Hello? Keston. Okay. Perfect. All right. I will be talking about RIST, a new interoperable error correction protocol for the transmission of media streams. So the presentation will be divided in three parts. We will start with a general overview and history of error correction protocols. Then we'll move to talk about the new open source library, LibRIST. And finally, we will talk about some virtual image tools that are available for integration testing. All right. So let's start with the basic concepts first, the error correction protocols. What are the basics? We send media streams using UDPs because we want to maximize bandwidth usage and we want to achieve consistent and reliable latency on a network transmission. However, because UDP has no acknowledgement mechanism like TCP does, and because of this without error corrections, there will be some packet loss. And the packet loss will cause video on audio artifacts in your transmission. There are several possible ways in which we can overcome this, right? We can add redundant data in the packet themselves to rebuild the drop packets. This is called for error correction. Or we can add two-way communications, hold on, adjust this, or we can add two-way communications such that the receiving side will recent for the lost packets and they will be transmitted in real time. This process is called an ARQ, automatic repeat request mechanisms. So the ARQ has been around, the ARQ and the FSM both, they have been around for more than 40 years in one way or another. And there are dozens of open and closed source implementations of both types of protocol. RIST is a new, officially published, interoperable standard to perform this error correction. What are the typical usage of error correction protocols? They're generally used for content streams from remote to the studio for mixing prior to broadcast, cable cast or streaming, for sports, news and opinion shows, foreign TV feeds, ethnic cable offering, mass shootings, etc. In today's world, internet connections have better uptimes than expected least lines. We're going to publish a study of two years of a very large provider that had a number of least lines all over the world and they had in parallel internet lines from the same places. The uptime was higher on the internet lines. However, unlike least lines, internet connections are expected to be lossy. There's an expectation that if you transmit any type of protocol that doesn't have acknowledgement, like UDP, there will be packet loss. So how does it work? The protocol itself. Typically, ignore the image on the right, there's just one particular implementation, but typically they all have the same type of mechanism. You use a time stamp and a sequence number, a sequential number on the sender side and you tag each packet and with this data, the receiver can easily identify any missing packet by looking at the sequence numbers. Upon detection of a lost packet, the receiver is going to request a retransmit to the sender for that missing data and this is all done in real time. Finally, upon the receiving of that missing data, the receiver inserts the packet into the buffer and then this all happens before that part of the contents is delivered to the receiving player or whatever that's on the other side. So what are other additional requirements or a wish list that we would like to have on an error correction protocol? Well, typically implementation of the protocols have to account for the fact that one or both sides of the transmissions might be behind a net with no public IP address, right? Or perhaps a bandwidth is not enough on one ISP for the quality they desire and they need to combine two or more ISP links. Some of these can all be achieved using tricks and techniques like port mapping, VPNs, and bonding. But that would mean that in order to use an error correction protocol, you would need to be also a networking expert to set it all up, right? So instead, these features are in most cases added to the different implementations of error correction protocols out there. So error correction protocols, right? Here's a shameless pitch. DOSER is my proprietary patented protocol and it's typically sold with a hardware or a VM containing a custom version of the Linux OS. DOSER has won several awards including an engineering Emmy for its technology. There are several other proprietary and patented protocols in use today. Most of them leverage their technology to sell reliable links as a service, not just to, you know, they don't just give you the devices. One particular vendor's implementation, High Vision, was published as an open source a couple of years ago under the name of SRT. I've been told that the source code release seems to have some inherent design issues with threat safety and with readability. And up until recently, it had no published specs. I think they finally published an official spec for it. But it is, you know, that particular vendor's implementation of an error correction protocol. So let's dive now into RISC itself. What is it and how it was born, right? Here's an excerpt from the executive summary of the first published RISC, simple profile document. I typically don't like read anything verbatim that's on the screen, but in this case, I think it's worth it. So it basically says, many solutions exist in the market for reliable streaming over the internet. These solutions all use the same types of techniques, but they are all proprietary and do not interoperate. This technical recommendation contains a protocol specification for reliable streaming over the internet so any users can mix and match solutions from different vendors. That pretty much summarizes, you know, why it was born. What was achieved with RISC was very unusual. A group of industry experts, including most, if not all, patent owners of different error correction protocols, they worked together to publish an interoperable standard that was free and clear of all patents, which also included the combined knowledge and experience of all these different vendors that have been using these technologies for the last few years. So this was not a theoretical exercise on the contrary. It was a culmination of a multi-year multi-vendor real-world experiment. So where does it stand now? It has been almost two years since the workgroup started, and we have published two documents. We have published one document and are about to publish the second one. They correspond to the simple profile, which is a TR-061, and the main profile TR-062. Here I also show some of the companies that are part of the group and that are very active. Actually, I forgot to include your company, sorry. You're in the forum. So we have collectively performed several interrupt testing events of each other's implementations. So it's not just one library that everybody uses, but everybody has written their own code and we've done interrupts among everybody. And most notably, RIST is now part of AWS as well as an INGIS mechanism. An important aspect of the design philosophy of the group is that we leverage existing IRFCs as much as practically possible to keep the final spec short and at the same time very well documented. So let's talk about the first, the RIST simple profile that has been already published for over a year and has been implemented by a number of projects. So the simple profile was designed with the idea of graceful degradation. In other words, senders that do not support RIST can still send their streams to receivers that do and vice versa. The one and only requirement is that you transmit your stream with a valid RTP header, which is pretty standard. In addition, when you want packet recovery, you open a second connection from the sender to the receiver and you exchange RTCP packets over that second connection. These RTCP packets can contain, like you see here, an example, timestamps, counter packets sent, et cetera. They can also be empty packets for, you know, like a keep alive to establish state over firewall, et cetera. Now, once this secondary RTCP channel is established, the receiver uses it for retransmission requests, among other things. We'll go more in detail later. So let's recap. Simple profile has its basic characteristics. The use of RTP, you can see that the use of RTP and RTCP were