it is welcome to vlog Thursday he knew what to say and i just had forgotten what i was going to say this is why we sit at the table together it's been a morning already so it's been a morning i don't know why marvin never thought to put the the combination of words together of chainsaw vodka and ice gates as a youtube search well i've put those words together before but i always landed me in trouble with the law yeah so if you put them in youtube something wonderful happens it certainly does it certainly does there's this guy in youtube that i uh i don't know why i subscribe to the channel and then vodka chainsaw ice gates what more do you need what do you need it just makes these videos and the guy apparently isn't cool but we're gonna stay on topic because that will promise maybe he will be a discussion we'll see if we can't get an interview with that guy that would be epic if he even speaks english i'd still interview sure but so far the only the only thing we've heard come out of his mouth is and a lot of vodka yeah so good vodka goes in comes out yeah anyways youtube search him and you'll see yeah well i will just leave a link below so you guys can enjoy it as well so the new year is upon us things are going well the video i just did seems to be popular which i did last yesterday i posted it which is the behind the scenes for how he produced youtube videos and it's kind of fun because i've been watching a lot of youtubers and how they produce youtube videos and it's kind of interesting and i get some people already commenting oh moved to 4k or moved to this and i've had this before i made that video and it's also part of the catalyst for that video is i don't look good in 4k he doesn't either no i don't not at all it will not improve things to us so it becomes a should i spend that kind of money on that and i i see a lot of people to get stuck on the gear they get really fast any with it i always refer back to kasey nice that's guide to filmmaking or if you want someone you're like yeah but he's kasey nice hat i'm like okay follow my cousin she does a excellent youtube channel she has her gone to snow dogs youtube channel she is not shooting with even as much gears i have and has a substantially bigger channel of me so there are people there are people that with very successful youtube channels that simply use a gopro that is not 4k i mean it's or you can't get a 4k you oh you absolutely can but the bigger point is it's all about the story the narrative uh sharing something with people if you're trying to get more subscribers you just keep putting it's you have to put something out of my wife is starting a youtube channel now about eating and stuff like that and it's it's all about creating the content that's you know she got hung up for a while before she started on all the other things related to it and i'm like there's not a lot here's the thing all so many youtubers myself included i not all of them but a lot of us all want to help all the creators we all have no problems sharing with how we do a lot of what we do and uh there's some channels you can watch and i might do a video on this like the best youtubers to listen to to get started at least in my opinion because they're ones who helped me uh i'll make a quick list of them i don't want to say their names wrong because i i probably pronounced them all wrong i don't know but i'm bad i but kasey nice had to be on that list but not all of his videos uh he's because he's an interesting topic for youtubers because he's if you really watch his videos he's an amazing cinematographer and he tells a story with cinema which is actually really hard to do it's it well it's not hard as much as it's a lot of effort there's a lot of hours i mean he talks about spending two or three hours every single day editing and that's just was producing his vlogs uh some of these other people there's a few other ones out there i mean it's there's a lot of effort and i'm not as much a cinematographer i have fun i play with it i have a personal youtube that i just do it for no purpose like i'm not doing it for the purpose of subscribers i i produce my other personal videos that i throw on facebook randomly i mean riding a motorcycle or whatever it's just fun and it's something i go back and look at going man i was doing that four years ago or five years ago and what's cool is i have old videos on there i recorded a video of my friend playing drums at a band little stupid stuff it's archives for me if people want to watch it i have i can link to my personal channel it's not purposed at all but even those videos are like you riding your motorcycle whatever you're still assembling them into some kind of yeah whether you know it or not some kind of story some yeah right an hour long video of tom doing circles on his motorcycle not exciting right no offense but edited down with you know interesting cut interesting or not cuts whatever but it you still assemble a story to it and that's what makes the content yes that's the most important part is assembling the story not the gear you use or anything else uh i like understanding the gear and i chose the 70d but that's actually an easy choice for me it's not like i had all these options out there and i simply narrowed down on this the 70s is actually because i was a wedding photographer for a long time so i shot canon so i have been with canon since my first tendy so that goes back to 2005 i think so i had all the lenses and a familiarity with the product line that canon makes that once you've been doing dslr for a long time it was a no brainer gun oh cool the 70 has video support on it i have all the lenses matter of fact i was laughing because i bought that wide angle lens i showed in there which i love we don't use it all the time on the channel but it's great for vlogging people like but that lens is like used five hundred four hundred dollars i'm like yeah i mean i had it already though i mean i bought it in two i had to recede i think it was 2009 when i bought it so i had a lot of stuff already so when i moved to youtube and started really doing this in 2017 awesome it was easy it was like cool i just had to figure out how to shoot with the dslr but there's a lot of less expensive options out there and that's not to say you need all that at all right just a camera that shoots video really i mean to just get started and a good and and a good story good story and a lot of determination you know you you were going to talk to dead air for a long time and i talk about this with my podcast as well people are like oh your podcast took you to microsoft and everything else and stuff and you know me and my friends have that similar podcast but but but we produced that wasn't we our first microsoft episode where they flew us out to seattle was episode 200 something i think yes 200 something produced episodes later you know where we just kept talking and we kept putting it out there but it takes up forever i mean it's years it wasn't like oh we just did a racked out a bunch of content the content is processed post it produced everything there's so much work that goes into it and then no one listens to it and you're disappointed and this is what happens i we've seen so many people like over at podcast Detroit we see as people get excited because podcast Detroit is a local podcasting guys are awesome bob and david been doing it for a long time consistently yes on mondays forever and people like but how do i get to be their channel i'm like um it's actually easier today to get started than it was when they started but still getting your content known youtube podcasting whatever it is don't expect it to come easy now i will make a slight exception that for people you may think it kind of comes easy to there if you can hook up with other influencers and you can kind of get in there and get a shout out from them awesome not easy to do because uh you are not the first person to think of that matter of fact no uh any of these influencers they will they will tell you they're bombarded daily some of them are like i they either hide their email address or like they've given up on email but like yeah they're getting like so many solicitation today they have to hire personal managers just to deal with that so but have good content and get that in front of them yes that's important that goes a long way to when you do finally make contact or in your next you know other attempts to make contact it's that oh well wait a minute that was that video that we saw the other day right that's that guy right all right i'll look at his email or i'll you know listen to his voicemail right so it's this and that's where i might be going to VidCon so you can go meet some person in person because when you go to VidCon or some of the bigger uh there's a couple of our industry events for you for youtube and content creators when you go to those events especially when some of the ticket prices are kind of high that filters out the people who are random strangers to go okay you've taken the time to fly come to an event uh you paid the price bought the ticket and the ticket was like eight nine hundred dollars you are here for like craters pass for VidCon it's more mile how much it is but it's more money once you buy the creators pass not just i'm a fan and i want to come meet my favorite youtubers those people kind of get the idea that you're serious so that's kind of how that works and the same thing with the the irony of the branding deals is really weird because it's hard to get into that you have to review lots and lots of products by the way if if queens manage the hot sauce would like to sponsor us huge fans of your stuff you love your stuff this is caffeinated hot sauce we've gone through half a bottle and it's been a day um i know i love that so getting those deals kind of means you have to go buy all the stuff and then because there's almost a little bit of jealousy you get when you look at some of the other big youtubers which it took a long time i mean any of them well the majority of them you're going to look at their videos roll to their earliest pose you're like if they didn't delete them and you're like yeah they did some really horrible they were trying to figure out how to do this product review thing and you look at them they're like oh wait they have like 20 google pixel phones just given to them a truckload one guy i i think was on box therapy and he had worked out some deal he would give away like 10 iPhones or 20 iPhones the new ones i mean in these it's it's so strange because when you get that big they actually just start contacting you we're only big enough we just crossed off officially crossed 14 000 this year beginning of the year and what they do is the company start reaching out to us so far we apparently have reached the chinese