Welcome, I welcome you all to this lecture in the course Sandhi in Paninian Grammar. In this lecture we continue studying the Hal Sandhi or the Consonant Sandhi. Hal is a Consonant and Hal Sandhi is the Sandhi that replaces the Consonant. We classified Hal Sandhi broadly into two, Ekasthanika Ekadesha and Ekasthanika Dvyadesha. Ekasthanika Ekadesha is one substituent replaced by one substitute and Ekasthanika Dvyadesha is one substituent replaced by two substitutes. Ekasthanika Ekadesha is further classified into two Purpanimittaka Ekasthanika Ekadesha and Paranimittaka Ekasthanika Ekadesha. Currently we are dealing with Paranimittaka Ekasthanika Ekadesha mainly and this can be described in the form of a diagram where we have A plus B in the Samhita mode where B is the Paranimitta, A is Purva and in the environment of B A is substituted by C. So this is Paranimittaka Ekasthanika Ekadesha. This is Paranimitta, this is Ekasthanika, this is Ekadesha. So A plus B is the input and C plus B is the output. The next Sandhi that we are studying after we studied the Scyttva Sandhi is Scyttva Sandhi. This is stated by the Sutra Shtuna Shtuhu 8441. The Sutra Shtuna Shtuhu consists of two padas Shtuna and Shtuhu. Shtuna is instrumental singular of Shtu. Shtu consists of shah and tu. Tu means Tavarga. Tavarga stands for the five consonants Tathadadhana. So Shtuna means in association with or in combination of shah and tu that is Tavarga that is Tathadadhana. Shtuhu is one slash one of Shtu which is of course once again composed of shah and tu. So Shtuhu means the substitute Shtu. Shtuhu is the word that is continued from 8444. Shtuhu is 6 slash one of Shtu and Shtu is composed of S and tu. Tu means Tavarga and Tavarga means Tathadadhana. So Shtuhu means in place of Shtu. Having put all these together the meaning of Shtuna Shtuhu is the following. In the close proximity of sounds in the combination of shah and tu in place of Shtu substitute shah and tu. I repeat in the close proximity of sounds Samhitayam in the combination of shah and tu Shtuna. Shtu is composed of shah and tu. Tu means Tavarga, Tavarga means Tathadadhana. In place of Shtu, Shtu is composed of S and tu. Tu means Tavarga, Tavarga means Tathadadhana, substitute shah and tu. Tavarga that is Tathadadhana. So in the close proximity of sounds Samhitayam in the combination of shah and tu Shtuna in place of Shtu, Shtuhu, substitute shah and tu Shtuhu. This is the meaning of Shtuna Shtuhu, the sutra stating the shtutva sandhi. We note that the principle of Yathasankhya our correspondence also functions in this particular sutra just as it operated in the previous sutra, Sthuhu, Shtuna, Shtuhu. What we mean to say is that there is Yathasankhya relation that exists between sthani or karyi and adesha or karya. So sthani and adesha or karyi and karya amongst these pairs Yathasankhya exists. We also note that also in this particular sutra there is nimitta of similar numbers. But there is no Yathasankhya between the nimitta and the sthani as well as nimitta and adesha. Nimitta and sthani or karyi and nimitta and adesha or karya they do not share this Yathasankhya relationship. So Yathasankhya relationship can be shown in the form of an equation in this manner. If we have Shtuhu followed by Sthuhu in the Samhita mode then this Sthuhu will be replaced by the consonant Sthuhu in the left hand side environment of Sthuhu. Similarly, if we have Shtuhu plus na, na occurs at the fifth position in the tabarga and so this na will be replaced by the fifth consonant in the set of the adesha namely na. This is how Yathasankhya principle will work. Now if we have para nimitta ka ekasthani ka ekadesha, this was the case where the nimitta was purva. So purva nimitta ka ekasthani ka ekadesha. Now in this case where you have the nimitta para and this para nimitta is causing the substitution Sthuhu then the substitute that comes in place of this is Sthuhu. Similarly, if you have Sthuhu plus Sthuhu then since Sthuhu occurs at the first position in the tabarga, this Sthuhu will get substituted by the first member that occurs in the tabarga that is Sthuhu. So Sthuhu plus Sthuhu will be the input and Sthuhu plus Sthuhu will be the template output. Then we have Sthuhu plus Sthuhu and similarly because Sthuhu occupies the third position in the tabarga. So this Sthuhu will be substituted by the third consonant D in the tabarga. This is how the Yathasankya principle will work. The nimitta and the Sthahani or Kari, they do not have any Yathasankya relation. Now let us also take a closer look at the peculiar mention of the word Shtuna. Shtuna is a very peculiar usage because this is instrumental singular that is stated by Panini and this case indicates the environment for the substitution to take place. But this third case neither indicates only the left hand side environment nor only the right hand side environment. This was what was done by the fifth case and the seventh case. The third case Tritya indicates both left hand side as well as right hand side environments for the substitution to take place that is why this is peculiar. So Sthuhu will be both left hand side as well as right hand side environment for Sthutvasandhi to take place. So we can have Sthuhu plus Sthuhu as the input where Sthuhu acts as the left hand side environment or Purva nimitta but then this Sthuhu will still be substituted by Sthuhu and the output will be Sthuhu plus Sthuhu. This is called Purva nimitta ekasthanika ekadesha and when we have Sthuhu plus Sthuhu where Sthuhu is the nimitta but this is Paranimitta now even in this case Sthuhu will be substituted by Sthuhu. This is called Paranimitta ekasthanika ekadesha. Here are the template examples. So if you have Sthuhu plus Sthuhu as the input and the nimittas are all Purvas Purva nimittaka ekasthanika ekadesha. So we have Sthuhu plus Sthuhu and the generated output would be Sthuhu plus Sthuhu. Similarly Sthuhu plus Sthuhu and the output would be Sthuhu plus Sthuhu. Remember the nimitta and the Sthani and the Kari there is no Yathasankhya but between the Sthani and the Aadesha between the Kari and the Kari there is Yathasankhya. So Sthuhu gets substituted only by Sthuhu and nothing else. Sthuhu with Sthuhu, Sthuhu with Sthuhu with Sthuhu and Sthuhu with Sthuhu. Then when we look at the Paranimitta ekasthanika ekadesha we have Sthuhu plus Sthuhu and this will be substituted by Sthuhu plus Sthuhu. Sthuhu plus Sthuhu will be the input and the output generated will be Sthuhu plus Sthuhu. Sthuhu plus Sthuhu will be the input and the output would be Sthuhu plus Sthuhu. Similarly Sthuhu plus Sthuhu as input and the output would be Sthuhu plus Sthuhu. Sthuhu plus Sthuhu will be the input and the output will be Sthuhu plus Sthuhu and sa plus na will be the input and the output would be shah plus na. Then we have tathadadhana plus shah, tavarga plus shah, tu plus shah and the output would be tathadadhana plus shah that is tavarga plus shah that is tu plus shah. Similarly, tathadadhana plus tah, tu plus tah and the output generated would be tathadadhana plus tah that is tavarga plus tah that is tu plus tah. Then we have tathadadhana plus tah and the output would be tathadadhana plus tah. Then we have tathadadhana plus dah and the output generated is tathadadhana plus dah. Then tathadadhana plus dah and the output would be tathadhana plus dha. And finally, we have tathadhana plus rana as the input and the output is tathadhana plus rana. Let us first study the purva nimikta ka ekasthani ka ekadesha, where we have shah followed by sir and the template output is shah plus shah. Shah is substituting sir. However, we must note that this output does not result due to the application of other rules stated earlier in the Asidna section of Paninian grammar. So, Suta A 241, Shadho Kassi states that substitute ka comes in place of shah in the environment of sir. This is obligatory, always this happens, where ka comes in place of shah. So, if you have an example, this shah plus shah plus t, which is the future tense, this shah plus shah plus t, this shah, then we have this shah plus shah plus t and then this shah will be substituted by shah. So, we have this shah t. Now, we have shah followed by sir. In this case, this shah will be immediately substituted by ka. So, we have dek shah t. Then this sir will be substituted by shah and we have dek shah t and when we join them together, we will get the form dek shah t. So, shah plus sir has got no desired output, template output as is shown on this particular slides title. Next, we move to shah plus t. And the output is shah plus t. So, we have the example, dusha plus t, where shah is immediately followed by t. Since, this is within a pattern, the samhita is obligatory. So, this shah is the nimitta and t consonant is the kari or sthani and this t is substituted by t. So, we have dusha plus t and dusha t. Similarly, dusha plus tavya. Once again, we have dusha plus tavya and then this t is substituted by t. So, we have dusha tavya. Then we have shah plus t and t being substituted by t. So, the famous word shahstha is derived by adding the suffix e after the word shah. And then once you add e, paninian grammar adds the augment tha to this e. So, we have shah plus tha and e. Now, this tha is substituted by tha. So, the output generated by the sutra is shahsh plus tha plus e. And so, we will get shahstha. Shat kati kati paya chaturam thuk. This is the sutra that states the agama tha. Then we go to the next example, shah plus the, shah followed by the, which is the input and 8441 applies and the output generated is shah plus d. So, we have the example where we have mush plus danda. This is a compound. So, samhita is obligatory. So, this shah follows this d and so, in place of this d now, we will have to substitute the third consonant of the tabarga, which is d. But first we will have shah being substituted by d and this will be triggered by the sutra jhalam jashonte which we have already studied before. So, we will have the next step, mud plus danda and then this d will trigger the sutra 8441 because of which d will be substituted by d and we will get the form mud danda. Then we have shah followed by dha and the output is shah followed by dha. However, this shah gets substituted by d. So, we have mush followed by dhana and then this shah will be first substituted by d, mud plus dhana and then 8441 applies and substitutes dha by dha and so, we will have mud plus dhana, the output would be mud dhana. Then we have, then we have shah plus dhana and dhana is substituted by dhana. So, we have ushan plus us and the next step is deletion of uh after shah over here. So, we have ush, nuh and us and then this nuh comes in the samhita mode with shah and so, nuh gets substituted by nuh and so, we have ushnah. Actually, in this environment shah plus nuh 8441 will apply first and we will generate the same result that is nuh will be substituted by nuh. So, we can say that 8441 is redundant in this particular case. Now, after having looked at the purva nimittaka, ekasthanika, ekadesha, let