Shook, shook, shook, look at that! Hello everyone! Today we are going to react to upcoming farming slash farming RPGs coming to the Switch.  Genre. Uh, that you love. Yeah. Here is Summer in Mara. Have you heard about this? Nope. Yes. Maybe. Doesn't it really? Is it 3D? Yeah. Look. Wow. I think you have full control of the camera too. Yeah, it looks like it. And it is such a cute art style and it's really green grass gaming. When is it coming out? Really soon. There's the farming. Look! Carrying the bucket. I like the music. So you get an island or? I don't know. There's at least a swimming. Oh, look at the pig! Yeah. Livestock swimming, farming. Oh, swimming actually. What? Oy! That looks like 2D swimming. And a boat and NPCs. It's almost as if it's a game. It looks really cute. Mm-hmm. It does. Are you gonna play this? Maybe. It's a bit Japanese-y. Is it? Really. But this is a Kickstarter game. Really? Yeah. And I am excited for it because it reminds me of my time at Porsche. The next one is called Story of Seasons, Friends of Mineral Town. This is a remake of the Game Boy game. That's too Japanese-y for me. Is it really? Yeah. Well, it's way too anime-like. Okay, wait to see the graphics. There you are, farming. Live the simple life in Mineral Town. They're chicken. That looks very... Monnie. Uh, what's it called? The Stardew Valley. Yeah, it's like a 3D Stardew Valley. In this game, you cannot control the camera, which is fine in this genre. Genre. Genre. You love that game. I love that game. That is a weird name. So you love that weird name. Mm-hmm. I'm gonna call all my livestock crazy names, like I always do. And you can marry. You know, marry. Stardew Valley. I mean, I like this, and I love this game. This Mineral Town is the best horror story in the game, I think. What did you say it was from? This game. Oh, it's a remake of Horror's Moon? Yeah, it's a remake of this game. But it's called Story of Seasons because of the name change. Oh, okay. Number three, I hope you like this one. It's just called Snackle. Wait. Is that the only thing? No, I haven't seen one. Stepping on the right. So yeah, it's a cat farming RPG. And this is not... I mean, do you mind this graphics? No, I like pixel graphics. But as you see, the environment is 3D. Fixed camera position, but the sprites of the characters, that is pixel. This looks very Stardew Valley, and you can't go wrong with cats. And you can see the bar with the items at the bottom.  I love things where you can build things. Yeah, customise everything. Because Yonder, for example, wasn't a farming game as such. But you can build buildings, except for those little ones on your plots. And I was just like, I like building things. This looks really good. It looks like you can customise a lot in the world. I don't know when this is going out, but it looks exciting. It looks exciting. It looks exciting. It looks really good. This is called Alchemic Cure. Walt. Yeah, Walt. It looks like Graveyard Keeper. Yeah. It's like Graveyard Keeper with the saturation or whatever is said to Max. I think this looks really cute. It looks... It looks a lot like Graveyard Keeper. Yeah, but it's clearly taking inspiration from Stardew Valley as well. You can see the text boxes and the little picture of the houses. I mean, that was what I was going to say. They're farming games. There's not really that much variation you can do. I mean, a farming game is a farming game. It's not like you can get like... Yeah, but you know, they are different. They're the feeling of them. They're different, but there's only so much you can do with this kind of genre. Yeah, but I love this genre. Genre. Crossed. Yeah, because it even has like jellies. Like it doesn't start a valley too. You know, you can make the slime hodge and they'll have little jellies. Oh, you can name them. Yeah, cool. That's cute. Yeah, like mini games. All farming games has mini games in them, I feel like. Oh, look at that. It looks like Graveyard Keeper just super fancy colors. Yeah, just not as depressing. Graveyard Keeper's good. Good. Yeah, it's good. Okay, did you like that game? I'll give it a try. Yeah, that looks good. I'm not sure how I feel about 3D farming simulators. I've never played one to be fair for like, I don't know. Well... I feel like that top-down view is like, good. Yeah, it's good. This is just called Dinkum. Dinkum. Apparently. I haven't watched this. Dinkum. Oh. Oh, that's cute. That is... What? Wow. It's a little bit Minecraft-y in a way with the blockiness. Yeah, and it's more modern-day with the motorcycle. Yeah. Build your town your way. Okay, full customization of the town, anyways. I'm farming and you could control the camera around. Oh, I love building. Yeah. Ooh. Yeah. And mining. Mining. Fishing. Those are required in a game like this. Oh. Metal detecting? Yes. Nice. I like that. Yeah, I agree with you. It looks a little Minecraft-y. An animal named Bob. Yes. Oh, I like that.  This looks really good. Yeah, this does look cute. Dinkum. Yeah, it looks really good. Dinkum is a weird name. Right. That is a weird name. Yeah. Oh. I think I'm going to like this game. I hope it is good. Oh, hunched. You can catch animals? Yeah. No, we killed the penguin. And you can do barbecue. Wow. Nice. Dinkum. Dinkum. All right. Call me soon. Wishlist now. What does dinkum mean? I don't know. What? What? OK, farm folks. Funny name. Did you know that there were so many farming simulators coming? No. No, I didn't either until I did my research. OK. Oh, I actually like the graphics in this one. Because it's very contrasty with the light and the dark. Look at those chickens on top of the box there. They were like, meh, meh, meh. This is actually really good graphics, I think. They're at least a little bit unique. Yeah, yeah, that's what I mean. Do you get to tidy up all that? Yes. Oh, I love tidying up. You love to tidy up. I love to tidy up. Look, cute chicken. Oh, so good. Oh, I like it already. I like it a lot. Yeah, that does look cute. What was it called, the farm folks? Farm folks. Wow. That's such a terrible title. No, I don't think it's doing anything. Oh, there's mining. Crafting and stuff. I think that's fine. Yeah, that looks cute. I like the animals, like the design of the animals, like the graphics of the animals. I like that design, too. Not sure. I don't, I'm not so... Oh, customizable character. But I'm not so fond of the look of the characters. Not me, neither. It's kind of like in Yonder. I didn't like the look of the characters. But the world was nice. Seasons? Yeah. Good. I love seasons. Same. I love seasons. We love seasons of tidying up. Seasons of tidying. I think this looks really unique. I definitely feel like I like it. Farm folks. That's such a terrible title. Yeah, now on Kickstarter. Alright, next one is called Kin Seed. And I think you may have seen this because it has been all over Twitter for a year. It also looks like Graveyard Keeper. This is, as you can see, it's more like, it's definitely pixel-pixel-y. But it's more like a simpler pixel style. Yeah, much more simpler. Like dated kind of pixels. Yes, I think that was what they were going for. I like the design of like the flowers and like this stuff around the environment. Yeah, it's actually really beautiful with the trees and the colors. And there's fighting, you see? Yes, fighting. Well, they have been working on this game for many years. They or the person. I don't know how many. Yeah. It could be just one person. Yeah, why do some of these farming sims are just made by one person? I don't know. It's like their passion project. Just like a single person. Alright. Okay, this one is called Little Witch in the Woods. That's the same kind of... Same graphical style, sort of. I like the character is super cute. It looks like you.  Oh, I like the interior. I'm getting some... Oh, I like when the characters are talking. Those sprites. Yeah, that gives me some Secret of Mana vibes. The bar there and like the thing is where the guy goes. Yeah, nice. The single ladies dance. Yeah, I think this looks really cute. It's a bit. I don't know. Yeah? Yeah. So there's a good end you have, yeah? Yeah, we'll film a video. I mean, it will be interesting to see. I may actually play it, so. Okay, this one I have known about for some year or two, I guess. Mineko's Night Market. How would you pronounce that? Mineko? Mineko Night Market. It is also a cat. Yeah, it's a cat. I think there are a lot of cats in it. Yeah, yes. Can't go wrong with cats. Can't go wrong with cats. Weird graphics. Yeah, these graphics are. They're a bit like Don't Star graphics a little bit. Tiny bit. Tiny hats. Tiny hats. This one I'm not too sure about. I feel like I'm more fond of full 3D. It looks more like an adventure RPG with farming elements. Elements! So yeah, I think it is that you have a market or you go to a market. Can you ride your cat?  Ride your cat. I think you're selling your stuff at the market and stuff like that. Okay, this one is called Ublets. I've seen this one. Yeah, this looks weird. I think this one looks really weird. I think it is the one I think it is. Look at the character model, you know. But the world and colors look okay. They're very pastel-y. Yeah, this one I haven't seen actually. Look how weird they walk and run. Oh, shopping.  They look like the Yonder characters. They're not good. Actually, they're really very looking. Very looking like the Yonder characters. I think this is also just an RPG game with farming elements. Elements? Elements! Well, you can customize your home a bit. Well, not in a very... I mean, we've just played Animal Crossing. Yeah, we have already done that. What? So yeah, I don't know about this one. I'm not sure. I don't like the characters, which is kind of a... makes it a little bit... This is an old game, Sora. But it's not out yet on the Switch. Really legend. But it has farming. I like the graphics actually, but I don't like the character. I don't like Japanese-style looking stuff. Yeah. I don't know what it is, it just turns me off. Look how satisfying the watering looks. The graphics are cute.  