Hi everybody, I want to make sure we're all live Three two one All right, we're good. Hello. Hello. Thank you everybody who came in early for today's live I see some of us waiting in the chat box Hello, hello. Let's see. Hi Katrina. I'm so happy you can make it to this live Hi, Tyga. Hello. Okay. First of all, give me a thumbs up if you can hear me and if everything is good Okay, Vivian's giving me a thumbs up. Good. Good. Good. Okay. Awesome thumbs up All right guys, so for all of my early birdies here, I always start off my lives if you're new here the same way We are all going to share something positive that happened to us this week No matter how big or how small I will go first. Honestly, nothing major has happened to me great in the last week I've just been a good mood in a good mood. I've been excited for the holidays I've been drinking one hot chocolate all day lots of sugar, but I've just been a good mood this week I'm really excited for the upcoming holidays to take a moment share in the chat box Michelle W. I hit my 20 pound weight loss mark. That is fabulous. That is a lot of working dedication Very nice job. Beth got all of her Christmas shopping done. Whoo cutting it close. Good job I actually picked up some things for Christmas today though. So I shouldn't be talking sweet gem society You just made it right on time. Awesome Jewels said my kids are getting over sinus infections. Good timing. Good timing. I'm happy they're feeling better Tyga had surgery Tuesday and was able to eat a little today Well, I hope your surgery went well and that everything is okay to you Let's see a niece. I got a promotion amazing and Southern Yankee Beauty said one of my subscribers sent me a $50 gift card for Starbucks That sounds good Let's see Tracy's relationship with her daughter is the best that it's ever been amazing My the kids are finally on winter break. So even if I if I have to come into work I'm happy. Well, that's awesome winter break certainly is the best Shonda's vanity mirror arrived intact. Well, that's always a relief, isn't it? Oh Merry Christmas Megan. Thank you and happy holidays. Whatever holidays you guys are celebrating We're aren't celebrating. I know this can be a hard time of years for some people I she got her new Sonya G brush that today, which one did you buy Ashley? Hopper received her fashion Nova order today and she's gonna be looking good for Christmas I never order outfits for the holidays or any like event. I should I was sort of something Shelby said her husband and I decided to move back to Arizona with our babies to be with family. That's awesome There's nothing better than being close to family So if he gets her booster this week, I need to make an appointment for mine I'm gonna get my booster soon This is so sweet Janella said my mom is visiting First Christmas you guys have had in four years that is awesome. Oh I see a makeup question From Kiki So the Natasha Denona bronze cheek palette is 50% off. Should I get it? Is it which bronze? Cheek palette is it is it the tan bronzing glow or the other one? Um Rachel said I'm getting the Odin's eye Judy palette for Christmas I am wearing the other two Odin's eye palette from that collection I brought them here for those of you asking if anybody comes in I'm wearing the Odin's eye and a net and then a couple shades from the fancy face So that's what I'm a is on my eyes if anybody asks when they come in hello from Tunisia All right guys. I'm going to stop reading the Positive thing here, but I always go back and read them after my life is done But here's the plan for today. I am thinking today is going to be a little bit on the short side I'm just going to do a live shopper drop since I haven't gotten a chance to a film one recently I have done a couple shopper drops, but I've been doing it on the bigger launches Have you guys been liking them because I did one Specifically just for the Bridgerton and Pat McGrath collection And then I also did a shopper drop dedicated to just the Natasha Denona release Because I feel like those are always the big launches that I get asked the most about when I do shopper drops I'm really just doing them for the main thing. So lately. I've just been Doing one quickie for the main thing and I've had a lot of fun being able to dedicate a whole video Just on my thoughts. So today There's a lot of other makeup that I haven't covered that I did want to talk about that I'm excited about in a lot that I'm not excited about so I thought it would be fun to talk about that I'm doing great tonight Bridget. Thank you. I'm a little tired I just had to rush a little bit because I was filming my best makeup of 2021 before this All right, let's head over to a trend mood right now Which is where I am going it to get all of the things that I am talking about today from So if you don't know for my shopper drops, I use a trend mood ones Instagram page And that is where I know all about the new makeup releases. So last I check it's been almost a month Since I've done a shopper drop on Instagram or on trend moods page. So we'll see what we have here We're gonna start off at the bottom So most of these items are released now, but some I haven't talked about so I did want to clarify whether or not I will be purchasing and I used to cover alamar cosmetics on my channel a lot So this is definitely an older collection, but they did launch a collab with Disney Which I think is an amazing for a small independent brand like them I mean, I don't know how small they are now, but they've definitely grown since I've first started using them And I just I'm so excited that they got a collab with Disney and it aligns with the brand and Gabby the brand owner so much And I think this collection is beautiful I did decide to pass on it just because I had too much going on But I'm excited for them and if you've never heard of alamar cosmetics their products truly are amazing And I love the color stories that their owner Gabby comes up with like look at this You can't tell me that this isn't adorable, right? Um These blushes look cute It wasn't something that I needed and you guys I'm about to say something absolutely crazy, but I think I have too much makeup And so a lot of these little extra releases that I would have purchased in the past I'm just allocating my money to the bigger launches. So launches like these is cute as they are I do look at them and I'm like, oh, I don't need it. Now. We have a close-up of this palette. This palette looks absolutely Stunning. Hi, Becky. I'm happy to see you here. I'm happy you could make it to a live I passed on it. I didn't need it. In fact, I do have an alamar cosmetics palette in my palettes to try thing My palettes to try bin so that would end up there as well So I just didn't need a pile on another one, but it is so cute and if you want to support A independent women owned brand. This is a good one and they have good products from all that I've tried Let's see if there is anything else that is interesting. I did want to talk about this guys Sorry, I'm reading the comments too. So this became available on Ulta's website And I believe it should be available at this point on Too Faced's website though. I could be wrong But this is their too fem collection And I was interested in this because it's the same format as their teddy bear palette And I talked about this when it was first leaked months ago and I said I was going to get it Now I'm rethinking that decision. I think this is an adorable eyeshadow palette, but I don't know. What do you guys think about this? I like the blue and the pink and the pastels. I think it's a really fun Collection, but are we over Too Faced? I've been over Too Faced for a while But sometimes they'll come out with a launch that I'm really interested in you guys know I bought their holiday palette And this blush kind of gimmicky but super duper cute Tyga said I am super over Too Faced. I don't like the sexy and kid stuff. Yeah I mean, I've heard a lot of comments about them mixing those two things. It's like, which one do you want to be? Um Too Faced isn't what it used to be. I used to love Too Faced even as little as three four years ago Loved everything Too Faced came out with now, which I'm getting tired. I'm a little bored, but I will say I I did do a tablet take with this palette and initially when I first saw it I was like I am absolutely buying this But now I'm taking it to step back. I'm going to evaluate the situation Gosh darn it another better than sex mascara it with A different packaging This not here isn't even that good. I swear And some new lipsticks, but anyways, um Tensative on the palette. I actually do think the palette's really cute and I don't think Too Faced has a bad eyeshadow formula I know they know how to do a good formula But I'm kind of lukewarm about that Too Faced is legit Too Faced Yeah, Megan says I'm over Too Faced as well. I don't really do much with pastels anyways very fair I don't either, but I think I do Hi patty patty Alonzo's in the chat. She said how is it spring releases time before Christmas? Every year I say that but they do it every year they come out super early It's been quiet in december. I've noticed the last couple of years not new many launches happened in december these brands much be bored um Very springy though, but we'll not be getting that What are these from color pop? Yeah Honestly, these are kind of cute. No, but let's do like I don't know if you guys remember a few years on youtube There's this trend called the pop effect. So what you do is you cover the pop shadows and it just looks like a boring Neutral palette so I want you to take your finger right now on the screen on the bottom eyeshadow palette Put your finger over the blue shade. Don't be fooled.  