All right, so welcome everyone to the Schubert seminar. Today we're happy to have Slava Naprienko from Stanford University talking about so many Schur functions, please go ahead. Hello, thank you so much for the invitation. And indeed I'm gonna talk today about so many Schur functions and how they appear everywhere in math. And I want to talk about how to generalize some of the Schur functions and why some generalizations are important. And I guess the main topic and the main theme of my entire talk is going to be trying to address and answer this question. And the question is, what is Schur? Many of the functions we feel that they deserve the name Schur and many of the functions they satisfy similar properties. But because they have different origin, they have different ways how you can look at them. So since the first part of the talk is introductory, I'm gonna talk about the classical family of the Schur functions, how they appear and what property they satisfy. And then I'm gonna go forward towards more general Schur functions. So the story begins with the classical Schur functions. Oops, sorry. The story begins with the classical Schur functions and the classical Schur functions which are denoted by a slender and parameterized by partitions is a symmetric function which happens in many, many different contexts and probably the most important context for this seminar is the context of the Schubert calculus. So if we look at the Grassmanian and you can think of the infinite Grassmanian, you can think of the finite Grassmanian and you look at the thermology ring of the Grassmanian. It turns out that the thermology ring is naturally even morphic to the ring of the symmetric functions and moreover, the Schubert class in the thermology ring exactly represented by the Schur function. And so this alone is already a very good reason to try to understand what Schur functions are because if we want to understand the combinatorics of the Grassmanian and being able to answer all of the questions from numerative combinatorics, we just want to understand what these Schur functions are because just the Schubert classes are represented by the Schur functions in the form of the linear basis of the ring of the combinatoric ring. Another source of the Schur functions is the representation theory. If you look at the representation theory of JLN or SN, the symmetric group, the general linear group or the unitary group, you will find that the characters of irreducible representations are also being equal to the Schur functions. So in other words, if we look at the character of the irreducible representations, it turns out that irreducible representations, polynomial reducible representations are often parameterized by partitions in these cases and the characters are again equal to Schur functions. So this is already two independent contexts where Schur functions appear naturally and it gives a very good reason to try to understand them in detail. All right, probably some other reasons which I'm not going to address in detail in this talk is the fermion-Bason correspondence which happens in the mathematical physics and integrability and some of the others are in numerative combinatorics and so on. So there are many, many different reasons to look at the Schur functions and try to understand the structure. So in particular, in the Schur calculus, if you want to understand the multiplication on the ring of the carmology and then expand the product, again, in terms of the Schur functions, you will look at the constants which are called the little with the richer concoctions and they play the important role. So this is some different context where we can find the Schur functions in the wild. Some natural questions like Schur calculus, the carmology ring of the Grasmanian or some natural questions like the character of the reducible representations. So now I want to talk about how to actually study and how to actually write down Schur functions, how to actually express them and where do these expressions come from? I want to talk about the expressions. And so the first way how you can write down the Schur functions is combinatorial and this is perhaps the easiest way how to do it. In fact, it is so easy that this is exactly what I always give to my students in research experience for undergraduate students in the programs because this is something you can give to anyone who doesn't know anything at all and nevertheless they can start feeling that there is some deep in the mental structure. So if you want to describe the Schur function, it turns out that it is just enough to look at the tableau which is just diagrams parameterized by partitions and you fill them with numbers which is called the semi-standard tableau. I'm not gonna go into detail because I want to talk a little bit of the big view and talk about the different generalizations but roughly you look at the combinatorial data, you assign weight to each combinatorial data, oops. And then you sum over all of these things. As a result, you have very, very explicit expression for the Schur function. It is so easy that you can give it to anyone who can write numbers in the table and you can write them down explicitly and it is very down-to-earth definition but of course it has some drawbacks and one of the obvious drawbacks is from this definition it's not even clear that the function is symmetric. If I give you some sum over all of these partitions and you look at all of these terms and sum them together, why would the sum be even symmetric? And how do you understand any of the other properties from the combinatorial sum? So it has some positive and negative sides and another definition which is probably some of the people learned first, I'm gonna call it a whale formula. It is the definition of the Schur function as the determinant. You can just give it explicitly as some determinant or rather as the ratio of two determinant and in the denominator we have the wonder month. So I'm gonna just write explicitly the expression for the wonder month and this definition is great for other purposes. This definition is allowing you to see the explicit expression for the Schur functions in terms of the variables but it has another drawback. If you expand the determinant and look at the terms in the expansion of the determinant you have lots of sine consolations. The first formula inherently just positive you just write Schur function as its monomials at every term that happens in the Schur expansion and the formula because of that becomes extraordinary explicit and you just write Schur function as one term plus another term and so on and it is just a positive sum. On the other hand, this one is more obscure because now we don't understand the terms so well but now we have the closed expression in terms of the determinant. The third one, which probably going to be the last one that I'm going to talk about is the definition in terms of determinant or I'm going to call it a Jambelli. So Jambelli definition is always the definition of the Schur function in terms of the very same Schur functions but of smaller order. So