They have been working on this game for years. I think I saw this game in 2018. Yeah. The first time. And it's still not out. I mean, the PC version is out, but it is an early access sort of thing. Early access is the devil, so... Yeah, it's the devil. So there are fighting, crafting, collecting these animals. Sticking your sword in water. Sticking your sword in water. Oh, that's a cute thing. Feeding your animals. Yeah. And riding them. Yeah, a little waltz. A little waltz. I think that was the taming animation. But if I remember correctly, this is going to have multiplayer. Online multiplayer. Oh, really? If I remember correctly. But as you can see, plastic fighting. Oh, opening a portal. Summoning. So yeah, maybe that. Yeah, there you go. Online multiplayer. That is always a thing that can be hit or miss. So we will see if that is going to be good. That was really legend, everyone. That was all the upcoming farming simulators. RPGs. That sort of genre. Coming for the Switch. What was the one with the fancy outside graphics? Was that Dinkum? Or was that the 3D one? I think we liked Dinkum. Dinkum was the one that had the most positivist response. Yeah, maybe. Maybe so. I don't know. The blocky one. I'm not sure yet. I like a lot of them. Actually, I'm looking forward to Snacko. I think it's the one that was like a graveyard keeper on crack. Okay, that one. Alchemicure. Yeah. Wow. Thank you so much for watching, everyone. We will see you later. We will see you later. Do you want to say something about the discord? No, not this time. Next time, maybe. Link in the description. Totally awesome. Bye. Bye.


The joys of phylogeny, how to? In the last video I showed how the use of inherited DNA markers are the basis of paternity tests. The same process of testing for inherited genetic markers is used by scientists to group organisms into phylogenetic trees, based on the similarities of sequence. I showed a single gene product, catalase, and how the homology of markers correlated well with the taxonomy of shared characteristics. Warning! What follows is actual science. Real biologists use these tools. There are no funny animations or lolcats beyond this point. It's just me and some cutting-edge bioinformatics tools up late at night. In this video I'd like to show you how to construct a phylogenetic tree on your own. Maybe I'm a bio nerd, but I find the process enjoyable, and the results are intriguing. It's also great to do with a friend or family member who is skeptical of common descent. If you have the responsibility of teaching science, this might be an excellent exercise for students for lots of ages.  There are many ways to do this, but I'm just going to show you the one that I use. Step one, open up a text file. We're using Notepad today. The format of this data is going to be called Fast A or FASTA. The way it starts is with a greater than symbol, followed by the name of the organism, with no spaces inside. The first space will break it up, and this information will not appear on the phylogran. Here's the protein sequence. We're going to grab this out of a database. But I wanted to show you the format and the basic formatting, so it's about as simple as it gets. I'm going to go ahead and clear this out. And we're going to go to the National Center for Biotechnology Information. Here's the link. It's publicly available. This is a database of all sorts of wonderful things. I swear I could spend weeks here just browsing through the information. For example, if you want to look at all the H1N1 influenza sequences that have been isolated. Lots of databases can be searched here. Today, I'm going to focus on homology, which is one of my favorite tools. What it's done is it's already gone through and found homologous genes for a variety of different organisms. The gene we're going to look at now is GAPDH. This is a really common gene to design assays for in a research setting as a housekeeping gene, because its expression is fairly constant. It's also highly conserved. So let's hit go and we'll run homology and search for GAPDH. Now the first hit we get here is GAPDH. So that's great. This is homology and record 107053. You see here a long list of conserved GAPDH genes. We've got everything from Homo sapiens, that's us. Pantroglodides, that's a chimp. Canis lupus familiarius, that's a dog. Boss is a cow. Mus is a mouse. Ratus, the rat. Gallus is a chicken. Danio is a zebrafish. Drosophila is a fruit fly. Anopheles is a mosquito. C. elegans is a round worm. Schizosaccharomyces is a yeast. Saccharomyces is a yeast. Cluveromyces is a fungus. This one is, I believe, a cotton fungus. This one is a fungus of rice. It's rice blast. This is a slime mold. This is a common research plant. Common name is Cress. This is orizocetava, which is rice. And this is plasmodium falciparum, which is the parasite that causes malaria. Pretty sure. So this is conserved in eukaryota. That means it's crossing across family lines. There's lots of ways we can look at this data. For example, I'd like to show you the alignment score information. So here we are versus Homo sapien. Here's the GapDH homology, or rather identity, for the protein sequence and for the DNA sequence. So you can see chimp DNA is very slightly different from the human DNA, but the proteins are identical. That means that the mutation that occurred here didn't change the protein here. When we look at dog and cow and mouse and rat and chicken and zebrafish, you can see as we get further and further away taxonomically from Homo sapien, we get increasingly large differences in the protein, but much more rapidly increasing changes in the DNA. And in fact, these substitution rates are a quantitative estimation of those changes in amino acids that cause the proteins to change that are caused by the DNA. So as we go down, we notice that even rice has a 71.8% similarity to the human sequence. But you'll also notice that none of these numbers are essentially the same, except in a few cases. But what we're looking at here is a great deal of diversity in the sequences that are being created. So let's go to the FASTA format, that's the one we're going to use for our gene. And here's what we have all the way from here to here. I'm sure there's better ways to do this, but I'm going to control copy and control paste. Now that's a lot of information here. And unless you want your filogram to have the GI number, the best thing you can do is highlight these and change them to something a little bit simpler, like dog. Hantrogloditis, we can change to chimp. I've already done this for this gene. I've created a file called GAPDH gone through and changed it to human, chimp, dog. Now some of these you'll see are Cal1 and Cal2. What's happened here is the gene is duplicated and we'll be able to see how recently it's duplicated or how much it's diverged between the two, what are called isoforms. So here's our GAPDH data in FASTA format. Going to control A, I'm going to copy this information. Now we're going to go to a new website. And this one is at the EMBL, which I forget what that stands for, but these folks have a cluster, which is the name of the program. Clusterl, I've never actually pronounced it. I'll add here, you can paste the sequence in if you like it this way. Or I've used it, I can browse directly to my GAPDH file, do that again, and then run. And I don't change any of the settings here. And it will take it about 30 seconds to finish the processing of the job. I'm going to speed time up like they do on the cooking shows and cut to an already finished product. So I've already run this job. What it's giving me here is a very plain vanilla alignment of all these sequences. Let's put the names next to them so it's a little bit more interesting to look at. It has allowed for gaps, so when you see a dash that's where it inserted space to allow for the alignment of the sequence. We'll see this in a much more colorful fashion. What I'm interested in seeing here is called the guide tree. So I'm going to click on that, it's going to take a second. And here is how the software sees the genetic sequences. We're looking at the number of changes that have occurred or percent changes. But it's going to take that and turn it into this graph. Now, this is a cladogram or cladogram. The resistance of cladogram is they all terminate at the right side of the graph. The distances here are less important. There's no supposition about the genetic distance. If we right click, we're going to have a little bit more editing option. I'm going to change the format from cladogram to filogram. And now the distances here reflect the genetic similarities or differences. So here's human and ship. I mean, they're right on top of each other because, of course, we saw the sequences were the same. Here's cow one and cow two, the duplicated genes. Those are obviously very recently duplicated genes. And they're related to dog. Down here, we had four of the isoforms from the rat. And they're all very closely related and they're very closely related to the mouse. Then as we go along, all the chordates are close together, chicken to zebrafish, to human to chimp. The invertebrates are, well, these insects, fruit flies, and mosquito are close together. The plants are close together, but there was one unusual fit and that was the slime mold here. I would have expected that to go a little bit differently. And then we have the two fungi here and then the three genes from the yeast. But it's interesting how far back these diverge. Yeast, pombe, and yeast cerevisiae are very distantly related, which still just amazes me. And then, of course, malaria is sort of our out group here because it's obviously not related very closely to any of these. That's it, you now know enough to make your own filogram. If you do choose to run out and make one, do a screen capture and post it as a reply to this video. I hope you are inspired to try a little phylogenetics on your own. Thanks for watching.


