What's up Mopar fam? I hope everybody's having an awesome time out there As you can see we got frostbite right here, and we are about to go to work on it We're gonna install a new modification. We are finally gonna ditch Trash can get rid of the factory bumper. This is a big old frozen chunk of poopy I've been meaning to do this guys for a long long time and I just keep putting it off because I got other things to do Finally we're gonna get rid of it though As you guys know I don't run the exhaust back here anymore anyways So it's really been bothering me to have the exhaust cutouts in the bumper when there's no exhaust coming back here so We're ditching the bumper and we are gonna be installing a solid steel roll pan from Street and show The link to this roll pan will be in the video description below so check it out It's a solid roll pan. There's been a few guys put them on already, and I think they look really good plus their steel You know I was looking at some of the polymer or the plastic roll pans and don't get me wrong The plastic ones look pretty good, but I'm kind of more of a fan of having some metal on the truck So we went with the steel roll pan from Street and show They're about 260 bucks, so you really can't beat the money, and they look good Plus it's gonna it's gonna save us some weight because we will finally be able to get rid of the rest of the factory hitch underneath the truck and Plus the factory bumper does weigh a lot more than the roll pan We're about to put on but let me go get this roll pan real quick, but here's the roll pan guys This is this the Street and show roll pan. I've already got it painted white as you can see It's in the bubble wrap. I'm not gonna unwrap it yet But we will get it on the truck and we will show you what we got to do to mount this thing on and give you a final Installation the parents on the truck.  I'm stoked about it They give you the hardware and everything to put it on also They give you the lighting the the light for the license plate and the hardware Pretty much a bolt-on dill so we're gonna get this old bumper off and get the new Street and show roll pan installed on the truck All right guys, so we are under the truck and To remove the stock bumper Assembly there's two bolts up here one there one up here and then My son is over here taking the rest of it off Sorry for all the jiggling here You have Up here you got two bolts on the bottom as well. I'm trying to bring you guys over here Showing to you a little better. There you go. There's one there and one there as you guys can see a long time ago I've actually cut most of my towing hitch off of this factory bumper If you're not aware you will be aware now that In order to Mount the factory bumper up The factory hitch and bumper is kind of an assembly You got to have the hitch mounting here to build and mount the actual bumper. It's kind of a pain in the butt So that's why I cut most of all the weight off of the bumper that I could and still be able to have the factory bumper on until We finally got rid of this thing So i'm happy we'll be able to get rid of all this stuff all this extra metal that's pretty heavy on both sides And we'll just have a nice clean flat steel roll pan back here from street and show But uh, we're gonna finish removing these brackets here and getting this bumper off I'm opar fan We have the new roll pan installed And i'm definitely liking it. It fits pretty good We only had to do a couple little bends and tweaks here and there and i'll show you where I did some of the adjusting But all in all the roll pan fit very good And very easy to put on not difficult at all So i'm gonna get the camera i'm gonna take you around the truck let you see it a little bit better And then i'm gonna get underneath and show you what we had to do also for the license plate light To be able to wire it up. We had to lengthen the wires and i'll show you how we did all that All right, so this is passenger side And we got it fit up pretty good This is going all the way around the truck here roll pan fits pretty nice Now i'm gonna show you a couple spots here that I had to tweak a little bit and i'm gonna have to get some touch up paint because I did end up dinging it a little bit As I was kind of rushing it not really Taking my time like I should have but that's just how I roll But anyway, so right here on the corners here The pan is very close. I'm gonna take you over here to the passenger side The pan is very close To the actual truck um, so what I did is When I had when we mounted everything up I took my uh one of my pry bars And if you see my finger here what I did is I took my pry bar and I laid the back of it against this The bed mount The tailgate mount right here laid it down here and I put it in here on the back of the pan Right here on the back of the edge where it's close to the Underneath the tail light here and what I did is I just pried out on the bumper a little bit or on the roll pan excuse me And that tweaked it a little bit to get some clearance right here And it fits good it doesn't rub it doesn't rub anymore Um, but I will need to touch up paint behind it just a little bit where I dinged it I'm putting it on Now your other option uh somebody else that installed the same pan what he did Is they ground down the back of the pan itself on the lip back here that will also work um And it may vary from truck to truck, but the pan is very close to The truck right here So you're either going to need to do what I did It just kind of bend it out a little bit tweak it some or grind the back of the pan a little bit And then I like I said the same thing over here on this side You'll need to do it as well over there if it's very close on your truck like it was mine Other than that the hardware they supply you with you have to drill Um five holes into the back of the truck Where these the pans already got uh slots for the screws But you will have to drill holes in the back of the truck So it kind of takes two people you'll need to hold the bumper or you'll have to hold the roll pan up Mark all your holes with a marker and then drill out the uh the holes to accept the screws And I'll show you the drill bit size that I used real quick Uh which worked very good for the screws they supplied And it's just a regular drill bit 1164 drill bit And that size worked perfect for the phillips head screws That they supplied in the kit And all you got to do like I said you're going to drill a hole through it The hole is a little smaller Than the screw obviously so when you start threading in this big phillips head screw It's going to tighten up against the Truck metal right here on the back of the bed So you don't have to put a nut or anything on the back Now if you don't want to use these screws you could use your own you can put bolts and nuts in it if you want to but Um if you drill the hole the correct size these phillips head screws tightened up very very tight. Um, I Honestly, I tighten the crap out of them and they are holding very good Now on the bottom side of the truck Now this is on the bottom side of the truck guys This is the passenger side over here on the bottom of the roll pan they have a metal tab that is uh Welded onto the bottom of the roll pan Which has a hole in it for a screw and then you will need to drill Into the bottom Right here the bottom right corner of the uh the bed More or less the bed fender or whatever Um, you'll drill a hole right there to attach one of the phillips head screws that they supply to hold the bottom of the Roll pan on and this also helps stabilize the corner Um, which is very nice on some of the plastic roll pans. I've noticed that a lot of people are having to put Uh three in or double-sided tape on the outside Um behind the roll pan to be able to hold this corner in Um, and sometimes those pop loose and it's just kind of a pain I do like this idea where there's actually a screw here to hold this So this corner of the roll pan will stay pretty tight and shouldn't be an issue And then it's the it's the same thing on the driver side So as you can see same thing Uh A little tab here on the roll pan For another phillips head screw And then obviously we've had to drill another hole down here to accept the Roll pan screw mount or the mount screw right here And then that's all there is as far as attaching the roll pan. That's how it's held on to the truck pretty simple Not a big deal at all And then for the lighting All right, now we're underneath the metal of the pan here Um, they supply you with an led Light mount that will attach on the other side of the pan with two phillips head screws Um, the wiring that's that comes off that light is not very long and then As I said, I had to lengthen it so we attached it to the factory connector here um I just cut off the factory connector where it used to plug into the The old bumper light and we wired in The led light that they supply you with And I can kind of show you so on the factory bumper as you know, you have two plugs For two lights on either side of the license plate Well, this one is the other one that I just got zip tied up here Um, but more or less, it's just like the other side except for I cut that connector off so that we can wire We just used the wiring coming out of the factory harness To wire in the new led light for the license plate And that's it. That's all we had to do for the Wiring side of it Pretty straightforward And then as well they supply you with two plastic, uh, little square mounts To pop into the roll pan to attach your license plate As well, but pretty straightforward. Like I said, um, obviously I don't ever run the tailgate I don't believe it's going to be an issue at all with the tailgate on there should be plenty of clearance here Like I said, there's another guy where actually I found This roll pan He has it on his truck and he's running his tailgate without an issue at all Um, he did have to do some of the same things I did here making some extra room Where it comes real close to the bed At these little corners right here By the other night it looks pretty dang good.  