Item No. SCP-2928 Object Class Euclid Formally Keeter Special Containment Procedures Agents globally embedded in law enforcement agencies and tabloid media are to monitor incoming information for possible SCP-2928 sightings and activity. Suspected SCP-2928 sightings are to be investigated by Mobile Task Force Beta-19, Nightingales, and confirmed instances are to be contained as possible or terminated if necessary. SCP-2928 instances are to be contained in separate standard humanoid containment units within sight. Personnel that come into direct contact with SCP-2928, including all members of Mobile Task Force Beta-19, must maintain a mental comprehension of SCP-2928 as outlined by the components of Operation Kudzu. Operation Kudzu is to remain in effect indefinitely. Operation Kudzu is designed to create and prolong existing media that effectively acts as an anti-meme towards SCP-2928. Creators of media that qualify are to be contacted in an effort to extend the duration of their work, but are not to be given any factual information about the Foundation or its goals. Once acquired, Kudzu content creators are to be placed under Foundation protection. Although the exact date of the breach is unknown, on December 2, 1996, it was discovered the effects of SCP-2928 had extended to all SCP-2928 documentation. As such, the memetic trigger within this document had been expunged to prevent perception alterations within personnel, and all possible future triggers will similarly be expunged. Those with sufficient clearance, and who have been effectively inoculated against the effects of SCP-2928, have been given access to an unedited interview containing otherwise expunged data. Description SCP-2928 are humanoids that, while in an alpha phase, cause hallucinations in those who observe them. An alpha phase is a voluntary action, and causes SCP-2928 to appear as the effective subject conceptually understands ██████ an effect which carries over to video and photographs. The most common hallucinatory effect is an inability to detect SCP-2928 due to the common stereotype of ██████ SCP-2928 are otherwise anatomically and genetically identical to non-anomalous humans. Most SCP-2928 display a rudimentary knowledge of other anomalies, and on rare occasions wield anomalous items as weapons and tools. SCP-2928 publicizing information to perpetuate the intended effects of being undetectable have been confirmed as early as the 15th century. The United States experienced a dramatic increase in media concerning ██████ during the 1980s, primarily in the movie industry. SCP-2928 activities showed a marked increase due to these spikes in public conception of ██████, and the resulting increased effectiveness of SCP-2928 being undetectable. In 1999 ██████ began the serialization of the ██████ series. The content of this series resulted in viewers regarding ██████ as much more conspicuous entities, weakening the intended effectiveness of the SCP-2928 anomaly. While it is unknown if the creator intended to combat SCP-2928, the Foundation successfully increased the duration of the series with the creation of Operation Kudzu, with the continued moderate success of Operation Kudzu, Object Class has officially been changed from Keter to Euclid. Displaying SCP-2928-13 interview I'm a ninja. Yes, I understand that. I can still see you, though you look like a Japanese theater stagehand to me. Worth a shot. I freaked the janitor out once. SCP-2928-13 ends alpha phase. Alright, go ahead. Can you explain to me what your organization hopes to accomplish? First off, I'm not a member anymore, you know that. As for what we did, we made ends meet.  That's really it, at least for the grunts like me. They're magical mercs for hire, nothing more. Same thing for hundreds of years. They just like doing it unnoticed. So they played with your database a bit back in, was it, 95? 1996. Checks notes. Can you tell me about the alpha phase, the cause of the hallucinations? It's a hidden discipline in Ninjutsu. Officially there are only 18, but this is number 21. We go through this ritual and we bind ourselves to an idea. So we're supposed to be ultra stealthy, you know, because that's what everyone think ninjas are. How have recent developments within pop culture affected the organization? It's ridiculous. My father didn't have to deal with this. He was a master assassin, one with the knight. I was two for a while, then in the early 2000s things changed. Any mission ran the risk of being a giant neon sign if the wrong person was around. We tried solving the problem the good ol' fashion way, but we kept running into problems. You guys, no doubt. Then things went wrong during the assassination of Somalia, I had to go into hiding. They clanned with all I knew, and now they want me dead. And this led you to attempt to contact us? Yeah, friend of a friend, yada yada. UIU threw me at you guys. Oh yes, one more thing, concerning the propaganda series created in 1984? The Turtles? I don't know. There was a lot of cocaine involved in their creation. Heh, I see. So they did not actually exist then. What? Oh no, they're real, I meant. There was coke involved in their actual creation. The comics were just us covering our asses.


This is stock number 11468Z. We are here at Summit Automotive in Fond du Lac, Wisconsin, near new and used sports car headquarters.  This vehicle only has 660 miles on it. They are original miles and that's at 660. This is a 2010 Chevy Camaro 2SS. Black clear coat is the color. We shoot all of our videos in 1080p 60 frames per second. So if you have HD capabilities on your computer tablet or smartphone device, definitely you're going to want to turn them on right now because it's like going back in time right now and it is definitely your best way to check out the quality and condition of the vehicle before seeing it in person. And if you want to check out all the photos on this car in the upper right hand part of your screen as a link to our website, click that and check us out there. Very clean down that side. No dents or dings. The thing that gets me most about this car is just how nice the rims and the brakes are on it. You get the 20 inch polished aluminum rims, not a scuff scratch on them and these are original Pirelli P0 24545 ZR20 tires and they have just about all the tread left. You can still see the little wear knobs on there. Once again only 660 miles on this car so it's not surprising but it's still kind of interesting to see when a car is 11 years old and looks like it just rolled off the showroom floor. Very, very clean on the hood. This one has the HID headlamps, the LED running lights, factory fog lights, front bumper and grille are absolutely perfect. The hood is absolutely perfect. The passenger side front fender, absolutely perfect passenger side rim. Once again just those brakes just are wild with how clean they are. And as you go down the passenger side take note of just how perfect this car is all the way around. We take these HD videos so if you are far away or even if you're close by you can still see the car, hear the car and have confidence in the vehicle that you're looking at before you even get here so that when you do get here there is absolutely no surprises. And that's why we offer the Summit Auto Fastpass option in the upper right hand part of your screen. A link right to our website where you can apply for financing, get pre-approved, see a payment quote, even appraise the trade all from the comfort of your own home so you can make this car yours without actually coming here. And when you do come here all you have to do is drive the car, love it and be all set to go. Back tires are like new as well and once again those back rims and brakes are just awesome. Didn't see any dents or dings on the quarter and as we come around to the back your bumper is absolutely perfect. Look at those exhaust tips. I mean they look like brand new too it's just this thing is like a time capsule. Do you want to point out that this comes with the original engine cover as well as a car cover so those will be included with this car and on the driver's side of course just as clean as that passenger side and for full disclosure this back rim very very nice as well. Do you get heated power mirrors inside the 2S package gives you the black leather interior there are no rips there are no tears on these seats they are in really really nice shape side curtain airbags and get the SS stitched into the headrest it still smells brand new inside this car if you could smell it it's it's pretty crazy. Formats are in nice shape Boston premium audio power windows power locks power mirrors you get that silver metallic finish to the doors there we'll take a quick look in the trunk very clean back here and then I do want to show you the RPO codes those are located right there but very nice and clean and we'll hop inside the car here so that you can see the miles and everything in the car there you go 660 original miles instrument cluster is very nice and clean you get that silver trim around there as well leather wrap steering wheel no scuffs no scrapes Bluetooth and audio controls on the right the SS logo on the bottom cruise controls on the left paddle shifters on the back there AM FM and serious satellite radio capabilities these front seats are heated door locks there you have your oil pressure oil temp volts and trans temp and then your stability control automatic transmission passenger side format and seat new and the headliner as you'd expect is absolutely perfect this car has never been smoked in map lights on star capabilities and we do have the original window sticker for this car so feel free to pause that at any time and a very safe vehicle to four and five stars up and down the board we'll take a quick look at the back seats but we'll also start it up the back seats have never been sat in or so it looks child safety locks or chat latch child safety system back here for your child car seats I would personally like to thank you for checking out the video today and hopefully from this HD video I've done a good job portraying just how clean this vehicle is all the way around the inside now under the hood we have the 6.2 liter V8 motor 400 horsepower engine bay very clean all of our used vehicles go up through a hundred hundred and thirty point safety inspection for the state of Wisconsin inspection process they get a pressure oil and filter change all the fluids get checked and tapped off before being made available to the public and this one is 100% ready to go I'm gonna do one more walk around here first I'm gonna turn the lights on so we can check out those HID lights in the front you don't see too many cars with this low mileage on them that are basically still in the wrapper so it's always really neat when you find one especially if it's car that you're looking for see those HID headlamps the LED running lights and I would highly recommend this car from a quality and condition standpoint and to see more pictures of this car one of our other 450 new and used cars trucks SEVs minivans Wranglers Camaro's Corvette challengers chargers Mustangs GT 500 team name it we got it go to that website right there www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summit auto.com if you want to check out more videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second you will see a link to subscribe to our YouTube channel on your left a link to more Chevy Camaro videos like this one on your right if you have not been to our website on the bottom link to this vehicle on our website click those check us out and we're super excited to be offering this extremely low mileage extremely clean 2010 Chevy Camaro 2 SS in black clear coat with only 660 miles thanks for checking out the video