companies just send us stuff which is kind of cool and start slowly reaching out to us you can't try to reach out to them but they also are bombarded with everyone wanting to become a content creator and get free cool stuff yeah it's you kind of have to prove yourself before they'll even listen to you and then they kind of seek you out as your brand gets bigger because they're always looking for places to market their product but you with no views is not really lucrative for them so it's really it's tough getting into the business once you get to the top as long as you're not as destructive as a couple of youtubers who shall remain nameless you can pretty much keep your channel and i yeah there's enough youtube controversy videos i don't feel i need to uh make fun of them right now where yeah address them it's it's goes out maybe we'll do an off topic tuesday and it goes outside the scope of it yeah well we definitely should yeah we may have some funny thoughts we'll share on it but the problem is by tuesday it's already old because here's a good part by next tuesday said youtuber who is super controversial may have done something equally dumb or stupid because it's a race to the bottom of stupidity occasionally so you're just watching himself destruct which is also it's like the car wreck you can't look away from people have taken lowest common denominator to a whole new level they're working hard at it they're putting the effort in burning midnight oil on how much of an idiot can i be somebody says well we fit the bottom now and they say hold my beer yes so jumping to lts creative and our efforts yay yay uh the website's live ltscreative.marketing and it'll be in the doobly-doo below the thingy here so we'll put that on there that's uh that's up and running we're working hard at expanding that uh we're also going to we still didn't get around to doing it we've moved all of our websites over for hosting so that's been kind of a fun project now here here's the thing about running a business people said well how do you just start a hosting company how do you just start another business and i won't lie it's a lot easier when you have a business and being able to kind of pivot and do something because i have experience doing running a business for the last 14 years and so we are just kind of expanding into it but one of the important aspects of a business and i want people to think about this is if you start something and you train nobody on it and you're the only one who can do it you have a job you may be working for yourself but you have a job so the important part and this is something i well here's my failing the hosting stuff you know who knows how to how do you set up a website how's my hosting work marvin i uh message tom and say hey tom so the the actual starting of my hosting company so i had a job hosting websites and i just never delegated that function out because i never tried to grow up very big and now that we're going to put some effort into it uh and we're working on putting the details on the website on there and what our angle is on it and that's i'm training kyle on it i'm training a little bit of steve on it steve's interest is a little bit uh but marvin and it's it we're creating a documented process that people can follow so it doesn't mean that all hosting is done by tom so that's part of it and the same with the lts creative marketing it's a team actually i'm less involved in it directly on functional sides of it uh i'm paying for it though so which is good yeah good for him because i've been paying him in the last month to do some of that right and here we are officially launching officially launching with with clients already with clients that's the important part there's it has to make money because uh the money has been going out no in your pocket well out of my pocket staying in the buildings it's the money has not left the building yeah it's just going from pocket to pocket that's all pocket yeah then it leaves the building well yeah then it goes to you know places like mortgage and whatever yes so i i actually there's always a question of can we do some more videos onsite and things like that uh we got one coming up that's coming up uh the construction company yeah that's uh we're friendly with the owners and we're going to talk about what they do a little bit we'll do the video camera i'm going to take the camera there and film it i'm i've got it cleared all with them but i think they're cool with the whole thing so yeah so we're actually going to document how they do it and talk with them as a business and you know services it's going to be an onsite job where we kind of show things uh we'll do that i did a rant yesterday that i didn't publish um and maybe you guys want to see it i'm going to let you decide whether i published a video i ranted about the status of it and maybe i got i was i'm occasionally jaded because i work at it and i love the creative stuff we like the social media we like this we like doing this building things and there's joy in creation uh we enjoy helping customers there's no joy in updating the rfms platform for one of my clients it is a joyless thankless like we get paid the clients very appreciative but there's a company called rfms that sucks and i'm just gonna i ranted about their software i showed what it's like to update their software because it doesn't violate any privacy rules we do it remotely so i'm sitting at my desk we have to reboot a client's server more than once to get their update to install and no update to software unrelated to microsoft not an update to the server just an update on a database program should require two to three reboots but there's does so they're and then it's like brace for impact because even the client knows that the update got released at the end of december but they wait a couple weeks because there's always another update to the update because the update had a problem yeah and we have this client this software is just suck and that it represents one of the problems with it where how you get burned out on this because you're not doing something amazing for the client and you're like oh the client should switch well the problem is it's a niche software they're a carpet company it helps them manage their carpet business and there's not another alternative out there that's good they've tried the other alternative and talked to other carpet places they hate it too yeah so if you are a developer going i am looking for a niche turns out people like carpet and flooring there's only apparently two good company two big companies and i don't know the other one's name at all okay i completely lose me but r4ms is the other one and r4ms does other things but they suck they are they're awful and it just uh that's such a niche thing though that i mean they do some r4ms actually they do carpet but they do a few other things yeah but here's the weird part for you for those of you who are going to have you heard of this their database is completely goofed up all the time it's massively oversized even according to r4ms they have no idea why it's so big it's dragging down on the system they told them to go find a sequel person to fix it i'm like you guys wrote the database really yeah but we don't we don't we can hire someone third party we don't work on databases i'm like but you wrote the software they won't log in and work on it they this is the stupid part too because the updates are so difficult to load because of all the server reboots and start and stopping services and all the details r4ms won't update the system needed they the client has to pay us to load the updates from r4ms and r4ms says well most of our other clients just do it in-house and they're like well we're not tech savvy and this is unknown like your process for update is this complicated yeah so well but they're one of only two so one of only two you're gonna use them or you're not basically so yeah so you use them or not and it's a pain in the butt but this is we see this a lot we dealt with the scanning software that just had a horrific amount of problems and it's something we used in a niche industry again the software is bad the support's bad we just spent time figuring it out we know it breaks randomly we're looking at you HP printers there's another one that clients just get kind of aggravated going wow the printers just quit first don't buy consumer printers second never buy a wireless printer sorry if you want to not be aggravated don't buy a wireless printers even the HP business ones they just kind of suck we have a client that it was funny because an update broke all the printers at once we don't know we the only thing we noticed that they all had the latest software on there I looked and there was a recent update and also did was un-set all the wi-fi for all of them and it wouldn't set back up until you went into the menu and hit reset i don't come right to the printer model but yeah it's kind of an aggravation the clients get mad when that stuff happens because they're like well I just spent money fixing printers um and first to disrupt my days I can do that I'm like yeah welcome to HP and speaking of big deals thanks Intel and a couple other companies uh I'm going to do something a little more in depth than this but this is the specter uh vulnerability flaw that was found that people are running around like just mad men over the how severe this is it is industry-wide it's basically a flaw found in processors they believe it may be an AMD it's definitely in the intels um and the solution to it could cause a 15 to 20 slowdown allegedly to patch it oh now that's at a data center hold it that was a hell of a tease anyways the problem is at a uh data center level it's at the consumer level it might be at the phone level as well uh but the the hacks are just crazy where it's a shared memory problem I might do a video on that I'm trying to read more on it to make sure I understand it so I can reiterate the how severe it is because it always starts up with the severity is here and we'll figure out in the middle where it really is other than that I what else we could go on here for business so that's uh oh process procedure videos I do want to do some of those yeah we should do some of those absolutely yeah yeah how we do things yeah people like to see that stuff I can't stop sneezing it's gonna be a lot of sneeze cuts there are gonna be sneeze cuts in here that's is that a technical term in the film industry um I know what a jump cut is yeah I I I've learned all the different cutting I think I would say that a sneeze cut is probably a sub category of like a jump cut there's in in radio there's the cough and sneeze button there is it just kills your mother's really quick so you can hit it and then yeah I learned that when I was on the