Hey, what's up folks? Welcome back to another 3D Hangouts. My name is Noah Ruiz I'm a designer here at Adafruit and joining me every week is my brother Pedro Good morning everyone. I'm Pedro as creative tech here at Adafruit and every week. We're here to hear We're here to share three printed projects featuring electronics from Adafruit That's right You know, I got this reactions thing. I'm gonna do the Adafruit Hello everybody, I forget what part I'm saying. This is the show we combine 3D printing fireworks and balloons To make inspirational projects With eyeballs Hello, everybody. Welcome to the show. This is episode 416 It is Wednesday, October 4th, 2023. We are hanging out in the discord chat room. Hello, everybody. Welcome to the show We have some some fun Halloween howl-holozy projects lined up for folks and We have some prototyping. We have a little bit of a shop talk Time-lapse Tuesday video and community makes all this and more on 3D Hangouts We'll take a moment to welcome everybody to the show live No, you want to say hello to people good morning everybody hanging out all over the YouTube's and the Instagram's and the periscopes And the linkedin's yeah linkedin periscope Facebook YouTube twitch discord If folks want to join us in the discord the link to that is discord.gg slash Adafruit Given shoutouts to do Wester, Rausen, Vince, Squid.Jpeg. Hello. Welcome to the show Let's jump into and Jason on the YouTube.  Do they have more I know but that's I want the dev kit so you can add your own It looks like it's just a powerful chain like how it fades in and out of the effect I like the the different layers that puts stuff behind you and in front of you Yeah, it's like blurring it to like the transparency of those balloons. Yeah. Oh, yeah in the portrait effect Then the studio you said you didn't like it. The studio looks kind of cool The kind of silhouette or and you can adjust it Vignette, oh, can I adjust the portrait? Yeah, whoa This segment brought to you by Simona Yeah, we know this one just was updated. Okay, let's go over what we're doing this week Yeah, first up. We'll do the freebies This week we have freebies Check out 80 fruit comm slash free for all the details I'll run through them right now for orders that are $99 or more You're gonna get a free PCB coaster with a golden 80 fruit logo. Those are lovely Aluminum PCB coasters with some really nice look screen of an 80 fruit logo if your order is $149 more you get the PCB coaster plus an 80 fruit kb2040. That's that lovely keyboard driver great for making keyboards and other projects if Your order is $199 or more you get the free kb2040 the free PCB coaster and free UPS ground shipping for constant until U.S. Only if your order is $299 or more you get the free ground shipping from UPS the kb2040 the PCB coaster and The all-new 80 fruit Metro M7 with partnership with digike Check out 80 fruit comm slash free for the details these get automatically added to your cart So that's really nice. No need for coupon codes But if you do want to use coupon code, you can use today's coupon code It's good for the next 24 hours and it's prototype Prototype and that's the coupon code awesome It's actually what we the largest portion of the show was showing off all the prototypes working on But I think to start off. We're gonna show off this week's Little bit of a project recap video right so There are a lot of Halloween projects and since we are still in progress of current projects Lamar suggested why don't we do a recap for 2023? And I'm on the eight of your learn systems just type in Halloween because we got a bunch of Halloween projects Particularly the ones that we have That I picked out this week We have the Halloween neon LED sign We have the Halloween M4 Tombstone we have the the blue fruit remote-controlled Canyon dispenser with a with a servo claw and What's the last one it's escaping me right now. I think it's the LED gem the emerald. Yes, that is correct Emerald so we have a YouTube video out that just kind of as them in a compilation and We thought that you know, they'd uh, they needed some They needed some what do you call it some some promo? Some recap promo. I think the LED flame is also there. I think that's a really cool one for folks that want to like Have a fan on a hot day, but still have like this cool light-up prop. So that's pretty cool Yeah, the one I have actually with me right now is the one of my favorites It's the tombstone Halloween M4 which will be in stock very soon Adafruit just got a big shipment of M4 chips that at CMD 51 That's the chip chipset that runs a lot of the I a project. So this is the Halloween M4 we have monster mask and and I think the M0 Halloween as well So this is a cool 3d printed tombstone. That's desktop size. It's a battery powered and it all snap fits It's got a couple of details on it to make it look pretty cool and it's got black LED acrylic with some neopixel lit Lights there to make this cool kind of spooky tombstone Rock yeah, the crumbled rock effect, which I guess vinyl, right? Yeah, this is all vinyl all that detail there This mask here is also Vinyl, which is a really good combination of like adding details to your to your props Nowadays we have the prop maker feather so you'd be able to kind of use that to make it more interactive So like if you had a time of flight sensor or proximity sensor You could like kind of wave your hand in front of it and it would like actually have sound So upgrading this with the feather RP 2040 prop maker will be a really good product idea. So maybe maybe next year. We'll have a nicer tombstone This year you did a tombstone already with the prop maker feather using the matrix So you big scaled but if you want to do a kind of a small one, maybe you can retrofit this one To do that. There's plenty of space on the inside here. Hey, it's very shiny And then there's like the USB port there for the Halloween M4 but see on the lookout for the return of the Halloween M4 All right, that is my pick of Halloween projects this year It's ripe for remixing Yeah, I can't wait to start on those eyeball projects again. This is why we've been holding off, but There will be more in store Yeah, there's a ton of Halloween projects the book Philby did an awesome job doing a bunch of different Not we is it Weegee? Yeah, Weegee. Yeah. Yeah, Weegee. Yes I think we can use the name or something. Yeah, Weegee board. We have that candy bowl We have like this googly eye. There's so many. Oh, that was cool. Yeah Yeah, when it came out, it was like, oh, yeah, we put it on a pumpkin. Mmm. Yeah There's so much stuff you can do with that Yeah, and that's just one example of many Halloween projects online at Adafruit.com So if you want to pick up The prop maker or any Neopixels or any other M4 dev boards that are in stock You get 10% off There are any other projects you wanted to highlight. Maybe the blue fruit claw Yeah, I think the blue fruit claw is pretty cool. You can open that one up This one could be attached to anything. So if you go to I think the assembly part of it the main claw part just attaches to the bottom of the Little ghost there so you can add this on to anything. Yeah, the drone I think I reuse some of the components when I did the drone claw So this makes it completely portable all you have to do is just screw it on to whatever other prop you want to use And it's all blue tooth controlled with your phone So you can add more functionality to it like lights or something like that or even Maybe hook up a sensor so it can be automated So if it sees something coming in front of you or if it like the techs heat or something it can do the You know dispense the candy that way so lots of ways to modify this claw On anything you want. Yes It's pretty simple. It's just the servo the BLE blue fruit CPX Yep, that's pretty much it just two components, I think yeah, and then the three from our part that like holds The combines the servo. Yeah board together I was surprised to see that the following the small flying ghost $20. It's still in stock They're still selling this thing. It's pretty cool. Yeah ratings like people still use Yeah, so it's basically a motor and a string and like has like a pulley system that drags the The ghost it's sound activated. So whenever it hears people knocking on the door saying trick-or-treat it'll It'll activate. Sorry. I'm trying to get rid of the discount. There it is So you can still pick this up. It's pretty affordable and it's a we we've you know We picked this up during the pandemic. So two three years ago now in 2020. I think Where it made sense to like have distancing, you know, but this is still kind of a cool prop to kind of reuse upgrade Yeah, I can dispense Kendi while you're like sitting on your couch Or you can you know use the servo to like open and close a door for candies to kind of fall out of something There you go. Yeah, so lots of cool uses for this Is this circuit Python it is circuit Python. Yeah, let's Clark put it together, of course And you can see here how it's working. It's using the the button It's up and down in the blue fruit connect app. That's free app for iOS or Android. So it's going to work with just about everything and it's a really cool kind of Simple project you can put together with not too much soldering. Mm-hmm Yeah, I think that upgrade for this would be maybe adding a speaker so you can like trigger sounds as well Have your own sounds being triggered. Yeah, I think Maybe a combo a combine The prop maker the new prop maker feather Somehow with with blue fruit. I don't know if you've done a project like that yet I don't know how you would do that I think we just used like the the nrf 52 Yeah, the other and then just kind of solder up to a proto board so that you can connect You know with JST cables a neopixel speaker. That's what we think we have pretty good audio support on the nrf 52 840 so if you want to do Bluetooth, that's the way to go. Oh, so that's a way we can update that next week next year Yeah, yeah, we got to start like you really need to start like in September 1st. Maybe then August Yeah Yeah, now it's like pick the kind of simple project So if you have you know, if you want something that lights up and matches your your cosplay We got this cool kind of light up Emerald mm-hmm And then again, this could be just you could just put insert this into a pumpkin as well have the yeah animations I'll be wireless or your candy bag Candy dish, whatever That'd be kind of cool. Yeah, I really like this one because it came in three different sizes and a lot of folks Stand up, which is kind of cool. Yeah, so I could just add that extra light to whatever kind of problem Sort of cool. All right But again, just type in Halloween and see what you get Lots of fun stuff the neon signs are always a cool one to kind of Adorn your your haunt with it's got a fun case on it and uh each each each sign has its own set of like animations that kind of match the sign itself Like the ghost has like this kind of cool trail the um The the the wolf howling at the moon has this cool kind of like Effect to it The moon rising Check this out. Um, if you want to make your own neon sign Um, I noticed like target always has the same kind of bat and pumpkin So these are kind of unique Uh, yeah Unique to me All right, any other ones that we want to talk about believe that was it, right? Yeah Yeah, I think so. Yeah, just four of them Props do obviously, but uh, I just wanted to pick five for this week Cool. Let me check in on discord and see if anyone's Yes question about the servos making noises. Are there any that have silent servos? I think those little ones from pinoco, right? Those are kind of exciting I think if you're gonna go with some silent, it might be a little bit more costly I haven't really played with any other