in particular the Jambelli sum of the Jambelli as identity are given us the Schur function in terms of the complete symmetric polynomials which could be given for example by generating series or just computed explicitly or doily we have the expression in terms of the elementary symmetric functions. So this is three different ways how you can just write down the Schur function give it to someone and so that they could look at this but before I go further, I want to take a moment and appreciate these three definitions and perhaps to think how long trivial it is for someone who doesn't know anything about the Schur functions and their applications why these three definitions would give you the same answer. If you look at these definitions, this is an explicit combinatorial sum from which it is not even clear that the resultant sum is going to be symmetric. Why would you write such a sum as the determinant with appropriate cancellations and why would you be able to write the very same sum as the determinant in terms of the smaller Schur functions and is it, which one is preferable? Which one is more natural and others just some of the formulas that you can derive from the first one. So this is a non-trivial question and the different authors take different approach. For example, Stanley in enumerative combinatorics in the second volume just starts by defining the Schur function as the combinatorial sum. And he writes that the following definition might be not motivated.  On the other hand, the whale formula, this is the approach taken by McDonald. You can immediately see that it is the ratio of the anti-symmetric function by the symmetric function and by some simple analysis, you immediately understand that it means that the function should be symmetric. And moreover, it is immediately clear that such functions form the linear pages of all of the symmetric functions. So this is a really good definition, but it has a drawback that it is not as explicit as the expansion in terms of the determinant. And it turns out that this definition is very hard to generalize. It is very nice that for the Schur functions, we have such a simple formula in terms of the determinant, but it turns out that for more complicated functions, there is no such simple expressions. But meanwhile, the combinatorial expression or the expression in terms of the Jumbellis formula is gonna generalize better. Okay, give me a second. So what we have at the moment is a family of Schur functions which appear in very natural contexts like in Schubert calculus and representation theory and there are different ways how you can see this Schur function. So I want to say that these properties are in some sense very fundamental and crucial. And the further we're gonna go, I'm gonna talk about generalizations. We'll see that these properties extend to every other Schur family. So let me go to the second family. And again, the second family is having a very good relation to the topic of the seminar. The second family is our first generalization is the factorial Schur functions which this time I'm gonna write the parameters here which this time depends on a new set of parameters on new parameters A. And how can you find these functions in the wild? What are they living their own life in various parts of math? Well, so one of the most important findings is that these functions describe them again the Schubert calculus. So again, a very, very natural thing to do is when we consider our Grassmanian and we want to consider the carmology ring, we find that the torus of the JLN is acting on the Grassmanian in a very natural way because it could just act on the planes by the torus. And it turns out that you can extend the carmology theory and instead of computing the regular carmology, you compute the something called equivariant carmology of Grassmanian where T stands for the action of the torus. And it turns out that this more refined version of the carmology, so again, very natural thing, we just look at the Grassmanian with the action of the torus. It turns out that it is isomorphic to the factorial symmetric functions which I will give you the explicit expressions for these functions in a moment. But of course, what is most important is that again the Schubert class is represented by the factorial Schur function. In other words, here is the very natural origin for the factorial Schur functions. And again, it gives the motivation to study the properties explicitly, in particular, the Richardson-Litterwood coefficients which were studied in many of works of the Sagan and Molyev, which was later used by Knudsen and Tao to give the combinatorial realization for the multiplication in the equivariant carmogenings of the Grassmanians. So there's another very natural family of the functions, but now I want to have a question. Is there representation theory origin for such functions? Before we, sorry, my pen seems to be more functional. So before we saw that the regular Schur functions, they appear both in the Schubert calculus and in representation theory. But now when we extend our definition to include the factorial Schur functions, there is a very natural extension to the Schubert calculus. Just look at the Grassmanian, but only with the action of the Taurus and look at the carmology. But at least I don't know what is the corresponding extension of the theory of the representation theory, what kind of representations we want to consider such that their characters would be naturally represented by the factorial Schur functions. So we lost one of the motivations to study these functions, but it turned out that we found another one and somewhat irrelevant. And another motivation to look at these functions is the interpolation theory. Interpolation theory of symmetric functions was developed by Sahi and Akhenkov and studied by Alshansky and many other people. And in short, the question is, if I have the symmetric function, I want to interpolate it, I want to expand it in terms of some coefficients and some bases. And it turns out that the factorial Schur functions form an extremely and extraordinary grade basis for expansion of the symmetric function any symmetric function in this basis. And the reason is because of the factorial parameters, the factorial Schur functions, they satisfy some vanishing property that makes the theory looks a lot like the standard, the classical Newton interpolation. I'm not going to go into detail about this, but what I want to point out is that now we have a new motivation, a new source where such functions appear naturally in particular in Akhenkov work. I don't remember the year. Akhenkov classified all possible schemas for interpolations of the symmetric functions. If we want to interpolate symmetric functions and have some good properties for the interpolation nodes, what could they be? And I don't doubt that there's only three families that satisfy these good properties and factorial Schur functions is just a natural family, one of them. In other words, it is another great source and inspiration and motivation to look at these functions. And now I'm going to