yer pays into your capital to be used for all the town so there's there's no separation between whether it goes to stormwater or highway or a building and there's a lot of towns that have really tried to get to that point so and as a taxpayer you know that that two cents is funding your infrastructure you're hired your buildings everything in the town everybody's paying it and everything costs one percent more if you run it through the general fund because we add one percent for the human services funding so the any of those capital transfers plus one percent more because of the bogey we add the one percent we add for the human services so and the human services is great it is yeah i'm not saying it's a bad thing but it's it's a reality that if there's four hundred and sixty six four hundred seventy thousand dollars of of capital transfers in our coming budget then forty seven hundred dollars is added to that yeah that we can give away so it costs one percent more and I would say the one exception to that should be the police which we should keep in the police budget so that we can properly account for the cost-sharing one thousand six dollars yeah yeah because you have a special deal but for everything else all your buildings your it the highway equipment stormwater especially I mean if you have and that makes it very easy for the taxpayer look say oh you've got your capital plans as this year you need six hundred ninety thousand dollars so your tax your capital tax is point three eight two and this year we didn't have a bunch we save some money we didn't have to spend a lot our balance is where we want it we'll set it at two cents it'll flux just like your highway tax I think your highway tax kind of went up and just stayed up it stayed it stayed at eight cents for a long long time and then we whittled it away to the zero yeah it didn't it didn't move around and that's for just highway though right in it specific for right or anything else need anything else for me anything it's just it's informational thank you thank you awesome thanks for all your hard work yeah is it a hand up no I was just gonna tell me could stay for an exciting it's okay we'll move on to the yeah the 5d the general fund balance so we'd hope to make some recommendations for you but the the audit didn't come in until well we got the draft version on just this past Thursday so Dan and I wanted to spend some more time really digesting that making sure we had grasp on it before we came forward with with specific recommendations you can have that by January 3rd we're I think we're in much better shape today than we were on Friday as we were putting the packet together yes yeah so but did want to keep it on the packet just kind of give you our preliminary thoughts which are to take the fund balance and that we're going to that we think we're going to have confident that we do have and apply it to two main areas which are reducing future tax rates we already have some money set aside to reduce future tax rates we'd like to keep doing that and capital needs because the other big one we just had that conversation that's probably firstly where you were going Ethan a couple other ones that we came up with talking that were not made it that did not make it in the memo the fire department had an instance where they bought a bunch of equipment towards the end of the fiscal year didn't get delivered until this fiscal year and best accounting practices you want to bill it to the year that is received not the year that it's ordered so so that they don't take a big hit to their budget this year we'd like to assign some money there it's about forty forty six forty seven thousand a thousand dollars and then there's some other money we have a health and wellness account that each each employee has access to a little bit of funding a few hundred dollars each year if that doesn't get spent by individual employees we're proposing taking that which is another four five thousand dollars yeah forty eight hundred and using it towards organizational health and wellness events so that's been everything from financial literacy in the past to we used to bring in somebody from PLCT to do some health screening so something like along those lines but those are the two big ones are tax reduction and capital what happened to the money that was initially set aside for the radios or equipment or whatever it was I'm saying they ordered it they had the money then it went into our it didn't get spent so basically it's savings and so rather rather than making them spend that money now and and either go over budget or have to defer another year on the another equipment this is kind of a you know they budget each year to buy some uniforms buy some radios wait no yeah I understand so we'd like to take the money they saved that they didn't spend last year and apply it towards that approach okay okay got it yes here I have an idea oh no be mad at me but I think we should put a hundred thousand dollars in the public works transfer capital transfer because if we're down two hundred thousand dollars and we have a year like this year we're going to be down four hundred thousand dollars next year am I wrong about that if things continue to happen the way that they're happening at the rate that they are right now how bad of a position will we be in next year in the public works standpoint for storm Ethan I don't have a good answer for you I would like to think nothing is going to break or fail next year or this year I'd like to have and that would be the perfect year for me but that's not reality at times it's quite honestly at the memo I put it we had two big ones last year but I also wanted to point out we had a lot of small ones right the twenty five thousand the thirty thousand the forty thousand that really eat up our operating budget capital is a way where we can take a big dent and at some of these future sinkholes or our conditions or issues we have with our existing infrastructure that we're finding when we're televising our system at this point we can start prioritizing those a little sooner and then get in the work done on those so do I think there's going to be another big one I don't know I can't answer that is there a possibility there's always a possibility of something like that happening again for our next meeting we'll get a list of what's available for for fund balance I think that's the time that we you can make those recommendations we can yeah and I would contend that you know rather than saying 100,000 to public works 50,000 here you know it could be one number just saying we're going to set aside fund balance and use it for capital transfer you know maybe it's 250k maybe it's 300k right something at your discretion so along with what you already have listed out we could say an additional amount right yeah I think part of what we'll discuss and what you'll have the decision on is out of that chunk of money do we put it all into undesignated capital and therefore as needed to rise over the course of the year we can pull from that we can replenish some of the undesignated we know we're going to dip into right or does it make more sense to say this is going to be for stormwater this is going to be for vehicle replacements I think that's part of what we'll be talking about presenting to you yeah yeah I mean my biggest concern is last year was 400,000 I imagine we're over we're over 100 this year probably in the bank of an eye right for 23 you know it's too alone had to well those are those those were sewer amount of our enterprise funds yeah but here's another water capital yeah it's to a certain extent I mean there's there's a cost to the to the to the to the town to the town to the town to the town to the town to the town to the town if it's fully 100% funded what's that there's no no one penny spent by the town on any of those the water the water rates the water sewer cover that fully yeah yeah yeah that's good you're welcome my well-failed and it was $12,000 out of my pocket the next day so just know that but residents I do say thank you Don because that's a common misconstrued argument because my kids go to public school and the firefighters take water from those hydrants and I use restrooms in this building and in many other places so I want to just throw that out there that we all be thankful for the water sewer department we do right there was actually I had a question about the the check board I did I didn't understand but now I do so I'm so yeah this you know I'm part of our general fund accounts for buildings we pay for water and sewer yep so yep we're our own customers yeah I didn't know that until I saw the war in the tri-city isn't it like a tri-city that owns the water sewer tri-town so tri-town Essex Junction owns the plant Willis and Essex Junction and Essex I'll have but we're all share involved with it to some extent and somebody else's name completely is on the bond right Bradford or Bradford yeah oh really he's picked up a leftover bond I already had a name on it because it's weird that was odd all right anything else that was was that fund balance where we just did yep all right so now we're moving on to the general fund budget work session minor updates from our last meeting see looking at the memo Dan Travis who's the HR director and I met with Passif about a week ago a week and a half ago no real changes to the budget it was very helpful in understanding how they set those credits how they come up with those each year but we still don't think we should budget any differently it fluctuates year to year there's not really a pattern to it capital we just discussed personnel Travis updated we'd filled some positions since we first presented the budget so we have a better sense of what they're going to be the wages and the benefits are going to come in at next year had a minor impact to the budget but those those changes were made I think it went dropped it down by about 10th of a percentage point yeah small but something Ethan and I have a meeting tomorrow about Essex Rescue with some of the other certain towns trying to come up with a response there senior vans still no word from Essex Junction as to whether or not they want to continue that at this point I would say let's just move forward with the expectation that it doesn't happen I guess we have another month or so if if something does change if we do hear something we can adjust it that way but at this point I would just say let's stop waiting and move forward on that and fun balance we just talked about we'll have have some more recommendations and thoughts on that for January 3rd did we find out insurance in the tree farm yes so the tree farm situation oh boy yeah so you have to think about it a little bit so we're tenants in common so it's a shared responsibility I don't remember them saying whether it was specifically on a certain amount of land like the tenant in common relationship just takes charge over it the dollar amount I don't remember being significant for that that coverage that we're sharing that was my concern about well yeah but is the town currently paying the the full fare for it no no it is no right I don't think it is yeah but we're we're paying yeah okay so it's shared that's your shared cost as well correct and it's it's minor because it's basically just on land at that point yeah but okay and how do we without hearing about the ethics rescue situation how can we warn a on a matter and we don't know what we're doing with fun balance yet either so I think right I don't think right the next two agenda items we won't move forward on is that the intent