servos other than like the really affordable ones That are your standard hobby servos. So I'm not sure, but definitely check out digikey. Maybe there's some that have rated for like Low noise. Mm-hmm. Yeah, I'm sure there are The claw, yep Oh, johnny's saying that they're celebrating cinnamon roll day here in sweden. I gotta get a cinnamon roll now hmm DJ Devin is asking if there's any plans to make the creepy dish with a bigger round eye display I would I have this we have the displays. We have the s2s. We just need code They're working on it. Yeah the libraries to like the firmware for it. Yeah, yeah, it's uh, it's coming together though Yep, we're ready We got the stuff. Yeah, we go to uh Tall talk to the hardware all nicely. Mm-hmm. Yeah, we're getting there Cool if we don't make it for halloween I guess we'll be making snow globes out of them, huh? Right, sort of Have you seen the one where it's the kitty cat on the um the litter box and that's the snow and the snow globe Oh my gosh I think that should be the the uh jiff that we put on there Yeah, that'd be fun Okay, um, let's see I think we're ready for prototype. Yeah Let's go ahead and jump into this week's prototype. You want to go first or you want me to go or I'll go first All right. Uh, I think I've shown you this A couple weeks ago. I finally have a hal 9 000 This is a fun prop from the infamous iconic movie from Stanley Kubrick 2001 a space odyssey. This is all 3d printed. We have a current project from Many years ago from phil b. He used laser cut parts. We won't he suggested that let's bring this to the uh the 22nd so 21st century with 3d printing instead of laser cutting So I went ahead and design a nice enclosure for this giant 100 millimeter diameter button So we press the button. I'm sorry, Dave. I don't have enough information We got a sample from 2001 a space odyssey of hal saying, you know, sorry, Dave Um in the back here, you can see it's just that button. These are really nice buttons They have a built-in led with a resistor. I'm using quick connects and then of course the prop maker rp 2040 feather So there you can see I have the wires all screwed in very little soldering Um, I just had to tend some wires really but this is nice because I can disconnect this Um, the speaker is uh the three watt eight ohm enclosed speaker So that's pretty loud. I'm sorry. I don't have enough information Because I have a kind of medium sized printer. I have it split into three And then I have my panel here split into two the last detail, of course, is the howl 9 000 kind of emblem that goes here And I may or may not do a back cover here Um, it is it is pretty big, you know, it's this big and I think um I was gonna say I think it takes a long time to print but Uh, I think it's worth it. It's a kind of big, you know thing we I made sure to scale it to the exact um Scaling of the actual prop Which um phil b kind of already did the hard work because He went in the rp Forms the prop rep forms and found folks that already painstakingly found like exactly how many holes and exactly dimensions of it So it's really nice that this button kind of already has that I might spray paint this to be chrome And yeah, it's it's a pretty cool prop We're gonna have it so that when you press the button it'll randomize the sample And I think to distribute this without any copyright infringement. We might just have you know mac os Uh text to speech do it or maybe tiktok or some other voice That that we won't want to do it. We'll just type it out and it'll kind of do it So right now I have it powered by usb here Um, I think it's safe to just have it powered by usb So there's no need for battery because you might want to mount this somewhere if you're a big fan of it Otherwise, it's it's a pretty simple project, you know, just showcasing the prop maker feather If I bring up the learn guide You'll see that man it is a lot of work back in the day to get an audio project I'm so go back to the learn guide and type in the howl 9 000 and if you haven't seen the movie I recently watched it a couple weeks ago And it's just so amazing how well it's filmed like stanley crubick did such an amazing job all the people that designed it It's Still like an incredible movie and it came out so long ago like 50 plus years ago That's how a lot of the movies are Star Wars, you know Nine inspiration from Yeah, so this is uh phil b's version. It looks really nice because it's you know spray painted and It's got acrylic that just has this really nice surface finish Wait, is the grill gold or is it gray? I'm seeing both in the movie. It's more gray But here i'm seeing it's a little bit of a gold. That's why I printed it in gold Which is fine I need to get some spray paint because you know the guy really covers like spray painting I was gonna 3d print this piece, but it has a lot of details That's like, you know, it's got the coil and the threading for the night So I really wanted to keep it simple and the whole point of this project is like to keep this like under a hundred dollars And here's the laser cut parts that I referenced Um, he really documents like the assembly of it like he's pretty good. Yeah But uh, yeah, he's got a label printer for it. I think I'm just gonna print it and do the hot Filament swap technique. Yeah, I was gonna say yeah, but you know building all the layers of the acrylic Um, can be a little oh my god, you know a bit of work. Yeah, I see, you know with the with the laser cutter These is a lot dude. Yeah But like, you know, they're still kind of expensive the 3d printers are cheaper these days in the laser cutter Um, and I haven't looked at the newest laser cutters from like glow porch because they're like Right now. I don't know what I think it's probably still a thousand plus dollars Mm-hmm Bet is I don't know how big it is and then your bulb breaks Burns out. Well, I mean, yeah So back then, you know back in 2000 what 10 or something. I think let me see let me just do a quick Uh 2013 actually is when it was first published 11 years ago Yeah Or 10 I think 10 because yeah So that's when it was published that when he started working on it. Oh, I see Right, so, you know, everything was Arduino. We have this wave shield Um, you had to like piece a lot of things together um Here's their Arduino code for it I think it's a lot more complicated Than uh, it would be in circuit python. Mm-hmm, but I think it was at dano or somebody re Redid it with um, oh This the the the cricket which is like kind of stock right now And it's kind of like a lot that is overkill because it is overkill because you know It's supposed to do robotics like motors and servos size of it. Oh, and you need a cpx on top. Yeah Well, that's again. This was even even this is out of tape, you know, like you could do it, but Uh, I think lemar wants to redesign this too much man with uh With an rp2040 because we didn't have the rp2040 when this came out And uh, it's still a lot, you know Here's the whole thing. I know This is what gives us the job security Everything that has to be remade Yeah, it's it's still a lot of work to remake everything nice and simple Yeah, and just making it 3d printable. I think is is going to go far. Yeah So, uh, that is so the project I got going on.  Because they know that we're gonna take photos and then you can have it But yeah, I think uh, I think I am gonna put a uh the lipo on here and then maybe Have like the um The screw thing for the back so you can hang it have it me for the kids's doors Cool, man. It looks so good. Even in the this light. Yeah, yeah Yep Yeah, everybody in the comments saying that yeah, they definitely gonna make one of these Oh, cool Squid says they're gonna make one all Andy Callaway says awesome doorbell. Yes.  So it sits behind it Oh, yeah Yeah, yeah, I'm a fan of custom doorbells Back in the day that was one of our first three printer projects We took an arcade button and we wired it directly into our doorbell because it's just a button And uh, just be careful, you know because it's like, uh 24 volts or something Oh, yeah Most arcade buttons are rated for like 24 volts. This one's rated for like 24 volts plus Um, so it's pretty chunky pretty industrial And uh, yeah, they're fun. I love these buttons. They come in different colors, of course And I want you can you can throw in any pixel in there somehow But right now it No, there is I'm just saying you could make it you can get the white one and then You know make it whatever color with a little bit of hacking Um, but yeah, it's pretty fun. It's pretty cool. I'm a big fan of Such an iconic movie. Mm-hmm Uh, it's events is saying that yeah the glow forge and the omtech polar are still the best to beat for entry level cutters Yeah, I'm curious like at some point. I do want to get a laser cutter, but it'll happen these days Yeah, cool. Next thing we're prototyping Next up next up in the prototype. We are almost done with this faz wrench Put all the components together Do a little demo. This is just the default code that comes with the prop maker and um Little buttons press the leds are hooked up. These are like fake leds. Happy the way these came out It's just a new a cut neopixel strip on the back I'll open it up next week, but Show like all the insides, but I think I need to make like a cover.  So the red doesn't bleed through Okay, but yeah Super happy with the dimensions feel super smooth prop maker rp20 40 like here and the on and off button all the components um Screw into the back. We have the countersunk screws to hold everything together Uh, super proud of the way we got the rotary on here. It's just the rotary on its side Uh, so it's like a knob, but on the side so it does the Squirrel wheel. Yeah, cool way to turn that into a scroll wheel because I don't think that they actually make something like that Do they or it's just a scroll wheel not a The There might be something on digit keys website, but uh, it's nice that we have that we stock those when I mean, right? Right. This is a stem aqt uh board. So it just plugs right in directly in without any soldering. It's really nice Um, yeah, I love to open it up to show you how modular all the components are. Yeah, it's really nice Everything has so happy with way everything plugs in even the screen Um, the screen also stemma. So it just yeah, let's try it in. We have soldering some headers, but that's it Okay, and um Yeah Just to give us some context. Um, this is a prop from five nights of freddy security breach ruin It's the latest dlc From the five nights of freddy franchise It's an indie horror game probably not indie anymore because it's like so widespread. They have a movie coming out Yeah, it has a movie coming out. So yay good timing that on the right for this one. So in the game Uh, this is a tool that's really inspired. I think by like the fluke Multimeters in the game you actually use this to unlock doors puzzles and um nodes in in the ar mode It's pretty cool Functionality wise. Yeah, you're supposed to plug it into uh the the unlock door and then you twist either up or down to Unlock and charge up these little these little wires to unlock the door So because it has a built-in accelerometer the prop maker feather It's actually going to change the sound effect depending on how it's oriented So we're going to use the accelerometer to change up the sound effects Um, the rotary wheel will be just be a volume control because you don't really use it in the game Like the rotary wheel. It's just kind of there. I mean I see that I see the the action with the thumb going like that As part of the animation when he's doing stuff, I see that happening But again in the game, you probably don't hear any difference to the thumb doing anything. Yeah And uh, it'll have a looping idle sound effect of like when you first pick up the the item in