Like I said, this is a solid still pan and uh Definitely like the new look Uh, makes frostbite look, you know, not so uh I guess the best way to put it not so uh Like it's ready to tow something down the road anymore Um, looks a little more sleek and definitely lighter now The factory bumper is pretty heavy, especially if you have all of your hitch your factory hitch still on This is the factory bumper Um, and as you can see, this is what's left Of my Old towing hitch, you know, there's a big tube here where the hitch would come out Which I've already cut all of that off a long time ago Um, as this truck does not tow anything at all anymore. That's why we got the big Cummins diesel now But you have to keep All of your hitch brackets To build a mount the factory bumper. You cannot just remove the bumper very easily Um Unless you want to take the whole thing completely off. There's no way to get rid of the hitch And just run your stock bumper. It's kind of a pain in the butt how the system works You have to have the hitch brackets to build a mount the bumper so it kind of sucks Um, but you can imagine how heavy this is Obviously the the stock bumper is steel is is steel also And then your your towing hitch is super thick metal very heavy And uh, definitely we shaved off some weight getting rid of this thing For the new pan Definitely pretty cool But there it is guys Sun's pretty bright out here right now. So I'm hoping the camera's picking it up pretty good Other thing I want to mention these are all the factory bolts that held on the old bumper and hitch assembly um And if I remember right these were 21 millimeter Bolts, uh, so you'll need a 21 millimeter ratchet and socket um, or a wrench I ended up needing both of them, but just a heads up. There you go. Looks like you got uh, was it two four Six eight bolts. So there's eight bolts you got to remove to get the complete assembly off the truck if you're running the factory bumper on your ram So heck yeah guys, there it is the new street and show roll pan Like I said, the link is in the description below. It'll take you to the ebay store. It'll take you right to the link to buy it Uh, my opinion, I love it. It fits very good very very minor Modification needed to get it to fit right Other than that simple installation And only 260 bucks. So it's hard to beat that for a steel roll pan. It's not plastic or abs This is a solid steel solid steel pan As you can hear And uh, it's super light that thing doesn't weigh hardly anything Definitely lighter than the old bumper for sure And it looks badass. So other than that guys, hope you enjoyed it Hope the video helps you out. As always guys, stay safe out there. Don't forget hit that subscribe button We'll see you on the next one


Alright so recall from the previous lecture that we were trying to define what a morphism of varieties is okay so we have pair of varieties, two varieties they could be either affine or quasi affine varieties and then we want to say when a map between them is a morphism of varieties okay and we use the analogy that I gave you in the last lecture namely the analogy from the topological spaces okay so if X and Y are topological spaces and F is a continuous map of topological spaces of course you know that continuous map pulls back continuous maps to continuous maps it is just a V statement of the fact that composition of continuous maps is continuous and but the more beautiful thing is that if you have a set theoretic map that pulls back continuous maps to continuous maps then it follows that that set theoretic map is itself continuous the proof is deceptively simple and you could say more or less topological but this is the but it is the importance is with the philosophy that you define a morphism as a map which pulls back good functions to good functions. So let me let me make this definition of what a morphism between varieties should be so here we go let X and Y be varieties by a morphism from X to Y, Phi from X to Y we mean a continuous map from X to Y such that for every open subset V in Y the pull back map the pull back of functions of regular functions I should say the pull back of the pull back of maps V of Phi takes regular functions on V namely O V to regular functions on U namely O U so the diagram is like this here is X, here is Y, here is Phi and here is the open subset and open subset V of course whenever I say open subset it is of course non-empty okay and in all these situations we are not going to look at the case when the open subsets are empty because we do not want it define regular functions on an empty open set okay. So of course I should tell you that where U is actually F inverse V okay so here is V and here is U which is F inverse V and this is also open that is because Phi is a continuous map of course X and Y are varieties so they have the Zariski topology therefore you know what open sets mean and you take an open set here the inverse image of an open set is an open set because and I should use not F I have messed up the notation should be Phi inverse here should be Phi inverse there as well okay and I have this map from Phi inverse V to V. Now this map from Phi inverse V to V will give you a map from O V to O U and what is this map from O V to O U what is an element of O V it is a regular function on V okay and element of O V is a regular function on V so what is a regular function on V it is a map from V to K a regular function on V is a map from V to K which as we had defined in the earlier lectures is a function which is locally given by quotients of polynomials where the polynomials are considered in the right number of variables in which V or Y is the right number of variables which is equal to the dimension of the affine space in which V or Y is sitting inside okay. So well here is V and here is Phi this is U so U takes Phi Phi takes U to V and then the pull back will be this map you pull back essentially means composition so this is this is first apply Phi then apply F and this is called as Phi upper star of F so this is F going to Phi upper star of F the pull back of F which is by definition first applying Phi and then following it up by F okay so this is the requirement the requirement is you take an open subset of the target per IT take a regular function on that if you compose it with Phi you should get a regular function on the source okay this is the condition this is just the condition that the map Phi is continuous and it pulls back regular functions to regular functions okay this is the definition of what a morphism is what you must understand is the following that if you go down from the category of varieties to the category of topological spaces that is you forget the variety structure and just look at all these things as and the underlying topological spaces with the of course with the Zariski topology then what will happen is if you give me a continuous map if you give me a morphism Phi of course V is continuous and if you give me a V and if you give me a regular function on V this F is of course going to be continuous because I have already proved to you that regular functions are continuous okay a regular function from a variety is always a continuous map continuous with the target K being thought of as A1 with the Zariski topology this is something that we proved last time okay so since Phi is continuous and F is continuous is very clear that F circle Phi which is the pullback of F by Phi this is also Phi of star F it is clear that this is continuous okay but what our requirement is it is not just a continuous map from U to K for the Zariski topology it should actually be a regular function from U to K for the Zariski topology that is the requirement okay that is what has to be singled out okay so the moral of the story is a continuous map such that if you take a regular function on the target on an open subset of the target and take the composition okay what you should get on the source a subset of the on the right subset of the source is not just a continuous function it has to be more it has to be itself a regular function namely it has to be locally given by quotients of polynomials that is the requirement okay so it is a philosophy that it is a map of varieties is a map which is continuous and which pulls back good functions to good functions and the good functions here are regular functions okay. Now so here is the so here is the so the point I want to make is the following so here is a so here is a nice little theorem the theorem is if you look at if you take a if you take a variety X and look at all the possible morphisms into A1 you will get exactly all the regular functions on X okay so morphisms of varieties from X to A1 is actually isomorphic to O okay so the regular functions are actually morphisms into A1 there is no difference okay order elements of O X they are they are they are maps into A1 which is just K with the Zariski topology alright and which are locally given as quotients of polynomials that is what a regular function on X means okay and what is a morphism of varieties from X to A1 it is also a map from X to A1 which is a map from X to K but then the condition is that it has to be continuous and it should pull back regular functions to regular functions okay and the beautiful thing is that there is no difference between a regular function and a morphism into A1 so regular functions are exactly the same as morphisms into A1 okay so let me write that that is regular functions are so in fact I should not even put isomorphic I should put equal to or morphisms into A1 so of course is A1 K where K is a fixed algebraic closed field over which we are working okay so it is a very nice theorem it says it tells you that your morphisms into A1 are the same as regular functions into A1 okay so so let try to prove this so you know so what you do is so what is a map of course this map is it is identity map okay it is the identity map but only thing is that when you take a regular function on X the target is taken as K and the target K you do not care about the topology on the target K but if you put a topology on the target K and call it A1 then you know a regular function is continuous so it is certainly a continuous map from X to A1 but the fact is it is more it is actually a morphism from X into A1 okay that is what this theorem says so let us prove this let Phi from X to A1 be a morphism okay what do I have to show I have to show that Phi is a regular function alright now so this means Phi up a star from O of V to O of Phi inverse of V for any open set Phi inside A1 okay so what is a morphism a morphism is a map which is continuous and it pulls back regular functions so if you give me an open set in the target which is an open subset of A1 then and you give me a regular function on that open set on A1 which is an element of O of V then applying Phi up a star the pull back should give me a regular function on Phi inverse V okay now what I am going to do is I am this way is actually very easy you put V equal to A1 itself put V equal to A1 okay then you get Phi up a star will go from O of A1 to O of X okay because Phi inverse of A1 is X the inverse image of the target space under any map is the whole source space okay I will get this okay and then what you and then we will use the fact that you know in