It's just a purple palette color pop is becoming very infamous for that So just be careful with that the packaging is super duper. Oh, what did I just click on? The packaging is super duper cute on this. Don't even lie to me You know, it's cute, but you know, we don't need it.  So I'm gonna judge you Uh, okay, let's keep it moving. I did review the vizier itwale Or itwale palette if you are curious, it is a bomb, but it is dark only for those who are brave enough to rock a smoky eye What is this? Jouet cosmetics radiant translucent soft focus. Don't they already have this The soft focus. Oh, it's radiant trans okay. Anyways, I'm moving on. I'm not interested in that What is this from good molecules? Very cool. I love good molecules. By the way, they are a very good affordable skincare brand We have the hyaluronic acid boosting essence So if you're looking for good quality skincare, very clean ingredients and still affordable I do recommend good molecules. I've had some good experiences with their products in the past This is done launched. Wow. I'm all the way back in november. Let me move up a little bit It's I just have been off. Have you guys seen this collection? I have this This is from revolution pro. It was a collaboration They with marylott minron marylin monroe. I don't know based on her the packaging on this is So beautiful you guys. It's even more beautiful in person. They did send me this I haven't tried it yet. I didn't I Everything was sold out online when I looked but I guess it just hadn't launched yet But if you like revolution pro, I've never tried revolution pro I've tried makeup revolution, which is like a sister company. I I do not like makeup revolution that much They have some hits and misses, but I am wary. I actually tried to mess scare from them That's really good though recently. But anyways revolution pro. I've never tried I'm really excited about this. I'm not as into marylin monroe I'm not a stan or anything, but the collection itself is beautiful. You might not have seen this But it is stunning if you haven't seen it just fy. I haven't touched it yet It is revolution pro so it's not It's like a sister brand to make up revolution But revolution pro is supposed to be a little bit more better According to the website. I'm gonna scroll up a little bit more because I think I scrolled up too much Oh, no, we ought to talk about this first because I have not yet addressed this on me channel And I wanted to talk about this. This is one of the main things that I did want to talk about um, we have The charlotte tulberry the beautiful skin foundation I have been waiting for charlotte tulberry to come out with a new foundation And if I'm being honest The foundation that she has Leave me wanting a little bit more because the one she has I'm not really satisfied with I do like What is it the the magic found it? What is it called? Okay the airbrush flawless foundation For full coverage, but it's not my favorite when it comes to wear time It was like almost there But not quite and the other foundations are just okay, but knowing charlotte tulberry I feel like she should come out with a transformative Glowy product and I haven't gotten that from her when it comes to her foundation range So I am hopeful this looks like the s. A. Lotter foundation Like the one that comes in the tube You guys know what i'm talking about. I feel like it's going to be very similar to that I'm really excited. It will be available January 5th on their website. You can 100 expect a review on this I'm super excited about it.  We're calling a concealer. I would like a beautiful skin concealer How does that sound? But yeah, becky said I was thinking as stay as well. Uh, but I will I'm really excited about this Uh, let's see science and color innovation foundation medium coverage and instant glow infused with hydrating hyaluronic acid And brightening rose complex to improve the look of skin every time you wear it Skin looks radiant plump and smooth in 30 shades. Sounds good to me charlotte You got a customer. So we'll see I don't think charlotte has the best record for good foundations personally. So i'm a little skeptical, but I am getting excited about that Okay, let's move on, but I did want to let y'all know how pumped I am for that I saw this. I don't really pick up uh, jivan chi very often but I like what I see, you know what I mean These lip things these marbled lip things are lip balms.  I never do tom Ford pat mcgrath Givenchy, I don't need a lip balm from you But you got me at this whatever this is the prismay Libre brush blush in rose tool Like doesn't that look so pretty? I bought a highlight from jivan chi. It was a quad similar Loose powder to this and the highlight was okay, but I didn't love the way it sat on my skin. I thought it did dry it out a little bit Does anybody have this oh it's coming january 22 22 if you have it What's your hookup because I don't expect you to have it but Okay, sophie said these blushes from jivan chi are amazing You don't say Like do you mix them all together like if you mix these all together Right with the highlight and the three shades that would make a pretty glowy blush, right? Or you could go pink and then you have I don't know I cannot guarantee I will pick this up Because I find jivan chi a little harder to get a hold of I know they sell it at sephora. My life is not hard, but I just never find myself picking up their new launches But this looks Like stunning and I want to oh hey jack lean is here. Hi jack lean So she said the jivan chi blushes are gorgeous. I will take your word for it. You know what's up so You can get the blushes from feel unique they ship to the us and their jivan chi Prices seem to be less than here. Thank you for that. That's awesome. Great tip. Okay so Positive feelings about this blush. I've never bought a jivan chi blush before I just have one of their highlights I'm always attracted to these so I think this one might be it for me Because I love the rosy tones in here and I love that pop of coral So I think I'm gonna do it If not when it launches if it comes to sephora, I would definitely be adding that to my cart I want to I want to get in on this. It's a spring collection that we're already looking at. Can you believe that? I'm a kaoli perfume fan now I only have smelled two scents from them But it's a 100 success rate y'all so Kaoli came out with this eden juicy apple perfume. It's already launched. I believed it sold out like in the first day Who has smelled it and is is it good? Will I like it if you don't know my my preferences?  