the game Um, I actually had to watch a walkthrough because I haven't played the game So I watched the walkthrough on youtube of like kind of the whole game um Pretty cool though. Um, it's really iconic kind of looking All the characters, yeah all the characters iconic the Story's kind of cool. Yeah, so it's a it's a cool prop. Um, it was really inspired by your son my nephew Gavin He's like, oh yeah, I haven't wondered how this is so bad. So You know shots of him for suggesting it So, uh, yeah, I think it's inspired by again like a multimeter That's what it looks like to me. Geez even the color and everything So that's the last step getting like the little lightning bolt detail going on there Like the overlay will happen so the handle has that black overlay The oh the antennas just came in so that plugs in here. No functionality, but Uh, this is a perfect case if you want to do some sort of hacking or something Like if we wanted to do that, uh, what is it the flipper that dolphin flipper? I'm hacking a portable thing. I don't know. Maybe this could be a case for that Like there's so much room in there. You have a 4400 milliamp hour battery. That's this entire side of it So you have lots of battery um To work with there and yeah, there's what it looks like, uh Of course gavin was saying hey, how come the scroll scroll wheel isn't as big as it is on the game with it being as thin It's like dude, you gotta think of physics like it would pop out the bot the back Yeah, so in the game, they probably have like a cube Transparency cube that like cuts it out so you can't visually see as it's rotating So it's not I would have to cut a thing out of the bottom and then like you'll see it on the other side It's like no, that's not how the real world how the real world works Yeah, I I guess it could be like half of a scroll wheel, but then you can't sit there and scroll, you know 360 But Um, yeah, we'll see. I think there might be a weighted Raise it up.  No to raise up the oh no, so the um, it's the board. Oh because the board that's right It comes down to the breakout board. Yeah, it is up against it, huh? Oh, yeah, it is up against it That's yeah, hope as far as I can go without any more Things getting bumped into or it comes down to yeah, it is size limitations. Yeah Compromising I I know of a very complicated way It would be kind of like a um a gear mesh Where it's actuating a smaller gear, you know, to me. That's the only other way I thought about that Yeah, that's too much But even this was a little bit like oh because the way this is being held up I'll show it when we type take it apart There's like a there's like a little hook that holds the rotary down. So when you yeah Roll on it doesn't push it like down because of the the force that you're applying on Just rotating it as a knob like that. I'd like push it down on it So you have to have like a little catcher thing Grab the the knob or the stem Yeah, is that what it's called? Yeah the stem Yeah, the stem Yep Yeah, so it's cool that we you know, we're going to use the accelerometer to kind of make it Okay, because squid is asking about the display. Yep. We have it is the lcd character display I believe it is the two Character display we'll show it. I think you're looking for that guy right there Yep It's been used a couple times the new thing is the stem of backpack that we have back there Yeah, again, we'll show it next week, but I have the Short headers on there because I'm already planning for one of the kids to break the screen And what happens I can just pop off the backpack and put a new screen on there Very nice So designing every single design now is with it breaking in mind at some point one of the kids is going to break it So we need to be able to quickly print that part again or quickly swap out that piece that they broke How did you mount it? Yeah, I haven't made a model of it yet. So you would you Yeah, I had to go in there with the calipers and just measure Yeah Yeah, the eagle catter there. So I'll be able to make a model Oh, I think it's just the backpack though Right, it is just the backpack which is fine You can look at the what what I did that's that lines up. Okay. If you want to use it for reference Yep It's just sketches though. I didn't I didn't model anything That's fine Cool So that is It is a little funky the way that the standoffs are You know where it's like, oh you mirror something and it is not Like all right, it's not like symmetric I had to go into one corner and like adjust it a little bit Keep printing out little little test frames to make sure that it all fit But yeah when they're perfect. Um, what other question was that just laughing at the At the plant the way that we have to plan Modularity with the With the intention with knowing that it might break or that it will break at some point. Yeah Um Let's see. I'm trying to think like if I want to do um A shop talk. I guess I have a really quick one. I have a camera I have a coke one that involves your the way that you're assembling Yeah, I think it's a little bit more useful. You got a little Getting the screws into some of these Centers right here. So it was super hard to get the screws into this area right here. So we got this 45 degree a bit With this anti slip a little bit in here. So this is a ph1. This is perfect for the like m3 and down so all the way down like m2 screws when you have to um Mount like say the feather prop maker RP 2040 the uh, the little screw amounts right by the terminal Those require m2 screws and that will fit this guy in there. So we need to get in a funky angle this could there go Nice and straight or I don't break it You can do your Angle in there You can reach in those crazy areas and you can hold on to this guy And I'll rotate around it and you can kind of see how this is working. There's like a ball socket in there It's doing the rotating At that 45 degree What do I what do I call it in um right angle? I think it's a 45 degree Drill bit I'm gonna find it should be in our Amazon It's it's quite a it's it's quite a ways back So I have to like the way do you filter now. I don't like it. It doesn't do like your entire search history So it might be in 2022 So we got it like words like drill We're trying to do that way Yeah, I don't see it. I do see the no slip Um, I just got this. Yeah these dudes here. Those look good pH one. I also got like pH zero and Yeah, I'm out Because all the drill bits we have are all like those big ones the That where the head just keeps slipping and breaking everything I'd love to switch over to the um the hex nuts or the hex screws, but Like when I have to take apart kids toys or what we're doing work around the house like All those screws are all phillips, man. I can't I can't change all that Or is this the style of it? Yeah, that's the style. Okay. I don't know if it's the one we bought because it's not the one we bought But it's pretty close Is it really 45 degrees? 30 whatever I mean, it's enough to get in there Yeah, because I want a really slim one that I think that's the slimmest just because of the way that you have to get that Yeah, some of them are really bulky Yeah, the first one that I was showing off that I used to make the master sort that one was huge Yeah, it's huge, right? But that one's like a Freaking nine like 180 You can completely bend it Right like this thing the flexible bit. Yes, that that's so big. It's too big, huh? Yeah, it doesn't really bend like at a precise 45. I mean this worked.  Is this yeah, or is this too bulky? I don't know what it would people is anyone in the chat have a good that looks bulky, but Yeah, if you go back there was one down there for the suggested go back and scroll down Yeah, right there all the way to the right all over the right 11 bucks. Yeah Hey that one right angled bit Chunky, but it looks chunky, but it looks like it might fit in that area. Yeah, I mean luckily you're not going into Do some searching because I do need to get one because I had to manually Yeah, it is getting fingers in there saying go me the last time. I'm gonna do that Yeah All right, good tip. Okay real quick for mine. We got 20 minutes. So I'll quickly go through it I got my bracket for my tripod overhead rig. This is from sun cut send. They have a 90 degree bend here um, this is a Oh gosh, I forgot one eighth inch thick aluminum So it's metal. It has some incredible strength. It's not going to bend It can hold probably a 20 pound camera, but I have a little slot here For a tripod screw and then some m4 holes here to attach this To the aluminum extrusion so that I have this right angled camera that can go straight down This came out really nice. Um, I don't know if this is I ordered one and they gave me two I'll take one. Yeah, I know so I'll send you one, but uh, it came out really nice I'll send you these bits too because these are like in a 10 pack. Okay. Yeah Yeah, we'll do a trade. Uh, so this is really nice. Um, otherwise I got this one that's just way too big for what I need. That's like This weighs like a couple grams And this thing weighs like maybe a half a pound. It's like heavy even though it's aluminum There's just too much metal material here for what I need. I just needed this So if you want your own custom bracket that has a bend to it and that's made out of aluminum And you don't have access to a CNC mill or bending capabilities. Check out send cut send. I designed this in fusion 360 Um a couple weeks ago. I think I showed off the um the sheet metal design and then you unfold it exported dxf Bring it into send cuts as a website and then you can define how much of a bend where the bend is Um, what the holes are you can have these um threaded if you want you can have this anodized Powder coated lots of great features. And this only cost me. Oh boy. I think it was like 20 bucks Um, which works out for me because this thing here Guess what is 20 bucks? So you can customize your own thing and you get two of them Like if I I said I only wanted one, but they sent me two And uh, you have the option of all sorts of aluminum's composites um Not just aluminum. They do steel as well. So if you want something that's like, uh, you know, uh magnetic you can do that counter-sink Um threaded and like I said, it's really nice. So send cut send Um, if I ever need another metal part, I will be sending it to them And it's cool that you can have bends. This is the most simplest kind of thing you can do with a bend But there's all sorts of crazy geometries you can make with folding metal And sheet metal designs especially infusion like they have a really good tool for making sheet metal um designs So, yeah pretty cool And that is my shop talk send cut send custom tripod bracket awesome With regards to the 90 degree drill bit Andy Calaway saying they have one of those bits and yes, they are still bulky Oh, yeah Yep All right, I'll keep looking. Maybe there's this, you know, whatever you have though. Oh, I'll uh find I just don't have the time right now to uh, we're through it That's all in the 10 minutes. Just searching against them. Oh, I'm dude. I spent was a while All right, let's jump into the time lapse. Here is our time lapse video this week It is very appropriate for the halloween season. This is called bonnie basilic it's from uh Me mitic 3d the designer on cults 3d. It is a printed place articulating skeletal snake You printed it in glow-in-the-dark filament It is a free download That's awesome adorable amazing design for a free download. I think it's a rattlesnake because of this tail Yeah, that's great. You didn't scale it up or anything. It's a hundred percent. Yeah, that's a hundred percent And like I said, it is the glow fill from color fab No support materials I just used um a brim just because of the bottom there Okay, but it did stick pretty well and I love the detail on him um I think the only thing I was missing is like a little mouth I'll hinge on the mouth but other than that. It's super cute little pokemon-esque Skeleton snake Yeah, it's got a cute face you can drop it up in this kind of cool Oh, yeah, yeah, yeah, so that looks really cool In the description it says that'll that'll lock in place, but my tolerance is it off or something That's what prints like as you saw in the print.  