us look at the purva nimittaka, ekasthanika, ekadesha. So, we have ush plus ush as the input and the output is ush plus ush. So, we have haris plus shahdha, here ush appears at the end of a padha and so, this sandhi is in between two padhas as part of the sentential combination. So, we have haris plus shahdha and the output generated would be harish and shahdha. So, when we join them together, we get harish shahdha. Similarly, you have manas plus shakara as a part of a compound and so, sir will be substituted by shah and you will get manas shakara. Then we have sir followed by t as the input and the output is sir followed by t. So, we have haris tika, here the sandhi happens in between two padhas, this is part of the sentence. So, we have haris plus tika and the output generated is harish tika, where shah substitutes sir. So, we have harish tika. There is a sutra written by Panini, chares taha. So, here we have chares followed by taha, where sir is followed by t and so, we have this sir being substituted by shah. So, we have chares and taha. So, chares taha. Similarly, manas plus tika and this sir will be substituted by shah by the application of 8441. So, we have manas plus tika, manas tika. Then we have sir plus th as input, 8441 applies and the output generated is shah plus taha. So, we have payas plus thakka as the input and this sir will be substituted by shah and so, we have payash plus thakka, payash thakka will be the output. Similarly, we have sir plus dha as the input and the output generated is shah plus dha. So, we have hares and dapaha and the output generated is haresh and dapaha. So, haresh dapaha, this will be the output. Then sir plus dha as the input and shah plus dha as the output. So, we have hares plus dhaukate. This is the example between the two words that is part of the sentence. So, we have hares plus dhaukate and 8441 applies and now this sir will be substituted by shah and so, we will get harish dhaukate as the output, harish dhaukate. This is the output and finally, we have sir followed by nir and in this environment 8441 applies and substitutes sir by shah. So, we have shah plus nir as the output. So, we have hares plus nakara. Once again this is the example of the sandhi that takes between two buzzers as part of the sentential combination. So, we have hares plus nakara and the output generated by the application of 8441 is haresh and nakara. So, we have haresh nakara. To summarize, we studied the second type of part of sandhi namely shtutva sandhi. We studied the sutra that states this shtutva sandhi namely shtunashtuhu. We also understood the literal meaning of the sutra. We also explained the meaning of the third vibhakti, third case tritiya vibhakti and then we studied paranimittaka ekasthanika ekadesha mainly. We noted down the template examples and studied the specific examples as well. We also studied the purvanimittaka ekasthanika ekadesha and we noted that these specific examples showed that the sandhi happens at different levels. Be it in between two buzzers external sandhi or be it in between the buzzer internal sandhi. We also noted that in cases of some inputs the combination outputs are not possible there the rule enjoys redundancy. Now we study next the remaining examples of shtutva sandhi in the next lecture. Thank you for your attention.


Alright, great. Well, welcome everyone to parts two and three of this last lecture series. There were some technical problems in the beginning we started a little late so I'm going to try to steal in this first half more or less on time, or maybe cut the break a little bit but try to add the second half, when it's supposed to. So we started talking about symbolic powers on Monday. And we're really focusing on the case of radical ideals. So the end symbolic power of an ideal is what I obtained when I take the ordinary power and a computer primary decomposition for it, and I collect all the minimal components. So you're going to take your power, you localize that all the minimal primes of I which in this case they're also the associated friends of mine, and contract back to our. So these are really the elements that live in your power up to maybe multiplying by something that's not in any of those minimal primes. Now, at the end of last time. I said a little bit about some of the many difficult problems about symbolic powers that people think about. And for most of today we're going to be talking about a problem known as the containment problem is very easy to phrase, but it isn't a difficult question and in particular. It's the question that sort of includes a sub problem, some of the other questions that I mentioned on Monday. So roughly speaking the idea is I'm going to hand you an idea. And I want to know which containments of this kind that can be so with symbolic powers are containing which powers. And many remarks to make maybe the first one is that this contains. contains some other problems. So for starters. This contains the quality problem that I mentioned last time. If you want to decide if a particular power is equal to the symbolic power notice. In fact, it was here in my reminders that the symbolic power always contains the power. And I'm talking about a sort of backwards kinds of containment. So really, if I can make these numbers to be equal. So, if a particular symbolic powers contain the power. That's really equivalent to asking for equality. So, in a way, you know what we really want to do this from a sort of best possible situation. And so, given the be I really want to find the best possible a that I can put in here. And the best case scenario is that I can make this number be equal to this one, a priority, it can be bigger it can't be smaller. So, you might, if you cancel this problem completely for each be finding the best a, you will in particular decide when you have a quality. But even if you don't have a quality, you can think of this question as a way of sort of comparing the, these two families of ideals you have your ordinary powers or smart powers. Compare the two really because you understand the powers really well, but the symbolic powers are much harder to understand. And so you want to sort of extract information about the symbolic powers from the powers. So last time I mentioned very briefly, that when you have a homogeneous ideal and a great ring symbolic powers are also homogeneous. And I asked about what are the degrees of elements in those symbolic powers and we saw examples where those degrees were sort of unexpected, right, the kind of the example we saw this sort of too low to be in the power but you might also, you know, see sort of unexpected things. Maybe let me introduce a little bit of notation that I actually will not use in the rest of the lecture but just to explain the problem. If I have a homogeneous ideal today. The smallest degree of a non zero homogeneous. The smallest element in J out of notice alpha. And notice that, you know, if you happen to know that a symbolic power is contained in a particular power. Then this automatically tells you something about these degrees. So if I want to compare the smallest possible degree of something in each one of these well. Obviously a bigger ideal might have things of smaller degree but whatever is the smallest degree of something in here that's also in here. And so this guy is bigger. So in particular, notice that the degrees of elements and the powers are really easy to compute like this is just the times whatever is the smallest degree of something I. I mentioned last time that getting upper bounds for this smallest degree is really easy, but getting lower bounds is what's hard. So somehow if you if you solve. If you if you get a particular statement of this kind, you might gain information about lower bounds on degrees on symbolic values. And in fact, there's been some some recent developments in terms of finding bounds on these lowest degrees that sort of involve not quite this containment but related related statements. We did useful to consider containers like this. And then there are the reasons you might consider this problem right as I said before it's sort of a comparison question. This is a question that first appeared in a paper of Senegal in 1985. But that really gains more traction. In the late 90s, early 2000s. And this starts, thanks to work of the NS one son. Who first understood a little better what it meant to say. Okay, maybe first let me say like this. So, chencel and others back in the 80s were interested in the question of when it even make sense to ask this. Right. So I was saying given a be I want to find the large, the best possible as the smallest possible a. But I haven't even addressed the question of whether that makes sense right given to be is there. We can make them all precise by saying that these two families of ideals are co final with each other. Maybe for the purposes of time. I won't write things. So precisely. But let me tell you about a theorem of nonsense, which was published in 2000, which essentially says that there exists an answer for the containment problem. So let me put it like this for all a is there's the. Oh, I think I'm switching the letters or no. For all these are existing. So really, there's an answer to the containment problem for all powers for this given I. So maybe let me clarify that I mean given I. So this is really equivalence to actually the existence of a constant see that presumably as I'm writing it might depend on your ideal I such that the CNN symbolic power is going to be the end power for all in. So you can think of this as sort of saying, if you can answer the containment problem. Your answer is no worse than linear, right the function that gives you the best possible thing you can can put in here for each end is worse case scenario linear function. And this sort of opened the door to trying to understand what what is this this constancy. So her proof didn't didn't give us, it gave us the existence of a city right it didn't tell us with what to see is explicitly. But even more surprising. Soon after inspired by this, there came an answer. Over regularings. So, I'm not about to write. I'm going to need a little bit of notation to write it was proved to receive I am not a fellow Smith, using the theory of multiplier ideals. And then soon after. They proved the theorem in characteristic P using type closure techniques, and then they use reduction to characteristic P to get the theorem whenever you're in the field. So it's going to be some theorem about regular range. And then, for a long time, this is all we knew. Very recently, thanks to Andrea solution of the direct summit conjecture using perfect like spaces techniques. We started seeing solutions to all these other questions and it's good to stick with opera. And one of the first things we saw. We sort of established a theory of multiplier slash test ideals and makes it interesting. And I think that's now officially, I want to say 2018. Do I have it here. Ah, yes. Their work require the ring to be excellent. And I'm not