talk about the corresponding expressions and whether they generalize nicely to the factorial Schur functions because we want to look at them because they appear in all of these areas of math. All right. So if we're looking at the expressions as before, we have the combinatorial expression and the combinatorial expression is if you want to give the factorial Schur function again, you can do it very easily. You, you know, you can do it very easily. You again consider the semi-standard tableau. Again, fill it with numbers the very same way how we did before. But this time we just assign weights in a little bit more refined way. Instead of just writing X1, we remember where the entry one occurred. So if it occurred here, I'm not going to explain why we have certain coefficients, but we can write the corresponding weight where each term remembers where in the combinatorial data it occurred. And because of this, it is perhaps something like this. Because, yeah, and we do the summation. Of course, because of this, now we have the refinement and this definition gives us immediately understanding that these Schur functions very naturally generalize the regular ones. If you set all of the a's to be zero, then you're just gonna collect the very same weight that you were doing before. You don't have any of the equivalent parameters and you go back to the regular Schur function. So it corresponds exactly to the fact that if your torus acts trivially, then you are just considering the regular carmology ring. Okay, so as you see, we still have the combinatorial expression for the factorial Schur function. And the combinatorial expression became a little bit more complicated, but still pretty easy. If we look at the whale formula, it turns out that it also generalizes very well. If you want to write the factorial Schur function as the determinant, you can still write it as the ratio of the determinants. But this time, instead of just having the variable x, we have the factorial power of x, which is just some shifted version of the very same power. And then the formula is pretty much identical. We again divide by the wonder month and our formula, our determinant formula remains the same. Okay, and of course the very same way we extend the Giambelli definition. And indeed the factorial Schur functions could be given as the determinant in terms of the complete factorial Schur functions, which could be defined by some simple generating series or even explicitly, or doily we can expand it in terms of the elementary factorial Schur functions. So you see the very same properties, they remained intact, but I want to point out that there is something very interesting happening and probably this is how I'm gonna make a break after I explain this. When we look at the Schur functions, at the original Schur functions, these three definitions, the combinatorial, the whale formula and the Giambelli, they come from different sources. So you can imagine that the combinatorial definition is really coming from the representation theory of GLN. Because you can think of the tableau as parametrization of the weights of an irreducible representation. So then it is very natural to write the Schur function as the sum over all of the weights. And it makes the combinatorial formula very natural object. You just sum over all of the weights in the irreducible representation, the character. And that's how you get the combinatorial formula. On the other hand, Giambelli formula, for example, is naturally coming from places like sugar calculus because the way how you can find these formulas is by considering the churn classes of the tautological bundle and it is very natural language to describe the entire ring in terms of the complete homogenous functions or the elementary symmetric functions. In other words, and the whale formula is coming from even another source which probably could be called crystals and some other structures, which I'm not talking about. But what I want to point out is that the way why these definitions create different definitions are natural, it's very different reasons. For example, the combinatorial definition in terms of the tableau in a way it doesn't make any sense in terms of in sugar calculus because what each monomial even means, we cannot expand if we look back here, we see that in our identification, the Schur functions represent the sugar classes in the caramology ring. But if we want to expand the Schur function in terms of the monomials, what could it even mean on the side of the caramology ring? You probably could embed it into something bigger but it is not immediately a not immediately natural object because we don't have any space into which monomials would live naturally. But in JLN it is a very natural object. So what I want to say is that these definitions are coming from different places. And when we go to the factorial Schur functions, Jambelly formula again could be thought to be coming from the Schuber calculus, but now we don't really understand what is the origin of this definition? What is the origin of this definition? Why this definition as the combinatorial sum of tableau is natural because as I pointed out before, it's not very clear what is the corresponding representation theory such that we would have some reducible representations and then we take their characters, we would get these factorial Schur functions. We would love to have some theory where we would have things like this. But as I understand, and there is no such theory, at least we couldn't come up yet. And but nevertheless a very similar formula that does a very similar job is there. And well formula is having something very similar, a connection to here if you describe the combinatorics of the representation theory. So in other words, we see that the Schur functions when you generalize them and when you can see there are more general versions coming from different places, they still have these three properties even if we don't know why. Even if we don't know why we have some of these properties, nevertheless they do. And this is going to be the feature for the further generalization I'm going to talk about. And at the end I'm going to talk about the ultimate generalization. Oh yeah, I see there is in the chart. Yeah, yeah, you can embed it to the matrices and then there is monomial expansion. I guess that you need to embed your symmetric situation into something non-symmetric to see this monomial. But I don't know if there is a correspondence between the representation theory because there is this result that connects the Schubert calculus and representation theory of JLN. You can show that these things, they have some sort of factorial connection. Meanwhile, in the case of the factorial Schur functions, it is very natural to consider Schubert calculus but it's not very clear what is the corresponding representation theory. Anyway, I think that it's going to be a stop for me and we can take the break. Very good, okay, so we'll take a five minute break.