a result of the design goals for the simple profile which was graceful degradation and leveraging of existing standards and specs. So pretty simple. It's somebody that has an RTP implementation. It will take them a day to add a packet recovery to it. Possible RTCP messages used, you know, these are standard messages and we leverage them for the protocol. On the sender side, we have sender reports, empty reports, source description, receiver, we have a receiver report, and the most important, the negative and acknowledgement packet to request the missing packets. All right. Here is how this NAC-based recovery works with a little bit more detail. An important thing to consider in this diagram is that, as you can see, we have the first packet loss not received and the receiver side does not send the acknowledgement immediately. There's a gap there. And that gap is important because we need to account for packet reordering. In UDP transmissions, there's always a possibility of packet reordering, not only packet loss. So the receiver might interpret a missing sequence as a loss when in reality it's just a reorder packet that arrives later. So it's important for us to have this gap before we request the first transmission. So the NAC messages send back to the sender, the sender processes and sends the packet again, the data packet, and then continues with the natural flow in parallel. And that's pretty much the mechanism. It's very simplistic, very effective. It's something that has been around for 40 years. And it requires certain parameters which are all specified in detail. We support two types of NAC messages. We use either a bitmask or a range and it's up to the receiver to request one or the other. One might be more efficient on the other depending on the amount of data loss the network is exhibiting. So we also suggest some defaults based on experience by, you know, it was a consensus among all the vendors and everybody that participated that for a typical internet connection from one coast to the US to the other or across the Atlantic or anywhere across Europe, these defaults work quite well. If you can sustain a thousand milliseconds of latency which is the size of the buffer on the sender side, these parameters will work quite well for any internet link. Well, in reality, if you see the graph on the right, a protocol can be implemented also to make those parameters dependent on the roundtrip times. It's not necessarily fixed. A good implementation will use a real-time measurement of the roundtrip time to adjust the parameters in real-time. So let's move now to the main profile which is the one that's about to be published. It's supposed to be published by, you know, today but it's still under review. It's going to come out in the next couple of weeks. So for the main profile, which came basically a year after the simple profile, the design goals were slightly different. We now needed to achieve multiplexing and encryption and some other requirements as well which we'll go over. For this, then we didn't need or require any type of graceful degradation. Main profile connections can only, you know, be established among two RIST devices. There's no longer the universality of having an RTP stream be the first thing that each other sees. So what does the main profile bring to the table? We needed a way to multiplex, so we used GRE, GRE tunneling. Why GRE? Well, one, it eliminates the use of an extra port. It allows for the multiplexing of streams. There are published encryption and authentication standards we can use on top of it. In our case, we chose ETLS and a former pre-shared key. GRE stands for general encapsulation. We can also separate another important side effect or having now one port and one multiplexing is that we can separate the connection initiation role from the packet recovery role. So this allows for the possibility that either side can be behind a NAT or firewall. It's no longer like in the simple profile case where the receiver side had to have either a public IP or a port mapping. Now either side can sit behind a NAT and we can establish the connection at the GRE level, at the tunnel level, and then on top of that, we can send the data with the packet recovery. An additional benefit or GRE that if they implement the desired set, it allows for the tunneling of any other type of data ground, not only UDP or streams, video streams. All right, so after the GRE protocol header, and we support two types of headers, if you look at it here, the typical use, you have a UDP header where you transmit your data and you have now the GRE header right here with the optional flags. One of the parameters of the GRE header is what protocol type is going to be your payload. So you can do a standard IP payload, which is a full datagram mode, and then this now becomes just an IP datagram. You're going to have another IPv4 header or an IPv6, whatever you prefer, and then you payload under it. But we also added support for a new protocol type that's not part of the normal GRE specification, specific for RIST, to use it for reduced overhead. The new type only uses 4 byte source port and destination port. And then it assumes that what follows is an RTP message just like with a simple profile. So you can do it as simple or as complicated as you want. So there are two possible encryption methods supported by the main profile. DTLS and PSK. DTLS uses SSL certificates and all the security complications that are associated with certificates. PSK, on the other hand, supports a simpler passphrase mode with the downside that now you have to get that passphrase communicated to both ends through some secure channel, a phone call, preferably a secure way. But now you have to perform that outside of the scope of the protocol. So what is the current status of RIST of this protocol? We have the simple profile. It was completed, integrated and tested. It's part of VLC, U-pipe, G-streamer, and others. It's on all the vendors that are part of the workgroup and people keep adding the simple profile on a weekly basis. The main profile that adds the GRE encapsulation and the encryption, it was finished and sent to review just a few weeks ago. We were expecting to be done by now. It's most likely going to be done before the month is over, probably within the next week or two. There's a new open source library that was created with the main profile called LibRIST. The main library is going to live under the umbrella of the VLC, JITLAB, code-based with a public group. It was coded and following the standards of the David decoder. Same rules that's applied for both. And we're waiting for the document to be officially published so that we can push the library to the repo. Right now, the repo is simply waiting for that document to be published. The main profile is scheduled to have interrupt between all the companies at California in the next two weeks at Cobalt's offices. And then after that, there's an immediate BSF conference where there's also going to be a demo of all the companies interoperating at about nine of them, I believe, showing the main profile with the RISP being transmitted from different parts of the world to a local monitor there. All right, so let's talk about LibRIST now. Basic features. It's a library, simple APIs, multi-thread safe. It has sample applications with it. The sample applications are just for a single stream, but the library supports any number of it. The library supports point-to-point, point-to-multipoint. You can configure every aspect of it. And best of all, it hides all the complexities of notting, port mapping, keep alive, sockets. You don't need to be a networking expert to use it or to implement it. With 20 lines of code on each side, you have a risk connection between two endpoints. Your code doesn't even need to open the sockets. So what are the more advanced features of the library? AS encryption, either DTLS or PSK. Right now the current LibRIST only supports PSK. Somebody wants to help out with DTLS. They're welcome. Multiple streams. We have an optional compression that is not part of the standard, but we found that it's effective in some streams. We can encapsulate multicast. And now we can specify which side is going to initiate the connection, independent of which side is