radio I've been on radio a few times that's kind of fun I co-hosted a radio show yeah way more organized than this we're spontaneous it's part of our charm that's the last thing I'll actually leave you with here on the topic of YouTube spontaneous and the unmediated all on the unmediated vision of the creator that was a sneeze coming up which is causing memory loss hold on we're gonna cut all this out right it's time allergic to I don't know all right here we go I mean didn't it's happy now okay so YouTube allows I I've heard that I think the nerd writer wrote this the unmediated vision of the creator so it's a direct connection between our audience and us and we can be very real now that's why I like editing because it's the vision as how we want to portray what information I share with you then we edit it to keep that same narrative and focus and I'd like that about that this is where you see so many youtubers this is the connection that was created between the creator and the audience and I think it's wonderful it's in this direct sharing is really cool then you have YouTube red and they are trying to produce shows and I've seen some of the youtubers that I really enjoy their channel and I much less enjoy the content that's created on the YouTube red with them it's like you drop them into a full production thing and I'm like meh it's just not YouTube red is the YouTube red is the paid subscription service and one of the things are trying to entice you with I which I'm a fan of YouTube red by the way because I don't like watching ads I had no problem paying the few dollars a month to YouTube for the ads I've done a review on it I'll do a follow-up review because I'm still in love with that as a product and oh don't confuse it with red tube don't even google that oh god no their naming is dubious in edgy so anyways back to YouTube red not red tube uh YouTube red is being able to connect directly with your audience versus the classic uh the way they produce a discovery channel series with a voiceover narrator who talks about the things that this guy is doing and they cut it all up and try to produce it I lose the connection right away I don't feel like I'm just watching a TV show that I can't get through and versus yeah I might do a topic on that because I think maybe if more YouTubers kind of complain about this YouTuber will get it and they'll stop producing BS like that it's not a movie the reason we like people and I'm going to say like uh Colin Furs love his channel I've tried watching a few of the YouTube red things he's doing I like him his projects amazing I'm not a fan I try to watch a few I'm like they're okay I mean they're good I've watched some of them but they're not not as much fun as when he grabs the camera and just is himself where he is putting it all together and making it all happen and just and it goes for other YouTubers as well that have tried this like them you're watching it for them so yeah it's it's I'm really it's analogous to like you know a comedian he's a really great comedian then they give him his own show and it just isn't the same right it's not the same once it all you have all the influence around him and it's not totally you went there to see that comedian not to have a producer and sometimes it does work when a producer around him but it's not always working right yeah sure enough but we'll leave you with that we have hot sauce to eat mm-hmm we got a jalapeno popper bacon bacon wrapped jalapeno poppers that we got a yes and so uh I might talk about this one of my personal things is I buy everything on clearance for food so I come in here with the clearance bag somebody talk about the clearance stuff because I'm I'm a very there's a there's a line between frugal and efficiency that I try to ride all the time uh where I will be frugal as long as it doesn't as long as it doesn't interfere with my efficiency and we talked about that because we were screwing around with a boom stand over here uh you know I didn't want to throw one out but it's interfered with my efficiency so now it's time to throw it out so we'll leave you with that maybe that's a whole nother topic also once again like subscribe tell us what you want to see more of less of um oh we'll address this we're working on improving things we moved the orange someone said that that would uh detract away from not knowing what things are so well we actually might do a background drop thingy behind us in have it for these videos so that's some upgrades are coming to that just simple stuff that branding and and uh I don't know stuff I'm not good at hi that's what I'm here for that's what you're here for thanks for watching have a great day time to time to eat some uh wake up with some red habanero and black coffee hot sauce and if uh queens manage she wants to sponsor us oh scottie ohade shared my son's video i mean well i made a video with my son scottie ohade shared it we're gonna do a scottie ohade i'll review i actually have a connection with them and we'll get them to uh sponsor and the only thing i want from them is sponsorship is just lay out all the hot sauces and all the rest there we go thanks see you


So indeed, so the subject of my lecture series is not contact tomology. And so this is some subject that we studied for a number of years. And in some sense, it can be viewed as applications of this symplectic field theory package to not theory or more generally to differential topology. So the series will have three parts. So today, I'm going to give some kind of introduction, defining not contact tomology in particular, but starting by talking about the Lausandre in contact tomology, which is part of this symplectic field theory package. And then try to get to the point where you can actually get the feeling for how you would compute these things more concretely, not just showing that the theory exists, but actually compute it. And then tomorrow, no, maybe not tomorrow, but this second lecture, I will talk about, probably continue with that, and then talk about relation to string topology. And finally, in the third lecture, I'm going to talk about relations to more physical theory. So like Cern Simons and the topological string theory, there was more recent developments of the subject over the last few years. But anyway, so let me start by giving some introductory remarks about the relation between differential topology and symplectic geometry or contact geometry. So there is somehow this basic thing that if you have a smooth manifold M, then it has a cotangent bundle, which is a symplectic manifold. In fact, Weinstein manifold, so exact symplectic manifold. And one may now ask the question, how much of the smooth topology or just the topology first of M does the symplectic geometry of this T star M remember? So the first, so I am not going to explain these results. I'm just going to state them so they see where what we are going to do fit in. So see if you have a symplectomorphism between T star M and some other T star or some other manifold N. Then, if you look at the zero section in here, M, that sits in there as a Lagrangian submanifold. And the image of that would be an exact Lagrangian submanifold in T star N. And there is a theorem which has some history, but somehow this full version is due to a Bosaid and Krog. And it says that if L is an exact Lagrangian submanifold in T star M, then there is a simple homotopy equivalence between L and the zero section. So in fact, the homotopy type of the zero section is remembered by the symplectic topology. And this proof goes via flow homology with local coefficients. So there is some history to this theorem that I want to tell you about, but there certainly were lots of contributions. Compact, yes, sorry, L, M, and L are closed manifolds. So that's right, so compact, no boundary. So the next question is, does this go beyond? Would the symplectic geometry feel anything more? Then the homotopy type. And the answer, again, is yes. So maybe the easiest starting point for such theorem is to start when M, in fact, sort of has no homotopy theories. So that would mean that M is a homotopy sphere. And then there is a theorem that builds on the first theorem in this kind of spirit. This is due to Abu Sayyid again, but this theorem is in a paper by myself and Prague and Smith, and it says the following that if sigma and sigma prime are all-dimensional homotopy spheres, and if the cotangent bundle of sigma is symplectomorphic to the cotangent bundle of sigma prime, then sigma is the class of sigma in the class of homotopy spheres. There are equal modulo boundary parallelizable spheres. So in this dimension, 2k minus 1, perhaps. All-dimensional, 2k. So when you look at this, this is some kind of classical differential topology, which I won't talk much about. But if you have a homotopy spheres, they form this age-corporealism group. And inside there, there's a subgroup, the boundary parallelizable manifolds. And we know that their cotangent bundle can be equal, symplective manifold, only if they're equal modulo of this boundary parallelizable one. So thank you, which corresponds to changing the orientation of sigma. So this is sort of not so serious. OK, anyway, so this theorem tells you that in fact the symplectic geometry of the cotangent bundle is pretty sensitive. And I would say that the proof that I'm not going to talk about, but goes beyond, you know, Fleur theory and SFT and the like. It's kind of different version where you use a modular space of allomorphic curves, not just to get some fundamental cycle or something like that, but it's actually a k theory class of it or something like that. So basically, you're using the modular space more than you're using things derived from it. So it's somehow a very interesting way of using modular spaces. But here it's a little bit ad hoc used. So it's very hard to use it directly. And so I encourage everybody to think hard about this and see if you can find maybe the expectation of what is the hoc curve, the sharpen. Yeah, so the sharpest expectation of this is this nearby Lagrangian conjecture will say that any exact Lagrangian sitting inside here, actually it's Hamiltonian isotopic to zero section. Do you still believe in this? Do you still believe in this? I'm not so sure. But then somehow you should ask Thomas Krog. So he's kind of the leading disbeliever, right? But anyway, I don't know. I mean, I don't know. So for example, yeah, I will mention something in one second in this direction. So now what we are going to talk about is not this, but we're going to talk about a relative version of that. So if you have a sub manifold, K inside the manifold, so again, closed, everything is closed, then we can associate the symplectic geometric object also to that. So and the natural thing is to take the Lagrangian