If I can't get the fenty I'll do kaoli Hmm. Is the fenty perfume good? Rebecca said I have it. It's amazing, but the smell doesn't last very long I've heard great things about kaoli if you haven't tried them and I do have one perfume that I love Hey, Jacqueline said you may like this kaoli eden apple. I got it. It's very much like a young fragrance. Yeah My mom says it sounds too fruity. I like fruit, but I do prefer sugary. That's for sure I won't like the fenty. All right fair. I'll take your word for it. I wasn't going to purchase it anyways I don't buy fragrances too often. They're a little Out of budget for me most of the time And I just am pretty content with my own collection, but I longingly look at perfumes because the bottles are so pretty the long So in terms of the longevity of kaoli, I think the one that I have is pretty good I have vanilla 28 if you like vanilla sense. It's Perfection. It's not the longest lasting perfume that I have but I it's solid for me So I don't have any problems like that You would not like the fancy perfume You guys are the best. Okay, so I missed out on this one Uh, this is from artist couture. I do love me some artist couture palettes most of the times This is the quickie palette. It is inspired by their iconic supreme nudes palette Which I will give them that too is iconic. I do love that one and I think this one is tiny I love this palette. I love the look of it. I think it is gorgeous I'm kicking myself for not picking it up when it first launched But also at the same time like bring me back to earth. I don't need that I don't know About artist couture though They have the capacity to create Beautiful palettes, right? We know that but they also Can create some pretty ugly palettes in my whole opinion I just don't know the aesthetic of their brand I just feel like it is so mismatched when I think they're going one direction Then they'll come out with a collection that's like cheap looking I don't know if anybody else feels that way, but I just don't feel like marketing wise They completely have it together and who might adopt I don't know anything about running a makeup brand But it's like I don't know the identity of the brand. I know mac daddy owns the brand But it looks so pretty Ashley willard said that palette looks like a smaller version of melts brunette. I was I think the melt brunette is a little bit More brown This one has that lower row of the cooler tones that brunette definitely does not have But I suppose right now I am content with the two that I have. I have both of the supreme nudes palettes But you're the top four actually you are right that does look like the brunette Palette it does it looks pretty The bottom looks like mount mary jane palette kelly. Yeah, I can see that Oh, I don't need it especially I think it's beautiful.  I love my neutrals But I just couldn't bite the bullet and do this one So this one is a drop. I haven't been saying shopper drop this one is a drop And fenty dropped their liquid kilowatts fluid freestyle highlighters if you pick this up Let us know in the chat box dropping this. I have a deep Running deep through my veins hate tread For liquid highlights. I can only name less than a handful of liquid highlights that I can tolerate I feel like fenty might be able to do it well But this is just a waste for me. I have no business A liquid highlight.  I give them all bad reviews, but that's more of a me problem than anybody else Ashley said no on this highlighter Yeah Not getting it.  I love the pinky look. Anyways, not getting this but Pretty pretty looks whoever the makeup artist behind that was Anybody else like lisa from blackpink their uh, korean girl group She came out with a collection with mac Hold on So she came out with a collection with mac I'm most excited about this cross body bag like This you get with any 90 dollar purchase from the collection like I want that cross body bag I follow her on instagram and i'm obsessed with her. My mom is too. She's just so beautiful Uh, but anyways, I nothing from this collection really is screaming out to me I love the purple glitter packaging don't get me wrong, but it's very warm. I'm not into the warm palette Pass. Yeah dropping it.   I love elf. They really do bring trendy products at an affordable bright price for you guys La la la lisa Okay, anyways Elf cosmetics came out with a glossy lip stain. I've tried a formulation like a glossy lip stain from elf before Or no from color pop I don't know how I feel about it. It's just like two worlds collided and I can't accept what they created I don't know if it is a gloss. I don't know if it is a stain. So I've been testing out It's the color pop fresh kiss. They're supposed to be a lot glossy lip stains And it just doesn't make sense to me. My brain can't comprehend it I can't like the product for some reason to pass on those from elf But Very interesting. They came out with a copycat Or a dupe. Well, it will be nice. They came out with a dupe of the patrick tall brow lamination. No Patrick taught it at first, but then abh Created more so something like this Hey, if you don't want to buy the abh, this is the more affordable option. This is why I love elf I don't really like products like that in the first place So I won't personally be picking it up sometimes elf sends me stuff if I get it So be it but I'm not I'm not going to spend six dollars for it when I have the abh Then I also never use It's a bit too intense for me this style of product Being bio girl said I love elf mean too. I've heard the brow product is great Well, that's awesome. That makes it a great alternative to the Um abh, but it actually said the brow gel didn't work out for me and never dried down and wouldn't hold my brows Well, if it doesn't dry down and hold your brows, what's the point elf? Why are you doing that? So I'm passing on those but Again, if there's any sort of a trendy makeup product that you want to try that you don't want to break the bank On quite yet. Elf is a good direction to Dip your toes in Oh, funny. Chelsea just said morgan. Did you notice the patrick tall blush palette is off of sephora? I did notice that today. I was linking it for a video that I filmed today and it wasn't on there So I had to link it to the patrick tall website. So I guess it really was limited edition Kaleidos came out with a new highlight. I have it. It's gorgeous Kaleidos is an amazing innovative brand. They are giving us what We've asked for for all of us makeup addicts. So they came out with a new highlight The space age gifted. It's very very pretty. I haven't used it on my face yet, but I've certainly played with it They do a great job with these mono multi chrome Highlights highly recommend if you're into that. I don't use them on my face.  They can do no wrong. All of their stuff is so good. We need a palette from them We haven't gotten a palette from them recently enough We love a multi chrome palette from them because we know they can nail that formula So Kaleidos somebody call them up. We need a new palette, but this highlight fabulous it just You know Do you need it? Do you need it? Probably not but They do a great job if you're into multi chromatic kind of highlights This I thought was so cool. I won't be picking it up, but um Physicians formula, I love these palettes from them and they made one that's very rich and deep skin tone friendly So that's exciting because these formulas are bomb The face palette that they've come with in the past Have worked for me and I've really enjoyed them very convenient. So I'm excited to see this It looks like it's going to work For pretty deep skin tones. So I think that that one is exciting I just wanted to share that And um Tuesdays for now. Yeah, December 25th Rare beauties launching bronzer and sticks and Setting powders I will be picking this up because I'm thirsty to review some stuff Nothing's come out lately and I've been missing doing my reviews. So I will be picking up a bronzing stick I love me a good bronzing stick and while I do not need a new setting powder Why not, right? I think it looks okay. So I think I might pick that one up What's this? Oh color pop color pop and kind of bored of you. I'm just gonna skip you But any hoosers, I will probably be reviewing the rare beauty I've done a whole video if you want my spiel on the Pemagrath and bridgerton collection I'm pumped mostly because I'm a bridgerton fan and all actually the eyeshadow palette really is not that exciting I don't know why she's doing yet another pink palette Do yourself a favor put your finger over the blue shadow And we have divine rose one divine rose two and all of the other pink palettes that she's come out with So I don't even know why she went so pink like one pink fine but I'm thinking in terms of the show There needs to be a navy in this palette. There needs to be like a yellow in this palette I'll even accept a gold Just get rid of some of the pinks, but I'm still gonna get it and I'm so pumped and I think everything else looks really excited but Give us more blues to play off of give us a navy Give us some yellows. Do we even have a yellow from pat macrath green? Bridgerton is such a colorful show if you're not familiar with