O on O of A1 see I have the identity map see the identity map on A1 is a regular function on A1 see the identity map on A1 is a map that sends every point of A1 to its every point of A1 namely every point of K to itself and what is it you know O of A1 if you want is A of A1 the ring of functions on A1 which is KX okay and what is the identity map correspond to it corresponds to the polynomial X identity map corresponds to the polynomial X the polynomial X evaluated at lambda gives you lambda okay so O of A1 is the same as A of A1 okay that is something that we have already seen O and A coincide for a fine varieties alright so O of A1 is same as A of A1 and identity map in O of A1 is actually that corresponds to the function defined by the polynomial X okay so this is so identity map is certainly a regular function identity map on A1 is certainly a regular function and what does it go to it will go to phi upper star of the identity map on A1 but phi upper star of the identity map on A1 is just phi, phi upper star of the identity map on A1 is by identity map on A1 composition with phi which is just phi and but then you are saying that this is here so you are just saying that phi is in OX so this will tell you belongs to OX so it is very clear that a morphism from X to A1 is certainly an element of OX okay so phi as an element of morphism phi as a morphism of varieties from X to A1 is certainly also in OX right so this is very trivial alright I have to now do things the other way around I will have to say that I have to start with a regular function and I will have to start with a regular function on X and say that that is a morphism okay so let me do the other way conversely start with an F in OX start with an F in OX right I want to show that F is actually a morphism into A1 so you know my F in OX means that F is a regular function defined on X its target is K and we have already seen that if this target K is given the Zariski topology and is thought of as A1 then this F is of course continuous okay we have already seen already seen that a regular function that regular functions are continuous so that means that F from X to A1 is continuous so what are the two defining conditions for a morphism it should be it should be a continuous map and then it should pull back it should pull back regular functions to regular functions so we will have to check we will have to check to check for every open set V in A1 and every psi in OV F up a star psi which is just psi F followed by psi is in O of F inverse V okay this is what you will have to check you have to check that it pulls back regular functions to regular functions alright so now you see what you must understand is that V is an open subset of A1 of course I am certainly not looking at empty sets alright so you know a non-empty open subset of A1 is actually a basic open set okay because you see what you must understand is that the open sets in A1 are complements of finitely many points okay and therefore the complements of finitely many points and there is always a polynomial with roots exactly at those points and it is the 0 set of that polynomial which is the complement of this open set and therefore this open set is defined as the basic affine open set given by the non-vanishing of that polynomial okay that polynomial which vanishes at those points in the complement of the open set you must understand that the important fact we are using is that A1 has the only closed sets in A1 are finitely many points and this is basically commutative algebraic reflection of the it is a reflection geometric reflection of the commutative algebraic fact that every ideal in the polynomial ring in one variable over a field is generated by a single element okay it is a PID alright so the fact is that so let V be D of G okay where G is an element of if you want A of A1 which is identified with Kx G is the polynomial in one variable right and V is D of G it is a basic affine open defined by G right then what is O of V then O of V will be O of DG and what is O of DG our definition as we have checked it is just Kx localized at G okay the regular functions on DG are the same as the A of DG and that is defined to be the localization by G okay so O of V is just this okay and so what is an element of O of V of the form it is of the form some H by G power M where M is a positive non-negative integer okay an element of O V looks like H by G power M alright this is how an element in the localization looks like and you are thinking of this H by G power M as a function on as a regular function on V and every regular function on V looks like that right and now if you so let me draw this diagram so I have X I have A1 and here is F and here is D of H okay which is my V and then I have F inverse V this is open of course F is a regular function it is continuous so the inverse image of an open set is open so F inverse V is open and then I have I have on D of H I have a regular function okay and that regular function is given by H by G power M this is an element of O of D of H and then I compose it with F to get the pullback this is a regular function into K okay sorry this is D of G should be D of G I am sorry should be D of G I think I have messed it did I mess it up somewhere there no I did not okay I mess it up here alright should be D of G right so yeah so I have H by G to the M which is a regular function on DG and then I compose this to get the pullback function which is F upper star of H by G power M which is by definition equal to first apply H and then apply first apply F and then apply H by G power M and so it is going to be well so if you calculate it is actually F's H circle F by H circle G to the M this is what it is okay so because this is what it will be when you evaluate it if you take an X here then it will go to F X and when you evaluate H by G power on M on F X you will get H of F X by G to the M F X so the effectively this is H circle F by H H circle G to the whole to the M alright and here of course and now the point is that what do I have to check I have to check that this is I have to check that this is a regular function on F inverse V I have to check that this is a regular function F inverse V okay so it is something wrong sorry this is G sorry you are right it is G circle okay it is G circle oops yes G circle F to the M right yes yeah please check that it is F followed by H divided by F followed by G whole to the M yeah thank you. So I will have to check that this is a regular function I mean if you think about it for a moment you will not hesitate to realize that this is a regular function okay but then if you want the way to look at it is the following the way to look at it is that you see the locus see F is a so let us look at what F is so F is a regular function on X okay. So you know I want to say the following thing I just want to say that if you if I tell you that H circle F is a regular function on F inverse V and G circle F to the M is also regular function on F inverse V that does not vanish on F inverse V then the quotient will also be a regular function on F inverse V I am just using the following thing I am using the following thing namely that suppose you have a regular function that does not vanish then its reciprocal will also be a regular function because the only condition for a regular function is that it is locally given by quotient of polynomials and if that quotient of polynomials does not vanish it means that the numerator polynomial does not vanish if they are in the if there are no common factors and if the numerator polynomial does not vanish then the reciprocal of the quotient is also a valid quotient of polynomials and that tells you that the reciprocal of a regular function that does not vanish is also a regular function alright. So therefore if I claim therefore it is very clear that it is enough to show that H circle F is a regular function it is enough to show that H circle F is a regular function on F inverse V G circle F to G circle F is also regular function of on F inverse V and G circle F does not vanish on F inverse V okay it is very clear that G circle F cannot vanish on F inverse V because if G circle F vanished at a point on F inverse V it will mean that at the image of that point under F G will vanish but then the image of that point is supposed to lie in DG where G cannot vanish so it is very clear that G circle F cannot vanish on F inverse V so the only thing therefore I have to prove is that H circle F or G circle F are actually regular functions okay but so let me write that down it is enough to show that H circle F and G circle F are regular functions on F inverse V okay this is all I will have to show okay now this is again something that is very very easy to see because you see see F, the F I started with was a regular function on X so F is given by a quotient of polynomials in the right number of variables the number of variables being the dimension of the affine space in which X sits alright so F is locally a quotient of polynomials okay so H circle F will also be a quotient of polynomials the same number of variables because H is just a polynomial in one variable when I take a polynomial in one variable and substitute for that variable another polynomial in some m variables the resulting thing will again be a polynomial in m variables it is obvious therefore the moral of the story is that it is very clear that since F is locally a quotient of polynomials H circle F, F is locally a quotient of polynomials on X okay then H circle F is also locally a quotient of polynomials on X okay so let me write that down this is obvious for locally F is equal to P by Q where P, Q are polynomials in the right number of variables which is a of a n with X sitting inside a n okay and you know and if H is equal to H of X is equal to sigma ai X to the i i equal to 1 to say some T then H circle F is locally H of P by Q which is sigma i equal to 1 to T ai T power i by Q power i okay which is a polynomial in K of X1 etc Xn divided by some power of Q so you are done. So the moral of the story is that if you really think about it it is very clear that a regular function is also a morphism so there is no difference between regular functions on a variety and morphisms into A1 there is absolutely no difference okay so the beautiful thing is that to define a morphism we started with the regular functions and then found that regular functions are themselves special cases of morphisms okay in that sense it should not be very surprising but you must understand that you see right from the beginning this is again you know amplifying more and more the philosophy of Felix Klein that you know the geometry of the space is completely