conormal inside the cotangent bundle of M. And what we are going to do is related to that, but we're also going to look at the Lagrangian conormal. So I'll define this in one second. Inside the unit cotangent bundle of M viewed as a contact manifold. So the Lagrangian conormal is the set of points in the cotangent bundle. So Q is the coordinate along the base. And P is the corresponding fiber coordinate. So that Q is in the sub manifold. And P, when you restrict it to the tangent space at this Q, is equal to 0. So it's somehow exactly the normal vectors of K, but thought of as in a line in the fiber direction. So this is obviously Lagrangian sub manifold. And the Lagrangian thing is this just LK intersected with, say, the unit cotangent bundle if it's the Riemannian metric. And that's the Lagrangian sub manifold. And what we are going to do is actually we're going to specialize quite a bit more. So we are going to, for this lecture series, we take K to be a 0 in M, which is equal to R3 most of the time. And sometimes, perhaps S3, it doesn't make much difference. So we will study a very special case of this. But before we go to this special case and I define the holomorphic curve theories, et cetera, that we are going to use, it's worth mentioning some results about this stuff and see how well it works with respect to things like this theorem. And there, so one should say, and that that's maybe kind of a good reason for talking about this, that this theory, so when you apply the holomorphic, the SFT package or some part of it to this lambda K, then it's quite successful. So for example, as we will see, the theory detects the unnot. So it will be, I'll explain this, so there will be a DJ associated to any note. And this DJ looks like that of the unnote, exactly only when it is the unnote and for no other note. And it is a pretty nice not invariant that knows about things like a polynomial of the note and et cetera, et cetera. But let's first consider somehow this counterpart of this in high dimensions, where there was some observations recently made by Dimitro Grurizel and then another student of mine, Ericsson Östmann, and it's the following. So if you start in R6, then in R6 you can embed three-sphere. So there is the standard three-sphere and the note theory here, in fact, is pretty simple. So if you appeal topologist, or C0 topologist, or maybe no, Lipchitz topologist maybe, or if you're Lipchitz topologist, then there is only kind of one note class. But there is an integer worth of smooth notes. And the invariant can be seen as follows. You take this embedding of the S3 in R6 and then you would find the four-dimensional cypher surface embedded, and you take its signature. So the signature is some kind of multiple of 16, and then you can realize all these notes. So there are these notes, three-sphere notes in five-space, which are actually differentially noted, but PL standard. So one might ask, would this lambda k, so k is k sitting? So what about this lambda k, which is now the conormal of S3? And topologically, so it's the boundary of tubular neighbors. It's S2 times S3. Does this lambda k, remember, smooth not in S? Is that 6 or 5? This is 6. So the boundaries would be in S2, right? So lambda k is if you morph it to S3 times S2, right? So it's a trivial, normal bundle. And the answer is no, because in fact, it does not. And why is that? So the observation is that actually, so let me draw the note and then take this tubular neighborhood, boundary of tubular neighborhood. Now the conormal lift can also be somehow, it's clearly isotopic to the conormal lift with the outward normal of this boundary of a tubular neighborhood, right? It doesn't matter if you lift right on the note, or you just fatten it up and lift a little bit along other vectors. And in fact, the boundary of a tubular neighborhood of the note k and of the standard one, even though the notes are not isotopic, the boundaries of tubular neighborhoods are isotopic. So this is some kind of just consequence of H-Cobardson theorem, or Smale's Handled Cancellation. So here you can define a function, Morse function on S, if you put S6 instead of R6. So you have a minimum here and an index-free handle here. And so the complement of that, you can cancel all the critical points. So that means that the complement looks like an S2 times D4. So somehow the complement retracts into an S2 sitting here. And the S2 is completely free in R6, right? Because it's 2 plus 2, it's too little. So that means that you can isotope this tubular neighborhood to that tubular neighborhood. And therefore, you can isotope lambda k to lambda S3. On the other hand, and this is somehow interesting open question. So the secret to this is that this weird note, the Hefliger note, it actually lives here somehow in a tubular, on the boundary of a tubular neighborhood. And one could, for example, ask the question that if you pick one of these Lachandrian isotopes, anyone, would it have to take, could it take a section of this kind of normal bond into a section of the other one? And probably, I would guess the answer is no. So that it still knows about this, but it doesn't, somehow it's some parametrization question, right? And does the Lachandrian isotope have to really mess up the parametrization? OK. So if that's not true, does it break this nearby Lachandrian conductor? No, no. It doesn't break really anything. But for the nearby Lachandrian conjecture, I think great question is if, so now this is in R6. And if you think about this T star S3, that's also a six-dimensional thing. And you have more or less the counterparts of this. You have the zero section. You have a kind of Hefliger counterpart to zero section and so on. And I think it's unknown if they are represented by Lachandrian embeddings. So I think this is a reasonable question. Can you find Lachandrian S3 in the isotopic class of the Hefliger sphere, in T star S3? And that would certainly break the conjecture, but maybe it's not that easy. I don't know. Well, OK. So this was end of the introduction, almost. But one could maybe say here that one of the things that little bit go wrong here is that the co-dimension is too big. So when you're in co-dimension two, then certainly this non-contact tomology, exactly as in the case of knots in R3, will be pretty powerful, because it fills a lot of properties of the fundamental group of the complement. It's OK. But that's enough of introduction to the general area. So we will now study this non-contact tomology. Should we think of the fact that lambda k doesn't remember smooth not in this as a shadow of the fact that there's no kL not in this? Yeah, I mean, so here it is. But so what I suspect is that lambda k, not as a submanifold, but as a parametrized submanifold, as a parametrized Lashornian submanifold does remember smooth not in this. That would be my guess. And that's, of course, I don't know how to prove. Otherwise, I'd give some other talk. OK, so. Do you think that the smooth morning is distinguished by the signature of the Cypher surface? So if you take those Cypher surfaces and put those in the co-dimension component, then what? Yeah, so here you wouldn't quite have a Cypher surface, but you would have a surface going. So if you have, so here's your S3, and then you have your strange not. So there you would have a four-manifold interpolating between the two. And you could take the signature of that. So that would be the counterpart of this Hefliger signature, I think. But this is just, you're just assuming now the knots are smooth. And then you're asking, can you actually find a Lagrangian representative so that this cubordism has non-trivial signature? And that's, if you can, you're famous, I think. Yeah. OK, so what I'm going to do next is I'm going to describe for you Lechondrian contact homology in a setting which is sufficient for what we are going to do later, but not completely in this unit called tangent bundle of R3. But I will start out a little bit more generally. So y is a contact, contact 2n minus 1 manifold. And the contact form alpha is the contact 1 form. And inside this y, we have a Lechondrian, so manifold. And what is this Lechondrian dj? So we'll define Lechondrian dj, it's part of SFT. So if you want to, just before I go into details, what is it? Well, it is the attempt. It is the answer to the following question. You try to do some kind of flow homology on the path space. So gamma, so here is lambda, and here is lambda, and this is a path gamma taking lambda to itself. And you try to do the flow homology for the action functional, which sends such path gamma to the action. And then you cannot quite do it, and somehow these SFT type splitings that you see forces you to use some other algebraic structure than just a chain complex. And that's what I'm going to explain. So since this is a lot of kind of technical business going on, so let me be precise. So we will restrict to, so we assume that there are no closed orbits in Y, which is the case, for the unit container bundle of R3, maybe not for unit container bundle S3, but anyway. And we will also assume that the first-gen class of the contact plane field is 0. And I think that I will assume that this Y is simply connected. And what else? I'll probably assume that the mass, huh? It was about to ask whether no contractable closed orbit could be enough, but since you're talking about Y, 0. It would be, but I want to somehow to get the thing sorry, maybe it's 0. OK, what do you prefer? OK, so and then, and I will also, I'll talk about this mass log class, but I'll take the mass log class of lambda to be 0, to have the theory graded. Are these assumptions really necessary or just to make it easier to explain? It's just to make it easier to explain. So they are not necessary, and some of them are slightly serious. So these two things affects the grading. So you'd have to do something about the grading. Right, so this is somehow is the serious. The serious assumption, and what would happen is I will now define for you an algebra which just generated by quarts, and it will be an algebra over some coefficient ring. But if there are orbits, then the Legendrian algebra would be an algebra over the contactomology orbit algebra that I'm not going to talk about. And that orbit algebra certainly does require a lot more of machinery of the nature that's being discussed here about polypholes or something like that, so abstract perturbations. Whereas this is what we are doing here, we can actually get away with the classical perturbation theory. OK, thank you. So I'm probably forgetting half of the more assumption, but it doesn't matter. So what is this thing?  