Hi everyone, this is Nico from the Advanced Imaging Conference in San Jose, and I got to sit down here with Adam Block, an astrophotographer, for a little bit here. And why don't you just introduce yourself, Adam? So I'm Adam Block, I'm an astrophotographer. I'm also an instructor in astrophotography. I create instructional videos that show people how to put together the data. And I work at the University of Arizona in the Department of Astronomy doing some research there. So that's basically what I did. Adam gave a presentation called Beauty and the Beholder for the Astro Imaging Channel, which is a weekly talk show on YouTube, all about astrophotography. And that presentation really stuck with me. You recommended a number of books, you showed a number of your astrophotographs. And one thing that I wanted to ask you about it was this concept of pre-visualization. And specifically, where in the process for you pre-visualization arises? There are some kinds of objects that you would take pictures of where they're well-known objects. So you might visualize that, boy, I would really like to take a picture of that. It could be a spiral galaxy or some well-known nebula. And you already have in your mind's eye what the ideal version of that is hanging up on your wall or something that you could in some way maybe share with other people. But I think the other form comes a little later where it might be an object that there might not be very many good pictures of or something that you haven't worked on before where you don't really have an idea until you look at the data and you actually examine it once it's in your hands because there is more information contained in the data that you can display on the screen at any one time. So just by manipulating the screen stretch and starting that process of looking at what you've captured that informs this pre-visualization of the kind of contrast you might want in the final image, the kind of details, the things you need to mitigate, like the noise, stuff like that. And this I feel is what Ansel Adams would do, the father of pre-visualization, when he would stare through his camera at some scene. He was already thinking about what he was going to dodge and burn in his laboratory just by being out there in the field and looking at the raw data, if you will. So speaking of Ansel Adams, do you find inspiration in art outside of astrophotography that then is directly related to maybe choices you make when you're processing astrophotographs? I think the answer is yes, but it's in a surprisingly different way. One of the things that I do as a communicator and a public outreach kind of person, popularizer of astronomy is that I'm always thinking of a way to present an image that offers a perspective. And art does that, right? Art does that by deconstructing things or displaying things or expressing things in a different way that makes the viewer approach the view or think about things in a different way than you might otherwise do. And I do the same thing in terms of astrophotography. So for example, there was a slide that was shown at the end of the presentation that we saw here today by Dr. Plate, which was a picture I took of Betelgeuse, one of the brightest stars in the sky. Now, who would ever stare at Betelgeuse for three hours and just get an RGB image of it just to see what's there, right? I thought that was a cool idea. I consider that idea just about as good as the final, the picture is, I mean, it's a nice picture, but I think the ideas really stands out in that picture. And I hope that a viewer would think, wow, no, I've never actually seen one of the things that are near Betelgeuse because it's so bright. Astrophotographers avoid bright stars. They don't go take pictures of them. So that would be an example. We're sort of being straddling professional astronomy and amateur astrophotography. Is there anything in the professional realm you think is going to trickle down? There are always things that seem to trickle down. There's some technical stuff in the days that I recall, for example, deconvolution, right? That's the obvious example where the Hubble Space Telescope was producing fuzzy images or you had the atmosphere producing fuzzy images from above looking down. There has been this concerted effort to try to do signal processing to make them clearer. Well, that trickles down to software that we all love and use to sharpen our images, right? But I think that there's other things. Professional astronomers have the same challenge when it comes to showing the public what they're doing. And there are many clever people to come up with interesting ways of doing that. And with my little radar, I'm always on the lookout for how other people choose to express that information or make it publicly available. So yeah, I look for that as well. One thing you showed in your talk last night was that the air glow in the red spectrum is really, really bright. It's really bright. But we don't sense that. So yeah, but so is that I mean, I know there's other limitations to shooting infrared from Earth. But is that one of the major ones? That is a big one.  And then there's other windows where the atmosphere literally absorbs the light at that wavelength. And so there are small little windows where certain wavelengths come through and others don't with water vapor and things like that. So yeah, it gets kind of weird when you start looking at these other wavelengths, how the atmosphere affects what we see. It just happens to be, well, it's not by chance, but it is transparent of the wavelengths that we enjoy with our eyesight. On the topic of wavelengths, is there, when you're reading like academic papers on objects, are there any wavelengths that a professional astronomer would capture that gives you a hint about something that may be visible in the visible spectrum? I think that the funny thing is that when you look at a lot of the papers, they tend not to have very good pictures. So it isn't so much the science that they're doing may or may not inform how interesting the object might be to photograph. But sometimes you can find hints at things because there are papers, for example, where one of the areas of interest is to find stellar streams around other galaxies. And if you look at some old papers, there are hints in some of these old papers because people study galaxies, they take survey images of galaxies all the time. The star streams were there, but they were just so noisy. I mean, no one would ever think that that was a feature that was something to go after. It just didn't have the sensitivity. And it wasn't something they were looking at, right? They looked at the same galaxies. But later, the study became something that was more significant and important. So you take these deep exposures that can even be done with modest equipment and now you're detecting stellar streams around other galaxies, which speaks to something about cosmological evolution of the universe. That's cool. That's a great Pro-Am kind of connective tissue. When you're thinking of the story of an image, are you thinking in terms of just the image or are you also thinking in terms of, and I could verbally explain this based on the image? Do you get what I'm getting at? I do. I think for me, the story is often a perspective is what I'm trying to show. So it isn't necessarily something that would necessarily need to be put into words. Sometimes it helps, but a lot of what an image communicates can be part of the physics of what's going on. So as an example, when you show edge-on spiral galaxies, right? If you process the edge-on spiral galaxy, you can make the dust lanes show up very well, but there might be more to it than that in the sense that if you apply too much contrast, those dust lanes become very opaque and difficult to you don't sense that there's light coming through where there is an attenuation of light of all the stars that are in the galaxy, that light shines through, right? So part of the story I wanna tell is that feature as well. That informs the steps that I'm going to do when I do my image processing is that there may be a perspective here that I wanna express, that I wanna be sure that the data shows me or displays in some way. And that's the story, even without words, I think that that's part of the story, that there's a certain naturalness, I think, in that. And that's kind of a style that I've generally done with my images through time. And it's that kind of thought process I can kinda use. I'm gonna mention a very unnatural photo you showed in your presentation where you put the full moon with Andromeda galaxy taken on the same night. Very true. Are you worried at all that if that photo circulates on the internet without the context that people will get the wrong impression? Of course. However, I was not the first to make that photo. The first of its type that became popular was done by an astronomer at NOAO. And