yeah we put it on there if you wanted to you can but at this point we have still a few questions as far as I'll have the meeting tomorrow before I say anything about ethics rescue yeah yeah so currently we're at 22 and a half percent yes tax rate increase as the as the current things are currently proposed right so that's that settles e and f we moved the CUD thank you guys thank you so much thank you before you do CUD I found my answer to the refund in my notes so basically they don't look at the split the town versus versus the city because it all is that tenants in common but they use basic expenditures for their rating whatever that means but today they look at it and then they they come up with the a standard of what it should be at the end of the day it's $60 a year toward $60 okay okay the truth okay okay that's fine yep okay use too much premium stage department and buildings wherever it goes the insurance premiums sorry say it you have the insurance premium all split out so that you know what everywhere what goes to public works what goes to finance space the entire insurance apart from workers comp we split out workers comp for fire and police all other insurance is processed through finance we do have the the schedule of you know what each building is and and those types of things but it's all paid through the finance department okay and they give you the opportunity to go through there and look at everything that you have that they're insuring yep because there have been discrepancies found occasionally a building that maybe isn't there or a piece of equipment that was sold or or something I just I'm sure you're on top of that I just would mention that you asked Dan asked a lot of questions ahead of time and they answered them all I think it's yeah we go through the annual process so in November we submitted our updated lists so that's the to assess you know our bill in comparison with other units I just I know that you guys do that sometimes what you get back from your insurance they may not have it they fail that occasionally to update their lists where you have even though you submit the list I just and like I said I'm sure you're all set but it never hurts to look again thanks Jeffs all right CUD okay so the there was a recommendation there's a recommendation from staff that we appoint Marguerite as the representative to the communications union district Greg is actually very busy is there is there anybody on the board who wants to would like to be the communications union district wrapped I'll give you a clue that I might raise my hand on this one but I'll defer somebody else really wants to do it I was going to say I would if nobody wants to do it but if you want to do it you have more time than I do my my most my most recent job at global foundries was involved with fiber with the optical fiber so some experience in it there's no problem Andy with that I have a conflict of interest and my father when I worked for Brown can talk to him so yeah so Andy somebody want to make a motion to want to make the motion we appoint Marguerite as a representative and Andy as the alternate alternate to the new CECC it's chinning county communications union district thank you thank you Don thank you Kendall any further discussion those in favor please say aye aye aye opposed say nay okay motion passes 4-0 first meeting is next week you know January 5th January 5th then Mary's not back by then probably not okay so I guess that might be all right we'll we'll come back to executive session discussion in a minute but consent agenda make the motion we accept the consent agenda as presented thank you Don thank you Ethan any further discussion probably do I'm not down yet what I said I probably have a comment but my computer is scrolling down through the stuff there's a check warrant saying it was a bit of approval and help off so and you pulled the communication on yep pull that one out I'm good all right all those in favor please say aye aye aye opposed say nay if I've corrected my my language here because you asked that question motion passes 4-0 reading file any question would have been that the excavation came in quite a bit lower that's great that's good thank you okay for reading file board member comment board member comments I asked this question about this dark preservation thing and it's it's for the water tower it doesn't actually say in there anywhere but it's for the the restoration of the roof of the water tower over in that but we did get one we did yes awesome so it's denied your yeah see the first time I probably was denied and this is their second time around that's um yeah Ann Gray deserves a ton of credit from the Historical Society she's been tracking down every available grant and putting in tons of applications and so major kudos to her for for getting this one well worth the effort thank you that's great any other comments I have comment I really like thank all the town's staff and employees and wish them a merry Christmas and happy new year and thank them for their hard work this year on behalf of these employees thank you and back at you Ethan I like that Don thank you for saying that and I made another trip down the road my tractor and then I about our discussion there and that it is Irene Irene Drive yep so this baffles me right because I've driven by there a million times I've never paid attention enough to see this until I'm in my tractor and there's people trying to cross the road well when you approach that crosswalk that's not being on the road there's crosswalk ahead signs and no crosswalk signs at all just crosswalk ahead so no lines I had that on the agenda to to have a letter from the select board go to V-trans it ran out of time no it's fine I just so it's it's there Aaron's Aaron's done a little bit of prep work on it already we are going to have to go to V-trans it's a state highway we're going to have to request permission to do that that's going to come from the select board that's the letter that has to get drafted up so that's what you'll see hopefully at your next meeting of you know requesting flashing beacons the crosswalk in the in the road to try to pursue that but it does have to go through V-trans and it's going to be a request from the select board to make that happen but is it is it a key thing that point out to them that there's actually a signs that say crosswalk ahead yeah that'd be a good crosswalk yeah there's no there's no sign there's no marking it's just crosswalk ahead yeah and who I mean maybe it was there and it got faded and nobody repainted I don't know so maybe it's easy I looked for broken poles or anything like that there's nothing because I was like I was like how did I never notice that's amazing fine yeah I'm gonna look for that when I as I've driven by every two days twice a day all right so let's any other comments if anybody off anybody somebody got the I make the motion select board enter executive session to discuss the negotiation or hearing a real estate purchase or lease options in accordance with one VSA section 313 A2 and to include the town manager thank you Don do I have a second second thank you Ethan any further discussion any discussion at all we will not be coming back after this other than to adjourn do we need to come back here to adjourn no we can adjourn up there so there's there's no more additional Scott you can leave and and we're not going to make any more definitely hang around and warn that we're going to do anything so we won't night Gina and so all those in favor we say aye aye aye opposed say nay okay motion passes four zero we'll adjourn upstairs


I'm going to start with a view of the Roman form, because part of the activities of the Luperchia Festival take place in the form itself, particularly along via sacra. And this is what we're going to be considering today. February 15th is the Luperchia Festival. We'll start with the protagonists and the context of the festival. We'll talk about it in the context of the Roman sources. That's not really the art that's going to give us an insight into the actual details of the worship at the Luperchia, but rather it's the ancient sources. So we'll be sure to talk about them. Then unwrap the ritual itself, the locations in which the rituals are taking place, some fun imagery to take a look at from antiquity. Then the famous case, the most famous case of all I'd say from antiquity is the moment in which Julius Caesar is involved and he uses it as a staging moment to push his special status in Rome as a, let's say, would-be king in 44 BC. Remember the Ides of March or around the corner? He's going to be dead on the 15th of March. This is then just before then by one month. And finally, how does this ritual that is so popular with Romans end? We'll talk about how the final nail and the coffin is hammered in, but not as, well, you think it would, with the Christianity coming in, with Constantine it would have gone out of use, but it actually has a much longer tradition. We go all the way to Pope Galatius. So let's take a look at the Luperchia. First of all, the basic concept is that it's also taking place the time of a festival called februa. And we think about fever, febris, febrile, with this term, februa, which is a ritual of purification. And we get this name applied into the whole month of February and associated with a particular deity, Juno febralis. And we even have this term for the date as a febrata. And that's the same day in which the Luperchia is taking place. So why is there this fixation with the idea of purification? Well, we already took a look at the entire month of February, just recently in another live seminar. And a whole bunch of the activity of the month is focused around a nine day period, the parentalia in which this Luperchia febrata is encompassed. And we need to take a look at and consider the earlier calendar system of the ancient Romans, which is the original calendar was a 10 month system, a lunar calendar. And the first month of the year wasn't January, according to the Romans, it was March. So the last month, the month where you're kind of tying it all together, ending and looking forward to something new was not December as it is today. And as it was the case with the later reforms in the Roman calendar, it was the month of February. So that period of purification is very, it just makes sense for the Romans in their own calendar system. The Luperchia, of course, is gonna have lots of associations going all the way back to the time of Romulus being tied in even before Romulus to the Greeks that are supposedly settling in there, according to a lot of Roman traditions, Evander, the Arcadian, and the Lysia is a worshiping festival focused toward not Faunus, as is gonna be the case for the Romans, but Pan, the Greek equivalent. And in that process then, we're gonna be talking about Romulus himself and how he's the one, according to other traditions, that sets up this ritual that's gonna focus around the point in the city where he is first with his brother, suckled by the she-wolf. And it's gonna be maintained by Roman families, two distinct Roman families, which is the case of a lot of other ancient Roman rituals in the Roman calendar. And it's something that ultimately through the participation of these noble families, these wealthy families, these old families, their participation is gonna then be the performance that leads to the well-being of the entire community of Rome. Okay, so who are the protagonists? We have the Pairantalia again from the 13th to the 21st of February, in which this is taking place. The she-wolf Romulus Remus here depicted on the famous altar from Ostia, now Museo Nazionale Romano. You see there at the bottom, the she-wolf suckling the twins and Pan oftentimes in these kind of reliefs is present or Faunus, this deity that we've also talked about being venerated in the month of February on his first temple in the Tiber Island. And Evander is a figure that looms large in the ancient sources.  