They're supposed to lock into this little Oh, I see a nub area right there. It's supposed to lock in there You go. I'm scared to break it I'm not gonna do that But it like you're saying that cool pose that they showed off in Yeah, that's super cool. Let's see it printed bigger. I don't want to see it bigger. Ah, yeah So, uh, again designed by uh me medics 3d or maybe it's mim Mime Anyway, meet me medics 3d Uh print a place no supports particularly need a fidget toy They have like a little story of the uh of the bonnie name, um Yeah, I'll Check out the comments in the discord and calaway. So it's supposed to be one of these guys Remember these kidding the walking lizards. That's yeah That's sick. Are they the hesus lizards? They walk on their hind legs And we had like the brown ones It didn't have the that parasol on the back of his um spine though I recall No, we're brown This might be the uh The bonnie's behemoth. It's prepared to perch on yourself. That's the highlight of your halloween assembly or stands Yeah That the halloween uh tombstone for your desktop decorations There's three different tolerances of it. So I guess you could try different ones. Yeah It's on things Tight tolerance loose tolerance Not sure which one you printed but I don't know. Whichever one was there Yeah, and you click download whichever one that gave you really? Okay All right, all right. Here's some support settings. Yeah, but check it out. It's uh Super awesome print. I'll put this link in discord if folks want it Not one issue with this one Yeah, I see you posted it on youtube and and uh Twitch very nice very nice Awesome So that is this week's timelapse Tuesday Let's stroll right into uh community makes this week We're gonna kick it off with another lightsaber This was posted up by monkey mk on printables They printed the new lightsaber rp2040 prop maker feather This looks modified. I see screws here Uh, there's no description on it But it definitely looks like they modified the design because I don't have screws Here I can see that there's some sort of screw situation going on here and here So that's pretty cool. Nice to see nice color After that we have something I found on instagram uh instagram user roger a not posted up the uh ghost neon signs And I think they're using different Strips It might be el wire. I'm not sure um So, uh But I'm pretty sure it's The ghost and maybe two different sizes So pretty cool. It just shows you that you can reuse Um, or you can you know use a different type of lighting You don't have to use a neopixel strip. You can use a el wire or whatever Maybe it's a noodle. I'm not sure what it is But I did see it and I was like, hey, that's uh the ghost that we made So shout out to roger for posting that up on their instagram And then uh after that we have another lightsaber This is from uh, nick oley They post it up there Hilt Looks like it's the standard hilt No modifications to it, but it looks good and black and it's kind of shiny I'm not sure if it's resin printed or what but it looks smooth. Maybe they spray painted it. Maybe they Did some sort of finishing post post processing technique on it. I'm not sure they printed it in resin Maybe We know it works in resin because I have mine printed in resin And I think after that the last one this week that we got is from uh, bow B lack art ick They posted and made a A rig for doing heat set inserts It looks like they modified it to fit their soldering iron and it looks pretty good So there you go. They have a whole little description here Saying works well super easy to print and assemble They modified the um the step file To hold to most people do you know remake the the clamp holder They're using a walmart 30 watt soldering iron I mean whatever works Yeah, they actually didn't like using it for soldering. So they're using it for heat press which works really good. It's a good way to kind of Use a crappy iron, you know as long as it heats up. It's going to make a good tool for a heat press inserts Yeah, so there you go. That is this week's community makes. Thanks everybody for posting your makes That's funny. That's really cool. I could see the cut out so bad on that one What depends on your camera confetti All right, so we got some projects that we got cookin um I think for next week. I'll probably have the hal night thousand we're not sure we're uh still kind of Toss these worth videos. Yeah, you know either that one or this one Yeah, one of these More another timelapse if we need more time Yeah, there'll definitely be more more timelapses All right, um, we got about 10 minutes left. I guess we can end the show a little bit early Yeah, don't forget if you want to pick up anything in the shop prototype is the coupon code Let me check real quick if there's any new products in stock The raspberry pi 5 was announced last week Or this week forget when There's a blur. It's been a blur a lot of things been going on, but they're they're coming in stock We don't have them in hand yet and we won't sell them until they're actually in hand And sellable no pre-orders or anything like that for us because we don't like to really go that way We really want to ship things that we have so that's why we don't do pre-orders But it seems like we're getting all the accessories for the new pi 5 And hopefully those will be in stock soon We got a new display that's going to be dropping soon the square rgb 666 tft displays Um, we're working on getting more support for the qualia New board with the round displays will be doing some projects with that Um, we have a planned kind of simple case for the usbc power delivery Um, we have a couple ideas to power some Projects some gadgets devices that have really odd power supplies It'd be great to retrofit those with usbc and this is one way to do that And it was surreal Throwing away all of those lightning cables it felt like So good, dude like Because everything else Yeah, but now when I come over I still have my iphone 15 not for long bro not That's funny. Yeah, I'm gonna I'm gonna upgrade next year. Yeah I want to wait it felt so good throwing away all those lightning cables Really? That's yeah, that's funny. Yeah, and then like You know all these cables that we had before that just sat there like the usb to hdmi Yeah, it works. Yeah, it just works now. That's great. I'm like, I remember when a little rig for my phone So it has like the monitor facing me. So when you do like a selfie Yeah, it's a big change. I remember when the 30 pin connector for the iphone switched to lightning And we just had You know, every week you get a different cable to replace that accessory that use the 30 pin connector With this case, we have all usbc. They've been here this whole time. Yeah, so Yeah, so the transition is way easier now so many things for usbc Do you know every single one of our cables the you know in the pantry we have like all the charging cables all usbc This is my air pods They're still use they're they're not usbc. They're new ones, but Still got them, but they're wireless charging. So I was gonna say I in I always That's a really nice thing kind of things Um, I still got this thing here. This is my um my magnetic tips Yeah, uh thing. So I have the lightning usbc and microbe all here still So Still sticking around Weird. Yeah The only devices that I have that are micro be Our old eight or three projects themselves that use like the m4 the picos the batteries the rechargeable batteries. Yeah They're gonna drop usbd next week I think they just call it pd whatever version usbc pd whatever um 2.1 I recently got a um an audio interface From martyro It's usbc. That's it. Does it it also has a a as a hub, but our uh The uh the soap dispenser You recharge it with usbc That's funny. So even my water pick usbc That's funny Yeah, my toothbrush uses AA batteries All the ports in the car. They've been usbc this whole time. Really? Yeah Yeah All right, um, I think that's gonna do it. What else can we rant about? That's it, man I gotta go. I gotta watch soka. See what how this ends and then Loki tomorrow. Let's see what projects hopefully more than just an led cube Hmm. Yeah, well the pruning stick is the tba bot baton thing That's the actual prop that you can get now from disney. It took them quite a while every time I go, which is, you don't see it I do not see it. Yeah So I wonder how well the uh what I want to look at. Yeah I think it's like a hundred dollars, right something up. Yeah, probably Yeah I pull it up, but uh Yeah, we'll do that next week. All right. Yeah. All right. So there will be more shows later tonight We still have the show until and then ask an engineer later tonight Yeah, I believe melissa It will be hosting the show until and then Liz Clark will be hosting the week after But there's still an ask engineer coming on at 8 p.m. So if you have any projects you want to share some inspirational things retro tech all that's cool come on at 7 30 p.m. Eastern time on discord And melissa will drop the link to the stream yard so you can join in Still got jp's product or jp's workshop tomorrow Tune in to jp. He's working on some cool um synth ios stuff with um A lego color sensor project at that that makes me think of the of zelda I can do the the laser with the crystals and I like play the theme You tried that No, I haven't but that that is a uh a video I've seen you can play notes um with the um With one of the zeno zeno zeno zeno devices pretty cool Um, let's see fridays are deep dives with Either tim foamy guy or scott Tune in And then from the desk of ladies on sundays on all the channels Mondays are weekly circuit python meetings Tuesdays product pick of the week With jp this week was the feather m4 because they're back in stock. I think that's That's it right now Cool. All right. Well, don't forget coupon code Prototype get you 10 off. We'll have another one tonight too if you want to use that one JP will have a coupon code as well And with all that said, I think it is time All right, everybody we'll see you next week, but until then remember to make a great day Let me play the