going to write a theorem about excellent rings. Thanks to work of the coming what I am. Who just a few months ago, so I think disappeared on the archive in November. So sort of doing similar things to my suite. I'm going to put 2021. This is not published yet. So it's very, very recent, but he was able to remove that excellent assumption so now we have a clean theorem for all regular ins. So this is going to be some answer to this containment problem. It's going to tell us over regular ring. Why is this constant C from Swanson's theorem. I just want some constant. That that is going to appear for a few weeks. For that I need a definition so I can write the theorem. You just tell me what the big height of an ideal is. So it's the maximum of all the heights of the associated rhymes of your ideal. Yes, in our setting our ideals are all radical. So you really just look at all the minimal times and deciding what's their maximum. So this is sort of a more honest version of the height than the usual one right the usual one is going to look at all the heights of your minimal primes and choose the smallest one. And I will choose the largest. So in particular for a prime ideal, right. So if, if I is prime. Notice that the big height is the site. But the fear we're about to write is a film that really requires this this big height invariance, we can't replace it by the height. And what is the statements. Well, let me say that I is radical of big height age. Do I need the assumption that the ideal is radical no I don't. But then we have to talk about, well we have to see a little bit more about what this invariant is the big height works but you can do a little better. I mean you can't do better for radical ideals this this is the constant that that you need to put in there. We also didn't define symbolic powers in full general. So the theorem. I talked to for so long you probably already guessed if you didn't know is that this one's in constant in this case is this big height. So, I'm looking at the time is maybe something I'm going to cut at the end so maybe let me make a comment right away. But as a beautiful consequence of this. We can actually take this one's in constant to be independent of the ideal. Because if you take D to be let's say the dimension of bar. That's the largest possible big height. Actually, we could take dimension of our minus one but let's not worry about that. It tells me in particular. If I take the D and symbolic power. That's presumably bigger than the H and symbolic power equal ideas, each or more. And so this guy is continuing here which is containing the power. But the amazing thing about this is that now we wrote a statement that doesn't depend on you, you have a uniform content to the works for all ideas. And this is sort of a beautiful thing that often happens. We have to sort of uniform behavior. So what we're going to do for the rest of this first half is I want to prove this theorem. So really we're going to cover the orchestra to make you prove in a computer to see P, and how we're going to do that. And, and the sort of really, we really will use very elementary characteristics techniques which I think, maybe to me this is one of the first terms I ever saw I really saw the power of characteristics techniques, because you know this is not, this is not an easy theorem. And, and the I was supposed to prove in a way, it's also sort of beautifully elementary in some sense, in the sense that you, you just have to show a certain string of containment. But it's actually very technical because each of those containments depends on some, you know, difficult properties of multiplier ideals. But I love how, you know, we turn this complicated theorem into something very elementary using type closure. So we're going to need a few, a few tools that you will prove as exercises. So, actually this one there. Well, okay, I'll write as exercise. It's spelled out with a few more details in the in the problem set. So first of all, we're going to need that if you take a regular ring of prime characteristics, then taking for being a specialist does not change if it would be a different. So, this is really a result of this can't be wrong. It doesn't actually need a ring to be regular but it needs the ideal to have funny projected mention. You write this down over a regular ring but the proof the right is essentially the same you're just going to use that you're able to have fun. Well, okay, maybe you'll use a little, a little more than that. But it is true more generally. So, one of the points of this is that remember last time we talked quite a bit about associated crimes and we said how one of the difficulties of dealing with symbolic powers is that it's really hard to study associated problems. And when you do things like taking ordinary powers. You lose control over your associate runs, but the beauty of being in courtesy P and being able to take for being as powers is that for being as powers do preserve associated problems. And this is going to be a key idea in the proof. And one more thing we're going to need. So we're going to prove a containment of two ideas. And we're going to need a very elementary factor the containment are local statements. So to prove a containment. You want to prove that I've contained in J. It is sufficient to prove that containment holes after you localize. Probably then this is an exercise when you're first committed as a book was. Maybe you did it for all crimes, or maybe you did this sort of final version that I'm going to need. I'm going to need that actually it is sufficient to look at the associated crimes of the larger. So if somehow you can control the associated crimes of the thing you're going to land on.  And now, thanks to this. The first part of the puzzle, I'm going to call it a theorem business call the theorem in my notes to me this should be a letter. This is, I'm about to write my very favorite version of the principle. So what is it. If I have a radical idea. If I have a high age in a regular ring. Then, if I take. So I want to prove something about the HN symbolic power being contained in the end power that's my goal. But now I'm going to prove that that's true for powers P. And I'm going to prove one better. I'm going to prove that I can land in the for being itself, which is smaller than your name. I'm going to prove. So step one, by the last exercise I just went down. It is sufficient to prove this at the associated primes of the potential larger. So I just want to focus on the associate of friends of this guy so sufficient to show after localizing. So the associate of primes. And of the convenience. But then the first exercise I wrote down was that the associate of friends of the previous power are very well understood to be associated friends of I. So we only need to prove this containment holds after we localized at all associate of primes of. Let me write Q instead of P, just because he's the character steak and having two things. Okay, so I need to prove this containment actually localized in the associate prime of I, I was some radical ideal so I'm really talking about the minimal friends I.  I localized an associate prime of it. Well, I just had an intersection of a bunch of primes and I localized that one of those. The remaining crimes are going to become the whole thing so I'll just get that one prime. So after localization, this is a statement about the maximum ideal. In what is now a regular local ring. And also the taking for being is powers. It's easy to show that that's something that commutes with localization. So again in the localization IQ is just the maximum ideal. So what we need to show. I'm going to rewrite a statement now in this sort of easier local setting. So I have a now I have a local ring in fact I have a regular. And I want to prove a statement about the maximum ideal. Well okay maybe there's a little bit more that I still need to do. So, and on this side when I localize, I is going to become the maximum ideal. And I'm going to take it for being it's power. On the other side. I have a symbolic power. The symbolic powers remember are the things I get when I localize at the associated crimes and saying, saying something different that's written here these are the same my guys back. I'm going to look like that each of those primes, and then look like the power can drop back. So if I don't take this and I localize again. So if I take my symbolic power and I localize I just get the ordinary power. Now I'm here. When I take. I hq. And I localize you. That's like taking IQ, which is our maximum ideal now remember, and just taking an ordinary power. Again, because I localize it on one of these. So on this side I have my maximum ideal. And I took it's ordinary. So what I need to show is that in a regular local ring. Something with less to understand here is what is the age have to do with anything. Well, it was the big height of I. So it was the largest height at one of these cues that I might have localized that. So what I know about this regular local ring. Sorry, I'm calling it are now. Well, it's dimension. Maybe let me write up here it's dimension is the height of this prime that I localized that. And that's at most the largest height upon us to see the final high, which is that the height. So I might as well pretend that each is the dimension of my ring because I know the dimension of my ring is that most worse case. And now we want to prove this. So this is what we'll start now. Now we can pretend this is the theorem. And this is what I'm going to do. And now yes I said earlier this is my favorite version of the vision hope principle, and this is a very easy application of the picture. Why, well, my ring is regular. I know about it. So since my ring is regular. I know that this maximal ideal is generated by at most each many things. Like, it might actually be that the dimension is something smaller right that this was a minimal primary smaller height that the big height but it doesn't matter I can always choose each things that are going to generate this and so really now I want to show that when I take an ideal generated by each element, and I take an HQ of power that is contained in the Q for Venus power. So I really want to prove it. Now, it is of course sufficient to think of generators of the power. The power is generated by monomials on these axes. So the generators here are things that look like monomials on the axis. And what you know about them. Well, I guess if I wanted to pick a minimal set of generators I could even be this equal to let me just say bigger equal than HQ. So for all the monomials of this kind I get a generating set for this ideal. And so if I prove that all these guys live in here I am done. But what does it mean to be in this ideal. Well, I just need to check that in this monomial. I need at least one of these powers so I mean at least one of these ai to be at least. Well, this is where the pigeonhole principle comes in.  