So you have some ideas projecting back the Lupercalia even before the existence of Romulus and Remus and giving it a nice tie to Greek ideas, Faunus, then associated with the Greek pan, Greek pan introduced by Evander. Evander, who at other times in the live seminars we've talked about is the one that meets Hercules when he's on his own laborers and passes through what will become the foreign boring. Now you're gonna have as the main protagonist in this ritual, two groups of men, originally from two families, the Fabiani and the Quintiani and each one is going to be affiliated with Romulus and Remus. And part of it is involved in the competition. These groups represent the original competition, the buying in a competition between the two brothers. And as we know in the end, in other contests, it's Romulus that's gonna be Remus and found the city of Rome. But there's a part of ritual competition in the Lupercalia as well. And there are big concepts. We're remembering the dead because that's a lot of what you're having in the month of February. We're having this idea of purification. A lot of the idea is remembering the dead and going through ways of purifying the community and then the city and then the individual. And then we have some questions about fertility because that's gonna come up as well. And ultimately this idea that's always percolating kind of a common misnomer that, you know, Valentine's Day is gonna take over Lupercalia. There's some sort of association going on there in popular theory and we'll see that doesn't actually prove to be the case. Okay, so the sources are Cicero right in the time of the famous moment when Mark Antony is trying to crown Julius Caesar in the forum at Dionysus Telecarnassus and Ovid are gonna be Augustine authors. Plutarch's obviously gonna be a bit later at the end of the first century AD and into the second century AD. And he has a great account in the life of Romulus, one of my favorites. And then we can go into later sources including Cetonius, like Caesar. We're just gonna also talk about that moment of time in which Julius Caesar is trying to be crowned symbolically. So the ritual. The ritual involves the Vestal Virgins, the Flamendialis and these Sedali Tatis, these groups of selected individuals from society. And the Vestals will make a sacrifice of Flamendialis is there as well, overseeing a lot of the rituals.  And when the sacrifices ended, you're going to wipe the bloody knife on the forehead of these Sedali Tatis members, two groups of 12. And afterwards the knife is wiped off with milk and wool as well for the off the forehead. The blood is coming off the forehead. But the response and getting your face wiped with blood is to respond with laughter. So there's some sort of ritual, there's some sort of function. We don't know if the laughter is warding off bad luck or evil eye or whatnot. But after this ritual, it's taking place at the Lupercal and we'll see what that is on the Palatine Hill. The exact location is still unknown and undiscovered. But then you're going to have a race, you're going to have running up and down on the via Sacra actually naked. And you're going to be whipping a lot of the crowd that gathers with the whips that are constructed out of strips of skin from the sacrificial goat. So there's all kinds of things that are going on in different locations. And a lot of the questions that is interpretation is this happening to be shepherding because the Enromance and Remus are shepherds and then they're suckled by the she-wolf. But then here's that dog, the dog is sacrificed. Why is the dog sacrificed? Because the dog is the enemy of the wolf. We're here in some way satisfying or remembering the she-wolf that suckled the twins. So we have a lot of different ideas coming on here of this competition between the brothers. And that's just this letticism, but also just various sources are telling us they're running down the via Sacra, they're running around the Palatine Hills, another kind of interpretation from other ancient authors. So is it also a kind of protective boundary that's being created by that running? A lot of different questions are being asked in the scholarship. And of course, we do want to think always about this original idea of purification at the end of the year. And you are doing something for the benefit of the community, a whipping it can be seen also as purification, not just as fertility, which is it seems to be a later introduction, a later idea that's introduced in terms of the interpretation of these men going around flacking their little whips. And then some women stand out to get hit and in the hopes of becoming pregnant to that kind of theme is introduced and also into the sources. There's a lot of different interpretation what's going on here. We are looking at a couple of images. We're looking at the Vestal Virgins. We're looking at the Flamen Dialis with this little hat and of course the capitalized she-wolf with Renaissance twins added beneath. Okay, what locations are we talking about? Well, the loop recall itself in the Ficus Ruminalis, this fig tree that grows up spontaneously by the cave where the she-wolf was suckling the twins is somewhere at the base of the Palatine Hill near where we have the Circus Maximus underneath the house of Augustus. We're gonna have the running on the Via Sacra in the Forum and then another fixed point it seems is another Ficus, another fig tree that grows up. This one's in the Forum by the Arostra. So this seems to be, according to some scholarship the end run on the Via Sacra, you're coming in from the Palatine Hill and the Vicus Tuscus from one Ficus Ruminalis at the loop recall, you're coming into the Forum and the end result is at the Via Sacra base at the Arostra with the Ficus Nivea, another fig tree. And of course that's where the roster is and that's where ultimately in the age of Julius Caesar that's where he'll be seated to be crowned. Here's a scene from the Arpacas, here's that same image from the altar from Ostiantica which is now in Museo Nazionale Romano. So we wanna think about these important locations, why don't you take a look at them now. So here's the Palatine Hill, there's an arrow indicating somewhere in that corner where there was the loop recall still to be discovered. Some people thought they discovered in 2007 but it's probably just an underground nephem but it is basically just below the house of Augustus and the temple of Magna Mater basically by sent Anastasia Church. Now we have the Rostra here labeled, that's a reconstruction but it is the basically Imperial Rostra of Julius Caesar and Augustus and we have the Ficus Nivea that was somewhere in the center of the Forum Piazza here it is depicted on the Anaglitha Triani which is now located inside the Coria. Next to the right there's a famous statue of Marcius also in the center of the Forum Piazza area. So that fig tree was there, it was a fixed point, it was a fixed tree and when it died they replanted it and up would come another one so it really was tied to the longevity and the success of Rome. If it died it was a bad omen when you planted another one and so forth but these fig trees tied into this concept of the fecundity of the she-wolf Aca Laurentia and this idea of fertility so that's always there overhanging the lupacalia, a location and lupacal structure. I just take a little walk down the Via Sacra and think about naked Mark Antony running down here in 44 BC and countless other lupercci that are running around and then flicking their whips and hitting various spectators were literally on the Via Sacra or heading down towards the Forum Piazza. Obviously the structure to the right here, there's the vestibule leading into the form of a piece of Aspecian, these are much later structures. There's the temple of Faustina and Antonius Pius. So not there in the time of Julius Caesar right to the left, on the left side there there was the Domus Publica. That's where Julius Caesar lived as the Pontifex Maximus until the day he died. But it's just, I think, fun to just imagine for a moment that reality, all that history that took place on the Via Sacra. Obviously this is modern pavement, there's some more original pavement further down, just to think there's so much history that took place on that street, the Via Sacra. Okay, Julius Caesar and the lupacalia in 44 BC, he's adding a third group, a third companionship called the lupacalia uniani. Mark Antony of the consulate time is one of them, basically running around butt naked and comes down and then ultimately tries to crown Julius Caesar before the crowd in the Forum, the crowd booze each time he tries to crown Julius Caesar and Julius Caesar refuses, the crowd cheers more and more and more. So basically it's staying on the part of the people of Rome, we don't want a king. Julius Caesar, no, don't take that diet. And it, but it seems to have been a publicity stunt to see, well, how far can we push this? Maybe everyone will cheer when he's crowned. He was just an initiator in the spectacle who's not running around butt naked, but here's a fun little image of that kind of moment with the teeming masses behind.  Here's one, a monument of Claudius liberalis which is now in the Vatican museums and you can see this particular, I think equestrian order gentleman.  He's got a little loincloth and he's got his whip in his hand. This is drawn by the way by my little 12 year old. If you need any artistic renderings of famous monuments or whatnot, be sure to let me know and I'll pass on her information. This one here is actually a terracotta of how to relief plaque that was found near the house of Livia on the Palatine Hill at the end of the 19th century. And what you see here again is something very rare. These guys are naked, one, two, three, four guys and some of them have their whips in hand. So this is the kind of stunning evidence that comes from ancient Rome that corresponds with the ancient sources in the description of these people and you think about the primitive culture and you think about that kind of perpetuation of that. If Romulus and Remus are running around naked, competing as they did in the Greek world as they did the ancient gods, well, so too can we be part of that primordial of Rome even at the time of the Vander if you follow other traditions and participate for the wellbeing of the community. How does it all end? Well, it's still mentioned, the lupacalia in the calendar of 354 which has Christian and pagan non-politistic traditions are recorded in that calendar already in the middle of the fourth century AD. Even though all rituals were banned at the end of the fourth century, we still have it going down until it's shut down by Pope Galatius I at the end of the fifth century AD. Absolutely incredible that this was something that was so felt and of course has to do with the wellbeing of the community. This is one that held on for quite a long time. And let's just remember and underline the fact that there really is no tie between the lupacalia and then Valentine's Day, this saint that's martyred in the third century AD. In fact, there are other ones with the same name that comes to take its place on the 14th of February. Lupacalia, February 15th, a very striking, unique, interesting and engaging festival. We still have a lot to discover about this incredible Roman ritual.