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hey you guys so it is where the end of April is actually April 23rd and girl we're still having issues with this dang-gone ransomware with my company and so um this is concerning that we will compromise a company this size was compromised you have to be a low-down dirty you know what to do this for a organization it's an organization that did it to do this when we're under the coronavirus and all this. Arizona has not been hit that hard but still is out there and I think now that it's getting better weather people have again have this false sense of yeah okay let's go out and have fun mm-hmm I cancel my lab appointment coming up I cancel my doctor appointment and super for a new doctor too I'm canceling everything because nothing is urgent right now it's not extention that I go to see a new doctor right now to develop a really you know develop a new patient doctor relationship I'll catch you later on I'm good so I'm counseling I've been trying to call them they're not doing tele what are you they call it tele appointments meaning virtual appointments it's only for them for their existing patients a lot of the time I took date JBN on Monday no Tuesday and I told y'all and my chit chat because he was complaining he had a y'all he was coughing he had a sore throat and a fever when I tell you I broke down crying because I was scared I'm like what the hell is going on because my baby hasn't gone anywhere so I was upset my husband got up he's like just take him to the doctor so we took him to the doctor and it was strep it was strep thank God it wasn't you know what I thought it was but that that rattled me a little bit and then I was confused how did you get it so my husband says that he's not washing his hands properly you know he's going to the bathroom and he's not washing and I'm like literally when you done when he's done with the bathroom he's not washing properly so I have mixed antiseptic a little bit of it with our hand soap because that acts like an extra layer or barrier for your for against germs and stuff it's the same bottle I had when I had my surgery it's the same stuff that surgeons use when they go into operating not only that but I ordered another bottle through Amazon recently so yeah I'm getting a lot of emails from now at school when I tell you we've gone from doing 70% of the school to 60% that's about 350% because school is done in about four you know three more weeks y'all and I'm done especially with stuff at work I don't have the mental capacity to be so glad when I started on the homeschooling stuff I don't have the mental capacity to do everyday stuff and they want me to do electives like they want them they have assigned them electives like Spanish art music PE girl please PE I'm chasing them around the house with a flip-flop that's our PE he got a lot so it is what it is but we are turning stuff in with that being said I keep telling myself it's only four more weeks oh y'all pray for me I'll pray for y'all I am praying like multiple times a day you know this is something that my spirit is telling me this is something that we have to go through it y'all heard me mention this before there is no going around this everyone's and this is this is the beauty almost the beauty of it this is not just my struggle it's your struggle it's my neighbor's struggle it's my husband's struggle it's my child's struggle so I can't see the parents say oh girl you won't believe it I went through the coronavirus last year no we all went through it the entire world went through it and so I really do think that a lot of us will be victorious at the end we just have to go through it I've been I've been meditating on the word I've been reading and I've been self-reflecting on almost what does what do you need from me God what do you need from me to do you know I've gone away from not necessarily gone away from but I'm trying to focus on others instead of myself because I think at the end of the day with me focusing on other people and how I can help others that will help me also and we will be blessed you know you Bible tells us you'll always be blessed and as as far as servitude goes y'all excuse me talking too fast as far as servitude go you will always be blessed so yeah you guys that's how I'm looking at it because for a while they're especially earlier this week with JB being sick and work I was getting really depressed I really was I was having a moment a couple of moments okay but I did a detox a watermelon detox ooh child when I tell you I lost three pounds oh yes I'm down to 172.6 I started at 175.4 or six or something like that so I lost three pounds doing that watermelon detox I include the recipe below what I use and she told me look she told me first of all I even I sent the message to my girlfriend I said girl what the hell I did this detox that you shared on Instagram I keep going to the bathroom is this normal she said yeah it's normal she started laughing she said yeah that's normal make sure you do a salt water flush in the morning I said I don't have any more for so I know we're not doing that I'm gonna drink a bunch of water I'm not having any meat think I did have a little bit of turkey yesterday though but I'm like no I'm not doing that I'm not doing a damn salt water flush after I had bubble guts bubble guts for 24 hours are you serious now we should go y'all these in the mask isn't this cute I got this one that says this to shell pass and then she has these for the kids and I got this one for JB this one with a little thing there and God we trust these are cute and so her name is up here can y'all see that hold on yes Shora designs and they are on sale for $8 look if someone is selling these masks I'm really upset that people are inflating prices this is cloth this stuff doesn't cost hardly anything to cost hardly anything to make excuse me so these masks should not be costing $25 I've seen people selling them $25 $30 $15 or less is how much these things should be costing but they're cute really really cute I think I got the what is to say if you can read this you're too close this is cute but I don't want that I think I got this to show pass yeah it makes it very difficult it depends all right so how would you make this JB come on I'm working yeah you're working how would you make this one two halves then two equal shares how else could you draw the line where else what else could you draw it I know of one easily but you show me you already just oh yeah good good good how else could you do two halves can I show you one good job JB are like some some asterisks hit the earth I've been getting beat up because they were taking over and your parents are right okay okay so they're already around the sun and really just get just like at all times when like when like when everything is orbiting around sun if they try the best to keep in front of her oh so they keep those asterisks from hitting us oh wow that's crazy so you did if you put it if you like no matter what it like Jupiter or like or like Saturn was gone then oh really yeah I didn't know that that's kind of scary so you do know that our astronauts are busy trying to find other planets that possibly live on so there