They sum up to HQ. If none of them was bigger than Q. Right if they were all up to Q minus one. Then no way they could together sum up to HQ. So this is automatically actually let me raise the need this is automatically going to get me what I want. I have each many things summing up to HQ with least one of them. And so therefore, sorry for the funny writing, this guy, this generator is indeed a different. And so the thing that we proved after all this so we reduced to the local setting. And then we apply the pigeonhole principle and show that the HQ symbolic power is always containing the Q's to be in this power. Any idea a radical idea of high, a big high age. So no, I can do better. When I was applying the pigeonhole principle. I only needed that at least one of these guys was at least. Yeah, it was at least Q. So I wanted to conclude that at least one of them was Q. So let's apply the pigeonhole principle a little more carefully. How do I make this fail. I want to conclude that one of them is Q that the worst or best case scenario depending on how we look at it is that of these age many things that they're all smaller than Q. Right. So, if all of them were Q minus one or less, actually follow them were exactly Q minus one right, they would sum up to eight times Q minus one. So in this situation, it would fail to have one of them to be at least Q. But now if I go and I add one more. Over here. Necessarily, at least one of these must be Q, right, because we took sort of like the extremal case and we added one to that. This is the best thing that the pigeonhole principle can possibly tell us. So we can improve our theorem to say that the HQ minus H plus one symbolic power I'm just distributing the age. It's contained in the Q for being a seller. Okay, so this was the key piece of the puzzle. And it was, like I said, it's just the pigeonhole principle. This is what I think makes it so beautiful. Now we're ready to prove the theorem. The theorem, this is the Hawks are going to be a paper from 2001. You have a regular ring. But now I'm going to say that it has crime characteristic B. I'm going to take a radical ideal. We've been high age. And we're going to show that the H and symbolic power is contained in the end power. We have already proved this in the case one ends of power. Now we have to do all the other things. So how do we do this. Let's fix and then we'll prove the statement for this particular end. So we're going to take a U in the H and symbolic power. And what we're going to show is actually that you. Well, I wanted to show it's in the pattern, but what I'm going to show is that is in the type closure.  You've been talking about type closure for months now.  Your ring is regular. If you like it, weekly F regular. And so that all ideals are tightly closed. And so in particular, the type closure of the power is just the power itself. And so by proving and living the type closure, you prove you are in. That's right. So I see a question in the chat. The maximum ideal should be generated by as many elements as a dimension of R. That's correct. So if we go back here, this is what we use in this group. We had reduced the problem to the local setting.  So this maximum ideal was generated by as many elements as a dimension of R. Well, but now R is not my original R. So this is my fault for you in the same letter, right? Now this is my localized ring, right? I took the original regular ring and I localized and associate a prime of I. So the dimension of this localized ring is actually the height of the primary localized that. And what you know about that prime is that it was associated to the convenience power. So it is associated to the original ideal. And by saying that H is the big height, I'm saying that H is at most, sorry, H is the largest of all the heights of all these cues. So for whatever cues that you localize that you always have this in the cloud. So, you know, and for the cues that have actually smaller heights, you know, you could maybe take less elements here, but for at least one of these cues, you will need, you know, the full on age elements. So I'm not saying these are minimal generators for any particular reason. Does that answer your question? Okay, thanks. Wonderful. Any more questions anyone want to ask? Please do interrupt me. Okay, feel free to interrupt me anytime now I open the chat. And so I will be, I'll be trying to pay attention. Okay, so coming back here we're trying to prove this containment. So we've remembered our ring is regular so we're going to take advantage of type closure. So we're going to take an element in the symbolic power prove it's in the type closure of the power. So I know you're all experts on type closure now this is the very final lecture series of this workshop. And so I barely have to remind you of this but it's early morning it's been a long few months so let me write down what we want. So, you will show that there exists some C. I guess my ring is a domain so I'm just going to say it's a non zero C such that C times you to the queue is in I to the end to the queue. Well to be in the type closure I only need this for a large queue, but I'm actually going to prove that for all queue this happens. I'm going to find a C independent of you that makes this happen forever. So it's very much in the cycle. Okay, so now you'll see it's just simple calculations. So what will we do. I fixed them to begin with. And I guess I fixed you but for now ignore the view. I fixed and so let's use the division algorithm, first thing you learn in the first out of the class. But division algorithm. Oh, I'm doing this backwards. I'm going to now take half. Okay, now. So for each queue. So for a minute, I'm going to fix you I guess in my calculation. But then in the end you'll see that what I'm going to end up writing we're not involved use at all. Okay so temporarily I'm going to fix the queue. I'm going to take this queue and I'm going to apply the division algorithm. I'm going to use the remainder so it's at least zero and it's smaller than them. So divide q by n is essentially the point. And now, and I guess I can say, also, a at least zero because choose bosses. Okay, so with this. I'm going to start with my you that we have done I to the age at this is where I started right remember, and I want to end something like this. This is my goal. I'm going to put it on the side so we can see it. Okay, so I started here. So if I take you to the a. It lives in the symbolic power to be a. So if you remember our lecture on Monday, we said that when you take a product of two symbolic powers. This lives inside a symbolic power. Well this is a product of multiple one, but when you take about two, it lives inside the symbolic power with order to some of them. So I took a product of a many things that were the same. I guess I'm going to add hna times. So I'm going to live inside of here. I'm not equal, but I have a team, which is all in. Next step, I'm going to now take my you to the a. And I'm going to multiply it by i to the agent. So this is really inside i to the agent times the symbolic power. I'm just using, I'm using the previous slide directly. Now, remember that we said that the ordinary powers are we contained in the symbolic powers. So you can think of this now as a product of symbolic powers, which is contained the symbolic power of the sun. I'm writing a really complicated looking thing. But I am going to do this one better. Actually, sorry, erase this, I'm going to replace it by something slightly better. I'm going to note that this remainder are kind of just by division algorithm is something that's strictly smaller than n. So if I take a smaller power, a smaller order, right, the power is a bigger ideal. So this guy is contained in here. And I guess I just said the power is contained a symbolic power. So here I'm just using and bigger equal actually and strictly bigger than our, but I just needed to be equal. And then I use the power to continue the symbolic power. And so I'm going to do the same thing I was writing down earlier. But now I'll play HR. Now the beauty of this is that this is I to the age times a n plus R. This is Q, right, it's up here. This is Q. So this is I, HQ. So so far this long string of things, I conclude, tells me that I to the age and you to the a is in I symbolic HQ. So this is at the limit that we put we call the theorem that for this one, the pigeonhole principle. What is the pigeonhole principle say he says that when I take the HQ symbolic power. So whenever I take a symbolic power that at each times about P, I land in a for being as power. So, I'm going to use this. This lands in the for being as power. So we're almost there. I'm going to take powers of n on both sides. Right. So, take a power of n here you get h n square. Take a power of n here you get a m. Oh, this is contains the exercise that we're going to use again today that symbolic or ordinary powers and convenience powers commute. That's not true. This is what I almost said online, right, ordinary powers. Community. For being a source community products. Elementary. I'm going to do just one more silly thing. Notice. Q is a n plus R. Let me write that Q is a n plus. So in fact, when I make a very silly statement. Q is at least a n. So if I had written I to the h n square times you to the queue. That would, that would be inside of here. When we write that out. And that would be contained in either the end. So what do we do all this. Because this power now. First of all, you see that there's no q's involved in that power there's just Asian n square, nothing else, no, no q's involved. So this is independent of the, and more over, you know, our is a domain. Our is a domain and I is non-zero. I should have said that in the beginning. Okay, I'm going to put that in my assumptions that I think we all agree that the theorem we're trying to prove is silly. So it's a zero idea. So we're not going to consider the zero ideal. When I take a power of a non-zero ideal in a domain, I get a non-zero idea. I have a non-zero ideal. There's nothing to do with q. I can choose a c that's inside of this power. And now choose that favorite c that's independent of you. And you conclude that this happens. In fact, this was true for all q. And so we conclude that you live in the tight closure of this power. And this is the definition of living the tight closure. I mean, better than that. But our reading was regular. And as we said in the beginning, the type, ideals are tightly put. So this is either the end. So indeed we proved either the hn is contained in either the end. And we started about eight minutes late. So I'm going to, I went three minutes over in this first part, but I think I'm going to, this is a good place to stop. I'm going to stop here. We're going to take a seven minute break. And then we're going to resume at the time we were supposed to at the, I was going to say, 9am, but that's not true for everybody. So that's the hour in six minutes. We will resume. But if you want to ask me questions in the meanwhile, you can. I'll pause here for a minute. See if anyone has questions. I do have one.