Probably you already discussed this, right? So this is somehow in the kernel of the alpha and normalizing, so this is equal to 1. And so the generators of our algebra will be rape quarts. So they will be quarts with n points on lambda. And the algebra itself, so a of lambda, will be the following. So it will be an algebra over the group ring of the second homology of y relative lambda generated by rape quarts. So this is a unit algebra generated by rape quarts. And these algebra is not commutative in any way.  It's just like that. And this is a. The H2Y lambda classes, they commute with rape quarts? Yeah, so right now, for the first words, I wanted to say this is a kind of simple version. So I will first take them to commute. It's not really necessary. So you can soup this up, and we will do that tomorrow.  But it's not really necessary. So this could be like some kind of module where you can put these things in between, and they don't necessarily commute. And we'll see geometric reason why you can do such things in a little while. So we are defining a dj, and we just defined the a kind of. So now the g, so the grading. So grading. So here is a chord C. And so what we do, we pick a path inside the Lagrangian. So this is some path inside lambda. And now, since y was simply connected, we could somehow extend. We can fill it in with a disk, right? And now, on the boundary of this disk, we have the tangent spaces of lambda giving a field of Lagrangian planes in the contact plane field. And when you have that path, you somehow you can take the tangent space of lambda at the endpoint and transport it to the starting point with the linearized rape flow. And you get almost a closed path. You have to close it up somehow by positive rotation. And you take the mass of index of that or the con disender index. So let me, I'll explain in examples how you compute this later. So anyway, the grading of C is equal to the con disender index of this C, which is this mass of index. I was talking about minus 1. So I'll leave it at this. It's just you have to think about this is somehow related to the homotopy class of this Lagrangian plane fields. And this is what normally enters into grading when you compute this indices. So OK. So we have an idea about the grading at least. And now what is the differential? This is, of course, the most important piece of the algebra. So first we fix an, so first we consider as was done before here. We consider the simpletization r times y. And here we take the symplectic form d e to the t alpha. I guess everybody saw this before. And we fix an almost complex structure, j, which is translation invariant, and takes the contact plane field to itself. And somehow this j of the extra t direction is equal to the ray direction. So this is probably everybody. You probably talked about this, right? Yeah? Oh, no? Oh, yeah. Oh, yeah. Oh, yeah. This was multiply-covered. This was multiply-covered. That's good. So yeah, I don't know if you should divide by one factorial or just divide by how many times it was mentioned. But anyway, so it's OK. OK, so you can recognize this thing. And then we have this notion, again, probably multiple-covered of finite energy. So we have the energy or omega energy. So it's an area in the contact planes. And then we have this cut-off area in the alpha energy, but maybe lambda energy in some other torque. So going in this other direction where we have to take a cut-off function. And then, as probably was discussed, at least in the case of orbits, we know that finite energy curves. So I'm just taking this a little bit in-precise. So finite energy curves, holomorphic disks is enough or asymptotic to ray chord strips at punctures. So indeed, note that by this requirement, if you take the just ray chord C times R, then this is a holomorphic strip. These are the trivial strips which counterparts the trivial cylinders from Helmholtz's talk. And now, if you have any such finite energy disk, let's say, mapping in there, then it has a number of positive punctures and a number of negative punctures where it's exponentially asymptotic to this disk provided that all the ray chords are non-degenerate. OK, and the modular spaces that we will use, they are modular spaces of a specific kind of disks with one positive and several negative punctures. A ray chord A and the word of ray chords B underline, which is B1 up to BM, we consider the modular space M sub A, which is this is, I'll explain what A is in a minute, A B is the modular space of holomorphic disks of the following form. So this disk has one positive puncture at A. And it has several negative punctures which appear when you go around the disk as B1, B2, B3, and then finally, BM, right? So that's determining this word. And finally, remember that we have these capping disks. So we can somehow take a little disk here, a little disk here, here. They're just, we just choose them, it's up there. If for each chord, we choose such a disk. So when we fill it in by these capping disks, then this creature, the holomorphic disks and the capping disks, they define a homology class inside H2, right? Relative. So that's what this guy is. So this is the modular space we'll use. And the dimension, the formal dimension of this MA in our case is simply equal to the grading of A minus the grading of B, which is the sum of the gradings of the factors in B. So the differential that we are going to define is simply defined by counting such things in one-dimensional modular spaces. So the kind of minimal dimension. Something interesting happens. So because, as you've heard about this Orin variant, somehow the minimal dimension of an interesting disk is 1. And so the differential from this algebra to itself, maybe I have lambda, satisfies Leibniz's rule. And it's linear on coefficients. So coefficients just go through. And on generators, it's defined as d of A is the sum over A minus B equals 1. And then number of R families in this modular space times the word B. And maybe I put here each of the A. So indicating we're in the group ring. And then, so this is the definition of the differential.  So d squared is equal to 0. And A d, let me not say too much about this, is invariant up to homotopy under deformations. Let's say under Le Chondrin isotope of lambda. So in the case that we needed, so in the case when the ambient space is a one jet manifold, one jet space, as we'll see the unit container bundle of R3 is, this theorem was actually sort of fully proved in work of myself and Etner and Sullivan. And that you can do without using abstract perturbations for some reasons. And maybe I'll see if I get to explain it. Otherwise, you can explain maybe during discussion. So what it says is that if you pick this j generic, then d squared equals 0. And also when you deform the thing, you get a homotopy. One would need to say what is this homotopy. But in particular, the homology of the thing is invariant on this. OK. Sorry, Tobias, A is the energy. A, sorry, A is the, this A is the algebra. No. In the formula for the differential, we have E to the A. E to the A, A here, yeah, right.  And then I write somehow, E to the A for the same thing in the group ring, right. So this is some integer number. And then times this thing, so it lives in the grouping. So it's just, you can think, if you want, you can think about it, it's just A. This is, OK. Right. OK, so let's consider the simplest example of this theory that was also the first somehow was discovered. It's called the Chekhanov-Iliashburg Algebra of a note, the Schrodinger note in R3. So consider the ambient manifold to be R3 with the standard contact sector dc minus ydx. So here, a Schrodinger note is a note which lies in the kernel of this thing. And so in particular, when you project it, so I should say first that the rabe, the rabe is just here, the vertical vector field, the z direction. So when you project the Lechonry note into xy space, then it projects to some, if you take it generic, it has double points. And it bounds zero area. If you kind of take the ydx integral, it's zero. And the rabe cores are very easy to spot. So they just correspond to double points, right? Because it's in z direction. And now one can pick the almost complex structure to be the pullback. So the contact plane field projects onto this plane so that there's nothing, I don't know what this is, bijection, I don't know. Funny thing is beautiful pictures on his website. Great. But anyway, so it's isomorphism on this plane, right? So therefore, you can take the standard complex structure and pull it back to the contact planes. And therefore, you can read off holomorphic curves in the simplectization by projecting them down and see that they project to curves in here. So in fact, it's possible to compute here by the following. So we need to distinguish what is a positive puncture and a negative puncture. So the rule is that at positive puncture, the holomorphic curve goes up the rabe coordinate, negative puncture goes down. So here you have such decoration. And then the differential counts holomorphic polygons with convex corners. So that's somehow this index, index, index requirement, if you wish, with one positive and several negative corners. So we need to say kind of few more words to complete this description. So here in this case, what is this H2 relative? That's just H1 of the knot. So there will be kind of one variable in the group ring. And so we fix a point on the knot. And what more? So the other thing is the sign. So here signs is the following. So remember that these chords, they have a grading. And in this case, I should say what the grading is. So the grading is the following. You start at the top. You go along the knot. So I assume the knot has mass loving.  So the grading of A is twice, so that's the mass love, times the rotation number of the positive close up, minus 1. And so there will be negative at the even, so let's see. So right. The polygons have to be embedded, or could they be immersed? They could be immersed. As long as they can certainly cover themselves, but they need no branch points. But they are immersed, and they have convex corners. And then now I'm kind of getting slightly confused. But let's see. So now what you do in order to get the, sorry, so I'm sorry. So somehow, I'm sorry, I should have gone a better picture.  