sending the stream. All that is supported in the library. For somebody that wants to implement advanced features, they're not part of the sample application that comes with it. It's very simplistic. So next, the virtual images. Right? How can we make it easier for people to implement the protocol, the standard, right? Well, step one is to provide false library, which we have already done. We have a list ready to be published. Step two is to provide an easy way to use a pre-wrap OS image that has the application and library already compiled inside and give them a simple GUI to configure it as a relay. So they don't even have to compile the library. They compile the code. They just grab the image, put it on the virtualization engine of their choice, and test their code against that image. That image will serve as a relay, receive it, let them play it in VLC, reverse ascending and let you play a content that you put on the image. Shameless speech again. The idea is that you will love the image so much that you will want to buy other flavors of images that have more functionality. So demo applications. Here's the workflow of a typical use of the image or the sample applications that's included with the library itself. On the re-sender side, we listen to a UDP port, read a local stream, UDP standard, encapsulating it to RISC and send it to multiple locations encrypted. Similar to what they've shown in several presentations today, that was done. On the receiver side, we read the re-stream, decrypted, and output to the next-stage device. It could be a player, or maybe you want to output as a local network multicast to be used locally in the receiver side for other purposes. So possible uses of the image, tested, learned, ad-hub, live stream, transmittal, a relay, development, whatever you want to use it for. Some more advanced use cases that are not available in the current sample application are, you know, virtual tap or tone interfaces. You can actually bridge two machines using top-tap interfaces using the RISC protocol and have zero configuration mode for the streams. Whatever you push on one side, automatically ships up in the other machine across the internet with the error correction on it. So this allows for the easy multiplexing of streams. We also support in the library already load balancing and redundancy and there are no limitations of any kinds for the use of the library in commercial applications. The license model is the same as the David. I forget if it's LG. I think it's not a GPL. It's an even looser one. So, thank you so much. There are a few questions. Does the library still offer a socket-based API like LibreSRT so people can drop things in? I'm not sure I understand the question. What do you mean by... Oh, I see. We don't have that now, but it would be a very easy to add. An emulator, yes. The code will be online and it's very clear or structured, so it will be easy to follow. I tried once to read the SRT code. Successfully. Firewall portal opening can be a problem in some organization. Do you have a mode? Is Firewall traversal like stun? I think so. What we have, we have the ability to initiate the connection from either side. So, if one organization is giving you problems, just go to the other end and get a public IP or a port mapping there and you'll be able to establish connection. A lot of the time, it's easy to get an outbound port open or it's already open and you don't have to do anything. Finally, are all these competing protocols a problem? It does stuff to after all and it's implemented in products. Well, it's a problem because until one standard dominates, you know, somebody that wants to create a new link is going to have to decide. Do I use RISC? Do I use SRT? Do I buy Dozer? Do I buy some other implementation? What do I do? So, I paid my money on RISC. But I'm biased, so... Another question from the floor. Do you recognize the room? The EBU from St. Ben who helped us film everything, the camera, and all of you attended and will now help us clean the room. So, please take all the trash that you can and put it in the trash can. Thank you.


What they gonna do with me now? I'm still a twerk of the town. I'm getting the sisters, I'm hooking them down. Hey, everyone, I'm your host, Enrique. Thanks for tuning into the Talk of the Town. Today, we got a very special guest on the show. Jean-Claude, what's up, baby? All right, awesome. So we're going to get started with a little icebreaker we have here called Rapid Fire Questions. So ask you some questions, and you answer them really quickly. All right. All right. So the first one is three things you'll take with you on an abandoned island. My three kids. So what is your favorite food? Tacos. OK, respectable. I like that. I can agree there. What's your favorite album? Take care. OK. Favorite song right now? Count these bands rushing slow. OK. So OK, staying on the song tip, what's one song you know all the lyrics to that isn't your own? Girl, you know I see naked. Don't be a pretender getting high as a condom. That's when they all come together. That's the name of that song again? It's Come Through. It's Drake's Come Through, finally. There we go. You got me there for a second. I was like, damn, you know the lyrics went off the song name. I used to get it. So what's your dream feature? Drake. Yeah. Nah, I figured it out. What's one song of yours you wish got more love? I can't remember the name of it. I have a terrible memory, but it's me on a drill beat, but it's not like a drill song. It's more like a pain song. I thought we'll figure it out and we'll put the name right there. What is your favorite thing to do in New York City? Be home. OK. And what show are you currently watching? Jiu Jitsu Kaisen. Oh, Word. Season two, or the first one? Season two. Yo, I got to get Crunchy Roll around the spot. Do you watch other anime, too? A word? Do you watch Attack on Titan? Yeah, that's my show. I didn't finish the third or fourth season, though. Because it's like you have to read the manga at some point, because it kind of skips a lot of stuff. Yeah, no. I definitely recommend it whenever you get the chance. Some top tier show. And then last one is one lesson you've learned in the industry so far. It's a ladder. It shoots in ladders. Get some ladders. That's a good one. Really good analogy. All right, but and with that, well, Randon, thank you so much for playing rapid fire questions. All right, it's a shame. How did your musical journey start? So my musical journey started. So my uncle died, I think, when I was like 10. And he used to rap. So I used to go to South Carolina to spend it with my aunt. And he used to be at my aunt's crib. He used to live with my aunt and my uncle. And we used to see him inside the room. Like he used to practice. I think he used to play clarinet. I think it was. And he used to be in there with his little tape recorder, his Jay-Z, his Jay-Z posters on the wall and be rapping. So I used to see that. And then when he died, it's like I kind of just slowly kind of pick up the mantle. Kind of picked up the mantle. I wrote my first rap when I was like 12. But then when I was in my senior year at high school, I wasn't really rapping. Sometimes I was just right. Like me and my friends would do something like Wildin' Out. When we was outside of my grandmother's crib, my grandmother had a porch.  We used to play like a game where we rap, but we talk in trash or you tell them. You're making jokes in a rapping form. This is before we even knew about Wildin' Out. So this is something we used to do. But from there, my senior year, my man, his name's Giz the Wiz. He just like, yo, bro, then we should start rapping. He was already like kind of into it. And then Rest in Peace, My Son Cash. He was like at the lunch table one time and then, you know, just do the beat on the lunch table.  