There are times when one's imagination doesn't do justice to reality, and the opening of God of War 3 was one of those times. The end of God of War 2 promised an epic clash between Kratos the Titans and the Olympian Gods, and the sequel immediately over-delivered, riding on the back of Gaia, ascending to meet Zeus atop the famed Mount Olympus, the tale commences. And so the game just thrusts you right into it, walking atop a behemoth fighting enemies, getting acquainted with the controls, when suddenly, Poseidon jumps from atop the mountain, taking a Titan with him into the water below, spawning appendages that start pulling at Gaia. The camera is fixed, as old God of Wars were, to frame the scale of this conflict in full, other Titans climbing in the background, when suddenly, a horse-like water creature with scorpion legs breaks through her body, and the first boss fight begins in earnest.  The camera returns control to you, dangling on for dear life as you fend off this hybrid creature from the bowels of the Lord of the Seas. Kratos overcomes this of course, with the aid of trusty quick-time events, and lands on Mount Olympus proper. As you make your way up, Gaia is still entangled with Poseidon's minions, so you rush to her aid once more. However, this time, it's Poseidon himself who appears, one of the three main Gods of Olympus, and the battle commences. The fight is relatively straightforward from a mechanical perspective, it is still the beginning of the game, but the sheer visual splendor here is astonishing. You have to dodge claws, aerial attacks, and electrified ground, but the hardest part of this is simply not staring at awe at what the PlayStation 3 is rendering. Gaia, although reeling, lends you her assistance, and you find a way to snatch Poseidon's body from within the watery chaos. The next part, quite graphic, is Kratos' maims Poseidon and the second person. After this, of course, you reach Zeus, who kicks you off the top of the mountain, and Gaia betrays you as you cling on, saying you were only a tool for the Titan's retribution. Thus concludes the opening 30 minutes of God of War 3. Part of what makes this opening so enduring isn't just the scale or the cinematography or pacing, but the sheer spectacle of it all. The God of War games are known to start off with a bang, but this was on another level entirely. Incidentally, the rest of the game never quite reaches the heights of this opening, perhaps with the exception of the Kronos fight. Regardless, few games even today I would argue can match God of War 3 in terms of pure epic spectacle. The word epic is somewhat superficial nowadays, more associated with memeing and internet slang, but there was a time epic referred to foundational stories in the midst of cultures. The Epic of Gilgamesh, one of the first stories in Mesopotamian culture. The epic is viewed as a core text in the evolution of storytelling, myth and heroic sagos. The epic used to be about universal stories of heroism that invoked the creation of cultures and civilizations itself, and now we associated more with pure spectacle. Beowulf, the inade, Mahabharata, these transcend cultures. Now we have the epic fail. Somewhere between these two poles lies a game like God of War 3, invoking the clash of gods and titans and archetypical story structures, whilst also being about pushing the PS3 to its limits to sell hardware. Kratos is hardly a heroic figure though, at least he isn't yet in God of War 3. He is an angry rage-filled maniac hell-bent on destroying the gods for tricking him into killing his own family. He is trying to defy fate itself, tearing asunder institutions and the world in the process. Every god he kills leaves the world in a more perilous state. How are we to read this story from an epic perspective, a tragedy, surely? Maybe in God of War 3 and games of this ilk, we see a new meta-narrative about our relationship to gods, deities and foundational institutions, a kind of want and disregard for authority of any kind. Let's take another game in my newly coined tradition of epic spectacle, Bayonetta. In it you play as a witch who is supposedly the unholy spawn of the lumen sages and umbra witches, which is of course historically persecuted in movements of mass hysteria, but here the marginal is rendered as heroic. Who are the antagonists? Why it is the church of course, angels and servants of God, an inversion of moral categories. Bayonetta has to topple a repressive dogmatic religious order, with the flamboyance and flair of witchcraft and demonic power. Spectacle also defines the opening of this game, as you take control of our witch atop a falling piece of debris descending from the heavens, being attacked by the legions of heaven. The game sees fit to inform you about the lore at this point, not that it's easy to pay attention to. The set pieces only escalate in sheer absurdity as the game progresses, fights against literal cardinal virtues. Like this one, jumping from pieces of geometry as a weird tentacle atrocity flings debris at you in the midst of a tornado it is creating, followed by a set piece that takes place on a highway, where you jump from vehicle to vehicle, and then take control of a motorcycle yourself, a clear homage to games of the past. Who can forget this boss against a creature reminiscent of a metal gear, as you surf across the water attacking its weak points, and then get dragged into a vortex that you have to surf around to finally incapacitate this behemoth. Perhaps the most memorable parts of these bosses is how you dispatch of them, using giant demonic summons to torture them into oblivion, clearly invoking the imagery of some well-known sadistic practices, Bayonetta herself, expressive and flamboyant, and as extra as you would expect a person doing these things to be. The game however saves the best for last, as you not only take on creatures of unimaginable scale, but ride atop a motorcycle going upwards before transitioning into an animal form, gravity be damned to reach it.   I could talk about Guide the Board's book, The Society of the Spectacle, where a critique spectacle is a force that replaces authentic human life with its representation. The media, commodities, these distort our perception of ourselves and the world around us. We are mediated by images and not reality. How does this relate to games? Games are a representational mass media form, yes, but they have been co-opted by industry and technology. New consoles are sold on the promise of spectacle that only cutting edge technology can provide. Rendering technology in polygons and ray tracing, spectacle has been commoditized and is used to sell immersive experiences to the masses. How does one overturn this? Perhaps by a process called the Tourne-Mont, turning expressions of the existing system and its media culture against itself. Or recuperation, the process by which politically radical ideas and images are twisted, co-opted, diffused and incorporated into a socially conventional perspective. I suppose you see where I am going with this. Kratos and Bayonetta are not conventionally heroic.  The epic has been co-opted by these games to sell spectacle, but spectacle in turn has been co-opted to reinstitute a new kind of epic. Enter Asura's Wrath, a game that almost strips gameplay away entirely in favor of pure spectacle. This wasn't instrumental in selling to the masses, the game didn't sell very well. But what it was was ridiculous in the best possible way. We play the demigod Asura who seeks vengeance against the gods who have wronged him, which sounds very familiar. Instead of Greek or Christian ideas, we get Hindu and Buddhist mythologies instead. The gameplay switches between arena style combat, on-rail shooting segments and quick time events, an experience that is often described as an interactive anime. These games all seem to want to start with a bang. Here you guide Asura through space as you lock onto enemies in space to be alike, a cacophony of screams and explosions lighting up the screen. To say this game has set pieces renders the term useless, the game is a set piece. Genres blending, cutscenes frequently interrupting, but the spectacle never abating. If it wasn't clear, Asura is angry. Of course we move towards destroying Deity's reminiscent of sacred figures and mythological text, but it's what happens on screen that is more of note. On the surface of the moon, against giant elephants and a space armada, I have never had as much fun mashing buttons and doing quick time events as I did in this game. It is unapologetically spectacle driven, that there is an earnest story amidst the chaos about a grieving father might make it more likeable. One part sees Asura laying on the ground when he is powered up by a mantra reactor and repeatedly mashing a button. Then you fight falling from a platform in aerial gymnastics to then proceed to space. See talking about what happens in this game is almost incoherent in the best way, you simply have to experience it. What is more readable, ironically, are planet sized enemies that use their finger to squash Asura, only to have his rage ignite the behemoth from within. Like stated, Asura's wrath is more anime and manga than it is game to some perhaps. As an experience though, it is way more than the sum of its parts. An epic about loss and wrath, couched in the symbolism of ancient mythology, but ultimately an interface experiment in handing spectacle to the player. It is interesting that God of War and Bayonetta are sometimes referred to as spectacle fighters. Their gameplay is spectacular in a different way. God of War and how you can brutally dismember enemies and chain combos using the blades of chaos, and Bayonetta with its instant dodging and witch time slowdown effects. Asura's wrath has combat but it is much more muted in terms of player interactivity. The thing is this might distract from the spectacle. The most pronounced set pieces in these games minimise interactivity because it can mess with the pacing it seems, on top of facilitating bespoke mechanics for different scenarios. This is also true of Final Fantasy XVI and its epic icon battles. Its mythology is far more wide-ranging than the aforementioned games, drawing from Middle Eastern, Asian and European myth, Bahamut, Shiva, the Freight.  