its intent, as was mine, was always to show a perspective. And so the genesis of that particular kind of picture was really another one of these perspectives is one of scale. It was this understanding of these objects in the sky they're so far removed from an understanding of how big they are, how bright they are, how faint they are, all of that kind of stuff. So to put the moon a half a degree thing next to the Andromeda galaxy, basically three and a half to four degree thing really offers some mind shaking moment of a perspective even though they don't naturally appear in the sky together because the moon is so bright because they don't come near to one another, all of that kind of stuff. It is a perspective that was worthy of the misinterpretation. In this particular example. Sure. Probably because of its intent. Sort of related, what is your opinion on narrowband imaging in general? I know that you do mostly true color imaging. And I'd like to explain why. One of the reasons why is because through time I was always administering these astrophotography programs as part of the public outreach that I did. And narrowband imaging takes an awful lot of time because you're looking at a small amount of light and you got to expose for long periods of time. So that was not amenable to any of the public outreach that I did because you couldn't invest that. No one would pay for that amount of time or spend that amount of time to somehow collect data just for those purposes. So broadband was an obvious fit for the kind of imaging that I was doing in those programs. Nowadays, there are other sources that I can tap into. Remote observing in Chile and other people's data that have been kind enough to give me their data. Things like that become other resources for me. And it's so recently I've started to actually work with some narrowband data. So I've never been opposed to it. But it is something that is, there's a different approach I think and it certainly has more freedom in the expression because the constraints are relaxed. There are no longer, you can put things in one channel or another channel, you can manipulate the contrast or the way in which you might deal with just true signal strengths, right? If you did that in broadband imaging, it'd be weird because you could just make green things, but everyone would look at that. But in narrowband imaging, we usually boost the O3 quite a bit because the HLF would just dominate others. But the story there then is really to highlight, perhaps the story, I mean, it could be other stories, but for me, the story might be, I wanna highlight the physics of where the gas is, right? So, and I think that that's generally the convention is that you're going to offer those intermediate colors or the striking colors where there is this differential in the emission of the gas. And so if the boosting of that signal is necessary to highlight those differences, to make that contrast, yeah, that's fair game, that makes sense to me. So I don't wanna hold you too long, but I want you to tell people on my YouTube about your educational efforts with your website and courses. Oh, so my site is called atomblockstudios.com and I really began the work and study and learning of CCD imaging when it kind of just started with amateur astronomy and this would be in the mid 1990s. So in the course of this experience of working with cameras and then working with the data, I've had the opportunity to experience a whole set of different software programs. And then subsequently because of this experience, create instructional content that helps people to learn how to use the software and learn how to manipulate images and learn just more about astronomy in general. So today my emphasis is on software programs like Vixensite that allows for the creation of these beautiful astronomical images. It's a huge, very sophisticated program that offers many, many degrees of freedom. And so it's ripe obviously for this instructional need to explain how to really take advantage of like any other program like Photoshop has that same kind of need, although it's well covered today. But that one is not dedicated to astronomical imaging where Vixensite is. So that's kind of the niche that I'm currently sitting in right now.


Bring it down. Down. Low. Catch. Circle. Chill. Catch. Circle. And we are super out of battery, so we're gonna land now.


our colleague Michael Murphy, who will present the opinion on implementation of free trade agreements, the regional and local perspective, own initiative. Mr. Murphy, you have the floor. Thank you, Mr. President, and thank you for the opportunity to introduce this opinion, the implementation of free trade agreements, a local and regional perspective. Dear colleagues, as we all know the world is going through unprecedented change, the global COVID-19 pandemic has had a substantial impact on all parts of our lives. And in terms of trade, the effects have been harshly felt around the globe. Recently, DG Trade published a macro economic impact review of the pandemic on trade new movements. And the results are, as expected, extremely worrying. In 2020, we can expect a decrease in global trade of between 10 to 16%, which translates to a reduction in EU 27 exports of between 280 and 470 billion euro. It's important to remember that behind those figures are SMEs, small companies and family-owned businesses, whether exporting directly outside of the EU are forming part of supply chains for exporting that function in our towns and cities and provide financial stability to our citizens, the same SMEs and family-owned businesses that invest, spend and hire local. The International Labour Organization in its recent research estimates 12 million job losses in Europe alone. This does not account for temporary layoffs. I try to reflect on this change in the opinion and deliberate on ways in which local and regional authorities can contribute to the restoration of global trade. Through the opinion I call the Commission to continue its work on addressing the started competition within the single markets caused by foreign subsidies. It's important now more than ever that we ensure a level playing pitch for all EU companies, irrespective of size. Furthermore, the opinion calls on the Commission to continue its important work on WTO reform and urges it to diversify global supply chains via the concept of open strategic autonomy. In the context of the revised MMF proposal, can I welcome a top-up to cohesion policy which can be used to provide important and crucial liquidity for SMEs, particularly in the hardest hit sectors and regions. In addition to this, influencing sustainability, promoting multilateralism and encouraging positive economic growth via open trade must remain an equal priority, and we should use these challenges and make them indeed opportunities for our industry. At the EU level, it is important to continue our support for the European Commission in its active attempts to ensure that sustainability and high labour standards are integral and necessary parts of all EU trade agreements, particularly through the TSD chapters. Negotiations of FTAs by the European Commission must be fully complemented by their implementation on the ground. The COR is well positioned to provide value to SMEs on the ground and give them the access that they need, the correct information most importantly in the right format. By working with the European Commission, we can ensure that the tools developed by the Union, such as the European entrepreneurial network, are fully utilised. It is local and regional authorities that are closest to the SMEs on the ground and most importantly understand the environment in which they function. Colleagues, we need to continue reminding the relevant stakeholders of our input into the formation and implementation of FTAs. We are the levels of government who work with SMEs on the ground and create a positive environment for their competitiveness. In conclusion, Mr President, can I thank a number of people, in particular my expert, Agata Kolodinska from the Irish region's office, for her support, her commitment, indeed, her incredible work over many, many months. The team at ECON, in particularly Efersini, the many stakeholders that we engaged with during the collaborative stage, particularly indeed the Commissioner himself, indeed the ECON members and co-ordinators who put confidence in me to be rapporteur, 21 amendments in total, 13 of which I tabled myself through my political group, the EPP. In terms of the 21, I'm supporting 18 and I count on your support. Finally, Mr President, can I thank you? Can I take this opportunity to thank you, Mr President, your team, indeed the Secretary General, for your leadership in recent months. Such leadership will be crucial in the months and years ahead as we not only tackle the challenges, but indeed grasp the opportunities as well. Mr President, thank you very much.