The fifth Pan-Communal Forum on Open Learning, PCF-5, was held in July 2008 at the University of London's Institute of Education. The forum is hosted every two years by the Commonwealth of Learning, an intergovernmental organization that helps developing countries improve access to quality education and training. The theme of PCF-5 was access to learning for development. More than 700 delegates from 70 countries attended the forum, representing Commonwealth governments, education institutions and non-governmental organizations. It was the largest ever Pan-Communal Forum on Open Learning. The forum was organized around four main themes, children and young people, governance, conflict and social justice, health and livelihoods. Over four days, more than 300 papers were presented around these four themes. Prior to the opening of PCF-5, the President of the Commonwealth of Learning expressed his hopes for the event. And the themes of this conference are designed to help us profile the much wider developmental impacts of learning. PCF-5 was officially opened by Sir Graham Davies, Vice-Chancellor of the University of London. He spoke about the university's role as the world's first open access university in both his keynote address and his interview. The forum is all over the Commonwealth and elsewhere, but from my point of view the most important relationship is the relationship through our external system. And there we continue to provide distance connections and distance education in, at the present moment, 180 countries, all of the countries of the Commonwealth. The forum's first keynote address was given by the Prime Minister of Uganda, Professor Apollo Ntibabi. The Prime Minister discussed the role of formal and informal education in achieving development goals and the importance of cost-effective solutions to educational access in his own country. The emphasis on affordable technology, affordable technology. The Secretary-General of the Commonwealth, His Excellency Kamala Sharma, spoke about the enormous challenges facing the Commonwealth today. He described of the 150 million children who don't go to school, 70 million are in the Commonwealth, 30 million of them out of primary education and 40 million out of secondary education. In his interview he also discussed these challenges. The old very, very daunting statistics is very clear they cannot be done entirely by conventional ways. You need to think of avenues in which you can really get the results you want in a much more flexible, innovative, technological, savvy way. Mr. Nicholas Burnett, Assistant Director for Education with UNESCO, provided the final address of the forum's opinion session. He explained the link between education and development, and our education is a right which leads to many aspects of development. Environmental sustainability, social and economic development, better child and maternal health, and women's empowerment. Parallel sessions were held on each day of the forum, offering delegates a wide range of topics related to learning for development and speakers from around the globe. The 2008 Excellence in Distance Awards education, we announced a PCA-5, recognizing good practice by institutions, learning materials, and by educators and students. The Commonwealth of Learning also named eight new Honorary Fellows, we have made outstanding contributions to open and distance learning. The latest edition of Commonwealth Education Partnerships publication was also launched at PCA-5, means Carol Bellamy reminded delegates about the plight of out-of-school children in a plenary address. The solution, she argued, is greater innovation in delivery of education. The key to education for all lies in the tapestry of new and innovative partnerships that have come together over the last decade or so. This is involving all sectors and all levels of society, from governments and funding agencies, to service providers and civil society representatives, to educators of all stripes, and of course families and children themselves. You, everyone here, you are all part of that tapestry of innovation that we so desperately need, and we need to weave in order to get the job done. Day two of PCA-5 began with the Asa Briggs Lecture, which honors the founding chairman of the Commonwealth of Learning's Board of Governors and the renowned British historian, the right-honorable Lord Briggs of Luz. Professor Brenda Gurley, Vice Chancellor of the UK Opening University and chair of the Association of Commonwealth Universities, spoke about new technologies, new possibilities for reaching the unreachable in ways that would have been impossible not so long ago. And I'm also enormously encouraged by how enabled by technology we are learning to share our commonwealth. The most abiding uplift for me comes from my perception of more and more people involving themselves in activities with purpose beyond themselves. It seems to me that it's especially young people who are demonstrating their understanding of what James Martin calls the awesome meaning of the 21st century. Dr Astrid Duff-Borg with the Global East Schools and Communities Initiative provided a plenary address about the challenges and issues of information and communication technology for education. One of the key challenges is the lack of knowledge about the use of ICTs. We realise that we know very little about what is happening in the classrooms. There is a lot of need for research on following what is happening, what kind of changes, what happens to the students, what happens to the teachers and what happens in the systems. Day three of PCF-5 featured a keynote address by Professor Lydia Brito, a university professor and former minister of education in Mozambique. Professor Brito offered an African viewpoint in a keynote address. Access to learning for health with particular reference to HIV AIDS. She warned delegates that we are running out of time in the fight against HIV AIDS. In order to integrate education into the social and economical processes, what we will need is to make sure that we have research, serious research that enable us to develop curricula, methodologies that can help education. PCF-5 also included a technology showcase, an exhibition of technologies and products related to open and distance learning. The keynote address on the final day of PCF-5 was provided by Professor Bani Pityana, Vice Chancellor of the University of South Africa. His topic was a decade of development and education in Africa, the promise of open and distance learning. Allowing broad access to quality education at an affordable price. In short, the growth of ODL has facilitated mass access to quality, higher education. Following summaries from the leaders of each of the four conference themes, the President of the Commonwealth of Learning, Sir John Daniel, reviewed the four day forum in his closing keynote address. The technology that attracted most attention through the conference was open educational resources, which we can think of as a kind of academic putty that allows you to create materials collaboratively and then shape them to our own institutional and individual needs. You saw applications for OERs in every area of learning, and it will be particularly interesting to pick up on this story at PCF-6. Sir John encouraged delegates to continue to collaborate after the forum to prepare for the next three year plan for the period 2009 to 2012. The forum gala was held at the Congress Center in Great Russell Street. Delegates wore national dress that reflected every part of the Commonwealth. The focus was on fun with lots of mingling and dancing to traditional Scottish Cain style music. With this successful forum in London, PCF-5 has taken its place as one of the world's leading international conferences on learning and global development. The next pan-communal forum on open learning takes place in India in November 2010.


I have with me today, Ms. Suzette Brown. Suzette is the TAP GPS Coordinator at Fleet Family Sports Center. And among other things that she does over there, but I brought her in today to help me talk about TAP GPS because while I'm not an expert, I am a customer of the class. So I wanna talk about some of the benefits and some of the stuff that even myself after 32 years in the Navy, I'm gaining from going to this class. So we're gonna talk about TAP GPS and how it is a benefit and an investment in you and it is not a chore.  It's funny, yeah, well, yeah, they're scared. And it's funny because one of the first things I ask, why are we here? Why are you guys here today?  And it's not just you, for a lot of people, it's not just that service member, it's family members, it's spouses. So it's a lot to prepare and to get ready for that transition, especially if it's a separation only. Retirement, you'd have a little stipend, you know, something to fall back on, but a lot of separatists, they do not. So there's a lot of preparation when it comes to making that next step. I always say writing that next chapter. When should somebody go to TAP GPS? And when should they go back, if they should? Separatees, it's recommended at 12 months. And retirees recommended at 24 months. And that's mainly because of benefits and things that you're entitled to, that, you know, of course, the separatist is not, that may take a little bit longer to prepare for. And so, and then it's recommended also to come back within six months of your separation, you know, the day that you're walking out the door, because the information may have changed, or if it hasn't changed, it's just a refresher to make sure that you're on track. And one of the things that we hand out during TAP is a milestones checklist. And it starts at the 24 month point mark. And it has different tasks, different milestones that you should have met by a certain timeframe. We have checklists and we have, you know, time charts and schedules to follow. And we've invested so much into our mission vision goals of our command's policy and the Navy's goals and the CNO's tenants and investing that time in ourselves and using that same kind of format that GPS has prepared, you know, for us to do, really does make this a little less overwhelming because there's a lot to think about when you separate, let alone retire. Don't wait for things to happen to you. Make them happen for you.


Vincent from Purdue University, we speak on one of the fantastic joint contributions of the orchestra and very clinically, tight closure. Thank you all. So I will talk about the work of Hoxster and Hewnecke mostly and how tight closure came about. And this tight closure is really the inspiration for this conference. And I thank Jugal Irma, just like Claudia, thank him. Jugal was really the main force behind this conference and more than year-long events in honor of Mel Hoxster and Craig Hewnecke. So thank you, Jugal. And we're getting more emails from him for further events and happenings. Yeah, so Craig is probably online and we really appreciate his presence, but Mel has not been able to log in. Instead, he is sending us this message and I will read it out loud. I would like to thank the organizers and the participants for listening. I count myself lucky to have had so many wonderful collaborators, colleagues, students, and mathematical friends. I wish everyone much joy in their pursuit of mathematics. This is a very Mel statement, and he has been a great inspiration to most of us here mathematically and also personally. And this is just another one of those evidences. So there is so much to tight closure. It's impossible to cover it in 60 minutes. So I will make some assumptions. I will not define very much. And most of the things that I'll talk about will be in characteristic P. Just it will make things simpler. So if I write some statement and I just say R is a ring, it's probably a ring of characteristic P, maybe I won't say it. That's standard notation there in tight closure.  