First, I'm sorry for the loss of your uncle and your friend. Yeah, thank you. And secondly, now I feel like it's a really honorable way to keep it going, you know, like picking up the mantle and look at what you've done with it so far. Right, I know you're proud. I know you're proud. I know you're looking at you're proud. So what were some of your influences growing up? Like outside of familial influences like on music, more like the people you would look to listening to music and be like, Dan, that's the kind of stuff I want to make. So you talking about like outside of hip hop? Music in general. It could be outside of hip hop. Music in general. Yeah, I know a lot of people, like it's crazy, you know, like we have a lot of draw rappers come on the show. Yeah. And then I'll ask them that question and they'll be like, honestly, Michael Jackson. I listen to Michael Jackson, but real, bro, I used to live in Colorado's village when I was younger with my grandmother. I used to live on the 24th floor in the bathroom. We used to have this thing to play music on or whatever. This is back where you still had to buy CDs. Wow. So I had the Backstreet Boys CD that my cousin had, the Usher CD. The one we're here on the cover is like Brown and beige. And he's like this on the cover. I forgot the name. Is that Confessions? I think that is Confessions. Yeah, my parents had the Confessions I think the Part 2 CD. Yeah, I think that was Confessions. So I used to get out the shower to switch the CDs from, I used to listen to, I like, want it that way.  What's the name of the song? You got it, you got it bad. That was my song. But besides that though, in high school, I used to listen to Classical Baroque. Oh, wow.  So did you play instruments in high school as well? Man, I tried. I don't have an affinity to sit there and learn. I get distracted quick. So I was like, I tried to learn how to play the flute. I tried to learn how to play the guitar. In those moments, I'll be pretty decent at it. But once, I don't have the bass no more. I don't have the focus enough to go back.  I try to learn piano in college. But I've learned sitting there and reading the notes. That's not my thing. I guess that's not my thing. So did you have a favorite composer, or even a favorite symphony? Man, it is so low-key. I forgot. It wasn't a Beethoven one, though. It might have been by Cicero. I'm not sure. I really can't. I think it might have been by Cicero, though. It might have been by Cicero. I can't really remember. Wow. Yeah, no, that's a deep cut, bro. I mean, I don't know if people are going to get that. I'm going to go with Classical Baroque. Yeah, bro. Honestly, that's the first. I've never had that as an answer before. But you know why that is, though? I had bread when I was younger. I was like, yo, people who listen to Classical Baroque usually has better memory retention. So when I used to go to sleep, I used to play it to sleep. Because I always had bad memory. So I used to play it to try to get my own, hopefully at helping it to help with my memory. So it didn't work. But I had some good tunes. Yeah, now, people are really sleeping on that nowadays. Crazy, when you take the words away and it's just like instruments of all different kinds. Yeah, it's satisfying, though. I used to listen to the besides that, though. I listened to my grandfather used to listen to it. My grandfather used to listen to a lot of jazz. And like, ain't no sunshine when she's gone.  Yeah, my mother used to listen to a lot of Patty LaBelle. And like, I forgot the other thing's name. But it was always like a little song where they sing. And it sounded like they're in a concert and they're talking. Like, hey, listen, child, you know what I'm saying? Those type of songs that he's listening to those type of.  Because real from my dad wasn't a big hip hop thing. He only listened to R&B. He listened to two rappers. And that was BMX and two poppers. And that was it. Wow. Wow, look at that. That's crazy. Of all rappers, too. Two of the best. But yeah, you got kind of look at them, they're similar. And they kind of functionality, like very bodacious characters. So my dad used to listen to only them, too. Wow. Damn, a whole host of influences. OK. So what made you realize that music was taking off for you, you know? So when I realized that music was my thing, that's something I really should, like, I should focus on. I realized that when I had these friends, I used to go to a school kids' studio. The thing was, Anthony, we had did a cypher.  So we marketed, like, it was, so Anthony put it out, like, it was the BT cypher, but it was just a bunch of kids from New York rapping, you know what I'm saying? Nah, it's tough. When I, because it was nice, like, the people I was rapping, it was nice. And then when I was reading through the comments, y'all, she ain't killed that, she ain't killed that. I was like, y'all, maybe I got something here. Maybe I got something here. And then another time that really sparked it for me was when I had a song called Cap and Gown. Drake was about to release, I think, he did that song with Whiskey. Oh, One Dance? One Dance. I need a One Dance, I think. If I'm not bugging, I put, I pulled the Soulja Boy, I put, I put Drake, I knew it was coming out 12 too. So that's 12 him when it's done. Drake, One Dance.  This ain't Drake, but it's hard. And then from now on, yeah, this might be my thing. It should, okay, I'm cold. Nah, that's good though, that's a great way to catch like a viral look, honestly. Especially back then, you know, before the algorithm was like really settled in themselves. The algorithm. Crazy. Yeah, now a day, it should have been awesome. It should have ruined itself. But, okay, so now with Count These Bands, it's, I feel like it definitely appeals to that virality, to like, to the social TikTok culture that we have now. You know, it's got a really great hook. It's also pretty short. What was the creative process behind that song like, and how did you approach it? Good man. So the way, the way that song came about, is literally My Boy Facts. I happened to walk in the studio, shout out Nigel. Nigel's studio, he's A&R for like Lil Durkin. So I'd go to his studio, I went to his studio and happened to walk in there. Vex making, he's working on a beat.  I'm like, oh, because I didn't even know, I didn't even remember about the Lil Wayne and Lois song. I heard that beat and all of the first thing I was thinking in my head was, picking up a master plan. What else is this? What is my hand? I couldn't tell if I could earn my money. That's the first thing I thought when I heard that beat.  This will be doing it? I ain't got it. You read it? I ain't cool. So I hopped in a booth. And so with a lot, most of my songs, I don't, I don't pin them. I just give them a booth and I try to, I'll freestyle two, three lines. I like two, three lines at a time. Keep punching in that with two, three, four lines. And that's how that song came about.  And I was like, oh, you got to show me.  I know this song. All right, let me see. We're back in like 30 seconds. That time I had wrote it down like 20, 30 seconds. Boo got in there and recorded it. I'm sure. Okay. Nice. Yeah, no, I really like it too. I feel like it's, it's one of those songs that utilizes a sample well. Thank you. Thank you. No, of course, man. I feel like sampling is becoming so prevalent. So prevalent nowadays. So I take, for example, have you heard that glow roller track with Fabio? Oh yeah, yeah, yeah, yeah, yeah, yeah. It's got the Uchiwale sample and the, but it's also got like some cha-cha slide sample interpolation on a drill bee. What do you think of it? As long as it's not, it's not my favorite song from her. Okay. I think I like that song with her and Cardi did, especially I like when I'm in the club and I watch all the women just tomorrow too. I'm like, what about Twitter? I'm like, okay, Rob, it's your Twitter, man. That's what's up, man. That's what's up, man. Rob, it's your Twitter, though. That's what's up. So yeah, that's my favorite, that's probably my favorite song about her. And Fabio, I like what Fabio's been talking to me. Like when he get on the beat, he start, like he start, he get on them like, let's say once on 13th, turn in 30, that's like probably one of my favorite Fabio songs. Wow. Yeah, I think my favorite Fabio verse is honestly his verse on off the grid. Really? Yeah, bro, I feel like, I feel like definitely because I'm also a Kanye fan. So that is like, you know, I'm definitely biased there, but I feel like that was such a big moment for Fabio and he killed it, bro. Now he did his thing. He outwrapped Kanye on his own beat. And I mean, Cardi was kind of just there, you know, like, I feel like he didn't really add too much substance. He definitely added atmosphere to it. Are you doing that song? Yeah. I'm not, I don't, I don't listen to much for that. Nah, you're good, don't worry. Donde was a minute ago anyway. But yeah, I feel like that was definitely, and even then, that was like the verse of that year too. That Donde album was fired. That album was fired. Like from production, I listen to that thing whole, like back and forth, back and forth, back and forth. I was like, yo, this, because of production, I'm like, hey, is this production screen? Yeah, that should be absolutely a moment. I feel like Kanye's just got like a crisp and clean ear. And Kanye is one of the ones. Absolutely, bro. Kanye is one of those probably most influential artists of like our generation, most likely. Like that's real for real. I would say top three for me, like when it comes to most most influential. For me, it would be probably like Kanye. I'd probably say Keith Keith. Yeah, absolutely Keith Keith. And lo and behold, I have to put, this is going to be the weirdest answer. I don't have to put like Lil V or Soulja Boy in there. Wow. They changed the whole ending that culture.   