are you you asked me about that yesterday and actually there are planets that are very similar to our atmosphere so darling I'm gonna read this so look it up you want to look it up right now okay we've only been able to do some testing of the atmosphere to see what what type of properties are there your daddy can go in that a little bit more cuz I felt organic chemistry okay so planets that are it is about four point two light years away Kepler 442 b and there's Kepler 452 see this looks very similar to earth doesn't it yeah looks very similar but I believe I don't know which one of these I believe one of these the days are extremely long I got some cheese cake and I was like oh it was two o'clock I watched power what did you get cheesecake from one more we not figured yeah I'm actually I'm actually filming you now chips baby that's all you eat JB you need to eat some fruit or veggies or something you want some green juice not you and me but my husband I oh it was another crazy party last night child those margaritas we go to our we've been getting these margaritas to go every nearly every week and when I wake up in the morning it looks like a sorority party has been has popped off in here like there's a cooler in the middle of the kitchen there's margarita glasses there's cake cut crumbs everywhere and it's just me Alex and JB so I'm like what hell be going on now I'm a type of drinker unfortunately I lose luch I lose train the thought of what happened the previous night apparently we we order margarita glasses through Amazon and my husband's like I showed you what they look like I said no you didn't he's like we were on the couch me you and I said these are the wine glass and then you said okay I said I don't I don't remember that so you need to show me what those in bless so let me back up because I think I'm gonna cut some part of the video out cuz I was looking crazier it is Saturday and our systems that everything was up Thursday morning when I tell you we were so excited you guys hey you guys I'm back in my room child is this is a disaster we're gonna have to get it together so yeah one of the ways that I like to decorate is by using pictures or decorations that are on sale seasonal so right now since it is springtime you will find seasonal springtime decorations all over my local fries is almost like one of those marketplace fries so they do sell home stuff and so I got these cute little paintings for you see that 59 cents I got this little sign that says blessed for 83 cents so yes I'm gonna put these in the bathroom and I'm gonna put this somewhere in the kitchen this is so sweet I just received this box of face products and it's a gift I'm not gonna read the note it's a gift from T thank you so much girl look at all of these face products y'all to put them over here with all my other stuff that's yeah those two baskets and all of this I mean there's serums in here it's actually everything that I needed JV's little hand bubbles what is he so sweet what is that caffeine energizing hydrogel eye patches we have something for our hair I've heard of this brand before good molecules look at that brightening toner move it out the way sweetheart can you pick that bag up he picked that little bag up for mama thank you this coloration correct in serum yes a lot of different serums in here we have niacinamide serum yes baby pick that I think that's a bar yeah that's a that's a bar a cleansing bar I think there's two clinton bars perhaps they're exfoliating powder I'm so excited oh this is so beautiful it was really beautifully packaged to one bar okay what's over here super peptide serum oh I think that's vitamin C powder booster I wonder how to use that would definitely definitely definitely look up videos on this my skin has been coming along I have to be a little bit more more consistent with you can see over here I have tons of stuff over there but this is going to take it to a whole nother level so thank you girl thank you so much this is very sweet hey hey hey yeah what is up with this kid why does the camera look like this they're a quick complainant y'all I'm tired I don't know what is up with JV sleeping pattern but JV is tired and he's fighting sleep so he's not going to bed to after 10 o'clock that can't work so then that forces me to go to bed between 10 30 and 11 and I don't play around as soon as my child goes to bed I go to bed because I wake up between four and five o'clock so this past week it's been a struggle I've been getting barely five hours of sleep and I'm tired I'm extremely tired today well that coffee is hot I'm extremely tired today and I am supposed to go grocery shopping and also go get we're supposed to go hang out at the pool at my neighbors they're not gonna be there meaning they're there but they're not gonna be outside girl social distancing they have their pool up year-round it's really nice and so they're like you can come over any time with with the baby and we'll just look at you guys since they're older they really don't want to be they don't need to be around us she was like we just look at you guys from inside and wave at you guys they're so sweet my neighbors from East Texas different pairs text so anyway yeah my sister y'all see those videos of my sister she is so crazy she was singing she was having a bad day I talked to my sister like every week we FaceTime so the babies can talk to because we have children the same age so she was having a bad day one of those days that we were FaceTime and so she was a little lit she had two two drinks so she was finding her wigs right I'm finding her wigs so she put on this one way it's a girl who do I look like I said shit I don't know you you look like a fluffy ass vanity so that's when she's or I should have never said that she's okay you sure it's right child she started singing vanity she's she saw at least two songs from her then she started singing Vesta Williams I heard the ending of that congratulations I mean she went in yeah I just only count put up a few seconds because my sister is wild anyway what am I talking about God knows again a little bit tired still have a lot to do let me come on in girl chop it a little bit of three pounds I lost I've gained back because that's just waterway honestly so I'm sitting at like 173 I was on a 171 when I was down with that detox but honestly that detox is something that I wouldn't mind doing every two weeks or so so I will probably do it again on Sunday yeah I'll probably do it again on Sunday do a light like light cuz we we're going in eating again Friday and Saturday make it some fried tilapia one day and the next day we're having chela chelaquilas I don't know the word for it it's a Mexican dish it's basically fried corn to Diaz with homemade salsa verde crumbled up cheese sour cream it's so good so I can cook y'all I can burn so I can look at two or three people cook and I'm good so my neighbor she's from Mexico and so she had she had served it to me a couple of weeks ago and I was like what is this she told me about it my other friend who's Mexican she told me about it I'm so young girl I cooked it