So here's the definition of tight closure. I won't read it out loud. But why would somebody, so, algebraists, we solve equations. That's what we do. But why would somebody make you solve infinitely many equations simultaneously? That's really hard. Well, it turns out that this gives a really useful notion. This notion didn't come out of nowhere, as has been pointed out many times, the work of Pesquina's Peron homological conjections in the 1960s, the proof of Hoxton and Roberts on rings of invariance of linearly reductive groups acting on polynomial rings, being co-McAuley. That also used similar methods. Heunica's proof of the, Heunica eto theorem and power, integral closures of powers of ideals also used some methods. And what I learned on Monday from Craig Heunica's talk, there was also a preprint of, never published preprint by Mel Hoxter of deep local rings that also use tight closure type proofs. So this definition, we have to solve infinitely many equations at the same time, has unified some of those old proofs. But it does actually a lot more. So that's the whole power that it was, didn't just write one proof for all those previous theorems, but it also gave really quick, elegant proofs to some of the new theorems. And then there has been lots of activity forever after. And I will touch on some of those things in the next hour. There were several announcements and published statements before this first paper in the journal of the American Mathematical Society. This one was published in 1990. I studied from the preprint. It was a thick preprint, not teched. So when this came out, I didn't really have to use it, but that was really a masterpiece. And it still is a masterpiece. I keep using this paper for reference for all sorts of things. But what was so beautiful about this paper, amazing about this paper, it's not only it gave these basic definitions and it gave basic properties of how tight-closure behaves. If I is containing J, then the tight-closure of I is containing the tight-closure of J and all that. Not only it gave all those basic definitions that whenever you define something, you have to prove the basic things. And not only it proved, gave really quick proofs of those old results, but it proved so much more. And while it was proving so much more, it developed not just things in tight-closure proper, but there were things that never saw tight-closure in the statement or don't possibly don't need it in the proof. So I learned a lot of mathematics, not just about tight-closure from this preprint, it was very rich. And furthermore, when it came, at least when it came in this published version, they already had seven thick papers lined up ahead of time. I brought one of those thick papers, 80-some pages in the Phantom Homology that appeared several years later. So they already had a map, they already knew what was coming up. Anyway, I had a front seat, I was a student of Craig Hewnekes, and later I was a postdoc with Mel Hoxter, and some of the lessons that I learned from the two of them, and even from just their papers, not necessarily from their saying. So understand your methods and literature deeply. And it's worth taking the time to understand the methods really well. It will pay off in the long run, you'll be able to use them somewhere. And then once you understand the method, just play with it for a while. If you don't play with it, well, then it's just that stale thing somewhere in the back of your brain, but play with it, try to see where else it applies, and then apply it somewhere else when you can. And then again, the power of this is that it applies, these methods apply, not just in tight closure proper. And such theory doesn't happen all that often. Okay, so the first result is that if R is a regular ring, then for all ideals, I, the tight closure of I is the same as I. So for this, what you need to know is that the Frobenius functor is faithfully flat on regular rings of characteristic P, of course. Everything is characteristic P. So in particular, that element C is in the Frobenius power of I colon, the corresponding power of X. So that's in I colon X, Frobenius power of that I colon X. And if you take higher and higher Frobenius powers of I colon X, well, there aren't very many C's like that in the regulating. The only possible C is zero, but C is not supposed to be in any minimal prime. So then I colon X, if it's, cannot be a proper ideal. So I colon X, so whatever is in the tight closure of I has to be in the ideal. All right. So next, so this is already a beautiful result and maybe I should say, oh, I even say, rings in which all ideals are tightly closed as everybody in this room knows are called F regular, or sorry, weekly F regular. The next result, this one was not in the mountain of theorems that the tight closure simplified. So this was a new result that was getting proved with tight closure. Sorry with an L generated ideal or maybe it doesn't have to be L generated but it must have an L generated reduction which we hope L is strictly smaller than the number of generators of I. Then for all non-negative integers N, the inter-closure of the N plus L power of I is contained in the tight closure of N plus first power of I. So if we start with a regular ring then you can forget that tight closure there and so that is generalizes the Brians' code of fear from the rings of convergent power sears that was done earlier. Here's a Hoxter's question and this is one of the beauties that interplay between elementary, basic algebra and tight closure. So here is a fact. You start with a polynomial ring in two variables. So that's a regular ring and start with three elements, arbitrary elements, F, G and H and let I be the ideal generated by F cubed, G cubed, Z cubed. That's a three-generated ideal but in a polynomial ring, this ideal may not have a two-generated reduction but at least locally it will have a two-generated reduction. So if we can prove that inclusion that F, G, H raised to the second power is in this ideal locally then we'll be done. So it suffices to prove that inclusion locally and locally L is equal to two and then if we take N is equal to zero and then we have the, oh and we also need to know that F times G times H is integral over I so the square of FGH is in the integral closure of I squared. So this is an element, yes. Oh, oh, sorry, excuse me, Z is supposed to be H. I'm sorry. I saw, I read this many times. Okay. Yeah, Z equals H. So, so Hoxter's question is can you find an elementary proof of this fact? So if for any FGH, surely you can do that but can you give an elementary fact without using tight closure methods of this inclusion for an arbitrary FGH in the ring. Okay, so I won't teach you anything new today so but maybe by the end of the hour you can have a proof of this. Okay, another big thing that they proved with tight closure is colon capturing. So not every system of parameters is a regular sequence but if you are in a pretty good ring so module finite over a regular domain and if you start with elements that actually are in the base ring but in the bigger ring they form a system of parameters or part of the system of parameters then the colon of n minus one of them with the nth one well it may not be contained in the original ideal of n minus one elements but it will be in the tight closure. So that's, so at least if you know that you're in a weak left regular rings then you can forget the tight closure but in generally can't. And then here's another version of colon capture. Again you have a base ring A that's regular and R is module finite over it but in addition also torsion free and if you start with ideals in the ring they don't have to have anything to do with parameter ideals but if you do any kind of colonning or intersecting with extended ideals in R well it suffices just do your colons or intersections down in the base ring and then extend so that makes it quite a bit simpler. These are not the two most general statements that we can make about colon capturing they're much more general statements but suffice it to say over here. And this has some strong consequences so monomial conjecture is the easiest one that so if we start with a system of parameters of R then we want to show that the teeth power of a product of all those system of parameters is not in the ideal generated by T plus first powers of the parameters themselves. So you might as well go to completion to prove that and you might as well go mod a minimal prime so then we are in the theory in local ring that's complete and domain and if you need or maybe we should have passed on infinite residue field at some point as well or but then you just take a regular sub ring that's generated over the base field or sorry over the coefficient field by X1 through XD and then there that colon ideal so there the inclusion definitely doesn't happen and therefore it cannot happen by the colon capturing in the bigger ring. So monomial conjecture is very easy to prove once you have colon capturing and it's well known that the direct summon conjecture is equivalent to the monomial conjecture so we won't prove that. So there are these easy proofs with tight closure. I repeated the monomial conjecture and direct summon conjecture and then one of the consequences here so this is the Hoxter-Roberts proof that the rings of invariance of linearly reductive groups acting on polynomial rings like Colin McCauley they that proof and also that's the direct summon that proof use these basic tight closure methods and so what you can prove very easily with tight closure that direct summons of regular F regular or weak left regular rings have the same property and then all such rings are Colin McCauley so that gives the Hoxter-Roberts rings of invariance are Colin McCauley. Then I probably shouldn't read all these there are lots of vanishing theorems this vanishing theorem that I wrote here and I will not read is already appeared in that amazing paper but just sometimes you can guarantee ahead of time that certain tour maps are zero the modules themselves need not be zero but the maps are zero and this vanishing of tour this theorem in particular can also implies the direct summon conjecture there are much more general vanishing theorems proved with tight closure and subsequently and then there's the phantom intersection theorem that is also touched on here so the original theorem by Paul Roberts that was proved is if you start with with a complex of free a finitely generated free modules and you know that all the homologies have finite length and the zero of homology is not zero then the Paul Roberts proved that the mention of the ring is less than equal to the length of this complex and that can also be proved with tight closure and we'll see later with tight closure you can even do more of these intersection and generalize new and improved vanishing intersection theorem. All right, more that they did in that first paper if proven of the scissor theorem of Evans and Griffiths so let R be in a theorem a local ring of characteristic P let M be a finitely generated case scissor theorem of finite projected dimension and let X be a minimal generator of M then the depth of the order ideal of this element X so that's the images of in R of all the of X under all the possible homomorphisms from M into R so the depth of that order ideal is at least K the original theorem of Evans and Griffith had proved that the height of that order ideal is at least K but with tight closure that they proved more that's even the Kull McCauley the depth is at least K and one of the consequences of this is that any sub module of this M that's generated by up to K minimal generator so M has some minimal generators take a set of minimal generators and if you choose a subset of up to K of them that degenerates that is a free sub module and in this not quite this form in some of this that form what I just said was already proved by Auslander and Bridger and by Brunson Fetter but not in the greater generality that Hoxton Hewnecker did actually this scissor theorem of Evans and Griffiths was proved by Hoxton Hewnecker not by tight closure but something they called Kull McCauley tight closure so in their papers they introduced more than just tight closure proper but there are various other notions and I will not give their definitions so Kull McCauley tight closure is one in particular that was used for the proof of the scissor theorem and then there's also tight closure with respect to family ideals the original family is just the set of all principal ideals generated by elements not in any minimal prime but you can take more general families then one thing I did not define and I'm not planning to defining is tight closure of modules in characteristic P or otherwise and for modules you don't necessarily need to assume that modules are finitely generated so in that case you might need some kind of approximated approximation so finitistic you can do the regular tight closure definition but you may want to bring it down to something that uses finitely generated modules so that was finitistic tight closure or also absolute tight closure and then another thing that I will not talk about is tight closure in characteristic zero we need some there's a lot of machinery that goes into this and it's the one other thing is maybe you don't necessarily care about tight closure in characteristic P or characteristic zero but the machinery that brings tight closure questions from characteristic zero to characteristic P is worthwhile learning and there's a lot of really amazing tricks that help you understand what is really going on and reduce the questions into the bare bones what is going on just like what Craig Hewnecker was saying in his talk on Monday this is typical Mel but also typical Craig reduce your question is what is the true question what is the gist of it and so what does it mean to be in the tight closure collect the data translate