Signs, right. So you shade at each even, even index crossing, you shade somehow half of the corners like this. And then in the disk, so we're going to have to look at papers to get this right. But in the disk, you count the number of shaded corners with a minus 1 to something. So for example, for the unknot, there is nothing here. So what is the differential here, d of a? So this is a. First, let's see, what is the grading of a? So grading of a is 2. It rotates once, right, when you do it. So it's a 2 minus 1. So that's 1. And there are two disks, two rigid disks, this one and that one. And one of them does not pass through this chosen base point, so that's a 1. And the other one, there are no shaded corners because there are no even corners at all. And the other one does pass through this base point, which means that we kind of view it as going once around the knot. So it is 1 plus, I know what to call it, maybe mu, which is the homology class of the knot, right? So you see somehow that the DGA of this unknot is sometimes, I mean, most often is acyclic actually. But if you take mu equals minus 1, then it is not acyclic, so it has something. So that's a. Mu was the mass loss. Mu, sorry, mu is the generator of h1 of lambda. So this is coefficient, right? So the algebra. You want q? Mu was mass loss. OK, maybe, I don't know, t is sometimes used. Let's put t. So t, t is the generator of h1 of lambda, which is here the relative coefficient, OK? So I was kind of, I'm now, the time is flying here. I still don't know this. But anyway, so I was asked to give some exercises. So let me kind of give exercise. So exercise, of course, is to compute this for some other knot. So compute is for the trifoil. If I can do it correctly, I'm not sure. I think that's correct. So compute is something wrong? Yeah, it will go. It's topological term. Sorry, yeah. This should go down, right? Down, under, over. Like that, right? I think that looks better. So compute dj for this. And also, think a little bit, what is the significance here of t? So this, of course, is a harder question. But yt is equal to minus 1. It's something, a kind of special thing here, so on. OK, good. So the next step, so we see that this theory is actually very computable in the simple case that we are in R3, or maybe surface times, or something like that. We can compute this thing. But we are actually aiming for something a little bit higher dimensional. So we're aiming for the unit-potented bundle of R3, which, in fact, is the one jet space of S2. So the next thing I want to explain is how this thing can be done in one jet space. So one jet space. Oops. So if you have a manifold m, then the one jet space of m is just a cotangent bundle, thought of as differential of the function times R, which is the function value. And on here, there is a nice contact structure, which is dc minus the action form pdq. And pretty much as in the case of the plane, where this is actually a kind of special case, when we take this m to be R, and this is one jet space of R. So we can also here use, we can find, so pull back the almost complex structure from an almost complex structure on t star m. So in other words, we take an almost complex structure on t star m, the contact planes, maps again isomorphically onto the tangent place of t star m, and we pull it back to the contact planes and extend it in the usual way in the other direction. And then we have a similar description of the holomorphic curve. So again, so holomorphic disks now correspond to holomorphic polygons of the same nature, but now with boundary on the projection of lambda, which is now a Lagrangian manifold. Inside this t star m. So basically, it's the same thing as four nodes. But now our Lagrangian is higher dimensional, and it still has some number of double points. And we have to find out how to count the polygons. But first thing to observe is that wherever it went here, that this notion of positive negative corner is exactly the same. So you have a crossing, and at the positive puncture, it goes up the rape chord, and at the negative it goes down. So we have somehow exactly the same dictionary. Now the question is, how can one possibly count these things? So here we are somehow we're lucky in the sense that we're basically using Riemann mapping theorem. But when the ambient space has higher dimension, there is no such easy way to find the holomorphic curves. But the idea is that one can degenerate the Lagrangian towards the zero section. So let me try to explain this. So just could you raise the board up behind this? Sure. So now we have some projection of lambda sitting inside t star m. And the idea is the following, that if here we have the zero section, vm, and then this lambda somehow is exactly Lagrangian submanifold here over here. And now what we want to do is we want to scale. So we take the, we have some almost complex structure, and then we scale. So now you take q comma p, and you map it to q comma, maybe I'll take sigma times p, where sigma is tending to zero. So what happens is, of course, that this thing is getting skinnier and skinnier, and gets closer and closer to zero section. And then one can prove that the holomorphic curves, so the basic case of this is very old. And the flora, that the holomorphic curves, when you have a graphical one, they correspond indeed to gradient flow lines of the function difference that this graphical thing defines. So when you have more complicated things like here, then you cannot say that they correspond to gradient flow lines, but rather they would correspond to gradient flow trees, which locally have, locally have the, looks like a gradient flow line, but then it's some sort of tree that is being drawn. So let me try to explain what those are. So I'm probably not going to finish that explanation today, but anyway I can start. So that's somehow the next main subject of what I'm going to try to explain. So this is called gradient flow trees. And I will have to wait till next time, but what I can explain is at least the grading formula. So grading. So when you have this Lagrangian inside the one jet space of M, we projected it to T star M, which was somehow holomorphically important. But we can also project it to the zero jet space of M, which is just M times R. And there it looks, what happens when you project the Lagrangian is that you get the front. And so here is R, and here is this M. And for example, the unnote that we drew before has the following front. And the intersection points, self-intersection points, well, how to reconstruct. So here we reconstruct the p coordinate, pi, is equal to the partial derivative of c with respect to qi, where you have a graph, then you have certain singularities, which I'm not going to talk too much about right now. But at least you can see that the double points, they correspond to points on the front. This is a little bit too good. But anyway, points on the front where the tangent planes are parallel. So here there's one chord in the middle. And now I want to give you the grading formula. So the grading of such a rave chord A is equal to, I should say, one more thing. That the singularities, singularities of this front, they are not so hard to describe in low co-dimension. The highest strata of the singularities are so-called cusp edges. So they look like that. It's a semi-cubical cusp. So c squared is equal to x cubed is the local thing here. And then you just multiply it by r in the other direction. And those are all the singularities in co-dimension 1. So if I pick a path from top to bottom, then I will hit only these type singularities, no kind of this co-dimension 2 or anything. I don't have to describe. And the grading of A is the number of down cusps. So that means I go down the cusp in the C direction, minus the number of up cusps. Is it the opposite way with the arrows? It's the opposite way with the arrows. So I go up in the C direction, plus the Morse index. So the Morse index here is that I have a critical point. If I take the difference, the top minus the bottom, I have a critical point of some function. And the degeneracy condition is that this is a Morse function. I take the number of negative eigenvalues of the Hessian. And then I subtract 1. So for the un-note here in the picture, you see I start here, I go down one cusp, that's 1. And I have 1 for the Morse index, that's 2. And so then I subtract 1, I get my 1 back. OK, so then we can expand. I will stop at this, but we can expand. You can now do an next exercise without any kind of calculation. So you can compute the higher dimensional un-note. It's this thing, which is a, now here this is an, oops. Here you have n dimensions, right? x1 up to xn, and this is z. This is the front. So this is an sn minus 1, cuspital edge, and so compute. And so here you can just compute, because you don't have to know anything about trees or anything at all. So you can compute the dj very easily. So I will stop at this and continue on Wednesday. And then I will continue first with the trees and then somehow try to cover moment here. Thank you. Just for Tobias, can you just say where the Morse index comes from in the picture again? Yeah, so the Morse, so in general here, so when you have, when you're at the point in the base where you have two parallel tangent planes, if you look at the function which is the difference of the upper graph and the lower graph, then you have a function which has a critical point at that point. And that's a Morse critical point, and you can take the Morse index of that with the positive function difference, so the top of the rate minus 1. I don't think the right most double point should really change that example, the real exercise. But do you think that exercise, the trifolding? The trifolding. The right most is wrong. The right most is wrong. Thank you.  Thank you. Yes. Sorry. Somehow. Some convention. That needs to be the same at both ends. OK. Any other questions? So like, the theory, it's, if you have a, how to say it, the hyper-circuit is an m cross r, and then you tell me something about it. But if I took that whole thing and I was multiplied by a trivial factor, I'd go up a dimension by taking that hyper-circuit as 1, so how does the theory change? The same theory, or what's the other one? So if you multiply it by s1, then the theory changes. It's actually one of my exercises I want to give you. But indeed, the theory changes.  So you have these s1 families, right? So you have to perturb it away. So you get one, something sitting over the minimum, something sitting over the maximum. Over the minimum, you have exactly a copy of what you had before. And over the maximum, you get, so here, here somehow, I have a sort of a generator A hat, corresponding generator A here. And when I want to compute this DA hat, then I get, let's say, gamma of DA. So this, what is this DA? DA is equal to some sum of monomials, b1, b2, up to bm. And the gamma of a monomial up to size. So let me forget about signs. So it's doing the following. So it's b1 hat, b2, bm, plus b1, b2 hat, b3, bm. Plus, and then so it goes. So I just move the hat once. It's like some kind of homotopy operator, if you wish. So that's what it does when you multiply by s1. And when you multiply by r, you kind of have to choose whether you want to live here or you want to live here. So it's not so clear. I have to say what you do at infinity. OK. Thank you for this again.