Okay. Well, thank you very much. I'm honored and thrilled to be here. So the first thing to say, I guess, is happy birthday, Dirk. I guess is very belated at this point if I'm not mistaken at some time in July. So Dirk was a very important kind of mathematical influence on me about 15 years ago when I arrived in Boston, where Dirk was spending half the year at the time. I started talking to him and learning about his work on the half algebras of renormalization and thinking about how these structures could be kind of lifted to a categorical level. So in fact, today's talk, which is sort of based on recent work is very much, at least in my mind, related to that set of ideas. And over the years I've had the pleasure of visiting him in Paris and then in Berlin and I have great memories of those visits. So thanks for all the inspiration, Dirk. All right, so let me, let me get started. So the main idea of this talk is that one can interpret things like the half algebra of rooted trees or the half algebra Feynman graphs, as well as a number of other combinatorial half algebras as hall algebras and what's a half algebra well a hall algebra is an algebra whose structure coefficients count extensions or short exact sequences in a category. And so, so I will talk about these types of categories, and I will, the ultimate goal is to describe the construction which, which attaches to a project of TORG variety, a half algebra. And this will arise as applying the whole algebra construction to some some category of coherent sheaves in the, in sort of a somewhat strange setting. So, my plan is to is to first talk a little bit about hall algebras in the kind of traditional setting they they are a tool that is important in representation theory. And so for people who study quiver representations and and quantum groups and things like this. But the, the setting in which we will ultimately apply them is actually somewhat different, which are sort of categories that are combinatorially defined which are non additive, but, but nevertheless one can do the same thing. And then I'll, I'll discuss some some elements of sort of the algebraic geometry of monoid schemes and, and the kind of combinatorics we see in that setting. Okay, so what's the, what's the traditional setting of of hall algebras. It has been sort of, they have been used in, in representation theory since at least the 80s. You start with an abelian category which has some strong finiteness conditions so it's this is called being finitary. And it means that the the set of the set of morphisms or the set of maps between any two objects as well as the, the set of extensions between any two objects, or finite as sets. And this, this is pretty, this is not so easy to, to achieve somehow because, you know, many, if the, if the categories linear over over some field that field better be finite or else a finite dimensional vector space is not going to be a finite set. So the main sources of, of examples of these types of categories are quiver representation so quiver is a directed graph and representation is, well we attach vector spaces and linear maps along the edges. So the category of quiver representations over a finite field has, has this property, and another geometric source of examples is the, as the category of coherent sheaves when, when x is a projective variety or a finite field. Okay, so these are the kind of two main examples one one can have. So what is a whole algebra well as a, as a vector space, it's just functions on isomorphism classes in the category so we just take this, this is the most naive version of all algebra I should say there are more sophisticated versions but just take functions on isomorphism that have finite support. So they're non zero and only finitely many isomorphism classes, and you can equip these with a type of convolution products so the convolution evaluated on the isomorphism class of an object M is obtained by summing over all sub objects and of M and evaluating F on the quotient and G on the on the sub sub object. If you squint your eyes and replace the summation sign with an integral here and think of M mod n as x minus y and, you know, and as why then you can see why this is called the convolution is reminiscent of convolution of functions and harmonic analysis. And a basis for these finitely supported functions is given by, by functions on just individual isomorphism classes delta functions.  And that's the following, or the structure coefficients correspond to the following numbers so you're counting the sub objects of K, which are isomorphic to N, and such that K mod the sub object is isomorphic to M. So, up to some automorphism groups, which you're counting are short exact sequences of this form so n goes to K goes to M. Okay. So that's what I meant when I said that's the structure coefficients of hall algebras count short exact sequences. And, and of course this implies that the structure coefficients are non negative also right since they count things. So to, I'm going to try to sort of connect this stuff with with sort of quantum groups and when if you've seen quantum groups you know they're a bunch of powers of cues floating around. And to, to get those, we have to take a slight twist of the multiplication. So you introduce something called the multiplicative Euler form and you. So, so here is a formula so of course the for this formula to make sense you really need a category where, you know, X are are non zero only in in finitely many degrees so something of finite homological dimension. And you can think of this as as basically Q to the power of the ordinary Euler Euler form. And so, so we take our old multiplication except we multiply through by this, what will ultimately basically be be a power of Q that depends on Eminem. Okay. And then the theorem of wringle and green is that is that if you have a finitary billing category, then these these these algebras either the one with the Euler form or without it are our associate of algebras. Okay, so you get a you get an associate of right. So if you want to study co algebra structures. This becomes a little bit more subtle so you, if, if a happens to be be hereditary so that the, the, the global dimension of a is less than or equal to one, then you can, you can equip this with a with a co product and an antipode. And get a get a half algebra in some cases this this won't, this will be something like a topological half algebra because the, the co product might not might land in the completion, for instance, but roughly speaking you get a get a half algebra but only in this in this nice case where the global dimension is less than or equal to one. And now, the claim is that that if you, if you see if you look at what you get, and as these hall algebras you get sort of interesting quantum group type things. So, as I said the kind of two main examples of categories were that are that are finitary and a billion being quivers and coherent sheaves on some on some projective variety. So, so here's the, the first theorem tells us what happens when, when we look at quiver representations. If I take a quiver I can view the underlying graph undirected graph as a dinking diagram for for some for some cuts moody algebra, and the theorem states that that this that this hall algebra that we computed by counting short exact quivers contains sort of a positive half of the quantum group corresponding to this to this cuts moody algebra so roughly speaking, just like ordinary. Let's say semi simple because moody algebras these quantum groups have kind of triangular decompositions, and roughly speaking this plus means that we're looking at the kind of upper triangular part here. And this map is, is, is an isomorphism in in sort of finite type so when the, when the, when the dinking diagram is of type edd, then this is actually an isomorphism and there is then kind of a procedure by using using the the Drinfield double, which you could then use to to recover the entire quantum group so I guess what I want to emphasize here is that if we hadn't learned about quantum groups from from Drinfield and Jimbo we could have discovered them in principle by using this this whole algebra construction. And another thing to kind of point out is that this, the, the order of the field, which is q right this q is a prime power, the square root of this thing appears as the, is the deformation or the quantization parameter here. Okay, so, so somehow prime powers have something to do with quantization and and I'm not sure if anyone really understands why that is. And so, so this was, this is a theorem that somehow tells us what happens with quivers and as a just a sampling I'll mention this theorem of component of and castle Bowman which tells you what happens if you take the category of coherent sheaves on just P one or you know simplest projective variety you could have over a finite field. And then also you see a quantum group type object you have. But now it's a it's a quantum affine algebra so so roughly speaking this is this is what happens if you if you were to to quantize the loop algebra vessel to rather than just vessel to itself. So, so in both of these cases we get some some interesting kind of quantum group. And there's been lots of work on this by, by, by many authors so just work of bourbon Schiffman, Eric Vasero, Capron of, and, and many, many other people. And so, so as you as you increase the so in the case of coherent sheaves. If you increase the complexity of the of the variety, this thing gets complicated fast so already already for elliptic curves it's it's it's not it's not easy to see what what happens and you get interesting algebras like the sort of double affine heck algebra show up. Sort of more generally, this the study of hall algebras of curves over finite fields is sort of related to to the theory of automorphic forms on function fields so the the action of the hall algebra on itself corresponds here to to the action of sort of geometric heck operators. So, already for hygienists it's sort of, aside from kind of abstract results it's not easy to see what happens concretely and when when x is a variety of dimension greater than one than basically it's, you know, very little was known and understood about what these what these hall algebras look like. And, and also these these categories of coherent sheaves no longer have global dimension one or less so the sort of co algebra structure I mean you can write down a ring, but you know whether this is a or not becomes a much harder question. And, and so the stock is ultimately aiming to, to look at this last case of sort of higher dimensional varieties but in a certain kind of combinatorial limit, a type of classical limit. Okay, so, going back to to the formula for for the multiplication in the whole algebra. If we look at this. There's nothing about this formula which somehow explicitly requires the category to be a billion or added. Okay, so, so, even though historically, people are looking at quiver representations or coherent sheaves. There's this this formula makes sense and serve a more general context. And, and that's the context that will be interested in. When, when I started thinking about this. There wasn't really necessarily a very good framework for thinking about these non additive examples but since there's been very nice work of Dickerhoff and Capron of. They define a class of categories. They are called proto exact categories. Okay, and these are. These are somehow. These are generalizations of Quillen exact categories but which are allowed to be non additive, and which are somehow tailored to, to hall algebras. And, you know, there's a very nice formalism that that that that was developed by them and and sort of related to kind of higher categorical aspects of the story also. And one thing to note is that that any, any of these sort of proto exact categories has a has an associated algebra key theory. Okay, so you can, you can define a key theory of sort of higher key groups of anything that is, that is proto exact. The show is that if, if you have a proto exact category, which is, again, finitary so that the morphisms between any pair of objects and the extensions of any two objects are finite as sets. And then you can write down an associative algebra using the formula that we saw before. So everything works, kind of as, as expected. Alright, so. So now there are lots of examples of these proto exact categories that are combinatorial and non added.  