it somewhere see how you can play with it there okay and and then the other thing that comes up in the the other thing I want to say about tight closure in characteristic zero there are two possible definitions of reducing from characteristic zero to characteristic P one is where C's just appear when you are in various mod P's and one is where you're also collecting information about C those two definitions of tight closure turn out to be the same but that brings into the uniform notion so one thing that tight closure really forced us to force us or enabled us to do is to think about uniform results can use one test one C in the definition for more than one ideal for infinitely many ideals and I'll talk more about that in a little bit but there are a few more other closure operations that were happening at the same time Hoxter was developing the theory of solid closure in any characteristic that was a it was a hope that solid closure would be equal to tight closure and then you could prove things in equal characteristic rings but it pretty soon it came up that no they're not the same and then Hoxter with his student Juan Villes was doing diamond closure and Adele of Ratcho another student of Hoxter was doing special tight closure and there were other closure operations and okay and then Neil Epstein developed many closures in very fun abstract way all right oh there's also inter closure regular closure plus closure yeah they're all interrelated that's right regular closure also appears in Hoxter and Hewneck as even I think even in this maybe in this one of these two the white one all right thank you plus closure Karen Smith did a lot of work on plus closure that's another beautiful theory that came out of tight closure with test elements all right so in the original definition of elements of tight closure of an ideal for every element X that's in the tight closure you need to come up with that test element C that makes C times X to the Q be in the appropriate for binias power of I but can we find C that works for every ideal and for every X in the tight closure well that sounds really nice right there is no such thing there's no such notion of test elements for integral closure so for integral closure it is also true that an element X is in the integral closure of I if and only there exists C away from minimal primes such that C times X to the N is in the nth power of the ideal and that's very easy to prove with evaluation theory for example but there's no one C that would work for all ideals I and all X so I will say more about that maybe it doesn't work for ideals but then they're asymptotic if you are willing to change powers that's a different but it turns out that these test elements for tight closure do exist under some fairly mild assumptions on the ring and let's see the, oh before I get there so in the proofs of existence of test elements that's another rich part of mathematics that Hoxton Hewnecke wrote up so beautifully again even if you don't care about tight closure the existence of test elements well maybe they're technical but there's so much to learn there there's you'll have to learn about excellent rings and Lipman Satay theorem and generic smoothness and powers of discrete valuations amazing things that they do what trace can do there are all these things that come into play and there are many different proofs of this test elements because there are different assumptions and then different existence theorems for these test elements but one of the consequences of test elements is the persistence of tight closure under ring homomorphisms so already early in the theory of tight closure you can prove that tight closure respects inclusions of ideals that tight closure of tight closure is the same as tight closure it has all those properties that you expect you expect of a closure operation that are really easy to prove but it is not easy to prove that if X is in the tight closure of an ideal I in the ring R and you pass to an algebra that X is still in the tight closure of the extended ideal so what you do need is something like a test element and some other clever tricks that again are really good ring theory whether you want to do into tight closure or not and so when you do those tricks with you get that, oh yeah elements of the tight closure in the ring stay in the tight closure of an extended ring all right, now phantom homology and phantom acyclicity criterion so I assume here that most of you or maybe all of you have seen the Buxom-Eisenbad criterion for exactness so this is, I will comment on that suppose that R is a homomorphic image of a Koma-Caulley ring and is locally equidimensional and then we start with a G of finite free complex so finite complex of finitely generated free modules and this complex satisfies the standard rank and height conditions after tensoring with R mod the nil radical so standard rank and height conditions so rank of a matrix of a map is what is the large, at least if we're in the domain simplistic one, rank of a matrix is the largest integer such that the largest integer t such that t by t minors of that matrix don't vanish so that's over domain so and then you want the rank of a module to be equal to the rank of nullity of the next one minus the rank of the previous map so suppose you have, well we have these standard rank and height conditions in Buxom-Eisenbad you instead assume standard rank and depth conditions which is stronger than height conditions and then the conclusion here with the weaker hypothesis is that all higher cycles of the Frobenius power of this complex are in the tight closure of the boundaries in this cycle so in other words, that's the terminology homologies of all Frobenius powers of this complex are phantom Buxom-Eisenbad concludes that the homologies are all zero but here with tight closure it's well it's zero up to tight closure so this is a pretty powerful result and this first result is though for each one of the elements in each of the cycles you wanna prove that it's in the tight closure of the boundaries so you need the C for each one of those elements but with a few more assumptions on the ring you can even get this phantom acyclicity with the denominator as they call where you find one C that annihilates all of these homologies you do need some conditions but again it's beautiful commutative algebra developing those and so Ian Albertbach developed the phantom homology and modules of finite phantom projected dimension to make it into a theory that kind of resembles the theory of projective dimensions modules of finite projective dimension that turned to be so then there are more notions related to tight closure and so Coal McHallifier so this is like in this phantom homology things are homology is zero up to tight closure but maybe these Coal McHallifiers make them zero and if you multiply by sufficiently high power or maybe there's a uniform power or that makes the the converts the height condition into a depth condition so it converts the height into depth and then it end up with exact complexes so that's a powerful notion to two of Coal McHallifier's then why is that on the same line? I guess it was used there too R plus so R plus so we started with the domain and in the theory in a local domain characteristic P and we take the integral closure of R in the algebraic closure of its field of fractions so that is called R plus it's a hugely non-netherian ring and I see, yeah, I need to start with an excellent or maybe a complete local domain so R plus is a big Coal McHalli algebra so lots of good things are happening and I already mentioned there before if you if you start with an arbitrary ideal I in your ring extend it to R plus and then contract that's called the plus closure of the ideal and it's always true that the plus closure is contained in the tight closure but and then there was Karen Smith did a lot more with plus closure and proved equality in many other connection many other connections between plus closure and tight closure then these test elements in Coal McHalli Coal McHalli fires played also a large role in the uniform properties so Craig Kuhnike wrote the paper very influential paper Uniform Art and Ries Theorem in which he developed a huge amount of theories so in a pretty good, not such under mild assumptions character C0 character Cp if you take there exists a K such that for all ideals I and all powers N the inter closure right to the N is contained in the N minus kth power of the ideal I so that was a huge thing earlier I said that there is no test element for integral closure but here what we have is all right so it's not that C or one multiplies the integral closure of I to the N into I to the N it multiplies it into C being one multiplies it into the lower power of the ideal that was pretty amazing what else in the same paper there were other results and I guess I'll and uniform art in these that's the whole title of the paper uniform art in these results so if you take two finitely generated modules M and N then for all ideals I there exists a K such that for all ideals I I to the N times M intersect with N is in I to the N minus K times the the module N so that was also an extremely powerful result and there are many people who worked on then art and wreaths alike or uniform type properties and Hewnecker did a lot of that Ian Aberbach I don't know why I didn't write and I'm a little blanking out right now what else is who else was proved and I forgot to say who else worked on Brians and Skoda theorem because there are now uniform versions of the Brians and Skoda theorem as well there are many people who worked on that and I don't want to forget anybody why didn't I say that I didn't I did it I'm blanking out well with there will be a test at the end of this lecture and then what's the next thing on my list so huge amount of singularity theory also arose out of tight closure there have been several talks earlier today and previous days so singularity theory we're talking about F rational F regular F pure F injective lots of these notions and some of these notions correspond to the course geometric notions and characteristic zero lots of work here was Smith Smith Harrah Karen Smith Harrah Nobo Harrah Mehta Srinivas so rational log terminal singularities and there are these analogies going back and forth Smith and Harrah did a lot of work also in geometric interpretation of test ideals and then another huge part of that got boosted by tight closure and Hilbert Kuhn's functions they started before tight closure but I think they got second wind or more with after tight closure we already saw some talks same for Hilbert Kuhn's multiplicity so and we already heard about it today Monsky did a lot of work and then Hoger Brenner did a lot more work and then also the I should mention at this point Hoger Brenner and Paul Monsky they prove that tight closure does not commute with localization so this is one of the basic properties that you would hope that tight closure does commute with localization but no it doesn't but fortunately it doesn't destroy theory the theory is still extremely powerful even if that basic property doesn't hold and then F signature and F threshold we already heard more about that earlier today so I'm finishing a little early I don't think I have any more no I'm finishing a little early but here's a test quiz I couldn't possibly do cover all the things that are in tight closure that tight closure influenced and this was definitely influenced by my preferences and what I know but the quiz is please chime in what should I mention or what would you mention if you were giving this talk Craig probably has a lot of things but I want to hear from this audience first I mean for me for me personally this notion of solid closure was the true starting point so I so the the many P to the power E that was a bit too much for me and for me solid closure seems more conceptually and for me that was the starting point which so that is a great paper of Hoxter I think even if it doesn't work in equal characteristic exactly I mean in positive characteristic it gives really a nice interpret and surprising interpretation of tight closure by local comology like local comology behaves when you add an element to the ideal in the sense of forcing algebra so for me that was a very important point so I in fact so I could go around some some of the really tight closure stuff I see good thank you somebody else Ian you were a front seat driver too so I'm putting you in the spot well yeah I was definitely near the beginning of this I got to pick low hanging fruit it was nice I've been trying to think of something else because what I'm going to say is I feel like I'm just tooting my own horn I I think that the for instance the Brienne since go to theater theorem which look like in some sense it was mostly about regular rings and Craig and I were able to prove it for for a rational rings and generality I