Hi everyone, this is Chih-chou. Welcome to my channel and welcome to another comic book haul video and this is gonna be a quick comic book haul. We only got two comic books in this, okay? But they're beautiful. Well, all comic books are beautiful, really. Almost all comic books are beautiful, but these two are fantastic and Let me tell you what they are. Now the first one I'm going to show you is a comic book haul that I did before the second one. We bought the second one. And since we started talking about comic books, started getting back into live-streaming comic book videos and specifically live-streaming the comic book reading videos during the discussions, during a live chat on Twitch, and also on YouTube. The topic came up where people were missing the comic book hauls, right? So what I started doing was sort of started building up my funds a little bit to start, you know, nibbling at comic book hauls through eBay mainly, actually all of it through eBay. I bought some comic books at conventions and stuff, but that stuff sort of is On the down-low right now. It's not really happening, right? So all of these and they have been for the last few years, all of them been through eBay, really, right? So I started nibbling a little bit and I got my hands on a couple of books and one of the books was this, okay, and This is a beautiful book. We ended up picking this baby up. Let me tell you what this is. This is Kit Kalt Kalt Outlaw Number 107. Okay, check this out and This was published in 1962. Let me tell you who's on this. The cover is by Jack Kirby, the pencils by Jack Kirby and the inks is by Dick Hairs, right? And From what I understand, I don't know if this is rare or not. A lot of places say it's a rare book or whatnot. I don't know how rare this is, right? Because you can't find it, but it is sought after, right? And I think it's the only monster Kit Kalt comic book out there, right? And I Really wanted to get my hands on this because it's It's a monster comic book, Western monster comic book covered by Jack Kirby, pencils by Dick Hairs. The stories in this are written by Stanley. There is There's art. There's a handful of people working on the art on the inside covers of this. There's Jack Keller did three of the stories, two or three of the stories, three of the stories, I believe. Joe Manley did one of the stories and Dick Hairs did the artwork, the pencils and the inks for one of the stories. So there's five different stories in this and the cover for this says the monster is lifting me into So Kit Kalt says the monster is lifting me into the air by some strange power. I'm completely helpless. Right? Right, beautiful, beautiful. And monster comic books, they are sought after. There are genres that There are definitely avid collectors that seek out monster comic books. I personally love monster comic books, monster issues, monster magazines. I have some of them creep and some of the other ones as well, right? But I'm not solely a monster comic book collector, but this was a beautiful cover and it's signed by Jack Kirby and Dick Hairs at the bottom here. Take a look. I don't know if you'll be able to see it. It's really, really small, really small. And the glow of the plastic. Where is it? Right there on the boulder, right? So it says Kirby and Heirs. And this thing, let me tell you what the grade on this thing. The grade on this thing is the person that was selling it, graded it good. Okay. And I ended up paying 18, 1850 Canadian for it. So that would come out to around 1450 or so US or $14 US, right? So 1850 Canadian, $14 US and Kit Kalt number 107, right? So I was sort of building up my funds a little bit and you know, I'm low balling comics still, right? I'm trying to get a good deal because my funds are limited. So I'm trying to get as much bang for my buck as possible, right? And this is a pretty good bang for your buck. Okay. So that's one of the books we ended up buying. Now, what happened after I bought this book? And I was tracking some of their comics and stuff like this. When I ended up buying this book, I got one donation coming in through PayPal, right? And the only thing that said on the donation was comics only, right? So the donation was to be used, that the funds were to be used to only buy comic books, right? And I'm like, okay, okay, we'll do, right? And that's Connor. Thank you very much for sending in the funds, right? So I started tracking the books I was tracking plus a little bit more and I was sort of trying to decide which ones I was really going to push for, right? And then while I was tracking some of these books within the week, because usually they end, I think this next book, it was a nine day period that once I started tracking it, the funds came in, it was, the timing was crazy, right? Because this series I'm about to show you is sort of golden grail for me, right? It's the number one of this series is one of my golden, I think they called golden grail or one of my most sought after books that I'm trying to get into my collection, right? And I've been trying to get my hands on this comic book for a very long time. It would have been better to buy it 30 years ago than it is now because the price is higher, but you can only buy what you can afford at the time that you can afford it, right? So while I was tracking issue number one, two and three of this series I'm about to show you from the same seller, local seller, right? These funds came in. Thank you Connor, comics only, right? So I was like, excited, excited, excited, right? So I placed my bids on one, two and three, right? And the number one of the series, it was going to be a lot more than what the funds came in, right? And then a couple of days later, we had a little bit more funds come in. Philip, thank you very much for sending in the funds. And Philip sending the funds didn't say comics only, just sending the funds, but I'm tracking comic books. It's going to go towards comic books if I can get it for a certain price, right? So I bid on all three of them and the price was kicking up. And number one, I was, I reached a point where I was like, okay, I need to go extremely frugal. I'm going to, you know, reduce my expenses on a few different things. But the the comic number one went above what I could afford to pay for it, right? And you could only buy what you can afford, right? There's one advice I can give people is when you're collecting comic books or you're collecting anything, if you're into the collectible hobby business or whatever it is, you have to realize that you can't buy everything. It's impossible. It'd be great if you could buy everything and have the space to keep everything and catalog everything and read everything and just enjoy everything, right? But you can't. And one of the pleasures of collecting comic books is the chase, right? Is managing your funds and looking for the bid and trying to get a good deal and the excitement involved in collecting comic books, right? So the number one of this issue went above what I could afford putting funds away for a few months, right? And then there was number two and number three. Number three was a lower grade and it went above what I was willing to pay for a low grade, very low grade for that, right? So it was a little bit on the expensive side for me, right? But number two was ended up being a fantastic buy and combined with the funds that came in from Conor that said comics only and Philip that sent funds afterwards, we actually have a little bit more funds left to do a couple of more or do more comic book calls, right? And by that time I'm going to try to increase the increase the budget and try to nibble at some of their auctions and I'm tracking, right? But it is a beautiful book, this thing, right? I'm very happy to have it in my collection. What we paid for it is probably, well, it is one of the more expensive comics that I have bought as auction on eBay, okay? Like much, much more expensive than 99% of the comics we've been buying on eBay, right? And let me tell you what this is. I know I'm dragging it a lot, I'm dragging it but knowing if you're a comic book collector, you'll have a phenomenal appreciation for this, okay? This comic book is from 1952, The Golden Age of Comics. It is one of the most important comic book series in the history of comic books from one of the most important companies in the history of comic books. It is issue number two of Mad Magazine or Mad Comics, right? From issue number one to number, I believe 21 or something, it was called, it was comic book size and then it went to magazine size, I believe, right? So this is issue number two of Mad, we'll call it Mad Magazine but it's Mad Comic Books and it came out in 1952 and Harvey Cursman, let me tell you who's on this thing, right? Harvey Cursman is the editor and he did a writing on this too as well, I believe, Al Feldstein, Jack Davis, John and Mary Severin, Wally Wood, okay, Harvey Cursman and Bill Elder, okay? And the cover of this is obviously, this is issue number two, well not obviously, I guess it could have worked on issue number one, but it's the first cover by Jack Davis from Mad Magazine and Jack Davis is huge, she did a lot of, I'm going to take it out of this mylar, I put it in mylar right away, right? Jack Davis is quite huge and he's done a lot of work in the film industry, posters, advertisement and did a tremendous amount of work for Mad Magazine obviously, right? But let me take this out and we ended up, let me tell you how much we ended up paying for this and I wrote down the information at the back here, right? It came out in December 1992, issue number one came out, it was a bi-monthly series Mad Magazine or Mad Comics, right? So it would have been August, September, October, November, so October would have been issue number one and issue number one, it was a low grade issue, it went for, it was a fantastic deal by the way, what issue number one went for, it went for $850, $60 or so, right? And that was above what my budget allowed to buy, $860 Canadian and it was graded at good, right? Which is still a very good price, okay? This comic book, we ended up paying, it's graded at very good, okay? So 4.0, we ended up paying $152.50 Canadian, which comes out to $112.40 US or so, okay? It's got tape on the spine and it's got three extra staples. So the person grading this grade is very good. The presentation of this is fantastic. Let me make sure you put the tapes here so they don't snag the comic and show you the comic without the glare of the mylar, the bagging there. And it's a beautiful cover and by the way, what we're going to do is we're going to read this comic. I haven't set the time yet as to when we're going to do the next reading and we're going to do do the reading of this live, right? Thank you very much Connor and Phillip for sending in the funds. I hope you enjoy the reading when we end up doing the reading, which is most likely going to be within the next two weeks, okay? So right now we're on June 22nd, I believe, 2020. Within the next two weeks, we're going to try to read this and let me show you that. I want to be careful with this, right? And this is obviously the lowest mad magazine thing that I have. It's a great cover. And I flip through this, right? Usually I don't try to, I don't flip through readings that we're going to do if we did comic book calls, but I flip through this. It's beautiful. It is beautiful. Okay. It is absolutely beautiful. The artwork inside is phenomenal. Okay. What a treasure to have, right? And what does he say here? I feel it in my bones. Someone is giving me the evil eye. Right? They're like this. Too funny. Too funny. Awesome. Awesome. It's beautiful. Okay. I'm very happy to have it. It does have the tape, this brown tape on the spine, but we'll take a closer look at it when we do the comic book reading. Okay. So good, you know, 4.0 graded for what was it? How much did we end up paying for this? $112, let's say $113 US, $153 Canadian. That's a great price. That's a great price. And a comic book like this, I am very glad that it's not slabbed because a comic book like this requires reading. And we will definitely be reading this together, gang. Possibly this week, possibly either in this set that I'm going to announce or the next set that we're going to announce, we're going to read. And we'll have, we're going to do this one first, for sure. And I'll try to go through my boxes and have maybe three or four, five other choices of comic books that we're going to read. And there's been requests for us to do a superhero comic book readings because we've been doing a lot of romance comics and science fiction comics and war comics and whatnot. And we haven't done too many superhero comic book readings lately. So we're going to do superhero comic book readings. And I haven't decided if we're going to read this one yet. Either way we might. So this is what we ended up getting. Okay. Kit cold number 107 from 1962 and mad comics number two from 1952. Okay. I thought you would get a kick out of this. Connor, Phillip, thank you very much for the funds. We wouldn't have been able to grab these without it. Right? Like 1850 for Kit cold was on the high. And I was willing to willing to willing to bid right because I was slowly building up the funds.  