The simplest, the simplest examples that is not additive is perhaps is the category of pointed sets. Okay, so. And sort of related examples are, if you take a monoid and the category of modules over the monoid whereby module I mean appointed set with with the action of the of the monoid so things that are by people in semi group theory or called acts, sometimes. Other examples are, you know, you can take a quiver and instead of putting vector spaces on each vertex, you can put pointed sets. And again, things can be made to work more or less as before. Other other structures in combinatorics such as pointed matroids. And then the examples that come up in renormalization, things like rooted rooted trees and forests, as well as Feynman graphs are examples of these, these proto exact categories, which means as I mentioned already that that therefore they have associated algebra k theory so which which we know is interesting because I mean I'll get to this in a second but these these hierarchy groups are somehow known to be very interesting. But the thing that will be of the main interest in this talk is this last example which is the category of coherent sheaves on something called the monoid scheme so I will this this monoid schemes are basically sort of versions of algebraic geometry and in a non additive context and sort of correspond to sort of combinatorial units of ordinary ordinary schemes, if you will, but they are they are a good source of these sort of non additive categories where hall algebras still make sense. So, my goal is basically to do the following so since we know that we know that hall algebras give interesting quantum groups. And, and so, so in particular if you have a higher dimensional variety something like a surface and beyond, you would expect to, if by looking at this, this hall algebra of coherent sheaves over FQ you would hope to get some sort of interesting, maybe quantum group like object but this seems very hard. So, so let's try to do something simpler. And let's try to compute as classical limit so I want to take the limit as the deformation parameter. This Q goes to one and see what happens to to this whole algebra. Okay, so it should, it should become somehow more commutative in this limit. And hope to to use this information about this classical limits to understand something about the, the original structure of the thing that we were really after which is which is the kind of quantum object. And this somehow ties in with this, this kind of philosophy of doing things over the field of one element and this, this stuff comes up when you're, when you look at limits of calculations over finite fields as, as Q goes to one. So this is, this is an old story and, and you know, kind of a set of, I would claim it's more of a set of sort of interesting analogies and ideas rather than than maybe a sort of a complete theory at the stage but, but the ideas are kind of neat I think so let me give a couple of examples here. So for instance, let's consider the enumerative combinatorial problem of counting subspaces of n dimensional vector space over FQ over finite fields so in other words I want to count the number of points of this across over FQ. So if you do this, it's an elementary exercise to see that that this is given by a rational function which is called the rational function in Q which is called the Q binomial coefficient and choose K. And if you take this rational function and it has a has a well defined limit as Q goes to one, in which case it's this that limit is just the ordinary binomial coefficient. So, this, this sort of leads to this idea that the, that the limit as Q goes to one of the category of vector spaces over FQ is something like the category of sets or maybe better pointed sets. Okay, because you want some some something corresponding to zero in your, in your quote unquote vector space. So, again, this leads to this idea that a pointed set is a vector space over F4. Let me just mention another sort of classical observation here this is due to teats, is that if you take, if you take a simple algebraic group over FQ and you, you count so you count the number of points of this group over FQ and you, if you take the limit suitably normalized here as Q goes to one, what you will find is that you get the order of the vowel group of G. And so, so this again sort of led to this notion that maybe, you know, if we if we had a good theory of algebraic groups over F1 then then the so F1 points of an algebraic group should be the vowel group. And to some degree, this has actually been been made precise in, you know, the work of, of Lorscheid and and Konkensani and others. So the, I'm not going to get into this very much but the you know the basics of the sort of dictionary is is the following so the category of vector spaces over F1 should be something like pointed sets. So an algebra over over F1 should be a monoid. So, all these, all the structures over F1 are somehow non additive. So, so, so you lose addition there.  So the notion of the module is becomes a pointed set with an action of a monoid. And so it's not surprising that the notion of kind of a scheme or algebraic variety over F1 should also be something built out of Monoids. So, let me, let me say a few words about what when monoid schemes are. So, I have this one additional slide here. So, you know, in, at least in my mind, these various sort of proto exact or proto abelian categories that are non additive are somehow, you know, can be in some cases at least sort of thought of as as limits. And it goes to one of, of, of sort of additive things. So, so these, these are somehow the, the analogs of, of abelian categories, abelian or exact categories over F1 things like matroids and graphs and things like this. And in this combinatorial setting. So I mentioned already that this, if you're working over FQ the the issue of the existence of a co algebra structure becomes kind of subtle. You need some conditions to to define a co algebra structure, but if you're working with these combinatorially defined categories you can do something very simple minded so our whole algebra is functions on isomorphism classes. And most of these combinatorial gadgets have some, have a kind of a co co product in that category which more or less amounts to disjoint union or wedge some which is kind of the pointed version of this joint union right so we have two Feynman graphs we can take their disjoint union. If we have two rooted trees we can take their disjoint union and get a get a forest, and, and so on with with combinatorial objects, the co products or somehow more or less disjoint unions and so. So you can define a co algebra here co algebra structure which is sends a function to the function evaluated on this disjoint union or wedge cell. This turns out to actually be compatible with the product for in these combinatorial categories so you, you get something which is manifestly a co commutative hall algebra or a co commutative by algebra. And it's, you can it's also easy to see that there is a natural natural grading by by kind of a positive cone inside the growth in the group, and this thing is connected so so you always get something which is, which is kind of graded connected co commutative half algebra and so, at this point we can apply the Milner Moore theorem it'll tell us that what we have is an enveloping algebra. Okay. So, and this, this, this Lee algebra, this this Holly algebra is just corresponds to indie composable objects so so things like, you know graphs that are connected or trees that are. Or I mean, things that are honestly brooded trees and not not for us and so on. I should say here that in connecting the sort of hall of a story with the usual story of the half algebra of graphs or trees, what we're getting here is the dual. Rather than, then, so we're getting an algebra which is non commutative but co commutative as opposed to how, maybe most of the time the these these half algebras are viewed. So, so let me. So let's, let's, let's see how this kind of this classical classical limit idea works out so we want to we want to use this kind of story about hall algebras together with this sort of f one philosophy to to compute some classical limits so Well, let me just give, give a couple of examples so if you, if you take the, if you look at the category of modules over the sort of the, the free monoid and one generator. This is the monoid, which is just powers of tea. Then then this than the, the whole algebra of this category that you get is is is basically a dual of Dirks half algebra of rooted trees.  Which tells you how T acts and then you can see that the type of graphs that can rise or are either rooted trees or sort of cycles with with rooted trees attached. And if you take, if you take the, if you take a quiver and you look at at the representation of that quiver and pointed sets which somehow you should view as the kind of kugos to one limit of the category of ordinary quiver representations. What do we get. Well, so the naive guess would be that I mean the sort of quote unquote classical limit of what we had before which was the positive half of the quantum group should be just the sort of the positive part of this, of this cosmode algebra. What you actually get is, in general you get this module a certain ideal, which I'm not going to describe here but this somehow reflects kind of a non flatness of this this kind of q goes to one limit so something non trivial happens this q goes to one. Something which is kind of maybe smaller than expected. However, if the if the quivers of type a. Everything works nicely so you get exactly the, the enveloping algebra of upper triangular matrices. So as we know in mathematics, everything works nicely in type a and then then it doesn't work as nicely in other cases. And so the, these, these hall algebras applied to other to other kind of combinatorial categories recover sort of other types of. Well, for for Feynman graphs we get the dual of Dirich's algebra of graphs and for for matroids you get the dual of Schmitz matroid minor half algebra, and, and so on. And as I, as I mentioned these these categories have have have have an associated algebra k theory and just to indicate that this k theory is interesting. In the simplest case if we take vector spaces over f one which is pointed sets, and these k groups correspond to the stable homotopy groups of spheres. Even in the. And this is somehow the simplest case so so in several other cases like for instance these, the case of matroids, you can show that this, that this k theory here is at least as big as homotopy groups of spheres in the sense that there's, there's the, the, the k theory of f one vector spaces sits inside of these things, quite often. So these are these k groups are are are interesting and and somehow hard to to compute. Okay, so, so let me, let me finally talk about these. These trying to do algebraic geometry in this kind of non additive setting, which will ultimately lead us to tutorial varieties, or, or rather to their kind of monoid versions. We know that that you know an ordinary scheme and algebraic geometry is obtained by gluing spectra of rings. And you can do the same thing with with spectra of Monoids. So if we have commuter to Monoids you can define prime ideals, you can, you can define as a risky topology and, and, and do the same exact same thing you do for rings. And, and what you do, what you obtain when you glue these things together is, is a space which is a, it's a minuital space so it's a topological space with a sheaf of Monoids on it. And this is, this is what a monoid scheme is it's the exact same story based on commutative Monoids rather than commutative rings. Just to just to give you a sort of a flavor for for this so so what are what are some of these kind of simplest schemes. The thing to kind of notice here is that these schemes have very few points. So, if we take the affine line which is which normally a spec of polynomials. So instead, in the Monoids version we would look at spec of a monoid on one generator and this thing has only has two points. So it has, it has exactly one prime ideal the one generated by T and it has the kind of generic point corresponding to zero. So, so the kind of monoidal version of affine and space is you take the free commutative monoid on n generators. And you look at prime ideals in that and in effect, these correspond to subsets of these variables exactly the kind of