it It's like a garden of beautiful flowers in the springtime. That's what bridgerton is There really isn't that much pink in the show. I swear. Or anyways Uh, I love you pat, but like I don't want any more pink, you know We could go away with the pink. Yeah, so if he said Sophia said I'm done with the pinks Becky wants the blue as a single The highlights do look gorgeous Yes to the blue, right But She's selling us based on that single blue. I know that's a fact She needs to give us more than just one of those pop shades, you know But I'm so excited about it nonetheless. Anyway, so I've already talked about this I think we're scrolling through instagram early today. I said hold up What's that? This is jason woo beauty. He came out and these are available With these stunning eyeshadow palettes. These are giving me like kkw vibes without being kkw I'm sure there's lots of redundant shades in these palettes. I've never tried jason woo beauty, but Oh, the aesthetic of the brand looks so clean like the kkw vibe And these color I'm attracted to this It's like a whole lot of shadows that I don't need and I already own But has anybody tried jason woo beauty? Because I am into this Ellie jane said the description of the new collection said it's eye blush Anyways more pinks. Anyways, I just had to quickly go over this because I thought it looked stunning Um glam light if I have any glam light fans, they came out with the icy collection. I do I did pick up some glam light palettes for black friday Really excited I haven't gotten the chance to use them yet because I've been reusing a lot of my older makeup for my roundup december videos Lately, I'm passing on this. I don't need a blue palette. I don't need a red palette I don't really like icys that much. They didn't get me with this collection with their drink collection that they just did They totally got me with that.  Oh, thank you. Welcome. I love me some brick clark She's awesome. But anyways, I'm sure this is good But these are very very vibrant colors that I certainly will not use so I won't be picking it up um Yeah Not into that personally I don't know what this is. I don't know this brand, but is anybody watching emily in paris I started watching it today. I think i'm on Season five that show kind of makes me mad or season five episode five That show kind of makes me mad, but you know, I still am watching it Shamelessly watching it still finished selling sunset by the way too But there is a emily in paris collection with the brand Spectrum won't be picking it up, but it's cute. Love the vibes of that um Yeah, not gonna get it though drop Let's keep it moving Oh this I recommend well, I haven't tried it. So Take this with a grain of salt, but I did get sent this palette from color prop. This is the mega matte eyeshadow palette Immediately what came to mind was vizier grande pro palette. If you don't know the vizier grande Uh pro palettes my baby I love it. Uh, it's the palette that I used in my makeup kits. I have another one that I use for myself personally This reminds me a lot of it. It's not exactly the same, but it's kind of a similar concept But the vizier palettes $150 This is $34 and I believe color pops on sale now. So you you should be able to get it for like 20 25 off This is a great alternative to the vizier art palette It's a great way to be able to get Neutrals and mattes of any desire you will ever have in one palette So I I like color pops matte formula. Is it better than vizier? I don't know, but I think this is a really fabulous alternative I think it looks really great and it will come in handy Especially for those of you that feel that you need a collection of different shades of neutral mattes in your collection Um, so fia said it looks like the dominate cosmetics transitions palette I cannot at the top of my head remember what that looks like, but okay um Rosie said I do want this color pop palette, but I'm still waiting on it. Oh Yeah, no rush on this at all and even if they stop selling this, I'm sure another one will come along from some brands um Becky said I don't think this one is included in the color pop sale. Well, what the heck that's unfortunate Melissa said the look of this gave me old school morphe vibes. I can see that I think color pops better than morphe eyeshadow formula wise, but I can totally totally see that So anyways, I just wanted to let you guys know that this is here I think it is a good option I did put my review up yesterday for the natasha denona mini biba palette and this rose cheek duo So if you are curious about that, it will be linked in the description. No, I won't But it's on my channel. I won't be linking that in my description box um Did anybody pick this up from sonia g? um Beautiful, right the story behind The wood on this collection how very exclusive I love sonia g brushes But I could not I could not even me Uh, $245 for the brush set and then the brush holder was made in very limited quantities I think like 12 if I heard that correctly The trees the wood that it's made of is very Difficult to harvest so it's $550. I didn't even post a link for you guys for this. I mean Did any of you pick it up? I was very I was excited to look at it, you know excited that I got to look at it Uh, wow that looks cool The brushes look beautiful, but $245 for two brushes even I was like and I also just have a complete brush collection, you know So this was something I didn't need. I'm very content with my brushes in my collection But you can't beat sonia j you really can't Uh, yeah, these look gorgeous, but no no no Right, we can admire the picture That's as far as we'll get the picture uh The brush tower is sold out. I I mean from what I've heard jennifer She only made like 12 only a handful of them. So it was extremely Limited sandy said no way ashley got the brushes Oh, did you get the brushes ashley you passed on the tower though? You're gonna have to let me know what you think of them. Actually. No, don't let me know. I don't want to buy Don't convince me The tower sold out in 30 seconds I mean, I'm not surprised by that, you know sonia sonia has Such a huge fan not a huge but a dedicated fan base So I'm not surprised, but personally I couldn't do that one I did see somebody ask me about this collection the Stadia jewel collection from color pop. She's cute I personally just have a lot of these quads from color pop so I won't be picking them up but You know the purple and the green look very pretty Right here and right here These are cute just to get an instant look in one little quad if you are interested in them And color pop quality in my opinion solid. It's not the best, but it's not the worst But you're you're not paying a arm and a leg But if you see a look you like but these I don't know I just haven't been as interested in those quads recently This is the makeup revolution mascara. I was talking about it's pretty good. You guys I know we don't really care about makeup revolution, but It's pretty good. Anyways What is this Oh, beauty bay palettes have been taunting me you guys Oh rosie said I did buy these quads and you're splitting them with your niece That's a great idea.  Um This looks really great for somebody who wants to be creative with their makeup. I love big palettes I'm super attracted to this but y'all know. I don't need this I'm attracted to beauty bay palettes because karen harris Always uses her beauty bay palettes and I feel like she gets gorgeous looks out of them. She likes the formula So it's always tempting to me I I love having so many colors close together And I think this is going to be fun for somebody who can create creative looks But I'm not going to get that because I don't need it And we have reached the end of trend mood. Honestly, you guys This is why besides the pat mcgrath and the Uh Natasha denona. I haven't filmed a shop or drop in the last month It's just a boring month Brands have already pushed their holiday collection in the time of bye. Bye. Bye for the sale and then It's just crickets. They just want you to buy things through the month of december for gifts They've taken a break from launches Based on we should be seeing the launches pick up towards the end of january Maybe a little bit into january. We will start seeing more spring collections But for now enjoy the lull Enjoy the break until three days from now When pat mcgrath launches her bridgerton collection y'all Can you wait? I'm just kidding when I say this but wait until 902 to order because I need this collection And I will fight you for it. I'm excited about it. You guys know Um, so I will be picking that up and I will put a link up for you guys too in the pat mcgrath collection launches Uh december 25th the rare beauty collection is launching the bronzer sticks and the powder if you want to pick that up And those are the major launches for now. Um, so anyways, I hope you all have lovely holidays Uh, I have one more video to film tonight and then I am taking off for the next couple of days for christmas eve and christmas So if you celebrate christmas, merry, merry christmas to you I hope you guys are getting some time off work and get to spend some time with your loved ones I'm sending you guys all my love and I am Going to end this here guys. Thank you so much for joining me on today's live I will see you tomorrow with a very good video in my 2021 makeup favorites Are coming tomorrow. I just finished filming it.  Bye guys. I hope you have a good rest of your night