controlled by the functions you choose on it so you know we started with affine space we started with n dimensional space Kn we chose the functions to be polynomials using the polynomials we define the Zariski topology on Kn okay and then from the Zariski topology we started translating back into commutative algebra and we came down to defining we first came down to guessing what should be regular functions okay for example on basic open sets and then generally what should be regular function what the regular function should be on a general open set okay and then after we defined regular functions once we defined regular functions we found that if you take affine varieties the regular functions are just polynomials okay and we also found that using these regular functions we could define morphisms and then it is not surprising that finally regular functions themselves turn out to be morphisms okay alright so that is a very nice thing it is a very nice result but now what I am going to do is that I am going to say that this is the statement here is only it is still a special case of a very very general statement okay so let me let me make that statement so again let us look at that statement morphisms of varieties so this is morphisms of the category of varieties from X to A1 is identified with OX okay and you know and I just want to say that this is isomorphic to homomorphisms of K-algebra from A of A1 which is which can be identified with KX to OX okay so you see now what I am going what I am trying to do is I am now trying to translate things see on this side the morphisms I have is in the category of varieties now I want to go this is geometric part to the geometric side I want to go to the commutative algebra side and I want to translate morphisms of varieties into morphisms of rings in this case morphisms of K-algebras and this is the this is the way I do it what I do it what I do is I think of OX as the as the I interpreted as being bijected to the set of all K-algebra homomorphisms from the A of A1 which is KX to OX see you know there is this universal property of the polynomial ring in one variable which says that a K-algebra homomorphism from a polynomial ring in one variable is completely dictated by the image of the variable X okay so any K-algebra homomorphism from KX to OX from KX to any ring is simply controlled by what you are sending X to so more generally I am so let me recall universal property of KX of RX okay where of course R is a commutative ring with one what is the universal property the universal property is that if B is if A is any R-algebra then A home R-algebras from RX to A can be identified with A by simply sending a map F from RX to A to FX to the element FX of A because it is a substitution it all R sending a map from RX to something means that you are substituting X for something in every polynomial in X with quotients in R so it completely is controlled by what you are substituting X with if you substitute X with some lambda then you have to substitute every polynomial in X with X in place with lambda in place of X it is controlled by that this is the universal property and in fact this universal property is also valid in several variables more generally homomorphism as R-algebras from RX1 through Xn to A is isomorphic to A to the n where you simply send a map F from RX1 through Xn to A to the tuple FX1 dot dot dot FX to the n tuple that is a map an R-algebra homomorphism from a polynomial ring in n variables is dictated by the images of those variables this is these statements are restatement of the universal property of the polynomial ring over a given ring okay. So and I am just applying instead of R I have put the field K and instead of A I have put OX so the homomorphism from K-algebras from KX to OX is just OX and that is what this is okay and now let me tell you how this statement generalizes the statement generalizes like this okay it is very beautiful so it generalizes like this. Homomorphisms from X to A1 can be identified with homomorphisms of K-algebras from A of A1 to X okay and morphisms from X to An can be identified with homomorphism of K-algebras from A of An okay and morphisms from X to Y okay where Y is a fine okay so instead of taking the target to be A1 I can take the target to be An instead of taking the target to be An I can take the target to be an affine variety. So the morphisms from any variety into an affine variety can be identified with homomorphisms of K-algebras from the affine coordinate ring of that affine variety sorry this should be a Y and mind you this AY is the same as OY there is no difference because Y is affine and the in particular you see in particular if X is affine the last statement says that the morphisms so here of course these several morphisms is varieties on this side it is a geometric side there are morphisms between geometric objects and this side is the algebra side the combative algebra side. So the morphisms of varieties from X to Y can be identified with homomorphisms of K-algebras from AY to AX and mind you I can replace OX by AX because OX and AX are the same because X is an affine variety okay. So this is the these are the two important statements this one and why are these statements important these statements we will prove these statements okay and they are just you know generalized versions of this first statement which is just the simple statement that the regular functions on variety are the same as morphisms into A1 okay it is just a generalization it is a grand generalization of that but how grand it is is that it actually gives you an equivalence between the category of affine varieties and the category of finitely generated K-algebras that is the reason why this is a very important statement. You have category so category so let me do that in the next board so that I have a little bit more space to write down what I want to write down so what I do is now I can really complete the picture that I stay I gave several lectures ago and then I was just you know throwing statements at you so here on this side I take the category of affine varieties okay and here the objects are affine varieties namely irreducible closed subsets of An for some N positive these are the objects in the category and I am going from that to the category of finitely generated K-algebras that are integral domains sometimes instead of writing so much people just say the category of affine coordinate the category of affine rings over K the affine rings means they are actually rings of functions on affine varieties okay so and abstractly they defined as finitely generated K-algebras that are integral domains which means that you are just taking a finite you are just taking a polynomial ring in finitely many variables over K and going more low prime ideal so that you get an integral domain okay and you know I have this I have a I have a functor that takes objects here so what it does is that if you give me an X it takes this X to well A of X okay so it tends it takes X to A of X and it takes An to A of An and it takes this closed immersion to a quotient okay and you know what that map is if you call this closed map if you call this closed inclusion as I X you know what this map is this is just I X star you can check that this closed this map the inclusion map is actually a morphism of varieties and you can check that the pullback I X star that induces that it induces from the O of this to the O of this which is the same as the A of this to the A of this is simply the restriction you can check that okay so this I X gives you this I X star okay and what are the what are the morphisms the morphisms here are well if you have a if you have X and Y to affine varieties I I get you you have a morphism F then that will give rise to a map on this side that will go the other direction so it will go from A Y to A X and you know what that is that is just F star it is a pullback so the fact is that if you give me a morphism of varieties the pullback map is actually a ring homomorphism okay that is something that you can very easily check it is obvious and in fact it is a K algebra homomorphism so the morphisms on this side are K algebra homomorphism they are ring homomorphism which take one to one which respect the vector space structure they are K linear so they are K algebra homomorphism and the fact is that this is this is the functor now A is a functor it is a functor because it goes not only does it associate an object to an object but it associates a morphism to a morphism okay to every morphism varieties you get associated K algebra homomorphism so this is a functor and the fact is that this is a this is an equivalence of categories this is an equivalence of categories because there is an inverse function which is which as I told you is given by max spec the max spec functor starting with a starting with a finitely generated K algebra A I can give you I can look at max spec A that is a variety okay that can be identified with a variety and if you give me a K algebra homomorphism G Phi from A to B then what you will get is you will get a from the max spec to the max spec you will get a homomorphism in the reverse direction namely max spec Phi and this is just pull back of given a prime ideal in B I mean given a prime ideal in B the inverse image of the prime ideal will be a prime ideal in A and the fact is you can check that because these are finitely generated K algebra which are integral domains in K is an algebraic closed field if you take a maximal ideal in B and you pull it back you will get a maximal ideal in A and so it will take max spec to max spec and this is the inverse functor and these two functors are inverse of each other in the sense that you start with an object you go then and come back what you get is an isomorphic object okay and then similarly if you start there you go here and come back you will get something that is you will get an isomorphic K algebra so if you start from here and go and come back you will get an isomorphic variety if you start from there with an algebra go and come back you will get an isomorphic K algebra okay and that is why these two functors are called inverse functors and we say that each of them defines an equivalence between the geometric side which is the category of affine varieties and the commutative algebraic side which is the category of finitely generated K algebra which are integral domains and you know it is easy but and certainly not an exaggeration to say that this is the full blown form of the Hilbert-Nulstall-Ansatz okay with all the other definitions in the right place this is the grandest form of Hilbert-Nulstall-Ansatz okay so with that I will stop this lecture.