Not at all. And you know what's crazy? When I listen to like, when I hear sexy red, listen, like young, sexy red, like that's the bass god flow. Like that young bass god, that's the bass god flow. So I've been listening to him like oh, she's just like a female bass god. She's setting the trends right now. Yeah, nah, he really set the whole, yeah, I mean, he set the trend for this entire thing going on, dropping all that music, all those mixed tapes online, direct to fans. And like in such saturation too, I feel like pretty much like laid the blueprint for a lot of these artists are doing now. He made an opening for like, for people just to be able to make whatever music they want to make. But if you want to make this kind of music, go make this a lot. He showed people that there's an audience very much. There's literally an audience for anybody. Yeah. And shit, he's still popping to this day too, which is- Yo, that's great. He's talking about a lot of things. So, with, so you've kind of like, for a while been in the melodic trap genre, trap hip-hop adjacent genre, do you see yourself like stemming out of that or like dabbling with other genres? Lo and behold, about my original genre was hip-hop. It was 90th hip-hop. My original genre was like me rapping like that, that is anything you need to get in the song. Okay. And just do back to back words like that. That's an easy- Yeah, boom, bad rap is easy for me. It's harder for me to do melodic trap. I don't know why it is, but it's just harder for me. I feel like maybe because when I do like melodic trap, I know it's more flexi, but when you do like boom, bad rap, there's more just skill, like how nice are you? How much, what can you put together? But I got a country song. I got like a song. Yeah, I listen to country music too, man. Really? Yeah, I'm not, I can't say I'm too deep into it, but I feel like ever since especially Lil Nas X did his whole thing with Old Town Road, like I feel like I've definitely seen a little more of the country genre and like the crossover into hip-hop. You know what's crazy? I've been listening to country before that. Word? And you listen to country since what? Since the, what was that song that Nelly had with those country guys? Oh, Nelly was one of my favorite artists, okay. A word? I know what song you're talking about though. I know exactly what song, I was just, it's crazy, I was just listening to that album. It was actually that song that's only just a dream, right? Or am I bugging? Ah, I can't remember. It wasn't a movie, right? I can't remember it, but I was. This is like a last one, but I was just listening to Nelly's album to see what haven't been touched, like to see what hasn't been touched, like what sample people haven't touched yet. You know what I'm saying? Like Nelly got some joints and nobody, and it's crazy, it's crazy when I was doing that, I think like a month later in the lead drop, it's hot, yeah, yeah, yeah, I was like, yo. That's simple, it's crazy, yeah. I was like, yo, great months, think of life, cause I was really thinking like, yo, I was really thinking of my head, yo, I should do that, where they at, where they at, if you wanna come and take a ride with me, but they didn't, they didn't ride wave, you saw him like that too? If I'm not bugging? He just did the apartment, he didn't do it. Hey, okay, so I knew it. I knew I wasn't bugging. I'm like, yo, Nelly had some hits, but before we switch the question, I just wanna lay this out, let me not forget Young Thug is also one of the biggest influences on rap, cause right, I gotta make sure I pay homage to that, cause he helped him in the future is the reason that I started doing a lot of tracks. Oh well, yeah, that's crazy, I was thinking about that the other day too, and not necessarily about bug, but more so about future, and really Drake and future, because I was thinking about like, Drake's been around at this point for what, like 15 years, right? So far gone, dropped to 2008.  So, nah, I'm over here thinking like, damn, back when What A Time To Be Alive came out, like that really, after that, I feel like melodic trap just like blew up, I'm completely- Yeah, crazy. Yeah, bro. Crazy, but my all time favorite Drake album will always be Take Care. Yeah, that was, yeah, I remember being 13 years old listening to that show. It was crazy. Marvin's room had like 13 year old me crying about the ex-girlfriend that I've never even had. I used to get mad at my ex and listen to karaoke. Damn. Everybody wants me, can't you?  Never been. Man, no, Drake is really one of them ones, that one, if anything. No, he's, you know, he's V1 right now. Nah, he is, the boy is. Like Akai is the most influential, but Drake is like, I don't care what the way he say, he's like the Michael Jackson of this generation right now because it's nothing Drake can't touch and it turned not gold, not just gold, but diamond. Anywhere, anything, especially in hip hop, if anything Drake get on, like what actor you saying? Stimulus package?   You out of here. It was like, it was like, wait, wait, wait. And to this day, I ain't gonna lie, I still use Drake's quote on drugs. Yeah, Drake's pen, Drake's pen is absolutely unmatched, like the, I'm sure you listened to him when it was at 8 a.m. in Charlotte. Man, nah, I just don't know that one. Yeah, oh yeah, it just dropped, it just dropped. Yeah, yeah, yeah. Yeah.  A word? Nah, I listen to like, at this point, I listen to like Tracy Catman.  I go back to DMX, like I'm like, I've been listening to music like that. Yo, actually one person I had listen to was Young Boy. Yeah, I can't tell you, she can tell you all about that. Young Boy is, I mess with Young Boy. He got a lot of pain in his music. Yeah, he's got a lot of, whole lot of music too, bro. I feel like him, I could compare it to like a low beat type, where he's just got like an absolute massive music. He dropped a lot, I think, like 10, 13 projects last year alone.   Okay, let me get right back on track here. So we're gonna play another game. This one is the last game, and it's a little shorter. So it's just the last time you do X, Y, Z. So what's the last album you listened to in full? The last album I listened to in full. It was an album that recently came out, I did that too, I can't remember, but probably I would say Young Boy Album. I would say Young Boy Album. What is the last movie you saw? It was an old anime movie called Godfather in Tokyo. Oh, now I'm, now you have a movie on, bro. Okay. What is it, what's the last thing you ate? The last thing I ate was waffle. Mm, nice, nice. Love me a good chocolate chip waffle. So yeah, what's the last thing you spent money on? My kids. Love that.   What's the last, are you a gamer? Yeah. Yeah, perfect. What's the last game you played? I think Wulong Dynasty, no, I'm lying, it wasn't Wulong Dynasty. It was, I was playing in the Hero Academia room. Oh, yo, I just started playing, that's what I said yesterday, that's crazy. Yeah, that's just fine, that's just fine, that's just fine.  That's just fine, yeah. I keep trying to play as Midoriya, and it's crazy because every time I wanna do that, everybody else is playing as Midoriya, bro.  