This starts as a quest for revenge, but turns into a journey to destroy the mother crystals. The icon battles bid two creatures of mythological proportions against each other. You play as Clive slash Euphryd, or sometimes as the phoenix. Once more we see battles of unimaginable scale come to life. The battle against Titan is a standout to many, but decidedly uncharacteristic rock score starts playing as you run at this Titan. Then you climb upon this monster and do battle with him as a sandstorm blusters around you. You make your way to a more stable platform and fight this boss in a more conventional fashion, but then you get launched into the sky and have to shoot at debris being thrust at you. Using his body against him isn't enough, and a final phase of you falling through the insides of this colossus takes place as triumphant orchestral music starts playing. Then there's Bahamut, which starts as a grounded fight in an illuminated arena, which then takes the skies in an on-rails shooter section, before literally taking you to space. The abilities of Euphryd and the phoenix combining, allowing you to choreograph your fight in the middle of nowhere. Again, the interactivity is somewhat minimal, dodge and attack, but that's almost missing the point. Spectacle isn't informing interactivity, as much as interactivity is in service of spectacle. What is the point of the spectacle, though? What are we actually doing here?  He has lived in suffering as a slave for years after the death of his family, only to find renewed purpose in challenging these icons of divinity. I'm not trying to argue that there is some hidden profundity to the spectacle in these games. They are just glorious to look at and play, but it is fascinating that there is a common motif across these. Anti-heroes driven by rage to topple a corrupt order of some kind, but invoking the symbolism of epic myth to represent that which must be torn apart. We side with the marginalized, the vengeful spirit and revel in the epic spectacle of games.


Good afternoon! Welcome to the UR Come live tour of the Maple Hill neighborhood. My name is Courtney. I'm a junior here at the University of Arkansas and I'm from Fayetteville so feel free to ask me any questions about the campus or the city or whatever you can think of. Behind the camera today is Channing. I'll let her introduce herself. Hi guys, my name is Channing. I am a senior communication major on campus and I am from Springville, Arkansas which is right next door to Fayetteville. So if you guys have any questions today, please comment them throughout the video and we will be sure to answer those for you guys. And let us know where you're from. Yeah, we're both from Northwest Arkansas so we like seeing where people are coming from. Before we go in I'm just going to show you what's surrounding us. So right under that awning over there you can see it in there. There's something called Club Red which is just like a little convenience store. There's snacks and coffee and drinks and a bunch of good stuff in there. I lived in Reed which is actually right over there and so on my way to class I would stop there and get snacks all the time. And then right down this hallway is the Fulbright Dining Hall which is your closest dining hall so you'll probably be going there a lot. And then if you can see over here in the bottom of this building there's a little restaurant and you can actually use your meal tray there at night so you can just go and use one of your swipe and they'll have like chicken nuggets and just all the good stuff there. I went there a time so that's really nice. And then there's this giant field that's used for all sorts of things. People are always playing frisbee or catch or football and then sometimes there's even events like they'll get a big blowout TV and they'll have a movie night out here so there's a lot of stuff going on in this neighborhood. Really nice. Looks like Carol says hello. Yeah. Thanks for watching. Is this a tour maybe right in front of us? I think this may be a tour. We'll go ahead and sign. Even as we spin. Bye. We have that so don't leave the door open. But you do have fobs for security so if you live here you'll just swab in and then you're good. We're actually in the common space right now. Maybe from the south. Yes we're in the south. I'll show you. Security. A big study space right here. Yeah this is really nice. Whenever you want to get out of your room and just hang out. Fireplace. Yeah cozy little fireplace. I really like this room. It's really cozy. It's a big good place to make friends. Common areas are really good for that.  These are pretty big neighborhood. I think about like 900 students all together by a few. So we're lucky enough to have CREs with us today. Do you guys want to introduce yourself? I'm the CRE or Hall Director of Maple Hall West. I'm Lene Patterson. I'm our third four south is currently out but that is Jake Talley. Yeah do you want to kind of tell them what you guys do around here? Yeah definitely. So a Hall Director is basically a live-in professional. We have master's degrees. We're here to serve you as our residents. We also oversee the RAs and we actually live on campus as well. So our experience is kind of similar to yours in that we go to programs. We interact with faculty and we also work within the housing office to make sure that the halls are safe and that you enjoy our event. So they're going to be going on tour with us today so if you have any questions. Got people that know it all. We've got the front desk right here. How does mail work in Maple Hill South? We've got different mail boxes that are out here so you'll actually be able to come pick up some of your mail from the boxes that are here in the lobby and if you have a package you should receive an email that says they have a package to come pick up. You can come to the front desk here if you have like a large package that needs to be and we do have limited hours when you can pick up that package so when you move in just ask your area for more information. Thanks. Hey good to see you there. Now they may see you. What's your name? Johan. Yeah so you may meet Johan when you come down to Maple Hill South. Awesome. Thank you. Nick said he was an RA here and he loved it so that's awesome. Thanks for joining us. Yeah we're going to show off some of the outside bases before we go. There's a lot of places to hang out out here. This is a really big neighborhood. There's a ton of green space here which is really nice especially if you're maybe from like Central Texas or something like that. Oh yeah. Lana Green. There's a lot of people from Texas. Oh yeah. And so now we're coming up to East and West. West will be on your left and East is on your right. Fire pit so sometimes like roast marshmallows or just different things. Yeah so we do have a grill. We do a lot of outdoor programming. We do a yoga class out here several times a semester. It's just a great space to like throw a ball around or if you want to sit out in the sunshine and get your vitamin D for the day it's just a great spot for that. Yeah so like we have those spots where students will come out and set up hammocks and just kind of relax and lounge around. The hammock. Yeah there's always hammocks. Big part of college. Yeah this is where you can find all of our residents like on a nice fall day or right before a football game they like to chill out down here because we're a couple minutes walk from the stadium which is a great feature. Nice. We have what 62 people watching so yeah just let us know where you're from. We love to know that. Yes. I like the red brick architecture quite a bit. It's a very classic university. You show the fob. It's a fob system. We also have a pool table in Maple East so if you want to play pool we have that improved for that equipment it's all behind the desk and that's also where you go pick up your packages as well. That's our study room. Very cozy. There's a lot of just open space. Sure. Now you did read right? I did. Did you ever come here? I did. I did hear a lot to study with friends. They have whiteboards in the study rooms which are super nice especially like I remember when I was in Anatomy we would always use the whiteboards in here to study. We just worked by a water facility where you can bring your own bottle and a lot of people do in fact do that is bringing their own water bottle. Carol asked if we're currently in East or West? East. Maple Hill East. So even if you're in West you'll pick up your mail in East and some of the study notes and spaces like common spaces are available to you as well here at West We've got a question for about fobs. Do you know are you fobbed by building or when you're with maples you can kind of move throughout the building? To my knowledge if you're a West resident you can fob into this space so this isn't actually residential it's not residential until you fob in again to go upstairs so the West residents don't have access to the East resident to my knowledge but this common area you would have access to that so that you can get your mail and enjoy some of the classrooms and common areas. Yeah some of the university perspectives are held here so you might have a foundation level course try and think what other classes have been held here I think some agriculture classes but don't be surprised if you might you know you might have a class in maple We're getting some questions about room measurements we are going to go up to a room a couple of rooms later on in the tour so if you have questions when we get to the room that'd be a great time to ask them.  