Attention Harvey Park residents. This is a community notification of a new sexually violent predator in your area. Please stay tuned to the following short program for more information. Hi I'm technician Ron Hackett with the Denver Police Department. The sex offender registration and compliance unit at DPD is responsible for the registration monitoring and tracking of all registered sex offenders and sexually violent predators who live in the city and County of Denver. Here's a brief history of sex offender legislation in Colorado. Our state laws trickle down from federal government mandates. In 1994 we had the Jacob Wetterling Act which mandated that states would establish a sex offender list. Megan's law of 1996 said that the public would have access to those sex offender registration lists. The Pam Litchner Act of 1996 stated that some offenders might have to have lifetime registrations and the Adam Walsh Act of 2006 unified sex offender laws across a country. In Colorado the legislature has determined that sexually violent predators by definition pose a higher risk to the community at large and therefore mandated that upon their release from the Department of Corrections the community must be notified. Sex offender notification in Colorado happens in two ways. The first is passive and ongoing through the sex offender registration process which is a list maintained by local police departments. The second way is active via community notification for those offenders determined to be sexually violent predators by the courts or by the parole board. Most sex offenders in Colorado are supervised by the criminal justice system in our communities. Most sex offenders engage in crossover behavior which means they may have been arrested for one type of crime but be apt to commit another.  There is no typical sex offender but all tend to be deceptive, manipulative and secretive. 80 to 93 percent of sex offenses are committed by someone known to the victim. Sexual deviancy begins in mid to late adolescence.  The community has a vested interest in helping offenders to be successfully managed in the community. Sex offenders have the same need for housing and employment as any other citizen.  There are approximately 16,500 registered sex offenders in the state of Colorado. About 65 percent of convicted sex offenders are placed in the community on probation. The remainder are in the Department of Corrections or community corrections. Offenders may be caught for one type of offense but be at a high risk to commit another type. Crime of conviction is only one indicator of risk.  The offender's residence must be verified quarterly by the Denver Police Department. The full sex offender registration list is available by calling the Denver Police Department Identification Bureau at<PHONE_NUMBER>. Convicted felons and those with multiple convictions are posted online at denvergov.org slash police.   Now here's a look at the newest sexually violent predator living in Denver. Here's an overview of the registered sex offenders currently living in Denver. There are 2,474 total living within city limits. In Denver Police District 4, there are 479. Precinct 422 has 85 registered sex offenders. Of those, 56 have felony convictions and 29 have misdemeanor convictions. Brandon Ray Esquible is a sexually violent predator currently living in Denver. He's 38 years old and was born on December 4th, 1980.  He's currently living at 2030 South Irving Street in the Harvey Park neighborhood of Denver. Schools located within one mile of this offender include Duel Elementary at 2520 South Utica Street, Johnson Elementary at 1850 South Irving Street, Gust Elementary at 3440 West Yale Avenue, Strive Prep Federal at 2626 West Evans Avenue, College View Elementary at 2675 South Decatur Street, Lincoln High School, Respect Academy and Compass Academy, all at 2285 South Federal Boulevard, Schmidt Elementary at 1820 South Balejo Street, Excel Academy at 1825 South Federal Boulevard, Shank Community School at 1300 South Quitman Street, Cuns Miller School at 2250 South Quitman Street, Strive Prep Ruby Hill at 2626 West Evans Avenue. Parks located within one mile of this offender include Sanderson Gulch Irving and Java Park, Sanderson Gulch Florida and Raritan, Athmar Park, Harvey Park, Harvard Gulch West, LaLomita Park, Garfield Lake Park. Recreation centers located within one mile of this offender include College View Rec Center at 2525 South Decatur Street, Athmar Rec Center at 2680 West Mexico Avenue, Harvey Park Rec Center at 2120 South Tennyson Way. Bus routes located within one mile of this offender include Route 21 West Evans Avenue and South Irving Street.  He's currently on parole and registered with the Denver Police Department on January 28, 2019 to 2030 South Irving Street and the Harvey Park neighborhood of Denver. Past charges against this offender include attempted flight escape, traffic offenses, motor vehicle theft, assault, trespass, dangerous drugs, carrying a concealed weapon, marijuana possession. Brandon Ray Esquibble has been determined a sexually violent predator after meeting the following criteria. Criteria one, age 18 or older on the date of the offense or under 18 and tried as an adult. The offender was aged 21 at the time of the offense. Criteria two, the crime must have been committed honor after July 1, 1997 and convicted honor after July 1, 1999.  The offender was convicted on May 24, 2002 for sexual assault on a child, force, threats and ticemen of a child. Criteria three, the relationship to the victim was one of the following. Victim was a stranger to the offender or the offender established or promoted a relationship with the victim primarily for the purpose of sexual victimization. The victim was a 14-year-old female. The offender was known to the victim. Criteria four, positive results are the passing of a risk assessment instrument administered by probation parole staff and a qualified treatment evaluator. Positive results include an assessment for the presence of a mental abnormality, a level of denial regarding the offense, treatment appropriateness and motivation, presence of sexual deviant interests. The offender was evaluated by the Colorado State Board of Parole with positive results, determining him to be a sexually violent predator.


Hello and welcome to this session. In this session we discussed the following question that says simplify 2x minus 3y minus 2z minus 2x plus y. Let's see the solution now. The given expression is 2x minus 3y minus 2z minus 2x plus y. To simplify this, first we will remove the innermost bracket, that is this bracket. This would be further equal to 2x minus 3y minus 2z. Now we have to remove this bracket and there is a minus sign preceding this bracket. So the signs of the terms inside this bracket would be changed. So this 2x would be minus 2x and plus y would be minus y. And now this would be further equal to 2x minus 3y. Now that we have to remove these brackets and there is a minus sign preceding this bracket. So the signs of the terms inside this bracket would be changed. And so we have 3y minus 2z plus 2x plus y. Now lastly we will remove this bracket and as there is a minus sign preceding this bracket. So the signs of all the terms inside this bracket would be changed. So it would be equal to 2x minus 3y plus 2z minus 2x minus y. And so this is equal to 2x minus 2x cancels minus 3y minus y would be minus 4y plus 2z. So minus 4y plus 2z is our final answer. This completes the session. Hope you have understood the solution of this question.