Welcome to Customer Service Skills for IT Professionals – Communication. Good communication is arguably one of your most important skills because you provide customer support. In addition to having advanced technical knowledge, you must also be able to share information in a clear, concise, and non-condescending manner. Today we'll examine the communication model, apply it to both verbal and written communication styles, and discover how to be more effective and supportive IT professionals. Let's start by looking at the communication model. Communication is the exchange of information between two or more people. At a minimum, you need a sender, the person who initiates the message, and a receiver, the person to whom the message is directed. The sender encodes a message and sends it through a channel to the receiver, who decodes the message. This seems pretty simple until the communication breaks down due to problems with encoding or decoding the message – physical or psychological noise or broken channels. For instance, what if you send an email full of technical jargon to a customer? Using technical language that's not easily understood creates problems decoding the message. What if you try talking on the phone in a noisy room? The background noise impacts how the receiver hears the message. What if you send an email to the wrong email address? Now the channel is broken, so the receiver never gets the message. It's important to understand how people communicate to avoid these breakdowns. Communication takes place through many different channels. For IT professionals, the primary channel is verbal, meaning either in person or over the phone, with written forms such as email and instant messaging coming in a close second. While the communication model represents both verbal and written communication, there are some unique differences. Verbal channels rely on the tone of voice, the rate of speech, and non-verbal signals to help convey the intended message. Written messages rely primarily on the choice of wording including phrasing and jargon. Verbal communication, such as talking to customers either in person or over the phone, can be stressful. Customers expect an immediate resolution and technology being – well, technology – can quickly change the dynamic of a support call. This can affect the message being sent. It's easy for stress to influence your message because it's conveyed in your voice and body language. If it's received incorrectly, it can lead to a communication breakdown. Pay attention to customers' verbal and non-verbal cues because it helps guide you through the conversation. Watch for signs of frustration, a lack of understanding, or increasing agitation. All of these customer cues mean you need to change how you're communicating. No matter the type of verbal support, always start with a smile. Yes, even over the phone, your customers can tell when you're smiling. Actively listen without forming your answer to be sure you understand exactly what the customer is saying. Don't interrupt the customer before they've finished speaking. Use a welcoming tone of voice to help put the customer at ease.  As an IT professional, you provide written support in a variety of forms including email, text, internet chat, and technical documentation, each of which has its own unique challenges. When communicating through written channels, your customer doesn't receive any of the verbal or non-verbal cues to help them decode the message. Additionally, because there is limited feedback from the receiver, it's difficult to gauge how they've received the message and how it influenced their reply. Communication breakdowns happen faster and more frequently using written communication, so give special care to your wording. Before sending any digital message, ask yourself if the message resolves the issue, is clear and easy to understand, and is positive in nature. This includes adding a professional greeting and closing, using please and thank you, and avoiding technical jargon. If your message is clear, go ahead and send it. No matter what channel of communication you're using to send your message, follow these universal guidelines whenever you provide support. Show your customer empathy. Understand the issue from their point of view. It can be quite humbling for users to contact you for assistance in the first place. Not everyone is comfortable using technology and some struggle to understand what's going on. Consider your words wisely. By that, I mean, avoid using unnecessary technical jargon that confuses and belittles the customer because it only leads to frustration. And don't make assumptions because they quickly lead to communication breakdowns. One final word of advice. IT support professionals should focus on identifying and providing a resolution and let go of the need to be right. Understanding how and where communication breakdowns can occur makes you a better IT professional. You have completed customer service skills for IT professionals. Communication.


to talk about curves and surfaces with constant non-local mean curvature. OK. Yep. So thanks, Yannick, for the introduction. And let me start thanking Francesco mainly for the invitation. It's very nice to be here. So the title says curves and surfaces with constant non-local mean curvature. But the talk is a little updated. And the main part of it will be a survey on non-local minimal surfaces. So it's the same equation. Well, it's the same operator, non-local mean curvature. But I will start with how it started. Surfaces with zero non-local mean curvature that we call non-local minimal surfaces. And later, at the end, I will present you some results that exist for surfaces with constant non-zero positive non-local mean curvature. OK. So and by the end, you will know everything that is known about non-local minimal surface. Not everything, but most of it. There are works, but not so many. OK. And I think it's an interesting topic. So let's start with, I used to work before, but it doesn't work anymore. So let me start just recalling what is the perimeter of a bounded smooth set in a REN. Well, the perimeter, you know, is the house of measure, the n minus 1 dimensional house of measure of the boundary of E. But you can define it also in the following way through integration by parts or in a distributional way. By the way, I can send these slides to whomever, or maybe they will be in the web page, or I can send them. It is a simple equality where the vector field X is free with L infinity norm less or equal than 1, and nu is the normal to the set. And then you look at this quantity and you integrate it by parts with the divergent theorem. And instead of integrating with an E, let's say that you integrate in REN the divergence of X times the characteristic function of E. And now you integrate again by parts in a distributional or weak sense. And you see, you get the gradient of a characteristic function in the distributional sense times X. X has an infinity norm less than 1, so this supremum is going to be the L1 norm of the gradient of the characteristic. It's what we call the W11 semi norm of the characteristic, right? So now I'm going to introduce fractional perimeter starting from this, like saying, an academic, very academic way. But I think it's OK for our purposes. So now I'm going to do the same, but instead of taking one derivative, I'm going to take alpha derivatives, right? So I'm going to consider the fractional sub-left semi norm with a fraction alpha. Alpha is going to be always between 0 and 1. And I simply take this and, well, the sub-left semi norms, fractional sub-left semi norms, have a nice expression, which is this one, through of a function. And you would put here the function at X, the function at Y, subtract, and make the double integral, the X, D, Y. And when you do this for a characteristic, you get this, right? If X and Y are in E, you get 0. If X and Y are in the complement of E, you get 0. So X must be in E, Y must be in the complement, or Y sub-left semi norm, that's why there is a 2 here. So this is the expression. And this is the definition of fractional perimeter up to a multiplicative constant that you put here, positive constant. That depends only on the dimension n and the fraction alpha.  It goes to 0 and makes the whole perimeter, the whole expression, to go to classical perimeter as alpha goes to 1. So you have these fractional perimeters with order alpha. And as alpha goes to 1, you recover classical perimeter. And this is the expression. Remember, E, E complement. And the novelty is that here you have single integrals. Here we have double integrals. For those of you who know about the fractional Laplacian sometimes here, instead of alpha, one writes 2s. And I will always write it like this, m plus alpha, alpha between 0 and 1, which means that s is between 0 and 1 half. And in fact, if you have, let me say, this fast for those of you who know, you have the fractional Laplacian. And you consider, for instance, the Allen-Cann equation. And you do a blow down or you put an epsilon. Some of you know, perhaps, that when you have the Allen-Cann equation and you make the limit epsilon 10 to 0, you recover minimal surfaces. So let me just say, with the fractional Laplacian or the fractional Allen-Cann equation, when you do this game, if s is greater or equal than 1 half, the limiting configuration is a classical minimal surface. And it's only when s is less than 1 half that you recover a new thing, which is the fractional perimeter. It's exactly this perimeter. And non-local minimal surfaces are going to be surfaces which minimize this perimeter, say, roughly saying. But still, this only makes sense when e and e complement are bounded, sorry, when e is bounded. Otherwise, if e is not bounded, normally you would get infinity here. So we'll come back to this later on. Let me just say, whenever you have a geometric functional, like this, you wonder if there is an isoparimetric inequality. It would be nice to solve the isoparimetric problem. So this existed for a long time. There was an answer by Garcia Rodemick. So maybe these are the years in the 80s. Garcia Rodemick discovered that the classical Schwarz rearrangement, the classical one, also works with fractional perimeter. You give me a set, like the one before in the previous slide, I consider the ball with the same volume. It will have less fractional perimeter. This was known, Garcia Rodemick. But then Frank and Sirenger quite recently proved the uniqueness. I didn't write it here. I should write it. Balls are the unique. So I wrote this reference because it's also important to have uniqueness.  And this called the isoparimetric inequality. And then there is even more recent works with quantitative versions, Fusco, Mio, Morini, Ficali, and Francesco Maggi. So let's go into matter and let's say, what is the first variation? When you have a function, you do the first variation and you should get a PD, right? In this case, it's going to be a fractional PD or a non-local PD. And that's very easy to do. And this is what you can do it as an exercise. What you'll get is the following expression. You have your set E. This will make sense even if E is unbounded. So now it could be even unbounded. You take a boundary point, X. X is on the boundary. The boundary is sufficiently smooth. But the important thing, X is on the boundary. And this object, it's called the non-local mean curvature of the surface boundary of E at X. And it's simply this integral in the principal value sense. You center yourself at X because there is the typical power kernel, singular power kernel, centered at X. You're integrating Y. And Y moves everywhere in Rn. When Y is in E, you put a minus 1. And when Y is in the complement of E, you put a 1. So you see what you are doing? You are centered at this point, X. Think of spherical coordinates if you want because this weight is radially symmetric around X. And you count the number of ones, which are the guys outside E, the proportion with the number of minus ones, which are the guys in E. And these you ponderate with the distance of the points to yourself, right? X minus Y to a power. The points closer count more. The points farther away count less. And for those who know the fractional aplation, this is simply the fractional aplation of the function, which is minus 1 in E, 1 outside E, and say 0 at X, 0 at the boundary. And if you compute the fractional aplation of that function at X, you get this expression. So the non-local mean curvature is simply the fractional aplation of this function, which is minus 1 here and 1 here at the boundary point. And you put the value 0 there. OK. You have to analyze no problem at infinity. There is a cancellation at X equals Y because the ones and the minus ones, when you are very close to X, and if the set is smooth enough, it looks like a hyperplane. So there are pretty much the same ones and minus ones when you are very close. When you are very close to X, the set is smooth. Locally, it looks like a hyperplane. So at the first order, there are the same number of ones and minus ones that will produce a cancellation, will add a 1X minus Y that will make this integrable at the origin at X. Very good, but still this makes sense, as I told you, for an unbounded set. Of course, the simplest unbounded set is a hyperplane. So E would be what is below a half space. This makes sense, and it gives you 0. It has 0 non-local mean curvature. But still you can wonder what is the variational problem behind? Because the fractional perimeter or the classical perimeter of a hyperplane is infinity. It's infinity. So for classical minimal surfaces, what you do is, for instance, in R3, you take a wire. This is called the plateau problem.  