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I'm assuming With card number Hawks, yeah Got RPA to 75 Jalen Green rockets color match That actually started as an inside joke between me and rich MOOC Me and him when I first first started breaking back in New Jersey We were watching a breaker and he's like trying to show me different breakers and stuff And a guy pulled him a Matumbo. He's he was like Dummy gang Katungo, I'm like, what do you see even saying? Rockets Jersey to 99 Eric Gordon. It was just so funny at the time Eric Gordon Jersey to 99 Darius Beasley thunder. I saw a guy clip his toenails on stream I was like, I was like rich. I'm gonna do that He's like don't no pistons. All right PA to 25 Luca Garza Jersey auto New York OB Toppin on the back to 49 Like To 75 Harrison Barnes Kings I Grew up in New Jersey and we had Rutgers and I don't like them. Yeah, it's not even worth like That's what I'm saying Like the closest we had was like most New Jersey people end up liking up Pencil being like Penn State. 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I would like to start my speech by thanking the organizers of this session for accepting my contribution and especially Tobias Krupp for inviting me to visit the site of Amarinto this summer and to Samuel Verdan for his tour at the Temple of Apollo at Eretria this July. Today my presentation will focus on the connectivity of the Temple of Apollo at Eretria during the early Iron Age by giving you an overview of the site its main finds and reinterpreting them. So as you know the sanctuary of Apollo of Neforza Eretria is located in the center of the island of Ubiya facing the southern coast and it was in fact located around 200 meters away from the seashore which made it very accessible not only for those who lived in the island but also for the seafarers that would reach the Ubiya coast from the sea. The Temple of Apollo of Neforza was the main urban sanctuary of Eretria and the use of the site starts well before the archaic and classical periods. The three early Iron Age periods that well Xenia already mentioned are established by the protogeometric and the geometric buildings indicated with the red line drawings in the picture and most of them have these horse shaped structures one of them being longer than the others this one and it's located right in front of the geometric altar which would be here where only it will animal sacrifices have been attested and then we've got these smaller semi-circular buildings the one in the north having traces of metalworking activities and the northern sacrificial area where most egyptian and near eastern material were found. The function of these structures has not been clearly attested and so we will go through the finds to see how the site could have been used in the early Iron Age. The ceramics found inside the horseshoe structures of the temple have provided a number of imports from Attica, Argos, Corinth, East Greece, Cyprus and the Nearies. The Cypriot shirts are biochromelechithia, white painted wear and some black and red bowls. Some shirts of amphorae are from East Greece, Cyclades, North Aegean, Cyprus and Phoenicia. Some belly shirts decorated with concentric circles belong to Cypriot amphorae of phases two and three. We also have a Phoenician shoulder number 254 and a piece of a jar with a horizontal handle which is number 251 which also belong to phases two and three. These are the finds from the horseshoe structures but then in the north sacrificial area located at the northeast end of the temple there was also pottery as we've heard before. From all the ceramics found in the area most of them were being used for rituals such as Idria with the geometric and orientalizing styles and 10% of the ceramics were pots with different shapes, some of them open shapes as we heard ski foil craters or vases and others with closed shapes such as lechithia and amphorae. Amphorae seem to occur only in the archaic period of the northern sacrificial area. Those shirts have been found for the geometric period therefore based on the presence of amphorae shirts. We could say that the horseshoe buildings were connected to some kind of trade or storage whereas the northern area would not be linked to any of these activities but mainly to eating and drinking activities or the deposition of votive pots. Some bronze objects found in the longest horseshoe structure of the temple appear to have Syrian provenance and they present similar characteristics to those objects found at the Arion of Samos. Two horse blinders appear to have been made in a north Syrian workshop around the 9th century BC although the way they arrived at UBS still under debate and they reproduce an identical scene a naked central character wearing a line cloth who holds two lions and on the right a eagle is depicted on the top blinder and two rosettes are depicted on the bottom one which also presents an aramic inscription regarding a donation by Haddad to King Hazel in order to cross the river and this is precisely the same inscription found at one figurine from the Arion of Samos. A bronze statuette of a female figure with Egyptian traits was also found in the long building she's wearing a long cloth holding a lotus flower in each hand and she has a disc around her head some similar representations are found in Syria and Palestine and this piece was probably made with a mold using the technique of the lost walks the metal sheet is too thick for repuse it and it does not have any hammering hints and the details are incised afterwards the hairstyle and the disc are very Egyptian and iconographically it might represent Anak, Asaute, Asherah or Kedeshet a similar figure of raised arms same dress and lotus flower is found in Nimrod a masculine bareheaded figure wearing a tunic with short sleeves and sitting on a stool was also linked to Syrian or Phoenician manufacture and dated to the 8th century BC he wears a necklace and earrings and he's holding a conic bowl with both hands this figurine might come from Biblos or alternative alternatively from Encombe and Cyprus or even it might come from some western side and it presents similarities to a statue found again at the Arion of Samos a badly preserved bronze bowl is also tested from the eastern Mediterranean between the 9th and 7th centuries BC probably from the area of Assyria and according to Skiaka these plates are exported and imitated also in Etruria so here we can see some connections with the west as well the temple area yielded just a few examples of Egyptian objects a scarab made of Egyptian blue faience and two scarabs made of stone the stone one seemed to belong to the group of the smith from Lyre in north Syria and then the northern sacrificial area however gave a great amount of Near Eastern and Egyptian material different types of scarab white seals were found in this northern sacrificial area and they appear to belong to the group of the juror of Lyre as well representing scenes of musicians two men a sitting man and a palmerette which find parallels in the scarabs from Rhodes scarabs from Mialisos from Lindos and from Kamitos they are made of different materials including amber stone and glass and belong to different dynasties of Egypt some of them being suspected of being Phoenician due to its iconography such as scarab 168 which has an Assyrian looking tree and the scarabs from Kamitos in Rhodes and an example from Kythion also resembles scarab number 163 so that connects it even more to Phoenician manufacture other scarabs such as the ones made of glass resemble the ones found at the Erayon of Perakora some other scarabs found in Phoenicia in Syria in Rhodes in Sparta the Erayon of Argos, Kyos, Creeks and Cyprus other metallic objects were discovered at the northern area as well a few rings of silver bronze and electrode these present similarities to rings found in Rhodes, Creek, Amantus on Cyprus, Artemis Orpheus, Sparta and Egypt as well as these Crees and Almenon. Amulets in the shape of Egyptian divinities include Bess, Isis Hattor, Nefertum, Da, Tot, Sekhmet or Bastet and the presence of figurings of foreign divinities at a temple presumably dedicated to Apollo suggests a few things one option A it could be that these statuettes were only seen as exotic products due to luxurious commerce happening in the area that had no repercussions in the beliefs of local populations B that those people visiting the temple presumably eastern seafarers would at first only worship Egyptian divinities and later on it would become a temple dedicated to the Greek god Apollo or see that Greek gods were confused or associated with foreign divinities which is a similar phenomenon to what could have happened at the temple of Komod in southern Crete which is a sanctuary also associated to Apollo where we have found sculptures of Sekhmet and Nefertum and Sekhmet and Nefertum together with a form the Egyptian triad so this could have been associated to the Greek triad of Apollo let one items and the same phenomenon could have happened in Eretria in conclusion the temple of Apollo Eretria has several successive buildings for the geometric and geometric structures with a horseshoe shape below the archaic and classical structures and the northern most of these geometric buildings is where we would have had metal working the longer building of the same period is where the horse blinders and the other figurines were found the altar where there where would have been the animal sacrifices and the northern sacrificial area with Egyptian material so we can maybe say that one building had one function so each building would have its own function or we can say that a group of buildings would have had one function or maybe a group of buildings would have had several functions which is probably this case so what we have in Eretria would have been a religious area not just a religious building would have been a religious group of buildings um there would have been a space of dedication to the divinity at the northern area where votives would have also been placed a space for animal sacrifices at the altar followed by the construction of a building that could have been related to a temple even though up to the moment of construction there would have been no formal temple and probably religious activities would have presumably been outdoors and this space would have not just been a religious space it would have not just been a religious group of buildings but also a commercial group of buildings the portrait finds in the other buildings indicate that the southernmost building would have been probably used for eating and drinking and the elongated building provided us with shirts of amphorae some of them from Near Eastern origin and this could mean that the area was used for both purposes commerce and eating uh since protogeometric times um the presence of transporting storage jars as well as other kinds of open shapes could indicate the use of the building as a stopping point for merchants not just for resting and eating but also for trading and with the time or maybe around the same time as it started being used as a port of coal around the eighth century merchants and locals frequenting the site would have also uh reclaimed the need of a worshiping area so the establishment of an altar and later on of a religious building would have been organized accepting this assumption the second theory about the beliefs in egyptian divinities from the moment of creation of the temple could be accepted even though an association between egyptian divinities could have also occurred one more aspect to take into account is the international character of a temple with such a proximity to the seashore which attests connections with other aegean sites such as samos and specifically its temple dedicated to era which is a sanctuary that would have had similar characteristics and functions to the one from eretria as well as the temple of kition bamboola in cyprus where metalworking practices also took place and the temple b of komos on creed and possibly the port's temple of brulla in southern rhodes moreover eretria could have been a port of entry of egyptian and neo eastern objects to ubia even though sites like lefkhandi seem to have yielded a lot more of oriental materials it seems that lefkhandi maybe would have been an end to these exchanges where whereas eretria would have been the the port of entry the temple of apolodaph nephorus would therefore form part of the network of aegean temples integrated in commercial districts often controlled by oriental merchants and these districts would have been a stopping point where seafarers would have rested who worshiped their gods eaten and sold products therefore the structures forming the early iron age temple of the temple of apolo at eretria was where commercial exchanges between foreigners and locals took place as well as a hybridization of religious practices that denote that cultures cannot be considered in isolation thank you very much now