Thank you. So now we're in the residential area. Yeah. I think we're going to look at this study area here first. Yeah there's one of these on each floor. Oh that's true. They're all kind of the same I guess aren't they? Our first floor is the only one that's different because it has an actual stove top so the other floors won't have the stove but you can't come down to the first floor and cook on the first floor. And do you find that people do come in and do some cooking? Yes actually we do have students that occasionally come in and like cook their own meal or occasionally they really want cookies so that's always a blast to watch students come in and make their own cookies and stuff. Occasionally we do have programs that come in here and we'll do like a big cooking program. What was the program? We used to do midnight midnight breakfast. Yeah that was like a fun like finals event but we also did a cooking and chocolate class. So we did chocolate tasting and they got to make their own pasta dish which was really cool. Some of the students have never cooked before so we do offer some of those cooking classes. It's one of those adult-age builds. Yeah for sure. It's important. Can you get your bean supplies before the next two? Yes we've got some cooking sheets, some baking pans and stuff. There's I think there's a queue for utensils and stuff so you should be able to get those with the equipment that you would need to make. You just need to buy the actual ingredients yourself. That's always fun. We make cookies a lot. You definitely have your cookie cravings and you can always set it in the air. A lot of study space you smell like. Did you hear the shoes all right? I am which is weird because I feel like I just lived in Reed. I feel like I just started. It goes by unbelievably fast. Yes. It's really sad. And you're graduating? Yes it'll be my last year next year. Time flies so enjoy it for sure. Do you know what's next for you? TBD? I love the whole city. TBD. The maple east and west and there's also a lounge like this in south on each floor so what you see here is literally mirrored in maple west. Do you do a lot of floor level programming or is it mostly building level? So our floors we like to have a like very fun friendly community so we'll do like little cooking nights things like that. We'll watch movies but as far as like our educational programming or like social programming we tend to do all maples so all three of the buildings will get together. We'll do a cookout or for each specific building we'll all do something together so like maple west we did a sushi night a couple months ago and we all made sushi and talked to the japanese student association so we do a lot of things like that. That's fun. So let's go check out laundry I think and then there's a study space whatever you for? Yes several. Okay. Yeah I think so that's really cool I don't know that we have that many buildings usually you're either going up the stairs or down the stairs and I believe it's right here on the left and there are two per floor so that's good to keep in mind. There's a countertop we use. We have an app called Laundryler so you can see the numbers and like the scanning stuff and machines so that you don't want to come check and make sure that something's available you can just check the app and then when you are using it you can scan the machine and put the number you're using and you'll get an application way to your stuff so you don't have to sit in your way on it. Yes super convenient. Yeah it's very nice and it's nice that there's so many laundry rooms in here so it will be offer. Good wipe one. Yeah are these used for like reminders of RA's right side lines? They write all kinds of stuff so if I write like to write like little reminders of like things that are coming up and then sometimes like encouraging words or if we have a program coming up or an event coming up soon we'll usually use that as advertising. Nice. And these are open 24 hours so you can stay in here and there's a big white order on the wall. Will residents have to bring their own expo markers for the whiteboards or are those provided? We have some for checkout but we would recommend just picking up a couple that way you always have some if you're not waiting for someone else to be done first. Yeah there are four of these study rooms on each floor in east and west. We have one that's like this which is perfect for group projects so it's like a conference style and then the other one which you'll see in this packet is more of like a lounge so like the one we just saw. Yeah we're going to check out the lounge too. Yeah these are definitely in use a lot especially finals week study rooms are crazy everywhere. Yes. So like you'll come in here and people will already be here or what's the etiquette around that? Really it's just first come first serve. First come first serve. Yeah first serve so they nearly swim but this one's more like a living room and did you say there's four on every floor? So four of these smaller ones and then one main lounge. Right. And the lounges on the first floor have an oven so you can make those cookies and then on the other floors we have like a microwave oven so if you wanted to like pop in I don't know like a lean cuisine or something. Yeah I like I always like having the option of being able to put because it just makes it feel like more at home. Yeah Yeah and actually if you don't want to bring a microwave in a fridge we do offer them so it's through like a third party but you can basically go ahead and reserve that and then it'll be ready to go in your room that's always a feature we like to tell our residents about we just don't want to have to move that in. You can go to movein.ur.edu and there's information about how you can rent I believe a refrigerator or a microwave and maybe some other things. Yeah that's like a whole unit so it's awesome. Yeah so let's go check out 416. 416. Which in this case is a loft style. It has that area up above but the first floor that you're going to see is very typical of Maple Hill residences. Do you want to head upstairs first? Yeah sure. The lofts are really cool. Oh yeah. Imagine a lot of people put their game systems up here or they're going to attain the console. This wouldn't be the typical style we have typically it's just the first floor but we did want to make sure people who had a loft knew what it looked like. Chase wants to know if you have to use this furniture that comes with it. So you don't have to use the furniture but it has to remain in the room. That is to say we would expect it to like when you check in it's there when you check out it's there because you will be charged if it's not. We're going to show this one. So now we're going to order resident rooms. So all of the rooms do come with this setup so you do have a bed that is loftable which means that you can remove this and move it up if you'd like to move the desk underneath or like you bring a futon or something you want some extra room to work with. You also have a desk which comes with drawers and then a chair which is actually more comfortable than it looks. It's very comfortable. And then you also have a wardrobe so sorry I'm a little tango with you here and you have another set of drawers here as well as a drawer on bottom and then you have room for all of your clothing items. Do you want to show them the chair trick? The chair trick? Yeah have you ever seen it? No I haven't. No one will show me. It's kind of like a painting there. Oh sorry. Yeah. So they're just a little bit in the back and then. Wow that's crazy I didn't know that. So you have a little side table on it.  And then you have a little ottoman thing you put your feet up or something. Yeah. Isn't that funny? A lot of people like I didn't even know. How should I figure that out? I don't really remember. One day. It's too funny. Yeah so you always have that option. Also this um laptop here's like a core board so you can like hit up those and stuff. It's kind of cool. A lot of students don't know about that so little no facts. We have a measurement question. Um can we get the width of the headboard? Yeah feet five inches. Perfect. Um and Nicole and Sano if you loft your bed high enough to put your desk under is there room for a headboard? A lot of these are really tall headboards because yeah if you were to put it up it would be about like probably about right here would be as high as you want it to be safely. From top of the headboard or top of this to the ceiling it's three feet. Three feet. Because you've lofted someone underneath that probably. Yeah probably right here is where you want to be and then we do have a stabilizer bar as well just so that it's safe. And then when you do a ride you will need to loft it yourself but we do have arrays that can assist and we have mallets and all you do is you just pop it off and you can stick it on top so. Awesome. Jennifer wants to know the measurements of the corkboard behind the desk. And Kelly wants to know other lights on the desks under the shelf. There should be a little twist light. I'm not sure if it's plugged in right now. Oh yeah. There is one. Yes there is one. Yep it's right under. And if for any reason that's not working then you can go to housing.uart.edu forward slash fix it and they can turn in a request there they will come and fix it for you no cost. Yeah so if a light goes out or anything like that you just go to that website and then they'll come fix it for you. Alina wants to know the measurement from the top of the window to the floor. I don't know if you can reach that. Let's see probably with an actual analog type measure. Yeah. See if we can't get it that way. Because I can get to I can get easily from here. I feel a little bit of math. Let's see that is approximately 37 inches to right here. Yeah. Can you give me a measurement can you give me the measurement from the top of that to the floor. That is 4 feet 9 inches. 4 feet 9 inches plus 37 inches. We are not math people. But there you go. Lauren wants to know the measurement between the two beds. And it will vary between room. Okay. So if you have a two person suite which means you walk in and it's one room with two beds that will be different than this. Okay. Just so that you're aware a little disclaimer. So like this there's four feet eight inches between the two beds. This all this furniture is movable. Yes. So you can put in whatever configuration you want. Yeah. Yes. See these a lot of different ways so you can always move separately on them. People get very creative. But again the furniture does need to remain in the room throughout the year. So when you check in it's expected that it's here and when you check out same thing it's expected that it's here. Awesome. We had a request for the measurement between the mattress and the bed post. So is there any mattress and bed post? Yeah. Yeah. They're asking for a headboard. It's going to be very small. Yeah. So the bed will push a little bit one way or the other. It's probably a matter of an inch maybe. Yeah. It's about an inch or two. An inch. Could you get them to the wall to the to the headboard too? That might be helpful. It looks like they're trying to build something. I mean from the back of it to the wall there's about five inches but a lot of people will just sit headboards in here and I know mine was probably about an inch or two thick and I could fit between the mattress and that. Sherry wants to know if the rooms come with cable, TV and ethernet. Yes. So they definitely come with cable and HBO. Yeah. Wi-Fi absolutely. Yes. We have a service called ResNet that makes sure that happens. Ethernet may or may