branch double covers, then start with one and do some decompositions until you get down to a diagram of the other. And it leads to some conjectures. So I'll make two, then end with a proof of a special case of one. One is that if there exists a ribbon rational homology co-boardism from a three-manifold to the branch double cover of an alternating link L2, then L2 is alternating, then the y itself is actually the amorphic to the branch double cover of an alternating link. And a special case of this would be, well, on the level of links of related conjectures that if there exists a ribbon concordance from a knot k1 to a knot k2, where k2 is alternating, then we conjecture that k1 is alternating. OK, but let me give you the evidence and then I heard the bell rings and make the quick joke that lots of people are studying ribbon concordances these days from E and A to E and Z. So evidence for two, I could say a lot of things about lattices and support of it, but let me just bring it full circle. The case that L2 is a two-bridge link, and either of these conjectures implies that L1 or k1, however I'm notating it, is two-bridge. I'll give you the proof really fast and then we'll quit. So here's why, and here's my ribbon rational homology co-boardism to the double cover of L2, which is a lens space. And what Gordon tells us is that the fundamental group of Y has to inject into the fundamental group of the co-boardism, which is surjected onto by the fundamental group of this lens space. So this is finite cyclic, so this is finite cyclic, so this is finite cyclic. So geometrization then tells you why is itself a lens space, and then if you're trying to do the conjecture at the level of links, then Hodgson and Rubenstein tell you that this thing had to be the branch double cover of a two-bridge link, and only that. That's a little bit of evidence. I'll leave it at that, thank you. So the question is why are we using diagrams to look at alternating links as a, right, thank you. I guess he didn't know better.  It's monotonic, maybe, but it is monotonic, yeah. Then any time what could be a decomposing circle, you can decompose and get into smaller elements of your family.