It's like, it's a couple players that's a cheat. I just found out Dobby, using Dobby's a cheat. A word? What? Dobby's Bakugou, I know you watch everybody use Bakugou and they be like, just go hand in hand.  Ridiculous. And everybody else is just hopping around for the most part. But I just called like, I was playing yesterday, I called like two, three dubs and a matter of five games. Oh, word? Yeah, me and my minions, we'd be cooking up. Sure. Nah, I don't think I've played like 10 games total and I almost won once, but nah, I've just been playing with randoms, so like, kinda just going with the flow, but it's all right, definitely. What system you playing on? Yeah, Xbox Man or PS5, man. Actually PS4, man, still. Yeah, bro. We gotta get you into the mnugen, man. Yo, next month though, next month, cause Spider-Man's coming out this month and I gotta cop up on my PS5. Oh yeah, it is coming, I gotta buy that for my son. Yo, that's just gonna be crazy. And then last, last one is, what's the last song you made? The last song I made was He Can't Touch You, I'm Touching You. Please, if you want to, I forgot the name of it. I don't know if you want to. I forgot, but it's, I forgot the name of it, but it's like a love song. Okay, that's a love song, yeah. All right, bud. All right, so with Count These Vans having just come out, what can we look forward to next and during this last quarter of 2023? Last quarter of 2023, you can look for more music. You can look for a remix of Count These Vans to come out. Oh, sure, okay. Yeah, it might be one of somebody's favorite artists, you know what I'm saying? Yeah, okay. We, you know, from Count These Vans, you don't get it city, the country, the city of the state, the country, hopefully to go. Oh, heard that. All right, Sheen, thank you so much for coming on the show. It's been a pleasure. Why don't you tell the people? Oh, why don't you tell the people where they can find you? Oh, you can find me on IG, S-H-E-E-M-K-L-U-A-F. Yo, hit me up, send me some love, baby. So good a sign, I appreciate it. So I thank you for having me. Much love once coming up. Big coming up, be going up.


Okay, so I'm going to talk about, hi everyone, I'm going to talk about a random additive polynomial in the setting, and I will focus about the Galois theory. So what I want to tell you something is weird because I got this message. Okay, never mind. So what I want to cover is first the general Galois theory of additive polynomials, some model of randomness and, and in each model to tell you what, what is the typical Galois group and if time allows I will give you maybe a glimpse on some of the methods which, which are I find very interesting. So, maybe I'll start with some motivation or some introduction. What happens for a regular polynomial so not not not not non additive polynomials. So, two or three years ago I gave you a talk so I will use the same notation, I hope you remember. And so I have a polynomial and I take a polynomial over the integer which is uniform from the set of all polynomials of degree n and height. At most L, this man means that I choose a sequence of a random variables, which are independent and they take the values, the integer values between minus and L and L uniformly. So this is a my random polynomial. Okay, and I have a three models that I mean three natural models that are more but a to consider but before that, if the polynomial is a separate band, namely doesn't have a double roots I can view its Galois group as a subgroup of the symmetry group by action on the on the roots. And the three models are the three natural models is the large box model, well, I take the coefficient from a box. And the size of the box is growing and the degree, the dimension is fixed, so the degree is fixed and the height goes to infinity. And I have the restricted coefficient model where the dimension of the box is going but the size is fixed. And I said three but I meant two so. So these are two natural models for random polynomials over the integers. And some results that we have about this polynomial in the large box model, the Galois group of the polynomial is the full symmetric group asymptotically almost surely this is going back to Aletasy einer court, Vermeer Donder modern quantity versions, etc. And in the large box model, the big challenge is, is a is to understand what, how the Galois group that behaves on the on the complement when when the Galois group לא אסן, ובמקום הזה, אנחנו רואים הרבה פרשת פרקסטים, אולי שיש שם פרקסטים, ובמקום הרבה פרקסטים בגבולים הרבה יעדים שבארגיבה, שהגבולים לא אסן הם מבחינים בגבולים של פרקסטים. סמטוטיקל. Okay, and from this one can, and also it showed that if you are not ascended, most probably you are either S and minus one, which means the polynomial as a root, or you are A n, I will not get into this in more details, but I will just say that a numeric evidence showed that A n is very rare, but this is the best we can prove now. And in the restricted coefficient models, the situation is more difficult, and even irreducibility is a challenge, and here maybe the recent progress is by Kuniagin, myself and Cosma, בויאד ההמביאויום, וכהלבן הוא שם דמńskו כולופלוס ואז כוזמא. So let me not cover all the history I just give you two exemplary results, the first says that the probability that the polynomial is irreducible is always positive for every box that you take and it becomes probability one when the box sizes. אבל כשרונות בווקסה ה-35, כך אלי 17, וכך עד כדי pedestrians, זאת אומרת, אם אתם שערם בווקסים בווקסים בגלווה, אז עד כדי דבר היא שהגלווה קרופי הוא גריא, זאת אומרת, זאת אומרת, תגידה על איזה פרוביטי, שזה נמצא על פרוביטי גריא כדי איזה פרוביטי גריא. זה רק שם שם. אז זה לא מה שאני רוצה להסתכל על זה כי זו לא פלנומיאלים פלנומיאלים עכשיו אני רוצה להסתכל על פלנומיאלים פלנומיאלים. אז אולי נשאר איזה פלנומיאלים sorry, so what is an additive polynomial or slightly more general q additive polynomial? q additive polynomial is a polynomial that has only terms of the form x to the q to the i. So I assume that the base field where I choose the coefficient form contains the finite field fq. And I only allow terms that are of degree a power of q. And it's called q additive because it has some additive property as I wrote. And the point is that the zero set of f in the algebraic closure is a vector space, it's an fq vector space. Okay, because this is obvious right. Therefore, if f is separable, which in this case it means that the a0, the smallest coefficient is nonzero, then if f is separable, the Galois group, which acts on the zeros, but now the zeros are fq vector space, so the Galois group naturally embeds into the, into GLN q, so into invertible matrices over fq, because it acts on a vector space of dimension n. Okay, so now the group is not a subgroup of s and not every symmetry is allowed, because we have a structure on ZF. And if you randomize f in some way, then you get a random subgroup of GF, so the main question is, how this Galois group distribute for example, is GF typically irreducible subgroup of GLN, is it large and whatever interest you? Okay, maybe I should say that q additive polynomials is a very classical object and they come in, in the study of a Drainful module, etc., but let me not get into this too much. Okay, so the bottom line is that if we have q additive polynomial, then the Galois group is a group of matrices and not group of permutations. So, let me immediately restrict to the case where the base field, the field that I choose coefficients from is the rational function field in one variable over a finite field fq, and then I have, this is analog of the rational, so I have analog way to choose polynomial, random polynomial, so I take f to be a uniform polynomial of a degree, let's say monic of degree q to the n, and of height at most q to the d. More precisely, what do I mean by this? I just mean that the coefficients are independent random variables taking the values, polynomials of degree at most d, a uniform. Okay, so this is my uniform polynomial, this is my random polynomial. Okay. And here we have three models, the large box model where I fixed the degree of the polynomial in X, I fixed the finite field and I let the height, which is the degree in T goes to