Okay, so I'm Andrei Davidovich and I'm very glad that I have a possibility to take part in this conference in honor of Dirk and my presentation is on geometrical splitting and reduction of endpoint Feynman diagrams. Well, I want to start with some very simple slides describing what the Feynman diagram is and as an example we can use the quantum electrodynamics where electrons interact using the photons. So elementary interaction vertex is electron emitting a photon and we can also organize interaction between two electrons, electrons using a photon and also we can have more complicated examples of interaction where we have more photons and some of the photons go from one electron line to another electron line and in such way so we can get so-called closed cycles or loops and one of the examples here is a triangle diagram and another example is four-point function which is a box diagram. Now, when we calculate Feynman diagrams, so we are using so-called Feynman rules, so each vertex can have some indices, Lorentz indices, spinar structure and it's proportional to the coupling constant and may depend on the moment of the particles. Then each line connecting two interaction vertices, it's a so-called propagator and it has such a form where we have the four-dimensional momentum in the denominator which basically consists of the energy and of three-dimensional momentum and this is like a green function for D'Alembert-like equation and also each closed loop implies integration over four-dimensional momentum k flowing around this loop but as a result of this integration we may get divergences and so we need some kind of regularization to permit these divergences and one of the most common tools used in loop calculations is dimensional regularization. The idea is to use the space-time dimension, I denote it as a small k is n as a regulator, so we basically introduce some small epsilon to this dimension which is close to zero, so we change four-dimensional integration into n-dimensional integration and then if the integrals are singular then the singularities appear as one over epsilon poles and this is the simple example of dead pole diagram, so for example nu denotes the power of propagator and when nu is equal to one or equal to two, so we have divergences, we have a gamma function of epsilon which basically gives us one over epsilon pole. Now, so I'm going to speak about a little bit more general case when we have one loop n-point function and it looks like that, so we have basically capital n external legs here and in physics this might correspond to the processes say m particles to n minus m particles and in general when we consider arbitrary external momenta, arbitrary internal masses, so such an integral even a scalar integral would depend on half n times times n minus one in momentum invariance of such form and n internal masses, so basically the number of variables grows quadratically with respect to the number of external legs and this is the basically the definition of the integral, scalar integral, scalar frame and integral corresponding to the n-point function and it has n denominators like that and basically we integrate over the loop momentum which is denoted as q in this case. Now, coming back to this birthday, so how Moscow Hobart and Mines got connected through the story began in the early 90s and at that point, so I lived in Moscow, worked on such n-point Feynman diagrams using Mellon-Berns approach, hyperdramatic functions, etc. and Dirk worked in Mines also known as Mayans and studied similar Feynman diagrams using also some hyperdramatic functions but he was using Carlson R functions and in 1992, Dirk invited me to give a seminar at the University of Mines and if I'm not mistaken, this was our first meeting and later on for two years I was a postdoc in Bergen, Norway and Dirk went to Hobart in Tasmania and of course, I mean many of you know that Australia is called Down Under and Tasmania is under Down Under and he worked with Bob Del Borger and then Dirk returned to Europe and next year in 1996, so I was able to continue research work with Bob basically within the same project and this is how our work on a geometrical approach to Feynman diagrams was started and also I spent four years in Mines and of course we've had a lot of useful communications with Dirk, so this is how this presentation is related to Dirk and I have basically another three-point function here so that's how Moscow Hobart and Mines got connected to Dirk. Now back to the integral, so let's consider this endpoint integral with unit powers of propagators, normally these are master integrals that we need and use Feynman parametric representation for this integral, so we have n for integral with one delta function so this and alphas are Feynman parameters. So in the standard Feynman parametric representation, so we have quadratic denominator which contains some quadratic part multiplied by momentum invariance and some linear part multiplied by the squared masses, but we can using the condition that the sum of alphas is equal to one due to this delta function we can make the quadratic form homogeneous in alphas and so basically we multiply linear part by the sum of alphas and then we can rewrite it in slightly different form where we get these quantities Cjl and Cjl can be defined as sum of masses squared minus the corresponding momentum invariant divided by some masses and they can be associated with cosine of some angles and when this cosine is equal to one, so this corresponds to two particle pseudo threshold and when this cosine is equal to minus one then this corresponds to two particles threshold and of course direct geometrical interpretation through the angles and cosines of these angles is possible when the corresponding cosines are between minus one and one, so in this case the angles tau are real but in other regions so we just can continue can consider analytical continuation and instead of trigonometric cosine so you get hyperbolic cosines a simple example of a two-point function so basically we can associate with two-point function where we have external momentum k12 and internal masses m1 and m2 we can associate a triangle and this triangle has sites m1 and m2 and the third site is basically the absolute value of the momentum and also we will use the perpendicular which we call m0 so using this perpendicular so we split our triangle into two rectangular triangles and just to remind so the cosine of this angle has such form of course it's just trigonometric identity and again I repeat that at the pseudo threshold so these sites m1 and m2 are together so the angle tau is equal to zero and at the threshold so they just go in different directions so the angle tau is equal to pi so this is the geometrical picture associated with this simple diagram for the three-point function this situation is a little bit more complicated so we have three independent external momentum variance and we have three masses and the geometrical picture would give us a tetrahedron three-dimensional tetrahedron and we three sites all these tetrahedron are associated with the masses m1 m2 m3 and three other sites shown in red are associated with the absolute value of the external momentum of the three external momentum and here also we can drop a perpendicular from this point on to the triangle made out of these momentum variance and here we have three angles and the definition of cosine so this angle is here if you go to the four-point function so then we get already a simplex and this simplex should be understood in four dimensions so the this slide requires four-dimensional imagination so and we have four masses m1 m2 m3 m4 so the diagram itself is shown here so basically we have four external momentum but we have six internal external momentum variance because we also get mandelstam variables s and t here and okay so in the simplex so we have four masses and we have six momentum variance and what is shown in red is in fact a three-dimensional tetrahedron but the picture itself is four-dimensional because we also have these mass sites and also here basically important quantities are gram determinant which is the determinant of the matrix of these cosines d4 and also the basically the gram determinant corresponding to this red tetrahedron which I call lambda lambda 4 and the hyper volume of this simplex is related to square root of gram determinant and the volume of this red tetrahedron is related to the square root of this lambda which is also gram determinant and if we drop a perpendicular from this point onto the red tetrahedron so the length of this perpendicular m0 would be proportional to the square root of d4 over lambda 4 now using these geometrical pictures so we try to go from fine one parameters to the geometrical picture and on this way we make some substitutions of variables linear and quadratic substitutions and in fact what we do we change the argument of the delta function that now it has this quadratic structure which we used to have in the denominator and this quadratic structure would be equal to one because it's in the argument of the delta function this how we this is how we get rid of quadratic structure in the denominator instead so we put it into the argument of the delta function but while making this transformation so we earn some linear some linear denominator which we have here and capital C is basically a modified