up I've been cooking it like every week it's you can make it to where it's not as fattening honestly you could bake the tortillas if you wanted to but yeah I think I may have some Latin blood girl stop anyway I'm not doing any work work is busy which is good I'm very grateful I'm very blessed I ordered look I ordered let me show y'all this this whole was taken forever to order I had originally remember that y'all seen those detangling combs I'm gonna show y'all what it looks like let me let it zoom in let me let me darken this up so you see that the tangling comb right there right and it has to it has to flexi like eight or nine flexi rolls that when you use it it so I had mentioned in my community page a couple of months ago a weeks ago excuse me that I'm gonna be reviewing that what I did order it it was taken forever to come in like it wasn't gonna come in till May 30th so I canceled it and ordered a different one so I am gonna review that one once I was by the is by them oak and it looks like it has a sturdier hold I'm gonna review this one because it has the same type of design right then once that I'm gonna add it back to my car once I review it and it's okay because if it's a crappy thing I'm not gonna do a giveaway you know what I mean so that's why I canceled that other order so this is different one with the same type of design but sturdier once I order that and I review it if I like it then I'll do a giveaway okay I'll do a giveaway for y'all in a couple more weeks all right so in addition to Amazon I got some dresses coming in from ASOS I have a little fluffy flat fashion show for y'all I have some more face masks coming in the face mask I show y'all what's what's from Etsy I some more of those coming in cuz y'all the face mask I got from SoCal I don't like those cuz they they sit right on your face so you can't breathe I can't breathe or talk in those damn masks so I don't recommend those I really don't there's the link I've been sharing for you guys I don't recommend those masks anymore instead I purchased some masks from Etsy when those come in I'll wait let me wait till I get those and I'll let y'all know how I feel about those but they do point out that way and I shared the image earlier and I also ordered some N95s you can get those now I'm going to wait until I get those to the Chanel unit guys know where I got them from hold on okay the N95 mask I got from Canope USA the C-A-N-O-P-U-S-A group dot US I'm gonna put the link below if I forget remind me y'all remind me because this is the thing now there are certain stores that you absolutely cannot go into now if you don't have a face mask what is it Costco even though I don't go to Costco Costco has announced if your face isn't covered you can't go in there as a main fork you can't go in I have a good feeling there's certain stores will follow suit to where you have to have a face mask to go in so we have masks here I don't think my husband ratchet ass is wearing his he's gonna catch his hand I think he has a face mask in his car that's why but he needs to wear something when he's out yeah real quick I wanted to show you some of these look I told y'all this is so much fun for me creating this type of stuff in my opinion it's fun so what I've done is created these cute little images for any type of documents I'm gonna be creating for the homeschooling stuff so we have this typewriter that says that says brown boy excellence we wanted to name our school it's brown boy excellence the typewriter would go in the more informal excuse me formal stuff this Game Boy logo would go on the I don't want to call it a logo it will go on the more informal stuff this is one that looks a little bit different and so one of the things I've already done or started on is to also create a academic calendar so we have brown boy excellence academic calendar I couldn't find one on Microsoft already for the 2020-2021 school year so unfortunately I'm gonna have to move these dates around manually that's a little bit you know a little bit cumbersome but it's doable you know you just click on these things and so one of the things I also want to ensure is that we're capturing any school breaks and observe holidays I've already spoke to this I'm about this with my husband and so school for us will start August 17th and it will end June 30th and I get things may change things will change that's just how it is we will have the traditional Thanksgiving week off Christmas week spring break but we will also include our birthday weeks meaning his birthday week off my husband I birthday week off additional days will include because again this is our schedule days such as of course Martin Luther King's birthday but we will also be including Malcolm X birthday and Maya Angelou's birthday I will probably do one half day a month so our schedule will be Tuesday Wednesday Thursday Friday and for me to have a break so that I can have parent workshops basically get my everything together for the next month or the next quarter I'm gonna take half a day for a Friday every month yeah so I'm super excited this is something I could continue what else have I been creating I do want to show you guys I went through a site called teachers for teachers and you're able to download tons of resources so one of the things I purchased let me get the camera off so you guys don't see this were second grade goals for so yeah sorry these are the second grade common standard goals that just to make sure that we're on track we have one for math and one for English language arts and so this is stuff I already printed out this is my me and my swimsuit girl me and my fanny pack it is what it is waste goes in a little bit over there is that I don't know why there's some type of mark so yes girl I'm not gonna turn around we ain't gonna be showing my bone to everyone this child look at look at him what that Sam turn around so they see you turn around so they see you look look at this miss child he is ready all right let me put my cover all on


Hello, this is David Diga Hernandez, and you are watching Spirit Church here on the Encounter TV Network. The mercies of God are new every morning. When you walk with God, every day is the chance for a fresh start. I want to talk to you about new seasons in the Spirit and how the Holy Spirit brings out new beginnings. But first, Stephen Moctezuma is here with me. He's going to lead you in some very anointed worship, and then we're getting right into this message. Here's Stephen Moctezuma. So if you're in a season of life where you are praying for a shift, this message is for you. I want to show you something interesting in the Scripture, particularly as it pertains to the Holy Spirit. One of the symbols of the Holy Spirit is the dove. The Scripture says this in Matthew chapter 3 verse 16. After his baptism, as Jesus came up out of the water, the heavens were open, and he saw the Spirit of God descending like a dove and settling on him. That's Matthew 3.16. The same narrative is repeated in Mark 1.10 and John 1.32. And Luke chapter 3 verse 22 says something slightly different.  