infinity. I have the large finite field model in which I fixed the height and the degree and let the finite field go to infinity. And maybe the most challenging case is when I call it the restricted coefficient model where I fixed the degree of the coefficients and I fixed the finite field and I let the degree of the polynomial go to infinity. Okay, so these are the three natural models for randomness. By the way, feel free to ask questions. For example, now if you have a good time. Okay, but don't worry to stop me, it's fine. And I order them in this order, not randomly, because maybe you can think that it's alphabetically but it's not, it's by the level of difficulty of each model. So the first model is very easy to handle. The second model is slightly more challenging, and we use deep result from finite group theory. The first model is what I will focus about in this talk. Okay, so let's start with the first two models. So, So this is the large box modern and the large finite field model. So here in these two models we have a very nice and clean result that asymptotically almost surely the Galois group is GLNQ. But the proofs. So this is a theorem with, I plan to say it at the beginning, but I forgot. So this is a joint, all of this project is joined with Alexantine from, with Alexantine and Ailey McKemmy. And look on her eyes to see if I said it correctly. Yeah, but an Ailey McKemmy. So, in these two models, the Galois group is asymptotically almost surely the full matrix group. And in the large box model it's, it's pretty easy. We just, we compute the generic Galois group so when the coefficients are actually variables. And this, this, this is easy to do, for example, Dixon did it in 1911 when he studied the invariance of this group. And then we just apply a function field of Healbert's irreducibility theorem. So it's very similar to the proof of Healbert of that irreducible, that the polynomial over the integers in the large box model has a full symmetry group is probability one it's, it's exactly the same proof, but modify to the, to the second. The large finite field is, is more challenging I don't want to, to get into too much details because I want to focus on the third limit, but the main thing that we use is that there are a few characteristic polynomial of element in certain characteristic classes in maximal subgroup of GLM. So, such as I just gave one example which is the, the read product this is the group that, that acts on, on a factorization of the vector space into a direct sum of L copies. And, and this is a deeply, and this is based on, on a Fulman-Gorannik classification of maximal subgroup of GLM Q. It's a series of papers of them, by them, that, that is a key ingredient in the proof. So, so it uses a very deep group theory. And we don't know how to prove it without. Okay. So, let me go now to, to the large degree limit. And I want to start because it's slightly more complicated in the large degree limit so let me start with what are the obstructions for the group to be GLM. There are some obstructions that, that occur with a positive probability. So first of all, we have a separability obstruction, so I remind you that a polynomial additive polynomial is separable if and only if it's, it's, if the coefficient of X is non zero. So if we restricted the coefficient model, we choose, I mean the probability that a zero is zero is positive. It's one over Q to the D plus one. Because it's a random polynomial degree at most D so it can be zero. So first of all, we have to take care of, of this issue that occurs with positive probability. Another obstruction is obstruction for the irreducibility, when I say irreducibility I think of the Gallup group as a subgroup of GLM Q and I think about irreducibility in the sense that there is no invariant subspace. And it's possible and it happens with a positive or symptotic probability that if I view F, this F that I wrote it as a polynomial in X. So now I view it, I look at it as a polynomial in T, and I take GCD of the coefficient. It's possible that, of course, the GCD of the coefficient of F as a polynomial in T, always divisible by X because X devised everything, but it's possible that it has a higher degree. GCD, I call it the content of, in short, CTF, this GCD is a Q additive polynomial with coefficient in a finite field in FQ. And this, and the zero set of this polynomial is an invariant subspace of the Gallup group. So it's possible with positive probability that the group is even not irreducible. So it has invariant space. But this invariant space is very special. It's something over a finite field. Okay, but this happens with positive probability. And we also have a determinant obstruction. So I just gave one example. The probability that the determinant of all elements in the group is one is to say, I mean, if I meant bigger or equal, I wrote equal, but I meant to write bigger or equal. So think that maybe the frequent a zero is some power of Q, some b zero to the Q minus one. So no matter what I will do, the determinant of all elements will be one. This also happens with positive probability. So the first theorem that I want to tell you about is what happened if all of this obstruction do not occur. Okay, so this is the simplest theorem that I can provide to you in this limit. And in this case, if I condition on the content of the polynomial to be X, so I don't have the irreducibility obstruction, and I don't care about this determinant, so I just want to check whether SLN is contained in the group. So the probability that SLN is contained contained in the Galois group, given that condition on the fact that the content of the polynomial is X goes to one as the degree goes to infinity. Okay, so this is a kind of avoiding all the obstructions. But we, in fact, we also analyzed what happened with the obstruction, but I wanted before to say one. So this theorem use a very deep group theory to prove it, and we get a corollary that myself, I don't know how to prove without deep results in group theory. But it seems kind of, how to say, something that, yeah, something maybe that is of interest to some people, so if I take this additive polynomial, of course it cannot be irreducible as a polynomial, because X divide all the coefficients, because X divide a polynomial, but if you divide F of X by X, and this polynomial when N goes to infinity is irreducible as a polynomial asymptotically almost sure, and this is something that I do not know how to prove without going through our theorem, and in particular using deep, when I say deep group theory for me as a number theory, it's, the minimal is that I use the classification of find simple group, but it's much, much further. Okay. So I don't know how to prove this corollary without the classification. Yeah. Okay. So let me try and explain what is the general result that we get, because we get a full result in this thing, so I need to analyze what happens if the content is not one, and I need to, so. So let's take H to be a polynomial with coefficient in the finite field FQ. And, and I assume that this polynomial H divides the polynomial F. Okay. So the zero set of H is invariant GF subspace, and because H has a coefficient in a finite field and it's very easy to understand the Gallo group because it's only the four binaries and then if you do some computation you can show that the Gallo group is generated by the by the companion matrix, the matrix that you put once and the coefficients of the polynomial. Right. So, so automatically we get that the Gallo group is a subgroup of upper triangular block matrices, wherein, in, I'm not sure if it transform me or not. So, in the upper left side, it's a group, the group generated by D, this is the action of ZH. There is something in the upper right corner, and, and in the lower right corner, again, it's, I don't know anything, so at the beginning it's contained in GLN minus eta, just so the dimension will be n. Okay, so automatically I know that the group factors into this is contained into this. Another thing is that if I take some non zero C and some K, the divides q minus one, then, then one can show that, and I assume that that a zero is I have something on the screen that doesn't allow me to read and I don't remember the notation so I will