Well, minimal area, right? Minimal area. Within a ball, for instance, the set below would have relative minimal perimeter. Okay, that's the recled problem, which is called plateau problem for minimal surfaces. How do you do this? How do you do this in the fractional setting? This is the following. This is done in the following way. I have this unbounded set E, okay? It has infinite fractional perimeter, so this is not good. What I'm going to do is I'm going to try to count its fractional perimeter inside a domain, omega. So fix any domain, for every domain. Let me say it another way. Let's think of the plateau problem or the recled problem. What I'm going to do is, I'm going to take a domain and I'm going to consider a set given set E, which is the blue guy, okay? And I'm going to see, for the fractional laplacian, I'm going to see this part of E, which is outside omega, as given. This is given. And what I'm going to try is to minimize a fractional perimeter inside omega. So the game is this. Here, outside omega, you cannot touch anything. The set must be exactly this. But inside, you could be the blue thing or you could be the dotted black thing. You have the freedom to change it inside. And as a result, you have a set. And now, you would write the fractional perimeter as before. It has the interactions, points in E, points in the complement of E. But now there is this omega, so I can, let me write all the interactions. There are four types of interactions. You see, points here, let me write it just, let me do it with the pointer instead with my voice because it's a little, points here, with points here. So points in E and omega, points outside E and in omega. This is the first interaction. Second interaction, points here and points there. So in E and in omega and outside E, outside omega. Then a third interaction, this and this, points outside E, points in E, sorry, outside omega and points outside E inside omega. And there is a fourth that I forgot, this with this. But this is, since this is the unbounded part, this would give you infinity. But at the same time, this is fixed, so every competitor, the blue and the black guy, would have the same interaction here. For instance, if you cut it with a bigger ball. So you just forget about that, right? Because everybody would have the same infinite energy, right? So you forget about that, it's crossed here. You see, you don't put it and in this way here, always one of the sets, at least one is bounded and this makes sense. So this is the variational problem or the fractional plateau problem, say, right? And this was introduced in what we call the seminal paper in non-local minimal surfaces. This is the first paper where this functional is written like that and it's a paper by Luis Caffarelli, Jean-Michel Romjofka and Obidiu Sabin, 2010. So they write this variational problem and also the non-local mean curvature, okay? So the guy that minimizes this problem that exists, I will tell you about this later, it's going to be a surface with zero non-local minimal, with zero non-local mean curvature. It's called a non-local minimal surface, okay? In fact, the non-local minimal surface, sorry, the non-local minimal, no, sorry, the non-local mean curvature, it appeared in a previous paper by Luis Caffarelli and Taki Suganidis, 2008, where they studied threshold dynamics to approach motion by a new mean curvature, which is not the classical, it's non-local. They discovered here, in fact, the non-local mean curvature. But let's keep this slide and let's go more into matter, all right? So this slide is about the results in the paper by Caffarelli, Rocgioffre Sabin. They consider that variational problem and always they consider surfaces which minimize. You see, when you are with minimal surfaces, you could, many people define minimal surface and I will use this terminology. A minimal surface is a surface that has zero mean curvature and on local minimal surface, we can say that it's a surface that has zero non-local mean curvature. But sometimes when you make the theory, you start with minimizers because they have more properties, right? Minimizers and then I will say that they are minimizing minimal surfaces or minimizing non-local minimal surfaces. So in this paper, they study minimizers and they prove many of the things that exist for minimal surfaces now in the non-local setting. And this is very nice because minimal surfaces, maybe it's a unique equation, right? That may, for which there may be, there exist so many things as the one I will list now, okay? It has many, many properties because it's a geometric equation. Well, a non-local mean curvature has most of the same properties and this is very nice. I think it says good things about this whole field of research. For instance, first thing, well, we already saw that. Definition of the variational problem, good. Existence of minimizer, very easy. Lower semi-continuity, some compactness. Density estimates also exist and they prove them here. The Euler Lagrange equation in viscosity sense, this is the Euler Lagrange equation, but for smooth sets, the minimizer a priori, you don't know if it's regular or not. And that's the goal at the end to know if it's regular or not. So you have to derive an equation in a variational sense or in a viscosity. In a variational sense, it's easy because the problem is variational in a viscosity sense. This is in part one of the, and the equation is going to be this with the fractional Laplacian of ones and minus ones, but in the viscosity sense. And that's one of the toughest parts in the paper. This section here, it's quite involved and the proof is quite involved. And I think there is no simpler proof yet. Then improvement of flatness as in the classical theory, then an extension problem and a monotonicity formula. Monotonicity formula is very important, it's crucial in the theory of minimal surfaces and also it will be here in some applications, I will tell you, some results that will come later. And they prove it here, it's great to have this. The funny thing is that the monotonicity formula is not known, we only know of a proof and it's in this paper. And the proof, the only known proof, uses the extension problem that I will describe for you in the next slide. There is no proof of the monotonicity formula working in Rn, you have to go to the extension problem that you will see in the next slide, okay? And a classical argument on dimension reduction using the monotonicity formula in classical minimal surfaces also works here and all this allows them to prove the theorem in the paper, the main theorem say, you need most of this or all of it. And it says, if you have a minimizing non-local minimal set in omega equals big one, so we are playing the plot, we are playing this game, the plateau problem in big one, in particular this set, okay? This set has zero non-local mean curvature but only on big one, not outside because outside it was given arbitrary, right? Then in the interior, the surface is c one alpha except for a closed set of household dimension hn minus two of household dimension n minus two which means that for instance in the plane, in the plane this would be a set of zero dimension would be for instance points, isolated points could be singularities, all right? By the way, when you play this game in the plane is very interesting already, not for minimal surfaces because when you are in the plane and if you have a minimal surface which means a minimal curve, it's curvature is zero so it has to be, it must be a straight line. So if you play the plateau problem in the plane, you get lines, right? Or a combination of lines, straight lines but when you play the plateau problem, the plateau game, say the plateau variational problem in the non-local setting and you give me this curve outside, unit ball, what you will get inside is not a straight line, it will bend because it has to compensate for the ones and minus ones that come from the guy outside, right? So it will bend and you wonder, is it infinity or not? At this point it was not still known, it could have singular points, right? What is the extension problem? Maybe most of you know it, let me remind it for some of you who don't know it for sure. We are in a Rn, X in a Rn and we are going to add one more variable, Y and we are going to have a half space, right? S is alpha over two, okay? Alpha is two S, like in the first transparency. But here I will take, here I should change a little this slide, sorry, I just made it today fast. It should say one half because of what I will tell you later, one half. What you do is you take your function, U, which is minus one on E and plus one, or the other way around, one in E and minus one on the complement of E. It's a singular function. I mean, it has a discontinuity in E. You take this function, constant one, constant minus one. And you are going to extend it with a function V that also depends on Y, V depends on X and Y and it's going to solve this elliptic equation in the half space. It's like the Laplace equation, but with a weight here, with a weight which is the distance to the half, to the distance to the boundary of the half space to this power. And to be able to extend minus one one characteristic function, and so that everything is well defined, you need S less than one half, okay? And then you can prove there is a unique extension. V is a function between minus one and one. You see?  Now you are here in the sky.  