not be in your room. We've been in a transitional period with that but you have a lot of Wi-Fi. Okay. Kendall wants to know can you remove the black bar on the side of the bed? The stabilizer bar. I personally don't know offhand if it's low enough if you can or not. Do you happen to know offhand? If not we can come back in and answer that question. Does the stabilizer bar need to remain there at all times? It's good that it remains there because it basically keeps the two sides of the bed from like collapsing in on you. So I would recommend that you keep it up there and we do inspections every so often just to make sure that it is still present. If it does go missing then you would get charged for it. So I would recommend just keeping it up there for safety purposes and if you loft your bed you'll just move it down a bit. Awesome. Elaine wants to know if they can take the headboard slats off? They are not removable. No. They are built into the wood. Yes. That's what keeps the bed up. It's the part of the bed. Yeah but people do decorate them. Definitely. You don't have to decorate it or put a headboard in front of it, whatever you'd like to do. Why Christmas lights are a thing? Yes. There's a lot of options. I've seen some very cute rooms. Stacy wants to know if there's a rod above the window? There is. So there is one up there? There is not. This was probably a modification from a student last year. So we are still going through the rooms and making sure they're good to go for all of you. So typically there's not a curtain rod but if you want to add one with a command strip that's really fine just be very careful of the paint. And then tension rods are commonly used. I don't think that one would accommodate a tension rod too. There is a little panel on top but if you, I mean maybe, probably not though. But then you did read where we have those slats as well. They have, sorry, lines. Yes. Did you have any issues with sleeping and sunlight coming in? I really didn't. My bed was right next to the window. We never got curtains. We just used the blinds next time. So not a necessity. Julie wants to know the measurement from the desktop to the bottom of the overhang shelf. Okay. Overhang shelf. That's not in here. There's a lip here that's probably four inches. In Meredith we are in a four person suite right now with a loft. So behind this little lip it's one foot and ten inches but if I go to it where's my laser? It's one foot seven inches. One foot seven inches. From here to here. Including the lip. Yes. Okay. We had a couple questions about the bathroom. Can we go in there really quick? The shower. Yeah. Thanks. And again it will depend on which suite you have. So sometimes those two person suites they have a little bit more room but you do have a nice spacious walk-in shower right here. It does have a built-in shelf. Yeah. I would recommend you get a shower caddy though because you will be sharing it with several other people. Right. It does come with a shower curtain as well. So just make sure at the end of the year it stays here as well. And then here is the toilet. And then there are some towel racks over here as well. One for each person. So that's nice. And you have room for a little shelf right here or if you want to put something on this side right by the toilet for towels or any other little necessities. You have room for that. This is a very typical bathroom right? Yes. I would say about yeah about more than half have this style. Typically when you have a two person suite you have a little bit more room to work with but there's not a lot of variation between them. And on the second I guess on the first floor we have our showroom. Do you know if we have any two person suites on this floor? The showroom should be a two person suite. Okay. Do you know if we have any on here on the floor floor? Yes definitely. Yeah definitely. I can show you one. Thank you so much. Sherri wants to know who cleans the bathroom. Yeah. Which is good because it's a great way to become independent, learn about you know what it means to live in an apartment if you decide to do that you know after college or as a sophomore. So yeah you will be expected to keep the space clean and that is a challenge for some of our residents but our arrays are here to help you. We also have cleaning supplies at the front desk that you can use. Awesome. We had a question about the measurement in this space right here. Okay sure. All right.  And then if I go from the end of the wall that's about two feet deep. Two feet deep. Okay awesome. Hope wants to know if you change out the shower curtain is it a special size? Any standard shower curtain should fit. You can just have a little extra room if you get like a larger one but it shouldn't be a problem. If you do decide to use your own just make sure to fold this and put it somewhere so you can put it back up at the end of the year. That way you don't get charged for the shower Good idea. That's a great question. Thank you for all the good questions. Yeah I think we're caught up. Okay. Want me to go look at that two person? Yeah definitely. And if for some reason we didn't get to your question we will be going back after the video and answering the questions that we didn't get to. Right here. Yeah this is going to be a two person this week. This is 418. And just as a reminder the rooms in east and west are identical so although we're showing the rooms in east just know that west is going to look literally the same. There we go. We're moving around here we can kind of get the idea.  Are we going in here? Okay. Yeah. Make sure to see how you can move these wardrobes anywhere you want. Yeah. That's pretty moveable. I love these little corner rooms. They're really nice. You have two windows. Yeah good lighting here. Yeah. And again like I said you have a little more room in the two person suite that you don't have in the four person. Chase wants to know what about the maple south rooms. Will they be the same? Yes they're the same as well. Sorry I forgot to add that. All the maples are designed to be identical. Now some of the layouts of the floor is a little bit different. So in south you have a long hall and then short holes on the end whereas in east and west you have like it's like perfectly like three proms if that makes sense. So the hallways are a little bit different but the rooms are identical. Okay well it's so much to know if we can measure the distance between these two beds in here. Yes I got it. It's six feet and four inches between these two beds. Nice. Any other measurements? Not right now. Well let us know. Yeah you can always go back and comb it like we said and be sure to go through and look at those and get them answered for you. Yeah it takes a little time because we're going through all the questions from the beginning of the York home live series but eventually we'll get here and we'll go back and answer those questions even if we answer them by voice. Bring less than you think you need because sometimes we do see students they get in and they're like I don't have room for anything so I would just say just bring less than you think that you need and if you want to decorate or bring more things you can always run home and get stuff on the next time you go home like if you go home on the weekend or we have lots of great furniture stores you can teach you math or just like that so if you want to buy a little something through your room that's a good option. Fable funky? Sure yeah it's a little other store. I just want to say like get excited and get, I'm putting my word but get pumped for the area. Yeah. I get decided to learn more about your roommate and campus and everything else that comes with living on campus and have an open mind to be willing to meet people. A week is going to be amazing so definitely like don't miss out on the events go to as many events as you can get to know your RA that's going to help you as a student and you're going to feel like you're really home while you're here. Yeah don't be afraid to go to your RA if you have any questions that's going to help you and make you feel welcome here. Make lots of friends because I really love you guys. It's awesome. I love all your fans. Yes. I have a question here so much and yeah it's just it's like a link you know. Oh yeah.  Yes. I just started it's crazy but I'm glad that I can show you guys around. Thank you for tuning in and be sure to check our website for our schedule for the other tours we're going to be getting. Yeah. Thank you.


People will provide an increased level of protection tomorrow. United States Marine Corps, aviation combat elements, rotary wing and tilt rotor squadrons. As you see, we're very, very busy.


Islam preaches us to stay united but at the same time we have to tell our generations about the injustices caused by those revered by members of the other sects. How do we draw the fine line between maintaining unity along with telling history to our younger generations? Unity is not that I hide what I believe in, it's that I recognize that there are others who may have reached different conclusions to me. I can still give lectures, I remember there was a certain time in the Iraqi community in London I remember when I was lecturing maybe about 12 years ago where people were saying that you know don't mention too much about Imam Ali and Ghadir and Jamal and Saqifah and you know try you know let's talk more let's bring more unity. I did used to wonder at the time that you know maybe they're right maybe we don't need to talk this much about our beliefs then I realized no you talk about your beliefs openly but you recognize that there may be others who differ with you, there are others who've taken different theological paths to you, there are others who drink from tap water while you drink from avian, you know you got to appreciate that these things happen. So secondly I think trying to maintain as much respect while you're talking about certain sensitive issues as difficult as it may be when you talk about these tragic moments and Islamic history but now for example in the UK myself other lecturers we've had our times where we've debated issues within our communities we've had our times where we've discussed many sensitive issues but I think it's very important with Islam under so much attack at the moment that the Muslims try and find ways of working together and that these theological issues can be discussed with respect and in different circles in the right time in the right place and with qualified people.