we will have olivia dank we want to begin with a question is it a match a religious relations between the island of ubia and the calcidus north of aegean what are some there yeah thank you and i also thank the organizers for inviting me and yeah i think now it is time to travel from ubia to the north more precisely to my research area the khakidiki or khakidike and i will start with an introduction about this region followed by a study of the relations between ubia and khakidi and peninsular the first example of the ties between those two regions is represented actually in the famous philosopher Aristotle who was born in star gira on khakidiki and died in chalcis on ubia and speaking of chalcis on ubia i want to say it's also yeah controversial for khakidiki where the name for this peninsular derives and chalcis is one of the answers so and what i want to note in advance since i discuss both the khakidiki and the ubia in city chalcis i will use the adjectival form khakidikian for khakidiki and khakidian for chalcis in hope of avoiding confusion just to let you know the khakidiki is a peninsular in northern greece itself trident like shaped with three promontories named palena in ancient times flekara modern kassandra also the first finger the first leg as you say in gree and then syphonia and you have aphels and octel and those three promontories extending into the gnc and today the territorial border of khakidiki is shown by the following red line missing of course the independent region of mount aphels and i have expanded my research area what i call khakidiki a little bit and defined it by geographical aspects rather than political the west east border is formed by the temai gulf and the stremonico while the inland extends to the edges of the coronea and the boulder lake and just describing like a boundary curve as you see here but of course i'm leaving out tessaloniki and also argilos yeah just a short introduction my doctoral thesis called since century on khakidiki is an official project of the swiss nation science foundation based at the university of vasel in switzerland and together with my two supervisors professor martin kubisberg from vasel and professor butiras from tessaloniki i'm seeking to present the first overview of the sacred landscape of the khakidian peninsula beginning in the late rome sage down to the roman empire and in this regional study the sites are evaluated with the help of literary epigraphic numismatic and archaeological resources and in total i deal with 25 places and about 12 sanctuary sites if i want to use this term here and the number it depends on how you want to count them you see i put there some question marks though and the results seek the results seek to complete the religious studies in north and greece where the regions of upper and lower macedonia have been already analyzed already out of stuc tested the khakidiki a special existence and the latest version for the definition of khakidiki comes from stapanos gemaciles who divides the area of north and greece into different micro regions and for khakidiki he says that this is the song with the strongest saufan greek influence and this saufan greek influence is especially connected with the impact of the ubeans so here's the connection and their role in the early colonization of the northern aegean produced a discourse about formation of settlements on khakidiki and the rich resources made khakidiki really an attractive area for settlers because the peninsula provided so much like mineral deposits timber and also natural bays and fertile land so the khakidiki became like something we can call a colonization hotspot especially in yeah in terms of scholars who want to see it like this this is an old perception and modern scholars have only very recently cut free from this colonial ideology that dominated the discipline from its beginning and with my first example i will show you why this traditional view of ubeans as colonizers of the north needs an update i start with dikaya dikaya for a long time the location was uncertain and the most recent evidence plays it in the region of nea calicatea as you can see here and from literary sources dikaya is known as a colony of erratria also an onomastic studies done by denny knöppler and immanuel erratiras proved the attribution as a writing colony now let's see what the numismatic evidence can tell us i show you here three coins without any name where you might yeah get an idea where it comes from and this like it's not just a test for you it was like you see they share the same types on the uppers you can see a cow standing facing its hind leg raised to scratch its muscle and on its back we have two types here this is also a bird while the rivers is with a middle sail in cues for german windmühlenziegel and yeah now you can argue is this carnage from the same place if i give you the solution you see both of them two of them are from dikaya and one is from caristos which is on ubea so i just informed you before the dikaya was supposed to be a colony of erratria so why we find in dikaya coins that have relations with caristos another example from the carnage here you can see the well-known coin type for erratria with the cow on the uppers and the octopus on the rivers so the left one shows you the one from erratria you can guess it from the epsilon and on the right there's an example from dikaya so coins from dikaya shows also the same types here another interesting comparison on the coins from dikaya is also the cock represented which is just known from the carnage of caristos you see here an example of the rivers on the right side so what we can recall so far that the carnage of dikaya is combining the types like the cow the cock the octopus used also by erratria and caristos and the traditional view presumed that ubean carnage influenced coin production in dikaya rather than vice versa because the scholars are thinking like in this way of course if erratria or let's say the ubeans are colonizing the moth then dikaya should follow um yeah the ubean carnage but i didn't put here a date for a purpose actually the well-known or prominent numismatist pete van alvin delivered in his paper about the beginnings of the ubean carnage the following explanation the picture that emerges of the beginnings of ubean and dikaya and minting suggests that the coin production began earlier in the so-called northern colonies than it did in the mother cities to the south to explain everything in detail we don't have time here but one of his main statements is this picture effectively reverses previous thinking which plays priority of minting with the ubean mother cities informed to some extent no doubt by suppositions that colonies would be dependent followers rather than independent innovators and this suggestions suggestion aligns as well as the argument made elsewhere of northern colonies initiating carnage before the south on the tropolas so here we have to really change our point of view and think a little bit vice versa because the normal idea is about that everything is coming from the south that are colonizing the north but actually here we have a really good example because for especially dikaya we have those coins away earlier or the same at the same time like we have the carnage from erratia or canisters and actually it was the opposite so the ubeans came into the north and saw this well-established carnage system and they adopted it also recent studies demonstrated that the north venetian colonies were some of the first outside of asia minor to adopt coinage after its invention indelidian and ion in heartland and therefore it's important to know that the rich gold and silver mines provided perfect conditions to feed developing mines because especially on Chakitiki we have a lot of mineral deposits and also Mount Pangaeon is close by and I would I wanted to show a quick you can also divide the Chakitiki into zones east and west which the so-called here ubeic ionic standard and a reduced Malaysian one in the east and it's interesting that this ubeic ionic standard moved actually also this is a modern term moved from the north to the south it's extended into ubea and this is why we found all those types in carristos and erratria for example. What we can learn from this is that the shared types of the cities of dikaya erratria and carristos showed that they would have been acceptable for payments in all locations so this was in terms of trade a really good thing to do. For the coinage of dikaya exist until now no study but from the few dozen examples that survive of this coinage they can come in a surprising range of varieties so and all those arguments we have until now they stress that the north was way earlier than we have it on ubea. I am sorry just um here a card or a map you can see the deficits so they had a lot of material to use on Chakitiki. Now we move on to aphytos modern califea to a cave and this cave is situated in a seaside sanctuary which belongs to the nearby ancient city of aphytos as you can see here and this is a modern view so we just focus on the cave and the attribution of a cave to a particular diety is not always clear especially codes of Dionysos are rarely detectable. The exception is the cave of califea which is one of the few securely identified caves for Dionysos in Greece and the cave fits into the Dionysian landscape where the god was associated with several features like mountains, woods, caves and springs and also we know already from Homer in the hymn to Dionysos that he has a strong connection with caves and he was also raised by the names of Nesa so for this cave we have literary evidence that also reveals the therapeutic function of the place so we know this from Xenophon so I just give you a short overview so this is actually the entrance to the cave what you see before just ignored for the moment and behind you see a staircase and inside the cave there is nothing bound unfortunately but we have some other evidence and here I make a comparison of aphytos and the school of Aristotle because both share the same reconstruction in the fourth century where this staircase was added to reach a niche the upper one as you can see here I know it's a little bit difficult to to look at it and just to give you the proof that it's actually for the Dionysos we have inscribed shirts for the Dionysos then we have a model head and inscription with a priest of the Dionysos and also we have the numismatic evidence where you can find images from which are related to the Dionysian canon like a calphoros or also crepes so and what I want to show you now is Katja Spoon was mapping the sacred caves of Greece and has shown that other caves of the Dionysos are only known through literary sources the list is quite short there's just Yubia, Naxos and Mount Pangeon where you can find a cave connected to Dionysos so this makes the importance of the cave of aphytos even yeah more important yeah the cave of aphytos becoming more important and yeah this cave on Yubia we just know it from Pozanias and it's still yeah we have to find it this would be interesting comparison then and now some other small ties between Chakitiki and Yubia I just want to show you Arephosa it's a place on Chakitiki located here in the north and here it's interesting on Chakitiki Arephosa appears at Poseidon's wife and together they had a son named Abbas or Abantas and this son of Poseidon and Arephosa is declared as the guinarish of the Yubians which is quite interesting so for Chakitiki Arona Perez has shown a different move in connection with Poseidon and Arephosa and according to this move Poseidon had intercourse with the young mortal Arephosa and then abandoned her and then we have Hera and she took mercy of Arephosa and transformed her into a spring so in fact as we find a spring of Arephosa then because we are talking about a lot of Artemis I just put this in on Chakitiki there's also a Lagoon sanctuary for Artemis which might be for Limneia or for Pithia and Artemis was here to worship between 7th and 5th century and it was really you can call it Lagoon sanctuary which we already talked about so there certain similarities of course to locate sanctuary for Artemis near shore or in this area where you find those natural features and then because we were talking about Blackavi here is just my example for the one hilltops sanctuary I have on Chakitiki which is on Papenoras you can see the hill here so this one and the site needs more research of course but there's something like you see on top of this hill there is something like this yeah rocky features and you find some niches there but what is also interesting is the site is in the middle of an optical line which can be drawn between Mount Olympus and Mount Athos and seen therefore a special point in the landscape which is quite interesting for this hilltops sanctuary it's not clear which deity was worshipped there it can be related with Zeus but this has to prove still we don't know and the last example I