coordinate subspaces. So part of the reason why there are very few points is is so so as I will maybe say this monoid schemes are closely tied to kind of Torah geometry and and their points in this kind of monoid sense correspond to to Taurus and sub schemes in the in the sort of ordinary story of Torah variety. So there are much fewer of these sort of Taurus equivariant things than there are of points in general, of course. And so here I also give an example, well you can take two copies of the affine line to glue to to get to get P one so P one now. It has three points it has zero infinity and a generic point. Okay, so, so how is, how is our monoid schemes related to to kind of Torah varieties well. It's determined by fans, and a fan gives you a monoid scheme. So, so a fan in in the kind of Torah consensus is a is is a is a collection of cones. Satisfying some some properties let me just give an example. Yes. So here's a here's a fan it's basically a way of dividing our two into into three chambers in a nice way. And the way that so these three colored regions here these are the three cones. Each cone. So if you look at the, at the kind of lattice points that live within each of these regions you get a you get a finitely generated semi group and or monoid. And, and these, this picture kind of tells you how these monoids are glued together. And this data can be assembled to sort of gluing data for for a scheme for for for, you know, for monoid scheme. And if you linearize this object, meaning instead of taking the monoid you take the monoid algebra, you would the monoid ring you would get a Torah variety in the, in the kind of ordinary sense. Okay, so in the three cones in that picture and give us give us these three monoid so so Sigma naught is is the is the is the first quadrant here and and the the the semi group of lattice points here is generated by the standard basis vectors you want to need to. And so this corresponds to the variable sex one x two. And these, these other cones give us give us different, different semi groups. Okay, so let's, let me discuss what's what coherence sheaves on on this object kind of look like so the story is again parallel with the ordinary story so if you have a, a module over over ring that module gives you a coherent chief on the, or quasi coherent chief on the on the scheme corresponding to that ring and the same thing here happens if you start with a module for the monoid, then using standard constructions you get a quasi coherent chief on on that on that monoid scheme that I described. Of course now this, these categories are not additive so you can't an ordinary algebraic geometry coherent sheaves form an abelian category on a monoid scheme they can't because it's not additive, but they do. They do form sort of proto exact categories in this in this Dicker Hoff Capron of sense. So that means that we have a chance to to talk about hall algebras of these coherent sheaves. Now, you kind of run into a certain problem which is to to to get hall algebras we need finitary conditions we need to objects to only have finally many extensions between them so only finally many short exact sequences between two, two objects. She fails in this in this monoid context, even when the the kind of the fan underlying the monoid scheme corresponds to something which is projected. And that doesn't happen in the kind of ordinary setting. When we, when we do ordinary algebraic geometry we have results of Sarah and and the tell us that X in that case just finite but but things can go wrong in this in this sort of non additive world. So that's a problem, but what we can do is to pass to sort of a smaller category of sheaves. So, so we define a class of sheaves called T sheaves. And what are T sheaves well, I'll show you a bunch of pictures pretty soon but these are basically these are sheaves which, which locally admit a grading by the by the semi group. So we've seen that our our our monoid scheme is somehow is covered by by by subsets corresponding to cones, each cone corresponds to a semi group. And, and so locally we want the sheaf to sort of admit a grading by this, this a signal. So the second condition, which actually this, the second condition is something. Something that comes up a lot in this sort of non additive world which is you want, you want to type of cancelativity and in these sheaves to to hold. And this actually fixes the finitarity issue. So, you get a, well, everything, what once you impose these conditions everything works. So how does this connect to to kind of combinatorics and other things well. The basic theorem is that this these T sheaves on affine space just corresponds to skew shapes and dimensional skew shapes and in the kind of ordinary combinatorial sense. Let me, let me give an example here in two dimensions but this works in any dimension. So, so here's a, here's a skew young, kind of young, young diagram skew partition and how can I think of this as a as a module for a monoid. Well, so in two dimensions I have the for for kind of the affine plane. So we have the monoid on on generators x one and x two. So how does this monoid act on this on this set. Well, x one moves one box to the right until we fall off the diagram and then things go to zero and next to just moves up. So any, any diagram like this can be thought of as a module. Over this over this monoid and therefore it can be thought of as a coherent sheaf. Okay. And so, I can make the remark here is that this, this, this is a picture of in this kind of monoid setting of a torsion sheaf supported on on the sort of third formal neighborhood of the origin, because three is the smallest power of all that kills all, all elements here so if you, if you, if you take any positive path of length, you know, at least three you're going to fall off this diagram and that's the smallest number that works. Okay, so here's some, here's some other pictures of sheaves. So these diagrams can be infinite. So, so here, I'm thinking of a diagram that continues off to infinity and the y direction and the x direction. And so this was correspond to a coherent sheaf on supported on the union of the x and y axes. This is a diagram which is just kind of, you know, has something missing in the lower left hand corner but is infinite beyond what I've drawn and this is a picture of a torsion free sheaf. So here's a picture in three dimensions. Okay, so, so this would be a picture of a, of a sheaf on a three supported on the union of the, of the three coordinate axes. And, and in general, if I have a monoid scheme, I'm going to glue these skew shapes together to get something global. Okay, so, so these T sheaves are just sort of objects that are that are glued together from from skew partitions. The problem is that, that this, that this category of these T sheaves is, is, is nice it's finitary is proto exact, and, and so you can define a whole algebra, and by all the kind of abstract nonsense I've said earlier. That's going to be an enveloping algebra. So, so in other words, for each torque variety we get a le algebra, and you can ask well, what, what did easily algebras look like so. Let me, let me just here give a, give an example of kind of how you would compute a le bracket here between. So here I've chosen sort of two torsion sheaves these are these are finite diagrams that they create this is in two dimensions so these are two torsion sheaves and in two dimensions. And so I want to look at all extensions between these two diagrams. And so this, this amounts to all ways of the product in the whole algebra amounts to always of stacking one diagram on top of another. And, and then anti symmetrizing this operation. So, so s times T is, is the sum of these three terms here, always of kind of sticking T to the right and up of s, and then we anti symmetrized so now we're sticking the diagram corresponding to s, up into the right of T. Okay, so, so would you would you get in as a sort of a byproduct of this is that for instance that the, you know, that skew shapes and dimensions have a le algebra structure and this under this bracket and this in fact these these the structure constants for this the algebra always plus or minus one and zero. Okay, I'm starting to basically run out of time here, but we, we are able in certain examples to actually compute these, these le algebras attached to Torah varieties, and you see stuff that looks like, you know, loop certain certain pieces of loop algebras like one, you get a certain piece of loops to GL two, which is, you can be thought of sort of a classical limit of kind of Kupronov's theorem that I mentioned earlier, where he was working over FQ. And, for instance, and if you take sheaves supported on the second formal neighborhood of the origin and a two so point sheaves. Again, you can look at the kind of hall algebra of this category. And in this case you get, you get a certain sub algebra of positive loops to to GL two. And there are other examples so so we're able to do, you know, P two. Well, we're able to exhibit a basis for P two and and and in some cases, when we truncate this le algebra we're able to sort of identify it with things that that are known but in general the structure of these things, which again are believed to be classical limits of some type of quantum group are still pretty mysterious. All right, I'm going to stop here so thank you very much. All right, let's thank Matt. Are there questions. Yes, I would like to ask a question on this black dots on the shapes you want this image twice this black dots to get to get a lead bracket. So, no no it was at the end. And. Oh, okay. After that. Yes. Yes. So, do you do you have some properties for this black dot for example is it a pre list or whatever. So I, I don't think in general, I mean it's certainly for for for general proto exact category I don't. I don't expect this to be freely because I mean this is more of a kind of intuition that I have more than a theorem but what freely is about insertion and sort of in a single spot. So, if you have these skew shapes the interact when you, you're not really inserting in a single kind of place like on a tree, and that ruins that freely property and so. So, so this came up I thought about trying to do sort of an insertion elimination type thing for these for these skew shapes and then things kind of fall apart precisely because when you stick them together they kind of that the interaction is non local in some some. Okay. Thank you. I had a quick question. You mentioned that the K theory of these, these categories. And in the very specific example of rooted trees, which have been studied in great detail what is then what are the, what is the K theory for those. It's So, I think we're free. So, I'm embarrassed to say I don't. It's something that again contains the stable homotopy groups of the of the sphere spectrum I think you can kind of, you can write it as a sort of more or less a sort of a smash product of that with something else but I don't, I'm going to get it wrong if I say it now but I can, I can look it up I think and tell you. I mean, the fact that the trees are like a co free kind of hope father but I mean is that, I mean I would have expected something trivial or something very generic for, for these kind of catering questions. What one wouldn't expect pointed sets to give you the stable homotopy groups of the sphere spectrum right. Yeah. So, so yes I agree that it's. You ask what happens for grass. Thank you. Well, I don't know but that that's I think that would be an interesting question. Yeah. Thanks. I think I have a question but cluster algebras are very popular in physics at the moment and they have people who say that cluster algebras are all algebras of quiver labs or something like that. Do you have a comment. No, I mean, so I've also heard this, I've heard people trying to kind of relate this. I mean, I think they arrive, they arise in a slightly different ways if you start mutating a quiver but but I don't understand the precise relationship. The whole story. Yeah. Thanks. Any other questions. I always find it very amusing that this F one philosophy it's almost the opposite of the way you do q counting where you would often start with a binomial identity and generalize it to the q form and here you're doing the opposite where you're taking something that makes sense at the q level. And going the other way. Anyway, if there are no other questions, then let's thank Matt again. Thank you.