Now, other Scriptures also speak about the dove. So we know that the dove is a symbol of the Holy Spirit. And by looking at how the Scripture describes doves, we actually see greater insight into that symbolism. So some Scriptures speak to the purity and innocence of doves, such as Song of Solomon chapter 5 verse 2. I sleep but my heart waketh.  Matthew chapter 10 verse 16 says, I am sending you out like sheep among wolves. Therefore, be as shrewd as snakes and as innocent as doves. So doves can symbolize innocence, doves can symbolize purity. Other Scriptures speak to the hiding nature of doves. Song of Solomon 2.14, my doves hiding behind the rocks. Jeremiah 48.28, you people of Moab flee from your towns and live in the caves, hide like doves that nest in the clefts of the rocks. So when you look at the dove in Scripture and you look at the biblical symbolism for doves, you actually get insight into the person of the Holy Spirit because the Scripture makes it clear that the dove is symbolic for the Holy Spirit. Now I want to show you something interesting here. In Genesis chapter 1, I'm going to read verses 1 and 2. You've likely heard these verses before, but I want you to listen to this. In the beginning God created the heavens and the earth. The earth was formless and empty and darkness covered the deep waters. And the Spirit of God was hovering over the surface of the waters. Now here we see in Psalm 33.6 that by the word of the Lord where the heavens made and all the host of them by the breath of his mouth, the Holy Spirit is that breath, the Holy Spirit is that wind. The Holy Spirit is that dove that was present at the beginning of creation. Now when the Scripture says that the Spirit of God was hovering over the face of the waters, what the Scripture is telling us is that the Holy Spirit was brooding or fluttering. That's what that word means, hovering. It means brooding or fluttering like a bird would brood over its eggs to incubate them. The Holy Spirit brooded over the spoken word of God to bring forth creation. The Holy Spirit was the breath at the beginning and we see the Holy Spirit of God and the word of God coming together to create, to cause, to bring into existence. Like a dove, the Holy Spirit brooded, fluttered, hovered over the surface of the waters. The Holy Spirit moves upon God's voice and he adds that power to it. The Holy Spirit is the power of God in action. He is the omnipotence of God. So we know the story, the Holy Spirit is there. He's present at the beginning of time. God creates all things and then of course creation falls. Man falls into sin. Man becomes a fallen creation. And so in order to begin again, God sends a global flood, a flood that overtook the entire earth. He sent that flood that he might begin creation anew. He sent that flood that he might begin a new season. He sent that flood that he might cleanse the earth of wickedness. Now again, we know that the Holy Spirit is symbolized by a dove in Scripture. And we know that the Holy Spirit fluttered at the beginning of time. He was present at the very moment that God began to create. The Holy Spirit was present at the beginning of time. And when God began to first create, we see the Holy Spirit hovering. Now this is amazing because if you look in Genesis chapter 8 and you read verses 6 through 12, this is what the Scripture says, After another 40 days, Noah opened the window he had made in the boat and released a raven. The bird flew back and forth until the flood waters on the earth had dried up. He also released a dove to see if the water had receded and it could find dry ground. But the dove could find no place to land because the water still covered the ground. So it returned to the boat and Noah held out his hand and drew the dove back inside. After waiting another seven days, Noah released the dove again. This time the dove returned to him in the evening with a fresh olive leaf in its beak. Then Noah knew that the flood waters were almost gone. He waited another seven days and then released the dove again. This time it did not come back. Now God created all things at the beginning. The Holy Spirit was present hovering over the commands of God. Creation falls, God has to begin again or chooses to begin again. He sends a worldwide flood. That flood wipes out creation as it was. And God preserves a man by the name of Noah. Noah and his family were preserved in the ark. When the flood waters began to die down, when the punishment and the judgment was coming to an end, God gave Noah the task of beginning creation anew. And just like we saw the Holy Spirit at the beginning of creation in Genesis chapter 1 verses 1 and 2, so again we see that dove present where God begins creation again. Noah releases the dove the first time. It comes back, no indication of dry land. Nowhere for that dove to land. Nowhere for that dove to mark as the place of new creation. Noah releases that dove a second time. It comes back with a branch. Noah releases that dove a third time and it goes and it found a place where it would land. The dove went in search of where God would create again. Now here's what's interesting. You don't see that dove land. The Scripture never records that landing. You don't see the symbolism of a dove landing for the rest of the Old Testament. It's not until Matthew chapter 3 that we see the dove finally landing. The dove finally finding a place where God can begin again. After his baptism as Jesus came up out of the water, the heavens were opened and he saw the Spirit of God descending like a dove and settling on him. And a voice from heaven said, This is my dearly loved son who brings me great joy. The dove came in hailing the dawn of a new creation. Announcing where God would begin creation anew. He did not land in the Old Testament, but he came to land upon not a branch but the vine. He came to find that place where God would begin anew, this time not a physical creation but a spiritual one, this time the work of salvation, this time the work that came through Christ himself. The Holy Spirit will always be found where God is creating anew. Why? Because the Holy Spirit is the active force of creation. This means that wherever the Holy Spirit broods, wherever the Holy Spirit flutters, wherever the Holy Spirit hovers, there is newness of life. Every promise that God has spoken over your life will come to pass. Every word that God has breathed will have the Spirit of God hovering over that word. The Holy Spirit broods over every promise of God. The Holy Spirit broods over every prayer you utter. The Holy Spirit broods over every declaration that God has made concerning you. The Holy Spirit will only land on the word. The Holy Spirit will only land where the word is in action. So the Holy Spirit is the one who brings new beginnings.     