From up there, maybe the ones are all below you, there are a lot of ones and the minus ones are very far, so I will not be one, I will be 0.8, okay? And if I go farther closer to the ones, I will be 0.9, but this function V is going to be between minus one and one strictly, okay? And looks for the quantity of ones and minus ones on the bottom. And then the theorem of Luis Caffarelli and Luis Silvestre is that if you consider this, the flux of this function when y goes to, when y goes to zero, I should rewrite this better, adapted to non-local minimum surfaces. When you compute this flux on the surface, on boundary of V, where the minus ones and the ones change, the flux here, that's going to be the fractional application of this characteristic function and that's going to be the non-local mean curvature, particular for a non-local minimal surface, this is going to be zero on the boundary of V, right? So let me just say that once again, you here is the bottom, you have the surface boundary of V, you put minus ones, you put ones, now you make this harmonic extension and then you make the flux but on the surface and these flux must be zero. It's like on the surface, the ones and the minus ones compensate and the flux is zero. So this is the second way, now we have two formulas for a local mean curvature. The first on the first transparency, making an integral of ones and minus ones and this is a second way, second way to compute a non-local mean curvature, okay? And this is used to prove the monotonicity formula. So now let me go into what is known, the main results about non-local minimal surfaces. So this is more recent works, 2012, 2013, Begoña Barrios, Alessio Figali and Rico Valdinoci. If you have a minimizing non-local minimal set and if you know that it's lipchitz, it's going to be C infinity. So the difficult thing is going to know if it's lipchitz or not, okay? And there is only a complete answer, there is a complete answer only in dimension two, up to now. So we are still in the beginning and this is a beautiful paper by Savino Valdinoci. If you take a minimizing non-local minimal set in the plane, it's going to be a half plane necessarily. Now I'm assuming, I'm not playing the plateau, I'm assuming that they have a curve in the plane and that it's minimized, it has zero non-local minimal curvature, mean curvature, sorry, local mean curvature. I'm assuming that it's minimizing in every ball. When I play this game of the plateau problem in the ball of radius one, but also in the ball of radius two, three, any ball of any radius, you're assuming that your surface, your curve is a minimizer, what we call a global minimizer, is a minimizer on every ball, okay? And then the theorem says that necessarily it must be aligned, right? This has a corollary that says if now we play the problem in omega in a bounded set, and you give me an any curve outside, any curve, and I get the winner, the set or a set that minimizes inside omega, a consequence of the theorem and blow up is that this surface is going to be seen infinity. It's not going to be aligned, I told you before, it's going to bend, but it's going to be seen infinity, okay? As a consequence of this global theorem, you get the local theorem also. Let me explain more why this theorem is interesting, because here you have, you see some enemies here. The simplest enemy is the cross, what we call the cross, is two perpendicular lines, straight lines, and the set E is the blue guy here and the blue guy here, you see? So I claim that this set at any boundary point, any point in the red part, it has zero non-local minimal curvature. Oh my God, today, non-local mean curvature. Sorry. Why? Take this point, for instance, compute the non-local mean curvature here, and do, for instance, instead of doing a spherical polar coordinates, do fubini, vertical fubini. When you integrate on this line, the minus ones and the ones cancel, because the kernel, that is that power kernel, is symmetric with respect to this point. Now take another line here, the same thing, the two distances cancel, a minus one and a one. And the same for a line here, now the minus ones become ones and the ones minus ones. So because you see this point, the distance to x is the same as the distance of the reflected point to x. And therefore the kernel is the same at this point and at this point and then everything is canceled. The same for any regular polygon. If you take a boundary point and now you do fubini perpendicular to this line, you will see the cancellation. So all these guides have zero non-local mean curvature. They were being candidates for being minimizers. They are not infinity because they have a singularity here. They are not leopards graphs at the vertex. But the theorem of here says that if they are minimizing, these guys are not minimizers. The only minimizer is the half line globally and locally are infinity. Okay, so R2, everything is understood. Minimizers are infinity, right? What is known in R3? This is the main theorem that exists up to now. It concerns graphs. So now I'm going to take a set in R3, which is the graph, the boundary of E is going to be the graph of a function phi of two variables. So sets in R3 could bend like this, right? Could bend and this is more involved geometry. But I'm considering the simplest ones first are sets which are below a graph. E is what there is below a graph E, okay? And then Alessio and Enrico proved, well, graphs are only always minimizers. That's very easy to prove. If you have a graph with zero non-local mean curvature, it's going to be a minimizer because you slide it and it produces a polyation, okay? Like in the classical theory. So any graph with zero non-local mean curvature in the whole space R2, the whole plane, is a plane in R3. So it's straight. It's equivalent of the thing. So this is the Liouville and the rigidity theorem. In R3. So let me show you a third expression for the non-local mean curvature. We saw the integral with ones and minus ones, the extension problem. And now I will give you the expression for graphs. And this is the expression. Suppose that you are in Rn plus one. Now I changed from Rn to Rn plus one because I prefer my function phi, which is going to give a graph to be a function of n variables, okay? Then it's very easy to compute the non-local mean curvature doing Fubini, vertical Fubini, as I did before. You have this graph, take a boundary point on the graph, don't use the spherical coordinates. Instead, use vertical Fubini to reduce everything to an integral in Rn. And, well, there will be minus ones, there will be ones, and everything will depend on the height of this function, which is u of, no, phi of x, phi of x. And a simple computation, Fubini, simply, gives you this expression, look. A non-linear function that looks like this, it's a bounded function, which is concave here, odd, concave here, and tends to a constant at infinity. And it's the identity near the origin.  U equals phi, phi of x minus phi of y over x minus y. So, the incremental quotients, but then you make this non-linear truncation, say.  And F is explicit, pretty much, almost explicit. You see, if F was, capital F was the identity, then this would become the fractional appellation of u, or of phi, u equals phi. And F is the identity pretty much when the incremental quotients are bounded around here, which is the same as saying that phi is Lipschitz, okay? But you don't know if phi is Lipschitz or not, okay? The graph could be anything. This expression is very nice because it's a very simple way to show some properties like the following. If you give me an, if this is zero, because you have a non-local minimal graph in v1, in the unit ball, I can prove you, for instance, an L infinity bound for the oscillation of phi. Independently of what the tails are at infinity. Independently of what phi grows at infinity, right? And this, not even the Laplace equation has this property, the Liouville theorem for the Laplace equation says bounded harmonic functions are constant, but if they are not bounded, this is not true. So this is a property that minimal surfaces have, but it's quite mysterious for minimal surfaces. For instance, for those of you, now let me go a little fast, for those of you who know what is the Simon theorem says, if you have a minimal graph in Rn, classical mean curvature, and it has, you have a minimal graph in Rn, and n is less or equal than seven, then it has to be on a fine function. And that's quite amazing, right, the theorem, because there is a priority, there is no control on the behavior of the graph at infinity. And instead, in the non-local setting, it's quite easy to see that the fact that capital F is bounded at infinity, and this is zero. Independently of how is the graph at infinity, in the unit ball, I can prove you, and very easily, in fact, an L infinity bound for the graph. Right, independently of the tails, right? And this you will find in a paper by Enrico, and Ovidio, and Serena, probably, the L infinity bound, independent of the tails. Okay, so it becomes less mysterious, in fact, than classical minimal surfaces. Let's go ahead. Then there is another paper by Caffarelli and Valdinoci saying that if the dimension is less or equal than seven, like in the classical theory, but alpha is sufficiently close to one, remember that when alpha goes to one, fractional perimeter goes to classical perimeter. So non-local minimal surfaces go to minimal surfaces, roughly saying, well, here they do this rigorously, and they prove that in Rn, if n is less or equal than seven, and if alpha is very close to one, minimizing non-local minimal surfaces are smooth, and minimizing non-local minimal cones are flat, right? And this is proved through a compactness argument, because minimizers, you can prove that they are compact in some norm, in the L1 norm, for instance, as alpha goes to one, and this theorem is proved through a compactness argument, it doesn't tell you how close alpha must be to one. And after that, there is one more important paper by Juan Davila, Manuel del Pino, Junction Way, where they start, so you see there are answers in dimension two, full answer, some answers in dimension three, and what we expect is that the same type of smoothness should hold up to dimension six or seven, but everything is pretty much open in dimension three, four, five, six, seven, except for this case, when alpha is sufficiently close to one, and what remains to be done is what I'll explain you next. And it started, for instance, this is a paper where they start to study cones in higher dimensions and trying to see if they are minimizers or not. It's very difficult to see if something is a minimizer or not in general. But it's simpler, first you test the stability, because we will talk about stability later and you will see you have a formula, say, an inequality to check if something is stable or not. So that's what they do there. And these start, for instance, with the simplest cones, circular cones, sorry, the simplest cones, for instance in R3, imagine a circular cone, cones can be much more general than these, but start with the simplest cones, circular cones, and then it's easy to see that for every n and alpha, there is an opening of the cone that makes, that the ones and minus ones cancel. So given n and alpha, the opening of the cone is chosen so that the ones and minus ones cancel and the cone has zero non-local mean curvature. That's easy to prove, yet now you want to know, can this guy be a minimizer or not? That's difficult. So let's look first if it can be stable or not. And this is what they do there. I'll show you later how they do it. Well, they do it numerically because there are many hypergeometric functions coming in, but I'll show you the formula that they use. And the answer seems to be for circular cones, seems to be that six or seven will be the right dimension. Six, one less than here when alpha is very small. So I think there is one of these guys which is stable in dimension six when alpha is very small, if I remember well. They find the analog of the non-local catenoid, the helicoid also has zero non-local mean curvature, but I don't have time to go into this. And let me describe, yes. This is a result that extends the guan of Savin and Valdinoci here that used the minimizing at some point. So the proof worked with minimizing and then Eleonora Chimdi, Joachim Serra and Enrico Valdinoci improved it very recently, you find all these papers in archive. And they prove that in the plane also a stable, not minimizing, but a stable, which is less. Stable means second variation, not negative second variation of fractional perimeter. Instead of minimizer, you only assume that that you are a minimizer, but for small perturbations. You have a stable non-local minimal cone in R2, it has to be a straight line, okay? And for these they improved, they improved the argument of Ovidio and Enrico. And their argument will have another important consequence later. But first let me tell you what a paper of me with the Eleonora Chimdi and Joachim Serra, it will be in archiving within one or two weeks, okay? We are just reading it, it's almost ready. And what it says is we classify stable non-local minimal cones in R3 for alpha sufficiently close to one, like in the paper of Caffarelli and Valdinoci, but now where they had compagnet through, because they studied minimizers, now we study stable configurations, stable cones, and we prove that they must be flat if alpha is sufficiently close to one and you are in three dimensions, okay? And