want to give you is Posidi the sanctuary is of great importance because it represents the one safely identified sanctuary of Poseidon in the area of ancient Macedonia its position is here and it's on a as you can see in this picture it's located on a flat sandy cape on the Panela Palene Peninsula in Chakitiki and lies about four kilometer west of the ancient city of Mende and yeah what I want to stress out here is that Mende is always is also from literary evidence always called the colony of Aratria and Irina Lemos stated that Posidi appears to fit well the model of an extra urban sanctuary founded near a colony to strengthen the territorial claims of the nearby settlement of Mende but whether is this the actual reason for its foundation or whether in fact it may have been founded before the settlement will remain uncertain until the publication of the site is complete and she stated this actually some years ago and we're still waiting for the publication so this is actually still not clear but it's a really important sanctuary just to give you a quick overview this absolute absolute building ST as you can see here stated into this 10th century and inside there was also ash altar which is dated earlier which about started or we have the earliest evidence there from the late machinium period and just on the opposite you see building Rama which has two different phases and it's just like like the structures are kissing each other into it and it's super interesting because in the in this labeling of to call this the extra urban sanctuary of Mende we have to be a little bit more aware that although we have evidence for Mende that there is something in the 12th century because there we have found refuse pits and also we have evidence that you beings were there of course they have a presence but to call everything a colony of Heretria I just want to give you here more awareness that you really have to show on the details and to make a really more differentiate few on this and for example what I want to see here you see on the map also Mende and the sanctuary for city together it's it's a nice explanation to label the city extra urban sanctuary I mean it's just about four kilometers which you can declare the distance what makes sense for an extra urban sanctuary but still I I don't like this term for for this and also the knee clapper the knee clapper was asking the question if actually this code for Poseidon comes from you via actually I would say he was asking the wrong question here because as we've seen so far the whole day we don't have a main sanctuary for Poseidon on you via we know just from literary sources we have Garestus and I guy which is uncertain to late which is not certainly located and I would presume that the influence also goes here more from the north than to the yeah from the north to the south so this old perception we yeah we have still in our minds I want to have an update here or just to make you more aware of this yeah and with this I hope I could give you a quick overview about there are a lot of relations as you as you saw between Chakiriki and you via and I thank you for your attention


Like many others, I consider myself a huge fan of Elvis Presley.  His music and work is timeless, and like any good legend, the man's living quarters even became a historical landmark. Of course, Elvis owned properties fit for well, a king. I'm sure you've all heard of or paid a visit to the famous Graceland Estate in Tennessee, which we'll take a look at, but he also owned a gorgeous home in Beverly Hills and more. So get ready to take a trip back in time and see the places Elvis once called home. Elvis Presley, also known simply as Elvis, was a singer, musician, and actor and referred to as the king or the king of rock and roll. His energized interpretations of songs and provocative performance style, combined with influence across color lines during a transformative time, led Elvis to great success despite controversy at first. Elvis was born in Tupelo, Mississippi and relocated to Memphis, Tennessee with his family when he was 13, also where his music career began in 1954. He worked at Sun Records, recording tunes with producer Sam Phillips, who wanted to bring the sound of African American music to a wider audience. When Elvis released the single Heartbreak Hotel in 1956, it became a number one hit and with a bunch of TV appearances and chart-topping records, he became the leading figure in the new and popular rock and roll. Elvis has won a handful of awards and is the best-selling solo music artist of all time. With Elvis' rise from poverty to significant fame, his success seemed to embody the all-American dream.  The most famous place Elvis lived in was Graceland Mansion in Tennessee, which you can take a tour of in current times. He lived there from 1957 up until his untimely death passing away in the home on August 16, 1977. Although Elvis left us far too early, his memory lives on, some of which is thanks to the preservation of his estates. Hey guys and girls, it's Kara and today I'm bringing you an extra special house tour here on Famous Entertainment. You guys requested this one, so we're going to take a look at where the king Elvis Presley used to call home, including the famous Graceland Mansion in Tennessee, his Beverly Hills house, and more. If you like these videos, make sure you're subscribed and ring that bell to be notified when we post so you can always be up to date. We've also done house tours on the likes of Michael Jackson and his famous estates and we'll link to similar videos at the end. Call me on Instagram to chat and as usual let me know who's house tours next in those comments down below. Now let's get into this video. Elvis lived in a handful of homes with his family on his way to success, most being rentals, living at a grand total of 9 addresses in Memphis alone. Today, some of these places are nothing more than empty lots, but a few of the homes still exist. We'll start with the house Elvis lived at on Audubon Drive before moving into Graceland. This one story ranch style home was located in a residential neighborhood in Memphis, Tennessee. He lived here with his parents from 1956 to 1957 before moving to Graceland. He purchased the house when he was only 21 years old for $29,500, putting a down payment of $500. It was not far from the family's prior residence at Getwell Road either. This house became one of Elvis's more well-known residences and it had four beds and 2.5 baths with a car port and built a couple of years prior in 1954. A brick and metal fence was installed by the Presley family and the backyard had a motorcycle garage too. Elvis had several modifications done to the home during his stay here, like turning the car port into a garage with doors on both sides and extending the driveway to the rear of the house. He also enclosed the brick patio and turned it into an extension of the spacious living room which we can see photos of. Elvis also installed a pool in the backyard which was reported to be the largest residential pool in the city at the time and only in more recent times in 2006 was the pool removed. Originally, the house was painted green, then white, then green again. After Elvis's song Heartbreak Hotel became the most popular song in the nation, fans mobbed this house. The residence quickly became a focal point for fans, media and celebrities to visit, even magazines publishing pics of the home. Police would frequently be called to deal with the mob's dying the streets and it all became too much for the Presleys. After 13 months, Elvis moved to Graceland. This house was added to the National Register of Historic Places in March 2006, shortly before its public auction on ebay and was last sold for 1 million dollars. Although the house isn't currently open to the public, it occasionally hosts small events or concerts. Now for Graceland, Graceland mansion sits on 13.8 acre plot of land in Memphis Tennessee and it's where Elvis called home from 1957 up until he passed away in 1977. His daughter Lisa Marie Presley has been the owner of Graceland since his death and it's located in the vast whitehaven community about 9 miles from downtown and is not in his rule of the location as one might expect. The house was built in 1939 by Dr. Thomas and Ruth Moore who named it Graceland in honor of a family member. The elegant call a mansion faces west and is perched on a hilltop. It's described as colonial revival in style and is a two story home spanning over 10,000 square feet inside at the time Elvis purchased it. The king bought the home from the YMCA for around 102K, according to records and while living there expanded Graceland to span over 17,500 square feet of space adding more and more rooms. It has a total of 23 rooms with 8 beds and 8 baths. To the right of the entrance hall through an arched hallway is the living room where these days guests are greeted by a 15 foot white couch, white marble fireplace and sparkling mirrors. The music room is attached to this space and it has peacocks set in stained glass, a baby grand piano and a 1950s style TV. The kitchen and living room are also set on the main floor of the mansion along with a bedroom and a suite that previously was occupied by Elvis' parents. Interestingly enough the kitchen was a part of the home not open to the public until 1995 as Elvis' aunt Delta used it until she passed in 93. In the 60s Elvis enlarged the home to create a den on this floor known as the jungle room. It had natural stone walls, an indoor waterfall and Polynesian island decor. Elvis added a large wing on the south side of the main house that was a sidewalk between the music room and the pool area connected by an enclosed gallery. In recent times this area of the home is known as the trophy building featuring an exhibit about the Presley family. The second floor which had Elvis' bedrooms and other family members rooms is not open to visitors out of respect for the Presley family and to avoid any improper focus on the bathroom where Elvis died. This level of the home has been untouched since. After his basement hideaway you'll find some of Elvis' favorite rooms like the TV room where he often watched three TV sets at once. Here Elvis had his 1970s logo with a lightning bolt on the wall as well as built in TVs, stereo cabinets to hold his records and a wet bar. Elvis created many lavishly decorated theme rooms at Graceland. The games room also called the pool room for its large pool table was created in 1974 and he had the walls and ceilings covered with pleated cotton fabric. All in all it's said that Elvis spent 500k or more carrying out modifications to Graceland such as the field stone wall surrounding the grounds, a wrought iron front gate shaped like a book of sheet music, a kidney shaped swimming pool and even a racquetball court. One of Elvis' best known add-ons was the meditation garden where he would go to reflect on any problems or situations in his life. It's also now where he and his other family members are buried. After Elvis' passing in 1977 Graceland was opened to the public as a museum on June 7th 1982 and declared a national historic landmark in 2006. It's the second most visited house in the US after the White House with over 650 thousand visitors a year, hopefully one of which will soon be me. Before I wrap this video up let's take a quick look at a lesser known Elvis residence. Even Elvis had to have some property in Beverly Hills and according to records he and Priscilla Presley bought this home after they married in 1967 for 400k living here part time until 1973. This stunning estate is on a street dubbed Billionaires Row and most recently went up on the market for a whopping 30 million. This piece of Hollywood history spans 5,400 square feet of space sitting on over one acre of land with four beds, five fats and an attached guest house. While the house hasn't changed much from when the presleys occupied it, the interior has been redone and modernized since with upgrades like stainless steel appliances in the kitchen, new floors and floor to ceiling windows. Other features include an impressive master suite, private pool and spa, built in barbecue, fire pit and even some skylights within the home. There are amazing city to ocean views and the home is in a prime location to say the least. Elvis was famous for greeting fans at the front gate of this place to take photos and sign autographs. Alright so I think I'll bring this house tour to an end here. We gotta look at a piece of history today and see the homes of the one and only Elvis Presley. After seeing his residence it's like Graceland, the Beverly Hills home and where he got started. What did you guys think? All of this made me really want to pay Graceland a visit, that's for sure. Be sure to let me know what you thought about the King's Homes down in the comments. Thanks for tuning in, don't forget to follow me over on Instagram and let me know who's house tour is next. I'll see you all in the next one, bye!