matrix well basically we have the same cosines but they are multiplied by some quantities which are square roots of capital F's and capital F's are just partial derivatives of gram determinant multiplied by the corresponding masses and we can see that in fact the vector composed of these square root square roots of F divided by the masses is an eigenvector of this matrix C so and eigenvalue of this vector is just the gram determinant okay so and we also would need the generalizations of lambda which can be easily generalized in n dimensions and also the length of the perpendicular which is still proportional to the square root of these two determinants now we continue to work on the parametric integrals and now we try to make the quadratic form diagonal and we do the corresponding rotation and transform this quadratic form to the diagonal form and if all lambdas are positive then we can just rescale the betas and get the delta which corresponds to hypersphere to the hypersurface of hypersphere and then the only weight in our integral would be one of the parameters gamma to certain power and all the rest all the rest is basically the measure of integration nothing more and all the depend except for the pre-effector all the dependence on the momenta and masses is in these limits of integration which is a dimensional solid angle and amazing thing is that this n-dimensional solid angle is basically the same solid angle as we have here in basic simplex so it's so basically by this transformation so we got the integral where we have the integration over this solid angle and delta function gives us the hypersurface of the unit hypersphere so basically we integrate over this piece of hypersphere which is cut by this solid angle okay so and also from this expression we can see that we have special case when the space time dimension lower case n is equal to the number of external legs so then this factor disappears and basically we have just non-euclidean hyper volume or content how mathematicians call it and this special case it's basically a two point case in two dimensions or three point case in three dimensions or four point case in four dimensions and so and another important question is what happens if some of the lambdas which we get when we make the quadratic form diagonal if some of them are negative it means that in this case so we would need to we would get hyperbolic surface instead of spherical surface and all our equations or all our results for these Feynman diagrams can be obtained just by analytical continuation of the results which we get in another region for example for the spherical case but now again to compare these two approaches or these two representations this is standard Feynman primate representation so we have unfold integral with one delta function and it depends on the masses and momentum invariance basically through these masses and cjl in the quadratic form which is in the denominator of this parametric integral in the geometric representation well again except for this pre-factor all the dependence on the masses and momentum variance is in the n-dimensional solid angle so it's just here so there is no dependence left in the integrand and another important thing is that we can use this geometrical representation for splitting and I will explain what does splitting mean and for the reduction of the number of variables in separate pieces of the of the occurring functions and basically for the simplification of the result now let's continue with the two-point function so this is the basic triangle associated with our two-point function again we have mass m1 m2 and the absolute value of the momentum and our integration will go over a circle unit circle basically over the arc tau12 so this is the angle tau12 but if we use the perpendicular here then this tau12 would consist of tau01 and tau02 so if you put some point 0 here and all the relations I mean we get just using trivial trigonometric formula and the area of course will be proportional to the sign of this tau12 like in usual trigonometric formula but now what we can do here so if we now consider new momentum variance k01 squared and k02 squared and of course square root of k12 squared is equal to these two square roots then each of the resulting each of the resulting triangles will be rectangular triangle and the sides of these triangles will satisfy the Pythagorean theorem of course and we can split our integral which would go over this angle tau12 into two integrals one of these integrals would go over tau01 and another integral would go over tau02 and basically each of these pieces can be associated with new Feynman integral but with different momentum and masses so we split basically our original integral with k12 squared and m1 m2 into two integrals the arguments are shown here but what's important that now these arguments of each of these integrals satisfy the Pythagorean theorem so now not all three of them are independent but just two of them are independent so effectively we reduce the number of variables so if these integral dependent on three variables now both integrals on the right hand side depend only on two variables now of course I mean one of the variables we can just use as the dimension and if we speak about the dimensionless variables this means that in the original integrals integral we had two dimensionless variables and in each of the resulting integrals we have one variable less so starting with two dimensionless variables we end up with one dimensionless variable and if we look at the quadratic form in the Feynman parametric integral so the original one was this one but in each of the resulting integrals we can use this Pythagorean theorem and we get for example in one of the integrals we get just such expression which is which has two terms instead of three terms here and we can easily calculate the integral with such denominator which gives us in arbitrary dimension just the f to one hyper just house Gauss hyper geometric function now the three point case again so let's try well remember we have this special case when the space time dimension is equal to the number of external legs and here basically in this special case our result for Feynman integral is just the area of spherical triangle which is the spherical excess and if we consider these dihedral angles size so this would be just the sum of this size minus pi and this result corresponds to the result obtained by Bernie nickel in 1978 so we just reproduce the result his result in this simple case but in general case when we have arbitrary space time dimension so we basically follow this geometrical procedure so first we drop perpendicular from this point on to the red triangle which is composed of the momentum variance and this is the picture basically this is the spherical triangle or spherical or hyperbolic triangle so basically the integration goes over this spherical triangle but the the solid angle is defined by this tetrahedron so basically we have dual picture now so we drop this perpendicular so let's call this point 0 then we connect it with each of the vertices of this red triangle and we get corresponding connections in this picture as well and basically we split our original tetrahedron into three tetrahedra and in each of these tetrahedra we have extra two conditions on the variables which we get now just take one of them say this lower one along the points one two and zero and split it again into two tetrahedra so now I mean our original tetrahedron is split into six tetrahedra but by dropping this perpendicular so we get an extra condition on the again due to this category and theorem and if we look at the number of variables then in the original one in the original three point function we had six variables but one of them can be extracted as dimensions so we we get five dimensionless variables in the original one after the first splitting into three tetrahedra so we get two relations so now each resulting each of the resulting integrals depends only on three independent variables dimensionless variables and after the second splitting so we get one extra relation so each of the integrals depends only on two dimensionless variables starting from five we get two but we have six pieces and the original quadratic form of in Feynman parametric integral was this one containing six terms and if we take one of these lower tetrahedra so the the quadratic denominator would contain just three pieces so and this is basically an illustration so we started with five basically we reduce the number of variables by three so we go from five variables to two variables and using this representation with quadratic denominator containing just three terms so we can easily calculate it and we get for the general space-time dimension we get the result in terms of apple hypergeometric function of two variables and by the way all these arguments of the occurring hypergeometric functions have very transparent geometrical meaning so basically if you look at these pictures so it's just the length of corresponding line and that's it okay and now for the four point function for the four point function so we have these simplex in four dimensions and we have certain hyper-solid angles so to say at these vertex and and what this solid angle cuts out of hypersphere is a non-euclidean tetrahedron in fact which might be spherical tetrahedron or hyperbolic tetrahedron