You see, He lands on the Christ in you. The Holy Spirit wants to do something new. The Holy Spirit wants to do something fresh. The Holy Spirit wants to breathe on the promises of God and cause them to come into existence. The Holy Spirit wants to take you into that season that God has destined you for. The Holy Spirit wants to take you to greater depths in prayer. The Holy Spirit wants to take you to greater depths of the word. The Holy Spirit wants to take you to greater levels of holiness, to bolder evangelism. The Holy Spirit wants to bring you into the new season, not just for you but for those around you, that you might be pleasing to God. Are you giving Him somewhere to land? The Holy Spirit is searching. Where can I begin creation anew? I don't know about you, but I want to be one upon whom the Holy Spirit can land. I want to be that place where the Holy Spirit can settle. I want to be that place where that Holy Spirit power can begin to work in my life. I want to surrender all. I want to give Him everything I am that He might mark me as a place where He can create again. And just as the Holy Spirit hovered in Genesis chapter one at the dawn of time, and just as the Holy Spirit hovered above the Lord Himself, so the Holy Spirit hovers over you announcing a new beginning. If only you'd give Him a place to land. If only you'd surrender yourself, He would create anew. Father in Jesus' name, I pray you help us to become a place where you can settle. I pray Holy Spirit that even now, upon that one receiving this prayer, that you would begin to breathe life. Brood over every promise. Brood over every word. Cause that word to come alive in us. Take us into the new season Holy Spirit. We will follow, we will obey in the name of Jesus we pray. And I want you to say it because you believe it. Say, Amen. Well, I want to welcome now the new members of Spirit Church. There you are up on the screen. We love you. We are praying for you. I always say that because I always mean it. If you'd like to join the Spirit Family, our online church, just go to DavidHernandezMinistries.com www.spiritchurch.com Fill out the form and then you will be an online member of Spirit Church. Now to your comments. These comments come from last week's teaching, Uncompromised Walking in Total Obedience Toward God. Now, if you haven't watched that message yet, I encourage you to do so.  Now, when you're going and checking that teaching out, make sure that you're subscribing. If you're watching on Facebook or Instagram or YouTube, follow us or subscribe. When you subscribe on YouTube, be sure to click that notification bell so that you can be notified when we release new content. And if you'd like me to potentially read your comment on an edition of Spirit Church, then go ahead and leave a comment in the comment section right now. So again, these are the comments from uncompromised, walking in total obedience toward God. Robin Gennade writes, it actually feels like God's power moves through the screen when I watch your videos. Thank you for the message. Glory to God. Robin, that's definitely the power of the Holy Spirit. This is his channel. We've surrendered it to him. He does whatever he wants to do through these broadcasts. Jay Jorica writes, this was a cut above the rest of the Spirit-filled messages from Brother David. Surely Encounter TV is a platform planned by God. Obedience, obedience, and obedience is the key to please God. I have learned that obedience is the main tool that can give us victory. Your emphasis on do what is right and leave the rest in God's hands touched me. I am learning day in and day out. May God continue to use you. Seraphine Leobon writes, God inhabits the praises of His people. Thank you, Brother Stephen, for such anointed worship. May the Lord continue to empower you. Thank you, Brother David, for the message. It challenges and stirs my faith. May the Lord help every believer to stand firm in our faith at any cost. God's rich blessings. And Emily Laramore writes, thank you, Brother Diga. This word is so simple yet so important to stay in the perfect wheel of our Heavenly Father. I found that if you simply trust and obey, you may not necessarily get the same outcome you hoped for, but the outcomes always bring glory to him and often touch others in the process. I always look forward to these weekly teachings that give me so much hope each day.  Well, thank you for writing, Emily. These teachings go around the world and we receive testimonies from people being saved, being healed, being delivered, being encouraged, being touched by God's power, and even being challenged to enter into the ministry. So God's word is working, and I want to invite you to be a part of what we're doing here at Encounter TV. Don't turn the video off. I want just a couple minutes to talk to you here. I really do want you to be a part of this. I want you to join in on what God is doing through these broadcasts. God is using the media that comes out of this ministry, the videos, the teachings, the live streams that we do, the Holy Spirit School, which is training people with a free Bible training school online, and the Holy Spirit is using the events that we do all around the world. Now, here's how you can be a part of it. I'm inviting you to become a monthly ministry supporter. You can do that by committing to $10 or more a month. If you commit to $10 or more a month, we're going to give you access to our monthly partner Zoom calls where Steve and I jump on, update the partners, and interact with you. You're going to get event seat reservations for all of our ministry events. Any of them that you want to come to will save seats for you and your family members. You get 10% off all ministry apparel. You're going to get a special email update that's exclusive for our partners. You're going to get the world changers update, and you'll get a beautiful Dove lapel pin that you can wear to show your support of this ministry. Think about this. People spend money on gym passes, on streaming services, on all sorts of different delivery services, but I want to challenge you to give to this ministry on a monthly basis. I know some of us are struggling. Some of us are worried about the future, but think about this. It's not just the one individual. It's all of us together coming in unity to support the gospel. So become a partner for $10 or more a month, or you can sign up for $30 or more a month where you get all of those benefits I mentioned, plus you get to select the book that I will sign and send to you. And if you sign up at the $100 level, I will send you all four books and will double your discount at 20%. But again, we do this because we love the Lord, because we love souls, because we want to see this content continue to go out around the world.  On top of that, you get all of those wonderful partner benefits. I don't think there's anything better than that. So sign up today to become a monthly supporter by going to davidhernandezministries.com slash partner, or you can give a one-time gift by going to davidhernandezministries.com slash donate. Do that today. Give a one-time gift or become a monthly supporter. But whatever you do, do it now. Join in the cause. Join our army of supporters and help us continue to spread the gospel all around the world. And that is it for this edition of Spirit Church here on The Encounter TV Network. Until next time, remember, nothing is impossible with God.