Something I've been thinking a lot about is where the liability lies legally in terms of choosing software and what if something goes wrong with that software. I'm not picking on Kaseya, but I did do a previous video and Kaseya does represent a scenario where it has occurred. It's not theoretical anymore. The company was breached and they're a popular tool used by many IT companies. I don't have the exact install base to know exactly how many they have out there, but let me give you a quick overview. Kaseya is a tool that allows IT companies to manage servers for their clients at scale. And that's what we're seeing a lot of is a lot of tools so we can get insight into all of our clients. So we license the tools, get the software, and then we can manage all the servers for our clients more reasonably. Keep them secure, keep them patched. But what if that software became compromised? When I say what if, well this isn't a what if scenario anymore, it happened. It happened at Kaseya. So I'm using them as an example. It may have happened in other companies that didn't disclose it. It may be happening right now to a company that's unaware of it. These are real problems because the IT companies now have become a big target. We manage a lot of businesses. So now we are a target because getting the keys to our kingdom gives you the keys to all the places we manage. IT companies or the software and tools that IT places use are becoming targets. And we've seen this happen with a few other pieces of software where they refer to it as a supply chain attack by inserting something into a popularly downloaded software or a cleanup tool and then that in turn installs a virus. Now this is where legal liability comes in because we as an IT company recommend software to our clients or we simply make the choices for what software stack we're going to use to administer our clients. And what if there's a problem with that software stack? Well, this is a collection of cases that maybe will be the precedence that is used for this. And it's just thought provoking because you're going to have to understand how the legal system works and the legal system works on a series of case precedences. So you look at cases that are similar and they use that as an idea for how things will go in the future. So it's easy for some people to be dismissive and go, well, it's their problem. I know I chose to choose software and I chose the client. Now my clients hacked. They're going to be angry at me, but I'm telling you it's not my fault. It's because Seya's fault because they got hacked. I don't know how that'll fly. One, besides your brand reputation and your relationship with the customer, they may not go, well, you chose the software. Were they cheap? Did you choose? Did you vet them properly? There's going to be a lot of questions asked. And the bigger questions, of course, becomes the legal things. If it damaged their company and you're unable to repair damages done, then where are all the liabilities? Do you pay for their data breach? What if they're a HIPAA compliant? And now they have to file and notify all their clients that there was a breach. Do you pay that legal fee or today? This is where things can get really convoluted and we haven't had a ton of cases yet, but I pretty much guarantee we will. And the reason I say that is because, like I said, because Seya, I'm not picking on them, but this is an example of it happened. It happened to a tool that she used. It could happen again. I hope it doesn't. But nonetheless, I have a friend who does a lot of legal reading. I did not say lawyer. They are not a lawyer. I mean, this is not an illegal advice. This is just a place for some insight to try to gauge risk and try to assess a little bit and maybe do some thought provoking because in case you ever end up in a situation or when you're vetting these companies, making sure that it's a, you know, well secure company that goes through and does things and really proper methodologies and have gone through proper security auditing is just something thought provoking. So there's a handful of links here into different cases. And this is going to be linked below in the description so you can read, you know, and go through and read all this. And it's some detail that we linked right to the case descriptions, not opinions of the cases, but some of the case descriptions. So you can kind of see how things played out because a couple of the questions are data theft may constitute legal injury. And that is the terms that are going to use to say, all right, that is the risk that you caused the customer so you're liable and then you would then have to upstream that to the other company and what if the company's breach was so bad they go out of business, where does that leave you? Do you need insurance for this? These are things I'm kind of thinking about myself as my company and it's also because this was a mining attack that makes it a little bit different again because as a mining tax created an imminent or speculative risk. There's been cases on that and then basically because this was a crypto miner installed, all that really did was steal some CPU cycles. But you may know if you work in IT that once someone has admin access, even though they may have only chose to do that thing, they had the case of the kingdom, what did they do otherwise and cover their tracks and you just didn't notice. It becomes a really hard case to prove, especially when you're talking about companies that are under legal compliance that no one's data was stolen. Oh yeah, there's a person who did this only installed a crypto miner or did they? Maybe that's what you see running now. That's the big question is did they do something else while they were there? They dumped a bunch of data, closed those tools off so you don't notice they did it. These are a lot of thoughts that are just going on here, some case precedents and some of my thoughts. Getting this article that was written by my friend together. We've had some discussion back and forth because I think this is going to be a really interesting facet of our business that we're going to have to deal with and business as in the IT service industry. This is only going to be ramping up. These attacks never get easier. They get more in depth and once they find one foothold in there, they expand the attack. So we're going to see more of this in the future. I can pretty much guarantee that this is at least one that's happened in the past. So it's not theoretical anymore. It is what happened that I know of. There's no legal cases that came directly from this. Here's the question, did those IT companies that had the breaches even notify their clients or did they quietly just remove it? Is your IT company telling you what they're doing in the back end? That can be a whole other thing because they want to save face so they don't tell you. So this gets really complicated really quick. But I just wanted to get out there and share these links so you guys can kind of see where I'm coming from on this. And I'm curious about feedback on this. Maybe I'm just a little bit too paranoid about things, but I want to make sure that at least someone's thinking about this. And maybe someone has some more insight than I do on it and had some more links that maybe they add to this and keep the discussion going and keep it in the front of your mind when you're choosing software and what the plan might be if things go wrong. Because that's part of it too is these things can't happen. We are using third-party tools. I can't control what everyone does and I can't write all the software from scratch myself. So what do you do in those cases? There's some tough questions. And disaster recovery planning is always the first one for me but there's still, you know, it's still a lot to think about. All right, hopefully this was helpful or at least thought-provoking nonetheless or maybe just scares you out of being an IT. I don't know, share your thoughts below. Oh, and I just want to read it again. This is not legal advice. This is just to be thought-provoking. I'm not a lawyer. This was not written by an attorney. We just linked to some case precedences and hopefully stir up some thoughts related to this. Thank you for watching. If you like this video, go ahead and give us a thumbs up. If you have some feedback, leave it in the comments below. If you'd like to subscribe to our channel, hit that subscribe button. Hit the bell icon to let YouTube know you'd like to know about new releases on videos. You can also find new releases on our website, lauranceystems.com, slash blog where every video automatically gets posted so you can always find our videos whether YouTube notified you or not. Also, if you'd like to hire us for consulting services, go ahead and hit lauranceystems.com. Fill out the contact form. Tell us about the project you would like us to help you with. We work with a lot of businesses. We work with a lot of other IT people who need services done. Also, if you want to help the channel out in other ways, we have a Patreon. 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