try to use my memory and if it's nonsense tell me and I assume that a zero is C times u to the K so, so, so this is the determinant obstruction so if, if a zero is, is some constant time time some polynomial to the K, where K is the maximum possible, then, then I know that the, and I write and I write the group like this, an element in the group like this, then, then I know that the determinant of B will be some C over determinant of D to the I times the K power and so I know that this is an obstruction on the determinant of the lower right block and, and, and I call it a gamma NHCK, probably this is the thing that, that I was missing I don't know how to delete the, the mating is being recorded by those participants, whatever so, so I let gamma to be all matrices of this form that they, that they are in the upper left side I have some power of D, D is the companion matrix of H I have something A in the corner, in the right top corner and in the bottom corner I have some matrix B and the determinant of B is, is, is given by something like, satisfies this condition that I wrote, this is something technical but it's exact and then what we can prove is that the probability that GF is this group a condition on the content being H and A0 being a K power times the constant it goes to 1 as the end goes to infinity. Okay, so, so we, we, we managed to analyze based on the content which is, which we denote by H and the maximum power that we can represent A0 is due to the K time constant to, to analyze exactly what will be the group I should, I should say that this, this, this thing that we condition on happens with positive, with asymptotic positive probability so we really have to, to, to worry about each, each one of these and also I should mention that this exhausts all asymptotically it exhausts all cases in the sense that if I take the union of all these events on, on which condition I get a asymptotic probability once so, so this is really a full result but it's a bit technical so, so let me go back to to the, to the easy result where we ignore all the obstructions so, so let me tell you the methods it's just a glimpse about the method because there are some more points there but, but I think those are maybe the most interesting parts so, so I restrict to the case the first theorem that I told you that I just want to check whether SLN is inside my group and I condition on the fact that the only polynomial that divides the only polynomial that divides the only polynomial in X that divides F is X so that the content is X okay and yeah so GF is irreducible, is reducible it means that there exists invariant subspace of some dimension between 1 to N so between 0 to N and, and we can write it as, as the fact that there exist some additive Q additive polynomial of degree compatible Q to D, to DM that divides my polynomial indeed if I have the vector space V I can construct G by taking the product of X minus the elements in V and vice versa if I have G I can construct V as the zero set of G and something that happens in function field that does not happen in number field and this makes the number field case much more complicated is that in function field the height function is, is multiplicative so in some sense in the number field this is illustrated by the fact that the height function is multiplicative once you, but is almost multiplicative and the constant that you have to pay is exponentially in N something like this which cause a lot of problem when you want to take N to infinity so, but here it's multiplicative so, so irreducibility is slightly easier and I wrote some, some lemma I mean we can, if, if I have such a polynomial that divides F then I can get bounds on the degree in T and therefore I can bound the, I can bound the probability that such G exist so, so irreducibility is significantly, significantly easier than what is happens in the number field case and I want to emphasize this because in the number field case when I multiply two polynomials the height is not multiplicative it's almost multiplicative but, but the constant that I, so the height of F times the height of G will, will be comparable to the height of F times G but the constant will be, I don't remember now if it's exponential or even larger in N this is coming from going through the model measure which is multiplicative and, and when you take N to infinity exponential constant in N is slightly problematic because it makes all arguments fail so you need to come up with something different but, but here irreducibility we, we managed to do it I mean I skip some details but, but this is the heart of it and the, the, so this is one, one, one thing that we have height bounds and then we can prove irreducibility in this method and the second part is specialization method we want to specialize for example T equals zero and then and then I can lift the Frobenius so what does it mean to specialize F is a polynomial in two variables and after I specialize I mean I'm in polynomial I have a polynomial in one variable over a finite field so, so I have the Frobenius that acts on the roots and, and I can lift this Frobenius to an element in the, in the Galois group of the original polynomial and, and the point is that at least if F zero X is separable and this means that the corresponding point is unremifed in some extension never mind the details so if F zero X is separable then I get an element in GLN Q in the Galois group that have characteristic polynomial which is the same polynomial as my original polynomial but now every time that I have X to the Q I write just X so this is the characteristic polynomial of the corresponding matrix and, and we can show that this is in some sense almost uniform that I, I don't want to get into the details of that and then we get a matrix whose characteristic polynomial is, is almost uniform in some very strong sense and so again I want to prove that GF contains SLM so now that I know that I have almost uniform characteristic polynomial I apply finite group theory and here this is the part that I, that, that I learned I had to learn for this project that I learned from ALEE is that we have a we have a, we have the nine Ashbacher, Ashbacher classes of maximal subgroup of GLN and for example C2 is, is this groups like the Ritz product that I wrote before it's the groups that stabilize such kind of factorization we, we want direct sum with VT which have the same dimension so, so I have the symmetry group acting on the component I can transform them and then for each component they have GL of the correct dimension probably N over T that acts on each component so, so this is one, one type so, so we have eight, nine classes like this one of them is of the reducible polynomial that we already took care of of them and the point is that this is a deep theorem in group theory that although there might be a lot of maximal subgroups there are not so many characteristic polynomials as N goes to infinity so, so I remind you I have a matrix I know how to generate a metric with high probability a matrix whose characteristic polynomial is close to uniform so I have some constant time Q to the N of these with high probability but only a very small portion of them is a, is in one of these classes of maximal subgroups that do not contain SLM so, so the conclusion is that, that I have irreducible group that contains that is not containing any maximal subgroup so it must contain SLM okay and this proof use deep results of Fulman and Goranlik about the number of, okay all kinds of results and you also need to, how to say to enhance it with a analytic number theory in the sense of an atom of integers and this was done by Eberhard and Gertzoni okay so what I told you, I told you what is Galois theory of additive polynomials about three models of them I explained the results that we have in each of the models we have in two of the models, the large finite field and the large box we just get GLN with probability one but in the restricted coefficient model we get we get all kinds of variables restricted coefficient model we get we get all kinds of abstraction and each of these abstraction of course with positive probability but we can handle it and I gave you some hints on what is hidden behind the proofs and I think that's it thank you