depending on on our external invariance and so I'm trying to make this picture here which should be also understood in it's a three-dimensional non-euclidean tetrahedron basically either spherical or hyperbolic and now we also begin the splitting to reduce the number of variables because we have too many variables in the general case in the general case we have four masses and six momentum variants so we have 10 variables so we have nine dimensionless variables so let's do the splitting so first we drop a perpendicular from this point on to this red tetrahedron so their intercept is just one point so because this is one-dimensional object this is three-dimensional object in four dimensions so their intercept is just a point and this point corresponds to a certain point inside this non-euclidean tetrahedron now we connect this point to all the vertices of this red tetrahedron and also here we get corresponding lines and now we can so basically we split the original tetrahedron into four tetrahedron now we take one of them for example this one and drop a perpendicular from this point to the base of this tetrahedron now we split it into three tetrahedrons so we split the original one into four now we split this one into three and at each step of splitting we get extra conditions due to this Pythagorean theorem because we always drop the perpendicular so we use this Pythagorean connection many times so now take one of the resulting tetrahedra this one for example and drop another perpendicular from this point to this point to this side so and basically this is what we get so sorry we first we split the original tetrahedron into four then into three and then into two so basically we split it into 24 tetrahedra four times three times two so and now let's look at the number of independent variables in each of the pieces in the original one so we had 10 variables minus one dimension so it's nine dimensionless variables after the splitting the original tetrahedron into four tetrahedra so we get three relations in each of the resulting pieces so we get six independent variable sorry dimensionless variables after the second step we get four dimensionless variables and after the last step we get three dimensionless variables in each of the resulting 24 pieces so starting with nine dimensionless variables sorry and up by the functions which depend only on three dimensionless variables each so we got read basically by six of them and if we look at the quadratic form in Feynman parameter integral so the original one had 10 terms and if we just take one of these two sorry for example this tetrahedron so then the corresponding denominator has just four terms instead of ten terms and you can also see that normally we have partial sums of these Feynman parameters multiplying the corresponding invariance and this looks like a general feature so I will discuss it a little bit in the general table and yes and we can basically for each of these integrals so we can calculate the we can get exact result in arbitrary dimension and it would be a certain certain case of Lorechel's run function so fn so here is the definition of this function but it depends on three dimensionless variables so like we calculated by this Pythagorean theorem and here is the table showing the reduced number of variables for two three and four point function and also it can be easily generalized to arbitrary endpoint function so total number of dimensionless variables is two five or nine and this is the total number for endpoint function the number of pieces in in how many simplices we split our original simplex is two in the two point case six in the three point case 24 in the four point case and one can easily see that each time we just multiply it again so we get n factorial in the general case and the reduced number of variables is one two three and in general case it would be n minus one so we started with the number of variables quadratically growing here and we ended up through this geometrical method by linearly growing number of variables and also if you look at the quadratic forms so again we see that I mean there is a general feature that we get these partial squares of partial sums of Feynman parameters okay so now the summary so well so we suggest you propose this geometrical way to regulate dimensionally regulated Feynman diagrams all our momenta squares and masses require direct geometrical meaning and we also get this hyper solid angle which basically which gives us all the information about the dependence on the momenta squared and the masses and in the one loop endpoint case so we can relate the results to certain volume integrals in the non-euclidean geometry and of course it could be either Lobachevsky case or Schleffly case so we can study this but it depends basically it depends on our momenta variables and the masses and analytic continuation so can be can be done from basically from spherical case to hyperbolic case and in a number of cases so the results all the epsilon expansion so you get hyperdramatic functions but still we need to consider epsilon expansion if you want the results for physical quantities so some of them can be presented in terms of generalized poly logarithms in more complicated cases so we can get multiple poly logarithms and so on but we didn't consider the epsilon expansion in this presentation and geometrical splitting gives us basically straightforward way to reduce general integrals to those with lesser number of independent variables and the resulting integrals can be calculated and can be expressed in terms of hyperdramatic functions and here are the types of hyperdramatic functions that we get here and also maybe the last slide so I want to mention that there are several papers right now which use geometrical methods maybe similar to this one maybe sometimes slightly different from this one so I try to collect some of them but certainly I couldn't get all of them so my apologies if if I forgot something so you can tell me if I forgot something here but there are many people working basically using some of the some of these methods so thank you thank you Andrei thanks very much thanks for all the time you've put into these nice pictures I have one question just quickly you mentioned in the end that you did not discuss the epsilon expansion but what you did say is that you refer to dimensions right you had formulas with the hypergeometrics and arbitrary dimension so I was wondering because at the beginning you said there's something special about the two point function two dimensions the three point function three dimensions and so on these cases where it seemed like the dimension should be something very specific and now you said that you can actually do it in all dimensions I was just wondering if you could explain a little bit well I think in one of these papers maybe in this one this case of spacetime dimension equal to the number of external legs was explicitly considered for arbitrary number I think it probably was this one but I need to refresh my memories but if we look at the expressions here basically let me see yes so basically what we can see here in the geometrical representation when n lower case is equal to the number of external legs so basically what we have this denominator disappears because it's power zero basically and what we did is basically just the hyper volume of this piece of hypersphere which is cut out by our solid angle so say if we consider four point functions so this is the volume of the spherical or hyperbolic tetrahedron without yield factors and this is the property also in higher dimensions so for example for the four point functions it's a three dimensional non-euclidean tetrahedron for the five point function it would be four dimensional simplex but again it would be the hyper volume or content call it and so on so we will not get any weight factors like that so the situation is simpler but the problem to calculate such quantities it's still a complicated problem yeah and you're saying that this geometrical composition applies no matter if this factor is there or not I mean we know what what does it mean geometrically but geometrically even calculation of the volume of three dimensional non-euclidean tetrahedron is a complicated task so it was a non-trivial task to solve it thank you very much there's a question from David yes well really it's a comment to remind you about a rather interesting geometrical paper that you also wrote in Tasmania with Bob D'Oborgo about the volume of three-body phase space which you interpreted geometrically now that is taking us into elliptic territory it's the discontinuity of the two-loop sunrise diagram and since you did that work there's been a lot of interest in three-loop and four-loop sunrise diagrams so I found myself last week trying to help Albrecht Clem understand the four-loop sunrise diagram working out the volumes of the five-body phase space in two dimensions and going back to your work with Bob to remind myself how to do that so not only did you make contributions at the one-loop level where the multiple polar logarithms arise but you also opened up this field of elliptics and beyond which is the subject of many conferences these days okay thank you thank you David yes of course I remember about that paper but I had just 45 minutes for my why I didn't include it thank you very much let's all thank Andre again for the talk