felt very good about that and there had been results about rational singularities but they mostly applied to ideals generated by parameters I guess I'd add also something that Craig really originated was this idea of the Branson's go to theorems with coefficients that led to for instance led to early proofs that over regular rings the great associated graded being cone Macaulay and gave it gave the re-sring being cone Macaulay I think so those reduction basically that the reduction numbers the local reduction numbers had to be small I think in the regular case that Libman eventually solved without tight closure but I think that he only solved it because Craig open the door yes so this type of Branson's go to here with coefficients this again has to do with interaclosures of powers being contained in tight closures of ordinary tight closure powers or ordinary powers time some ideal coefficient and so this anytime I saw the theory of evolution of Eisenbaden-Mazer I thought of this Branson's go to theorem with coefficients but in a different way I would say that tight closure theory always sort of carried a lot of dramatic tension and excitement so like there was always that there are all these questions of like okay so you've got tight closure can you can can you characterize it in some other way and so like for instance with the you know Karen Smith's amazing theorem that it's well for parameter ideals it's plus closure well is it plus closure in general dot dot dot and then you know many years later of course you know Holger and you know and Paul Monsky showed that it couldn't be because that you know because that it doesn't commit with localization in general and plus closure does and but then there were all these other operations and I you mentioned some of them and but the thing is that a lot of them kind of are tight closure but they're just different at least in you know over complete local domains like the you know the diamond closure if you do it in characteristic P and the or are really close to tight closure so it's sort of created this this way of thinking about about the framework of closure operations as as kind of a thing in itself and then people were keep kept hoping to do this in mixed characteristic and I guess maybe people kind of are by now because these yeah perfectoid techniques but you know I mean I think so you were saying that like okay you learn tight closure theory it's gonna help you have a lot of techniques to do other things and that's true but I think it also you know always provided a lot of inspiration to try things which is you know also really valuable thank you so so one of the really nice theorems which you have not listed but it was mentioned in the week from by somebody is the relation of the symbolic powers and the ordinary powers I think this is really a very astonishing theorem and it's I mean there are proofs in other settings by I in Smith and Lazarus felt but so the much more general statement by by Unik and Hochstor about the uniform bound that is also one of my favorites I have to say so that should definitely be on the list okay and Alexander had a question so what I want to use this as also way to say thanks to the organizers for both the some the school from last year and also this what I'm about to say I didn't know until I had the lectures from Ian last year when we were talking about this uniform parents on school at some point you said that there was applications to the chemical property of these algebras so in 1996 there was this two results one from Johnson and Ulrich and one from Goto Nakamura and Ishida that were finding sufficient conditions for the resal to be going Macaulay and the one from Johnson Ulrich I'm very familiar with the uses reciprocal intersections they use different techniques instead based on this local reduction number that come ultimately from the study of uniform parents on school and rely on on this type closure theory and I didn't know about it until Ian talked about it last year and so the best outcome for me personally was going back to that paper and reading and understanding the last piece of my thesis that I was missing so thank you oh the man so one more I mean we still have we still have time so I mean the regarding so it's more maybe more philosophical remark I mean regarding the uniformity so my experience in my life is rather that there are also many cases where you do not have uniformity and so tight closure itself they are really infinitely many equations and you cannot really reduce it to finitely many equations so that's in that case you do not really have uniformity so that I think that was the hope somehow that you would have here a more uniform behavior but I think the generic case as soon as the ring and the ideal gets more is more on a difficult side of the spectrum of the rings we we have then you will not have that uniform behavior so I think in general you will really need a good reason for uniformity so don't expect too much uniformity in your life yeah so I didn't realize I would finish early I saw skipping a few things one of the things I was going to ask is so in light of the Ananyan and Hoxster's proof of the stillman or count example to the no sorry proof of the stillman conjecture is there some bound so if you're in a polynomial ring mod an ideal and you want to understand if x is in the title of java and maybe you even know your test element c it works for all of them so you know c so all you're looking for is c times x to the q contained in iq so you there are infinitely many equations but maybe you can solve this equation for the first 17 q's but then is there some pattern is there some uniformity or is there some bound on the degrees of the coefficients that you can take in front of your generators they're given x and the generators of the ideal can you bound in some way in the sense of greater herman or abraham sideberg the degrees of the coefficients so i that's wide open as far as i know any other what else would you have done craig probably has some craig are you there i'm here yeah i can say all things with um oh i don't think uh for this uh very nice talk and i wanted to thank the organizers one more time they put in a tremendous amount of work jugal in particular to organize this and i really appreciate it i'm sorry i'm not there i've been enjoying all the talks and i i'm glad they're on video because i'm able to see the ones i miss because it's in the middle of the night for me for a lot of the morning talks um the one well let me say a couple things when mel and i you know first started tight closure that was certainly one of the most exciting times in my own life and it's it's very good to be lucky in math i think it helps a lot but it also uh to me there's so much other work that uh tight closure connected to the f-split school which of course shrinivas is here knows very well the multiplier ideals and algebraic geometry and in a sense you're lucky that it connected but the lesson for me is if you follow problems which are interesting and develop things which will help you solve them it almost surely in mathematics will connect to other things and the timing just happened to be right for tight closure but as much as i appreciate the retrospective math is all about moving forward and i'm very gratified to see all the beautiful work being done on many different things that the speakers have done in this in the conference and in many cases tight closure has has disappeared from what's going on and is maybe only a faint noise in the background but that's the way it should be that's that's what you want is as math moves forward one problem that i would always wanted to solve using tight closure is already known it's a beautiful theorem of dale kukowski's about characterizing rational singularities by the square of of integrally closed ideals being integrally closed and i was always sure there should be a tight closure proof of this i've never been able to find it but i always felt if you could find it you would learn something new and that's something i've always personally wanted to do and of course the many problems still remaining about localization at one element or weak implies um F regularity or strong F regularity is very much an area of a lot of interesting problems i think which come up and i think ian's speaking about that tomorrow partly so thank you again it's uh it's been great so i can take any questions if there are any for me personally but thank you craig and said dale good to see you craig i can't literally see oh there you are what would you have said about tight closure um you know somehow i've i've missed out on this except for a just one vague comment that it looks a lot like almost mathematics that's i mean this whole thing about the test elements and then going to the plus closure and all of this i mean that it it's i remember the last msri that paul roberts was really excited about this uh this paper by um fault faultings where he had started this and and i'm i have no idea how he saw that this was the thing which would lead into the proof of the direct summit conjecture but somehow somehow he did he knew that was that was what was necessary that's right well height and of course had just done his right three dimensions yeah which is fantastic of course yeah and which is also very much actually it's one of the great regrets of my life in a sense of that a time constraint i was asked to uh sort of go over the manuscript of of gabber and maras and almost mathematics and i would have gotten in on the ground floor so to speak but i was so busy i turned it down that was real mistake on my part actually you probably probably was you probably wouldn't have had time to do anything else if you undertook that yeah that that was the problem we're going to enter into that you have to commit a huge amount of time it's always a question in math you know for everybody in the audience you know this very well that when you see a problem that you're interested in there's always a question of whether it's worth the time commitment to do it and you have to make choices and judgments about what the most valuable thing is and what you can expect to get out of it so i know that's something every mathematician has to do in general for um mathematicians and artists also especially for more senior ones there's always this trade-off is whether you should try to get into the latest latest hot thing that's happening or continue to develop what you've been doing and it's it's a hard trade-off and it's very hard i think i always i i always tried to do a lot of different things but it and then i couldn't go into as much depth sometimes as as i should have but it's a trade-off as you say i saw the comments that i found that conversation between dill and crick very interesting but i want to emphasize maybe um the point that that there's many ways to have fun in math and and and have a decent career in math and you can try to go deep in one topic or you can go broad in different things and i think it's it's a big 10 so you can choose what that is suitable for your personalities i think that's and the community of algebra is actually one of the um a good area for that because people are very friendly and and very tolerant of different styles i think that's i think that's very true and you have to understand who you are as you say that's two things that are comfortable for you and you have yeah fun doing that's right you have to do it the way you you want to do it yeah i agree totally yeah craig i've really enjoyed all your comments that you've been making this meeting and i see that you're becoming a very sage like uh like a person nobody ever called me sage before so i'll put that on a little plaque i think thank you getting old has some advantages i guess not many but i am really gratified to see all the young people in our field and they're doing so many wonderful things that it's just a joy for the people in the audience of which there are many who are sort of my age if you think back of what community of algebra was like 50 years ago i mean it's just had tremendous explosion of ideas and beautiful theorems and i expect the next 50 years to bring even more things like that so unfortunately i won't be alive to see them all but i can i get this almost tingly sense when i see things sometimes about oh there's a lot more there to do and it's a good feeling thank you very much craig and thank you


Protesters opposing the replacement of Enbridge Energy's aging Line 3 oil pipeline shut down construction in northern Wisconsin for a brief time this week. Enbridge spokeswoman Jennifer Smith says a group of about 20 protesters entered a work site outside Superior on Monday and vandalized equipment before leaving on their own. She says there were no injuries and no arrests. If you've enjoyed this segment of Lakeland news, please consider making a tax-deductible contribution to Lakeland Public Television.