They deserve better than being left on the streets of DC or being left in Martha's Vineyard. They deserve a lot better than that. These vulnerable migrants were reportedly misled about where they were headed. Told they would be headed to to Boston, misled about what they would be provided when they arrived, promised shelter, refuge benefits and more. These are the kinds of tactics we see from smugglers in places like Mexico and Guatemala.  Excuse me, uh, isn't Martha's Vineyard one of the nicest, richest places in America? Hello, and welcome back to another excruciating dive into the black hole abyss of self-awareness known as the view. This time, as usual, they are shocked that Democrats are being held to their own standards by their elected political opponents. No. No. No. No, not that one. No. Yesterday, undocumented immigrants were put on planes and flown from Texas to Martha's Vineyard in Massachusetts. Florida Governor Ron DeSantis said he used his state's funds to do that. That means taxpayers paid for it. And who exactly do you think are paying for all these illegal immigrants when they come here? It's almost as if none of these pro-illegal immigration activists have ever thought about it any deeper than what it takes to signal their virtue. That's the thing with Democrats. They're very, very generous with other people's time, money and space. We're gonna dive deeper into this, but first give me 30 seconds to tell you about this free coin offer from Noble Gold. Noble Gold CEO Colin Plume thinks that quantitative tightening is setting up the stage for a gold rally. In his interview with the National Desk, Plume said the tightening is pushing the dollar up. However, he predicts that by next year, the Fed will print money again to restart economic activities. If you're thinking of gold and silver right now, Noble Gold is giving away a free Gold American Eagle Coin with every eligible IRA or 401K in September. You can't go wrong with Noble Gold. Call the team now at<PHONE_NUMBER> to find out more or visit noblegoldinvestments.com. You can also use the link in the description or pin comment. Make sure to tell them DroneTech sent you. And his spokesperson added that places like Massachusetts and New York should take care of them since they're the ones inviting them here by calling themselves sanctuary cities. Yeah? So what are you complaining about? They came and now they're going to live with you. The people who openly invited them to come by the hundreds of thousands. But you know she's not even thinking that. In her head, these people always go somewhere else that's not bothering her. Now I call me crazy but I remember the big tall green lady, you know the one that's over on the river and I thought we asked people to come here. The Statue of Liberty in Ellis Island are in New York. The people who were coming to New York were processed. Unlike the open borders where people are just surging across by the millions. Some of these people are indeed being bussed to New York. And all they've done is complain about it ever since. So I get that I understand what they're trying to do. I get that they're trying to make a point. But it's these are people you're playing with. These are real live people with children and older people. And you know we can work it out. But if you're going to be a bonehead. Yeah. Who wants to play with you?  Oh okay. Oh you crazy. They were always people, children and old folks. Many of whom die in the dangerous journey to get here. Or they're kidnapped by human traffickers.  Whoopi and the rest of them just didn't care as long as they were going somewhere that didn't involve them. Now suddenly she sees it as a political stunt. But that was always the case with Democrats. Democrats went on for years about their desire to see border states and other red states get flipped blue by illegal immigration. Because of demographic changes in this country, I think that the Democratic Party is going to win Texas moving forward. And the Democratic Party is going to be in power for the next 30, 40 years. The demographic change that's happening in America right now gives the upper hand to Democrats. This census that just came out especially drives home the point that Texas is next. It's a state where the demographics are changing in ways that are favorable to the Democratic Party. Demographic changes that help the Democrats. Democrats for a decade now along with Arizona and Texas have had on this sort of long-term project of trying to take some red states across the sunbelt and flip them blue as demographic changes are taking place there. Democrats should be asking themselves as a matter of fact why aren't they dominating the political landscape. Two decades ago they influenced a book The Emerging Democratic Majority predicted they would due to demographic changes in the country. But unfortunately for them, things haven't been going that way. So now of course that they suddenly see no use for these people in their states and maybe even see them as a threat to their power, we get these completely transparent attempts to explain away their hypocrisy. I wonder really what is the scope of the problem because I think this is just political theater. Yeah. If Martha's Vineyard is my happy place, it's my home away from home. I spent the summer there. I wrote a book about it called Summer on the Bluffs and it's a beautiful place and I'm happy that they are there. Welcome to Martha's Vineyard. Unfortunately the same people who are displaying this ludicrous level of hypocrisy are the very same people who generate and focus outrage in the first place. So I doubt they'll be doing it to themselves. Which is exactly why you should support channels like mine and help them grow. You can do that by hitting the like button, sharing this video, subscribing, and leaving a comment to let the community know what you think. All of these things greatly help and I deeply appreciate it.


Hi, I'm Professor Nesheba and I'm here to tell you a little bit about Lewis acids and bases This is an introduction to the idea in which we're just going to use Lewis structures to Understand this this idea. So Lewis acid base chemistry requires a base And I'm just going to symbolize that as B. It's not any particular element I'm just writing B But the key thing is that this this Whatever the base is it has to have a lone pair of electrons So an example of that could be ammonia nitrogen with three hydrogens bonded to it, but it has a lone pair of electrons and So we think of the rest of this as B And there's the lone pair also water would be a good Lewis base because it has two lone pairs of electrons and The fluoride ion, you know because it has a full octet of Electron pairs would also be a good Lewis base. How about the Lewis acid? Well, the example that I'm giving you here is BF3 the main thing to note about the Lewis acid is What you look for is is an unfilled octet The point is that it has the capability of accepting This lone pair of electrons from the Lewis base and examples Well, I've given BF3 the silver ion so three-year-old good Lewis acids Now what's the stoichiometry of the reaction that happens? Well, the base with its lone pair combines with the acid to produce something called BA and the BA gets a special name in Lewis acid base chemistry and it's called the Lewis acid base adduct or just the adduct The thing to note about the adduct is that there is a bond between the B and A That bond also has a special name. It's called a dative bond and Finally the electrons that go into making that bond It's two electrons are the same as those electrons right there That is to say the Lewis base provided the electrons to make the dative bond


The study reviews existing literature on spatial navigation and postural control in healthy elderly individuals and Alzheimer's disease patients. It focuses on the role of the vestibular system in these processes and discusses the implications of vestibular deficiencies in both groups. The authors conclude that further investigation into the vestibular system is needed to better understand the causes of spatial and postural deficits in both healthy aging and Alzheimer's disease. This article was authored by Maria K. Chepeshiva.