But stay within your budget. Enjoy life. Don't make sure you don't get pressures of needing finances to take care of life's necessities. If you're playing with certain things that includes investing as well because if you're investing, you're really playing. You're really to a certain degree gambling in a sense. But when it comes to comic books, it's not just an investment. It's a way of life. It's a way of being it's entertainment, this enjoyment, as well as it possibly being a form of investment. So if you can get things on a great deal, you get things on a great deal, right? And we got mad magazine number two from 1952. Right? At some point, we'll get mad number one, we will 100%. And once we get it, we're going to read it. We're going to read every little word in this book. So we're going to read everything in this from beginning to end. And when we get our hands on mad number one, we'll definitely do the same for mad number one as well. Okay, gang. I thought you would enjoy this little, little, just a teeny, teeny, we need a little two comic book haul, but holy grails, really. Well, holy grail for mad. The Kid Colt one is beautiful book.  How many western monster comic books are there? I don't know. I'm not a specialist in the western monster comic books, right? But I'm pretty sure there aren't too many out there. And mad magazine, mad comics. This is one of the books mad magazine was one of the comic book or magazines that are comic book related that I avidly read when I was in elementary school and more in high school. Mad magazine as well as heavy metal. Those are the two magazines that I try to, when I could afford it, buy them and read them and, you know, get the Alfred E. Newman for presidents, stickers, play around with them and whatnot. And that was more in elementary school, right? Well, it's fantastic. Very happy to have this in the collection. And again, Connor, Philip, thank you very much for the support and the funds to get us a comic book haul. Okay. Aside from that gang, I'll see you guys in the next video, next live stream, next podcast. Okay. Bye for now.


We need you. We're all stand with me. Agree with me. We're all to survive. Survive. I need you to survive. I won't pawn you with words from my mouth. I need you to survive. This is where we need me to survive. You all need to survive. As we stand in this space, the place where both of John was killed, today we all have a responsibility to make sure his death isn't in vain. As children of God, we are all to call to be stewards and advocates of justice. And while many of us here we are tired and frustrated, some of us fatigued. Don't grow weary in the struggle. Don't grow weary, but keep on fighting for justice. Keep making noise. Now from what Max says, if you make noise, something happens. So we're going to make noise, we're going to march, we're going to protest, and we're going to pray for justice comes. So we have a responsibility as one church, a united church, that knows no color, the blood is red. So today we stand in solidarity, grab somebody's hand, grab somebody's hand. We stand in that secret strip in the times of weakness. We stand in that spot in the hoping moments of despair. And we're going to pray a proper prayer that Jesus taught his disciples when they were under attack. Let us go to the Lord and pray the Lord's prayer. Our Father, which art in heaven, hallowed be thy name, thy kingdom come, thy will be done, on earth as it is in heaven. Give us this day our daily bread, and forgive us our trespasses, as we forgive those who trespass against us. And lead us not into temptation, but deliver us from evil. For thine is the kingdom, and power, and the glory forever and ever.


Welcome back to a new session on dentistry and more. So today's topic is matching which is coming under case control study and further under epidemiology. So in epidemiology we have descriptive and analytical in the observational study and experimental study. So analytical study we have two types that is case control and cohort study. So in case control study one of the step was matching. So today's video is about matching, its definition, the types of matching, the problems associated with matching. So let's get started what is matching? Matching we have two definitions. So let's study this definition given by Leon Godis. It is a process of selecting controls so that they are similar to cases in certain characteristics such as age, sex, race, socioeconomic status and occupation. So why we are doing matching is we need to keep equal parameters such as age, sex, race, socioeconomic status and occupation in both cases and controls. So it is not easy way because the age, sex, race, socioeconomic status and occupation such parameters would be different but we need to keep in such a way that we select controls similar age or similar sex or similar such parameters so that we can assume that they are different only in the presence or absence of a disease. Otherwise what happens is all these characters or all these variables or all these attributes will act as a confounder or the third variable. If a confounder is there in the study it will distort the result. The result we get will not be the actual result. So we need to control the confounders. So we need to keep the same effect of all these variables both in cases and controls so that we can assume that they are different only in presence or absence of disease because anyway control is people without the condition or the without the case. So let's see what is design of matching. So matching variables such as most commonly we do age and gender matching. If we are doing a matching based on the age that is if you have a case of 5 years we need to always make sure that we select controls with that same age. So controls can be most commonly matched in two types. One is individual matching and another one is pair matching. So individual matching is very simple sorry individual matching and group matching. Individual matching is just like we are selecting a person with a disease. So we can select a person without disease but with the same age or same gender the same socioeconomic status or same race that is known as individual or paired matching. So we can do paired matching when there is two controls which are usually matched to each case. So we can always we take more number of controls. The ideal ratio is 1 is to 4 but minimum we need to have 1 is to 1. But group matching is a different strategy. We select a population of controls such that the overall characteristics of the case. Suppose if 15% of the cases are under age 20 ok so we are considering only age parameter so the controls also should be under 20. Because same group that is 15% controls we select under 20 age because cases are 15% or under 20. So that process is known as group matching or frequency matching. So we have two types of matching individual or pair matching and group matching. So what are the mistakes we face or the problems we face that is over matching. That is matched only on factors not to be caused of the disease. Suppose we are thinking that age could be the factor which can act as a confounder. So we are not addressing other parameters such as gender socioeconomic status. So we purposefully neglect all those factors and we concentrate only on one parameter which we would have thought that could be the contributing factor or that could be the confounder. So that process is known as over matching. We need to match as much as possible variables. So what happens is if we do power analysis by matching more than one control in general the number of controls should be less than four because of there is no further gain of power above that because maximum is one is to four. So there is no point of keeping more number of controls. So over matching has no statistical power also because the maximum power we obtain with four controls per case. And so other problem is individual matching on too many variables is time consuming costly and cumbersome and may lead to two less controls. So if we are trying to match with too many variables like age, gender, race, socioeconomic status income what happens is it will become very confusing and may lead to less number of controls because too many variables are coming up and which we cannot explore possible association of disease with any variable on which cases and controls have been matched. So what we have to do is therefore only factors which are not to be associated with disease are studied. So we don't need to match for all the variables. And over matching also have problem like matching on variables other than those are risk factors of the disease either in a plant or inadvertently we are doing over matching. Just one example like in a study of OCPUs that oral contraceptive pills as a risk factor for cancer if you use best friend friends as controls it is most likely that the controls would also be OCPUs. In effect we would have matched for the very factors we want to study. Suppose the controls if we are selecting they should be without this factor but if you are selecting controls from the best friends they also will not be considered as controls. And we can say that one another example that is if we have neighborhood control in a study on nutrition and tuberculosis we would be inadvertently matching for socioeconomic status and this nutrition. So always we should select neighborhood controls for a study on nutrition and tuberculosis. So what happens is we are matching for socioeconomic status and this nutrition. So it's are a few examples about matching mostly it comes under a short note for four marks or three marks. So only thing we need to write the definition and the types of matching that is pair matching and group matching and little bit about its problems that is over matching problems. And over matching has more than four members of controls means there is no power statistically. So one or two examples also you can write. So that's all about matching which comes under a case of control study step and further in epidemiology. So I will come up with a new session on dentistry and law thank you.