here, and if it's not a cone and it's a global surface, globally stable, say, stable in the whole space, it must be a plate. Here, with stability, you don't have compagnet, because a family of parallel planes, for instance, infinite parallel planes, these are not minimizers. If you play the plateau problem with this boundary data, you will not preserve all the planes. They have too much area if the ball is big enough. You will join some of them or do something or bend them. All right, and that's not a minimizing configuration, but instead, parallel hyper planes is always a stable configuration because you are only allowed small deformations and the fractional, if you perturb one of them or any of them, the fractional perimeter, small, with a small perturbation, is going to increase. So here, we don't have compagnet. In fact, proving compagnet is as difficult as proving this theorem. And we have to do a proof where, in fact, we can tell you how close alpha is close to, should be close to one, okay? We could get a value, but we don't compute it because it depends on too many constants, okay? But it gives you a quantitative value. It's not through compagnet. So I want to tell you what do we use to prove this theorem, okay? Here, and that's also in the original proof of the paper about minimizing lines by Savin and Balinocchi. The trick is, you know what you do. You take your set, the plane, and you translate it in a direction. You fix a direction, you translate it in this direction, in this direction, and also backwards. You make a cutoff function not to touch the tails and you compute the fractional perimeter of the translated, forward, backward, and you compare it with two times the fractional perimeter of yourself. And when you do this, you are comparing the fractional perimeter of yourself with these two competitors. Here, the stability, you will be able to use the stability to get some information. So it's through the morphisms. Here, we are going to use, for first time, we are going to use, well, it's also used here numerically to check the stability. We are going to use the formula for the second variation of fractional perimeter. So I still didn't show you what is a formula for the second variation of fractional perimeter. And this is here. This is our first ingredient. And this was found independently by, it's not a simple formula to find. This was found by Figali, Fusco, Maggi, Migio, Morini, and independently, I think, by Davila Del Pino way. More or less different ways, but independent ways. Okay, this is the formula. If you have a non-local minimal surface, which is stable, that means the second variation is non-negative, you will have this inequality. And this is, okay, this is like a fractional aplation but computed on the surface with the ambient distance in Rn. So you have this surface boundary of E of n minus one dimension in Rn. You are going to compute distances, but in Rn, not on the surface. And this will call the fractional Laplace Beltrami operator in boundary of E. We can call it like that, all right? Even that it's not exactly a fraction of any Laplace Beltrami, but okay. Or say a non-local Laplace Beltrami, maybe better. Non-local Laplace Beltrami operator on the surface E. Always using the ambient distance. And so this is the Laplace Beltrami. And then if you bring this to the other side, you will have here. Well, this is the quadratic form, of course, you see. It's a quadratic form associated to an operator that it's going to be a single integral psi of x minus psi of y, okay? And that's the non-local Laplace Beltrami. And then what you bring to the other term is this c square. So in fact, the second variation of energy is what we call the, in the classical theory, it's called the Chakobi operator, okay?  And it's going to be this fractional Laplace Beltrami of order alpha, let me write it like this. This is what there is on the right-hand side, the quadratic form. And then simply here, a zero-order term. X is on the boundary. Here, c square E. And this is a zero-order term. And this is some fractional derivatives there. And what is c square? C square is defined at the point x on the boundary. It's defined in this way. Normal to the set at x minus normal at y squared. And then the kernel and you integrate in y, okay? So this is what Davila and collaborators use to check if circular cones are stable or not, all right? And there are a number of integrals to be done numerically, in fact. And this is what we used in the paper with Chinti and Serra. We also use something, a more classical ingredient. The behavior as alpha goes to one of the optimal constant in the fractional hard inequality. And the third ingredient is very recent and it's very surprising and it's a very powerful tool that surprises when it was found. It's in this paper of Chinti, Serra, Valdinochi that says if you have a stable, same situation, a stable, non-local, minimal surface in a ball of Rn, sufficiently smooth. Then in the interior of the ball, half the ball, you can bound the classical perimeter. This is not the fractional perimeter. This is the classical perimeter. Using that is stationary and it's stable. You can bound the classical perimeter by the right thing, R to the power n minus one. A plane would have Rn minus one. And this constant that depends like that as alpha goes to one. And here the non-locality, the fractional perimeter is crucial. So we are realizing lately that stability in the fractional setting is a stronger thing in a way that in the classical setting. And you will see a theorem presented by Alessio Figali on Friday, or Thursday on Friday, or Friday on Friday, about the fractional Allen-Cann equation, which is very beautiful result with Joaquim Serra, that for the classical Allen-Cann equation still is unknown, as he will describe, and about stable solutions of Allen-Cann in R3. And related to the conjecture of the Georgie. So, stability is stronger in the fractional setting. It gives you more things, okay? And now how we use, let me tell you in one minute how we use these ingredients. We have this cone in R3. We take alpha very close to one. You have this cone in R3. And we know that it satisfies this inequality. Well, a cone in R3 is just a curve in S2 and then you project, no, not circular, but you project it through the, from the origin, right? It's like an ice cream. You have this and then you do like that. But maybe it's not circular. Then, well, we use this because you can reduce your prime always to S2, but listen. What I'm going to do is use this, I'm going to flatten the cone. I'm going to look locally at the cone and I'm going to pretend that it's flat. Well, I'm going to flatten it. This could be very dangerous if the cone had a lot of perimeter, because then I would not control this change of variables. But the cone has controlled perimeter. So when I flatten it, say locally, I flatten it and I write things, because I want to write things in R2, that cone is two-dimensional. So I want to write things in R2. I flatten it. I will control the Jacobian of this transformation thanks to this estimate. And then I'm in R2.  The cone is something homogeneous. When you write it in flat space, it becomes a hard inequality, because this is going to rescale the same as that, okay? You don't have an upper bound on the area for stable sets in general. Well, in R2, yes, but in R3, but in R4, it's still a non-local in a way, yes. Yes, exactly. When you write this and your guy is a cone and you write it in coordinates, for instance, in R2, you are going to get another quadratic form whose operator is the fractional Laplace. It's not going to be alpha. If I remember well, it's going to be this other power, but don't forget, let me just write beta. And then here you are going to get x to the power two beta and x is going to be in R2. And this is the operator and a constant, sorry, and a constant, very important constant. This is going to be the operator that whose quadratic form gives you the hard inequality. So now what are we going to do? We are going to take a radial function in R2 that saturates the fractional hard inequality, so that it almost achieves the fractional hard inequality. And knowing how constants behave with respect to, as alpha goes to one in the hardy here and there, we are able to get a contradiction if alpha is close to one, unless c squared is zero. But if c squared is identically zero, you are a plane, and that's what you wanted to prove. So this will be in archive within two weeks, something like that. And what I was going to tell you, let me just give you just a couple of minutes. The second part of the talk was going to be about surfaces with non-constant, constant, but non-zero, non-local, minimal, non-local mean curvature. And let me just tell you the results which are the equivalent of these two. The four sets, this is a classical mean curvature. The four sets with surfaces with constant mean curvature are called CMC surfaces. There are two, there are a huge amount of theorems, but the first two theorems, and you see they are quite old, are very important. The first one by, well, the second one by Alexandrov, saying if you have a smooth enough bounded connected set with constant mean curvature, it must be a ball. And then the one of Deloné years before, more than a century before, that says in our three, he proved in our three, but also in our N, there are unbounded sets which are periodic cylinders with constant mean curvature.  And this guy has constant mean curvature, classical mean curvature. So the same things are true in the non-local setting. And this is the Alexandrov theorem, it was proved by myself and Mustafa Foll, Senegal, Joan Solamorales in Barcelona, Tobias Webb in Frankfurt, and independently by Chiraolo Figali Maggi Novaga. It says that if you have a smooth enough bounded set with constant and local mean curvature, you must be a ball. And even they prove here in this paper, they also prove a very strong quantitative version of the Alexandrov theorem. That by the way, you can prove with the Alexandrov reflection principle, and it's even simpler in the fractional setting. It's much simpler than in the local setting because strong maximum principles are cheaper. And then in my paper with Mustafa, Joan, and Tobias, we also prove the equivalent of the De Launay cylinders. We prove, it's a bifurcation result, so we only prove that for a certain small parameter from a straight cylinder or even in the plane from a straight band that obviously has constant non-local mean curvature, there are also, from the straight band, a family of periodic bands bifurcate. And they all have the same non-local mean curvature. Later, we prove that the same holds in R3 and in R4. We even compute them numerically, the bands. They look like this. And here we follow them a little more. At some point, this cylinder and this should touch the picture is not very good, sorry, should touch and produce another type of configuration and I finish here, which is periodic configurations. That is my last paper, you find it in archive with Mustafa and Tobias that says that in the plane or in Rn, you can find periodic configurations of bounded sets, repeat it, but that you have a bounded set which is close to a ball, but not exactly a ball.  And also, we also find them at least when the distance is very large.  And to use the implicit function theorem, you have to analyze the linearized operator to non-local mean curvature, which is, the Jacobio is the second variation of perimeter. So we have to analyze this operator, but on a ball, in a single ball, or in a straight cylinder in the previous paper, and compute its spectrum and see that you can bifurcate, you can apply the implicit function theorem. So sorry for the extra eight minutes, and thanks for your attention.